Terranova Zl 032014 d

EXPLORING THE STRUCTURE AND DYNAMICS OF IONIC LIQUIDS USING

MOLECULAR DYNAMICS

A Dissertation

Submitted to the Graduate School

of the University of Notre Dame

in Partial Fulfillment of the Requirements

for the Degree of

Doctor of Philosophy

by

Zachary L. Terranova

Steven A. Corcelli, Director

Graduate Program in Chemistry and Biochemistry

Notre Dame, Indiana

March 2014

EXPLORING THE STRUCTURE AND DYNAMICS OF IONIC LIQUIDS USING

MOLECULAR DYNAMICS

Abstract

by


Experimental studies of solvation dynamics in imidazolium-based ionic liquids

(ILs) have revealed complex kinetics over a broad range of time scales from fem-

toseconds to tens of nanoseconds. Microsecond-length molecular dynamics (MD)

simulations of coumarin 153 (C153) in a series of imidazolium-based ILs were per-

formed to reveal the molecular-level mechanism for solvation dynamics over the full

range of time scales accessed in the experiments. An analysis of the structure of the

IL in the vicinity of the probe molecule revealed preferential solvation by the cations.

Despite this observation, decomposition of the solvation response into components

from the anions and cations and also from translational and rotational motions show

that translations of the anions are the dominant contributor to solvation dynamics.

The kinetics for the translation of the anions into and out of the first solvation shell

of the dye were found to mimic the kinetic profile of the solvation dynamics response.

This mechanism for solvation dynamics contrasts dramatically with conventional po-

lar liquids in which solvent rotations are generally responsible for the response.

The structure and dynamics of water as measured experimentally in ILs have

revealed local ion rearrangements that occur an order of magnitude faster than com-

plete randomization of the liquid structure. Simulations of an isolated water molecule

embedded in 1-butyl-3-methyl imidazolium hexafluorophosphate, [bmim][PF6], were


performed to shed insight into the nature of these coupled water-ion dynamics. The

theoretical calculations of the spectral diffusion dynamics and the infrared absorption

spectra of the OD stretch of isolated HOD in [bmim][PF6] agree well with experiment.

The infrared (IR) absorption lineshape of the OD stretch is narrow and blue-shifted

in the IL compared to the OD stretch of HOD in H2O. Decomposition of the OD

frequency time correlation function revealed the translation of the anions dominate

the spectral diffusion dynamics.

DEDICATION

To my complement, treasure, and companion, Kelly.

And Harrison Ford.

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CONTENTS

FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

ACKNOWLEDGEMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii

CHAPTER 1: INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Ionic Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.1 Polarity of ILs . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2 Solvation Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2.1 Solvation Dynamics in ILs . . . . . . . . . . . . . . . . . . . . 81.3 Vibrational Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.3.1 Spectroscopic Studies in ILs . . . . . . . . . . . . . . . . . . . 131.3.1.1 Spectroscopic Characterization of ILs . . . . . . . . . 131.3.1.2 Vibrational Reporters in ILs . . . . . . . . . . . . . . 14

CHAPTER 2: THE MECHANISM OF SOLVATION DYNAMICS IN [emim][BF4] 162.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2 Theoretical Methodology . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2.1 Solvation Response Calculations . . . . . . . . . . . . . . . . . 172.2.2 Decomposition of the Solvation Response by Solvent Component 182.2.3 Decomposition of the Solvation Response by Translations and

Rovibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2.4 Molecular Dynamics Simulations . . . . . . . . . . . . . . . . 19

2.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 212.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

CHAPTER 3: SIMULATIONS OF THE SOLVATION RESPONSE IN A SE-RIES OF IONIC LIQUIDS . . . . . . . . . . . . . . . . . . . . . . . . . . 353.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.2.1 Decomposition of the Solvation Response . . . . . . . . . . . . 393.2.2 Molecular Dynamics Simulations . . . . . . . . . . . . . . . . 39

3.3 Solvation Dynamics Results . . . . . . . . . . . . . . . . . . . . . . . 423.4 Charge Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

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3.4.1 Self-Diffusion Coefficients . . . . . . . . . . . . . . . . . . . . 573.4.2 Charge Scaling Effects on Solvation Dynamics . . . . . . . . . 60

3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

CHAPTER 4: REGARDING THE VALIDITY OF LINEAR RESPONSE THE-ORY IN SOLVATION DYNAMICS SIMULATIONS OF IONIC LIQUIDS 634.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.2 Computational Methods . . . . . . . . . . . . . . . . . . . . . . . . . 654.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 66

CHAPTER 5: A MOLECULAR DYNAMICS INVESTIGATION OF THE VI-BRATIONAL SPECTROSCOPY OF ISOLATED WATER IN AN IONICLIQUID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755.2 Theoretical Methodology . . . . . . . . . . . . . . . . . . . . . . . . . 78

5.2.1 Spectroscopic Maps . . . . . . . . . . . . . . . . . . . . . . . . 785.2.2 Infrared Absorption Spectrum . . . . . . . . . . . . . . . . . . 805.2.3 Spectral Diffusion and Decomposition of the FFCF . . . . . . 815.2.4 Molecular Dynamics Simulations . . . . . . . . . . . . . . . . 83

5.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 855.3.1 IR Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.3.2 Spectral Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

CHAPTER 6: MONITORING INTRAMOLECULAR PROTON TRANSFERWITH TWO-DIMENSIONAL INFRARED SPECTROSCOPY . . . . . . 986.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 986.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1006.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 107

CHAPTER 7: SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1107.1 Alternative Systems of Interest . . . . . . . . . . . . . . . . . . . . . 114

APPENDIX A: SOLVATION RESPONSE FUNCTION FITS . . . . . . . . . 124

APPENDIX B: MALONALDEHYDE TWO-DIMENSIONAL INFRARED SPEC-TRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

iv

FIGURES

1.1 The structures of imidazolium cations and inorganic anions studiedhere. These geometries were calculated with density functional theory(DFT) with a B3LYP functional and the aug-cc-pVDZ basis set. Thecations are 1-butyl-3-methyl imidazolium, [bmim], 1-ethyl-3-methylimidazolium, [emim], while the anions are tetrafluoroborate, [BF4], di-cyanamide, [DCA], trifluoromethanesulfonate, [TfO], hexafluorophos-phate, [PF6]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 The structure coumarin 153 (C153) with the differences in charge den-sity, ∆q, predicted upon excitation as calculated and validated byCinacchi et al.[1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.3 The experimental solvation relaxation time as a function of the solventviscosity[2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1 Calculated (black) and experimental[2, 3] (green) solvation responsefunctions in the range from 50 fs to 1 ns. . . . . . . . . . . . . . . . . 23

2.2 Fits of the calculated (black) and experimental (green) solvation re-sponses of C153 in the IL [emim][BF4] to a stretched exponential func-tion, Aexp(−(t/τ)β), in the time range between 10 ps and 1 ns. Thedata are shown as filled circles, while the fits are lines. The quality ofthe fits in terms of the correlation coefficient, r2, are excellent: r2 =0.9987 for the theoretical data and r2 = 0.9983 for the experimentaldata. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.3 The calculated total simulated solvation response (black) is decom-posed using the methodology described in Section 2.2.2 into contri-butions from the anions (red), the cations (blue), and the internalmotions of the C153 solute (purple). . . . . . . . . . . . . . . . . . . 25

2.4 The radial distribution function, g(r), for C153-[emim] and C153-[BF4]pairs, where r is defined as the distance between the center-of-masspositions of the relevant pair of molecules. . . . . . . . . . . . . . . . 28

2.5 The solvation responses of [emim] (blue) and [BF4] (red) decomposedinto contributions from translational (solid) and rovibrational (dashed)motions. For reference, the total solvation response minus the contri-bution from the internal motions of the C153 solute is also shown(black). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

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2.6 The residence-time correlation function (RTCF) for the anions andcations in the first solvation shell of the C153 solute. The first solvationshell was defined as any molecule whose center-of-mass lies within 5.6A of the center-of-mass of the C153 probe. . . . . . . . . . . . . . . . 31

2.7 A schematic depiction of the mechanism of solvation dynamics inC153/[emim][BF4]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.1 Optimized structures of imidazolium cations and inorganic anions stud-ied in this chapter. The cations are 1-butyl-3-methyl imidazolium,[bmim], 1-ethyl-3-methyl imidazolium, [emim], while the anions aretetrafluoroborate, [BF4], dicyanamide, [DCA], trifluoromethanesulfonate,[TfO], hexafluorophosphate, [PF6]. . . . . . . . . . . . . . . . . . . . 36

3.2 The calculated (dashed) and experimental (solid) solvation responsefunctions for [emim][BF4] (black), [bmim][BF4] (red), [bmim][DCA](green),[emim][TfO](blue), and [bmim][PF6] (brown) over the range 50 fs to 1ns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.3 Time constants for experiment and calculated response functions de-rived from a fit to a single exponential, Aexp(−(t/τ)), in the rangefrom 50 ps to 400 ps. . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.4 The calculated total solvation response (black) is decomposed intocontributions from the [BF4] anions (red), the [bmim] cations (blue),and the internal motions of the C153 solute (purple). . . . . . . . . . 46

3.5 The calculated total solvation response (black) is decomposed intocontributions from the [DCA] anions (red), the [bmim] cations (blue),and the internal motions of the C153 solute (purple). . . . . . . . . . 47

3.6 The calculated total solvation response (black) is decomposed intocontributions from the [PF6] anions (red), the [bmim] cations (blue),and the internal motions of the C153 solute (purple). . . . . . . . . . 48

3.7 The calculated total solvation response (black) is decomposed intocontributions from the [TfO] anions (red), the [emim] cations (blue),and the internal motions of the C153 solute (purple). . . . . . . . . . 49

3.8 The radial distribution function, g(r), for C153-[cation] and C153-[anion] pairs, where r is defined as the distance between the center-of-mass positions of the relevant pair of molecules. . . . . . . . . . . . . 50

3.9 The solvation responses of [bmim] (blue) and [BF4] (red) decomposedinto contributions from translational (solid) and rovibrational (dashed)motions. For reference, the total solvation response is also shown (black). 52

3.10 The solvation responses of [bmim] (blue) and [DCA] (red) decomposedinto contributions from translational (solid) and rovibrational (dashed)motions. For reference, the total solvation response is also shown (black). 53

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3.11 The solvation responses of [bmim] (blue) and [PF6] (red) decomposedinto contributions from translational (solid) and rovibrational (dashed)motions. For reference, the total solvation response is also shown (black). 54

3.12 The solvation responses of [emim] (blue) and [TfO] (red) decomposedinto contributions from translational (solid) and rovibrational (dashed)motions. For reference, the total solvation response is also shown (black). 55

3.13 The residence-time correlation function (RTCF) for the anions andcations in the first solvation shell of the C153 solute. The first solvationshell was defined as any molecule whose center-of-mass lies within thefirst solvation shell, defined as the first minimum of the cation-C153g(r). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.14 Calculated self-diffusion coefficients for [emim] (blue) and [BF4] (red)for varied unit charges. Experimental measurements (dashed) self-diffusion coefficients for this IL in the range of 298-303 K are reportedto vary from 4.4 − 5.4 × 10−11 m2/s for [emim] and 3.6 − 4.2 × 10−11

m2/s for [BF4].[4] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.15 The calculated (solid) solvation response functions for [emim][BF4]where the charge scaling parameter λ was varied from 1.0 (orange),0.825 applied to the entire [emim] cation(red) 0.80 applied to the en-tire [emim] cation (black), or 0.80 applied to the imidazolium ring(turquoise), along with experimental measurements (black filled cir-cles) over the range 50 fs to 1 ns. . . . . . . . . . . . . . . . . . . . . 61

4.1 The normalized solvation response without the contribution of the dyefor the nonequilibrium S(t) (black) and equilibrium C1(t) (red), andC0(t) (green) from 50 fs to 1 ns. The inset is the identical responseincluding intramolecular interactions of the dye molecule responsiblefor the large oscillations below 10 ps. . . . . . . . . . . . . . . . . . . 68

4.2 A comparison of two decomposition strategies as applied to C0(t) show-ing auto- and cross-correlation decomposition (top), to the alternativemethod defined in Eq. 4.4 that calculates the contribution of the rele-vant component relative to the total response. . . . . . . . . . . . . . 70

4.3 The normalized solvation response decomposed into anion (top) andcation (bottom) contributions for nonequilibrium S(t) (black) andequilibrium C1(t) (red), and C0(t) (green) from 50 fs to 1 ns. . . . . . 71

4.4 The normalized solvation responses of S(t) (black), C1(t) (red), andC0(t) (green) decomposed into contributions due to translational (solid)and rovibrational (dashed) motions. . . . . . . . . . . . . . . . . . . . 72

5.1 The orientational time-correlation function for an OD bond in H2O(black) and in the [bmim][PF6] IL (turquoise). . . . . . . . . . . . . . 86

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5.2 Vibrational line shapes for the OD stretch of dilute HOD in H2O andin the [bmim][PF6] IL. The spectra were arbitrarily scaled to have thesame maximum intensity. . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.3 Distribution functions, F (E), for the projection of the electric fieldprojected along the OD of HOD in H2O (black) and in the [bmim][PF6]IL (turquoise). The distribution of electric fields in the IL resultingfrom cations (blue) and anions (red) are also shown. The distributionfunctions have all been scaled to have the same value at their maximum. 90

5.4 Normalized CE(t) for HOD in H2O and HOD in the [bmim][PF6] IL.Also shown is a comparison between Cω(t) (red) and CE(t) for HODin the IL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.5 Decomposition of normalized CE(t) for the OD stretch of HOD isolatedin the [bmim][PF6] IL in terms of the contributions from the cations(blue) and anions (red). . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.6 Decomposition of normalized CE(t) for the OD stretch of HOD isolatedin the [bmim][PF6] IL in terms of the contributions from the trans-lational (solid) and rovibrational (dashed) components from cations(blue) and anions (red). . . . . . . . . . . . . . . . . . . . . . . . . . 96

6.1 Proton transfer reaction coordinate in malonaldehyde. . . . . . . . . . 99

6.2 (top) Potential energy curves for the intramolecular proton transfer inmalonaldehyde generated with DFT and SCC–DFTB. The DFT bar-rier height is 3.2 kcal/mol while SCC–DFTB predicts a barrier of 2.6kcal/mol. (middle) Free energy profile from a QM/MM simulation ofmalonaldehyde in water with a barrier height of 4.1 kcal/mol. (bottom)Anharmonic C–D vibrational frequencies as a function of the protontransfer reaction coordinate for malonaldehyde in the gas-phase. Thefrequencies were fit to Eq. 6.2, where A0 = 1534.0, A1 = 91.5, A2 =11.8, A3 = 2106.5, A4 = 42.7, and A5 = 7.0. . . . . . . . . . . . . . . 102

6.3 (a) C–D stretch IR absorption spectrum of labeled malonaldehyde inaqueous solution. (b-d) Chemical exchange 2D IR spectra for waitingtimes of 0, 15, and 50 ps. . . . . . . . . . . . . . . . . . . . . . . . . . 105

6.4 (top) Reaction coordinate time correlation function along with a fitto a single exponential with a time constant of 28.8 ps. (bottom)Evolution of the normalized volumes of the diagonal and off-diagonalpeaks in the 2D IR spectra as a function of the waiting time. Bothcurves were fit to a single exponential yielding time constants of 29.7and 28.3 ps for the diagonal and off-diagonal peaks, respectively. . . . 109

7.1 The simulated solvation response (black) is decomposed using themethodology described in Chapter 2 into contributions from the rovi-brational (dashed pink) and the translational motions of the fictitiousdipole molecule (solid blue). . . . . . . . . . . . . . . . . . . . . . . . 112

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7.2 The calculated solvation relaxation time as a function of the inversecube root of the molecular volume. . . . . . . . . . . . . . . . . . . . 113

7.3 The optimized structures of cations and anions. The cations are 1-butyl-3-methyl imidazolium, [bmim], 1-ethyl-3-methyl imidazolium,[emim], triethyl sulfonium, [S222], and tri(methoxymethyl)-methyl phos-phonium, and [Tmet]. The anions are tetrafluoroborate, [BF4], trifluoro-methane sulfonate, [TfO], 1-pyrazolide, [Pyrazo], 1,2,3,-triazolium, [Tri-azo], and bistrifluoromethylsulfonylimide, [Tf2N] . . . . . . . . . . . . 116

7.4 The calculated total solvation response (black) is decomposed intocontributions from the [TfO] anions (red), the [bmim] cations (blue),and the internal motions of the C153 solute (purple). . . . . . . . . . 117

7.5 The calculated total solvation response (black) is decomposed intocontributions from the [Pyrazo] anions (red), the [emim] cations (blue),and the internal motions of the C153 solute (purple). . . . . . . . . . 118

7.6 The calculated total solvation response (black) is decomposed intocontributions from the [Tf2N] anions (red), the [emim] cations (blue),and the internal motions of the C153 solute (purple). . . . . . . . . . 119

7.7 The calculated total solvation response (black) is decomposed intocontributions from the [Triazo] anions (red), the [emim] cations (blue),and the internal motions of the C153 solute (purple). . . . . . . . . . 120

7.8 The calculated total solvation response (black) is decomposed intocontributions from the [BF4] anions (red), the [S222] cations (blue),and the internal motions of the C153 solute (purple). . . . . . . . . . 121

7.9 The calculated total solvation response (black) is decomposed intocontributions from the [BF4] anions (red), the [Tmet] cations (blue),and the internal motions of the C153 solute (purple). . . . . . . . . . 122

7.10 The calculated total solvation response (black) is decomposed intocontributions from the [Pyrazo] anions (red), the [Tmet] cations (blue),and the internal motions of the C153 solute (purple). . . . . . . . . . 123

A.1 Fits of the calculated (black) and experimental (red) solvation re-sponses of C153 in the IL [emim][BF4] to a single exponential functionin the time range between 50 ps and 400 ns. The data are shown asfilled circles, while the fits are lines. . . . . . . . . . . . . . . . . . . . 125


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B.1 Chemical exchange 2D IR spectra for waiting times of 0 ps. . . . . . . 132

B.2 Chemical exchange 2D IR spectra for waiting times of 10 ps. . . . . . 133









B.11 Chemical exchange 2D IR spectra for waiting times of 100 ps. . . . . 142



x

TABLES

2.1 PARAMETERS FOR A STRETCHED EXPONENTIAL FIT . . . . 26

3.1 SELF-DIFFUSION COEFFICIENTS FROM MD SIMULATIONS . . 41

5.1 IR ABSORPTION DATA . . . . . . . . . . . . . . . . . . . . . . . . 88

A.1 IDEAL MULTIPLICATIVE CONSTANTS . . . . . . . . . . . . . . . 130

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ACKNOWLEDGEMENT

I owe many of my achievements and successes to the hard work, encouragement

and support of others. I am truly appreciative for all of the guidance, support,

and wisdom my advisor, Professor Steven A. Corcelli, has conveyed to me during my

graduate studies. His invaluable insight combined with his affable demeanor enriched

my graduate experience. I consider myself to be extremely fortunate to have been

surrounded by so many talented people throughout my time here. The Corcelli group

members, past and present, have been especially helpful in the conversations and

entertainment we have shared: Cory Ayres, Lindsay Baxter, Ryan Forrest, Danyal

Floisand, Mary C. Sherman, Clyde Daly, Jonathan Walker, Dr. Hannah Fox, Dr.

Ryan Haws, Dr. Laura Kinnaman, Dr. Carrie Miller, Dr. Kristina Furse (Davis). I

am gracious for the artistic and computational knowledge shared with me by Dr.

Kristina Furse (Davis) and Dr. Charles F. Vardemann II.

I have been touched by so many in my years here at Notre Dame. Mary C.

Sherman, Kelsey M. Stocker, Ryan P. Forrest, Steve Asiala, James Marr, and Joseph

Michalka provided me with the friendship and fortitude to withstand the isolating

and occasionally crushing nature of graduate school all while tolerating my antics

while in lab. When I reflect on the encouragement I received from those who inspired

me to go to graduate school, Torgny B. Hallin, Michael Seibert, Professor Scott Reid,

Professor Alanah Fitch, Professor Augustine Agyeman, and Mike Grady, I am forever

grateful. My siblings Lindsey, Ryan, Jacob, Kevin, Hannah, Julianna, and Luke and

my mothers, Kelly Hodge and Barb Maggio, have always generously provided love

and support. Dr. Kent and Dr. Diana, Tom, and Denise Nelson have additionally

xii

extended their love and help whenever necessary. Professionally I am appreciative of

the guidance and personal conversations shared with Associate Dean John Lubker,

Mimi Beck, and my administrative assistant Donna Frahn.

I am thankful for the helpful questions, comments, and challenges presented by

my committee members Professor J. Daniel Gezelter, Professor S. Alex Kandel, and

Professor Jeffrey Peng. In particular, I am very thankful for the advice I received

from my personal coffee connoisseur Professor J. Daniel Gezelter thereby enabling

my addiction. I would be remiss if I did not acknowledge Let’s Spoon Frozen Yogurt

for supplying 20% of my meals any given week. It was a pleasure teaching with Pro-

fessor A. Graham Lappin, who contributed greatly to my teaching philosophy and

personal edification. I am sincerely thankful for the assistance provided by Profes-

sor Ed Maginn and his group members, specifically Dr. Craig M. Tenney, Dr. Hao

Wu, Dr. Marcos Perez-Blanco, and Dr. Yong Zhang. The computational wizards

at the Center for Research Computing, specifically Dr. Paul Brenner, Dr. Timothy

Stitt, Dr. Dodi Heryadi, Rich Sudlow, and Jim Bulger, have been instrumental to

my success here at Notre Dame. Without their technical expertise and training, I

would not have averaged 500,000 CPU hours every month. Many thanks for the time

and input given by the additional multidisciplinary members CoMSEL supergroup.

I also want to thank Cheryl Copley, Deb Bennett, Mary Prorok, and Eric Kuehner,

and the additional staff in the Department of Chemistry and Biochemistry for their

help. Additionally, I am thankful for the office and janitorial staff of the Depart-

ment of Chemical and Biochemical Engineering for their kindness, cleanliness, and

coffee. I am gracious to our experimental collaborators Professor Mark Maroncelli

and Professor Michael Fayer for generously sharing data.

Finally, and most importantly, I would like to acknowledge the patience, support,

comfort, and compassion my wife, Kelly, and my sons, Jack and Owen, give to me each

day. The laughter and love that is shared in our house motivates me to continually

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achieve my best. I could not have risen to the level I am now without them.

xiv

CHAPTER 1

INTRODUCTION

Ionic liquids (ILs) are gaining considerable attention because of their attractive

properties as environmentally friendly alternatives to volatile organic solvents[5, 6]

and their applications involving the production, storage, and efficient utilization

of energy[7] while also demonstrating tremendous promise in a variety of liquid

separation and extraction strategies.[8] ILs exhibit unique physical properties rel-

ative to conventional liquids in terms of vapor pressure, viscosity, electrical and

thermal conductivity, solubility of polar and nonpolar molecules, and low melting

point.[9] Moreover, these properties can be tuned to specific applications by chem-

ically modifying the molecules that comprise the liquid, and/or by forming mul-

ticomponent mixtures of anions and cations, making ILs highly adaptable for a

variety of tasks. The use of ILs has made significant advances in electrochemical

applications[7, 10, 11], the processing of lignocellulose[12–15], and thermally stable

high performance lubricants[16, 17], the practical aspects of complete control of these

reactions lies in fostering an understanding of the complex dynamics of these liquids.

In general, dynamics play an important role in determining mass and heat trans-

port properties of reactions, which are crucial to many energy related applications.

Many proposed and actual applications of ILs involve charge-transfer reactions (e.g.

dye-sensitized solar cells, batteries, and many catalytic reactions), so understand-

ing the detailed microscopic mechanisms and time scales of solvation dynamics in

ILs is of pressing relevance. While the solvation response has been measured in a

range of ILs, the exact molecular mechanism responsible for their complex kinetic

1

profiles has not been determined until now. This dissertation sets out to develop

a fundamental understanding of the complex intermolecular interactions in ILs that

are responsible for microscopic structures and dynamics that ultimately manifest in

macroscopic physical properties by using molecular dynamics (MD) simulations to

calculate theoretical quantities directly comparable to experimental measurements of

solvation dynamics and infrared (IR) spectroscopy.

This dissertation is organized such that a brief overview of ILs and background

material concerning solvation dynamics and IR spectroscopy are presented in the

first chapter. The second chapter focuses on calculating solvation dynamics in a

common IL, [emim][BF4], thus allowing a direct comparison with our experimental

collaborators. Chapter 3 then expands the solvation dynamics study over a series

of imidazolium-based ILs in addition to analyzing the effects of charge scaling on IL

properties. In Chapter 4 the validity of linear response theory as applied to solva-

tion dynamics simulations in ILs over the entire response time is explored. The fifth

chapter describes the spectroscopic signatures of an isolated water molecule in an IL,

which acts as a probe of structure and dynamics within ILs, in addition to shedding

insight into water-ion interactions. Deviating from ILs, Chapter 6 presents calcu-

lations of multidimensional infrared spectroscopy of a non-perturbative vibrational

reporter to monitor the kinetics of proton transfer processes in aqueous solution. Fi-

nally, Chapter 7 contains concluding remarks and a summary of this work, as well as

proposed alternative systems of interest.

1.1 Ionic Liquids

ILs represent an important class of solvents with melting points below 100◦ C

composed entirely of ions and present a unique environment to test our theoretical

understanding of condensed phase dynamics. Unlike common inorganic salts such

as NaCl, these ions remain in the liquid state at ambient conditions due to weak

2

electrostatic interactions and frustrated packing that inhibits crystal formation. ILs

possess the advantages offered by aqueous solutions (i.e. nonflammable, high solubil-

ity of a range of compounds, efficient conductivity, etc.) and avoid certain limitations

by having a large potential window, excellent thermal stability, and the control of a

range of physicochemical properties.

Traditional molten salts were used in electrodeposition processes[18, 19] but with

operable temperatures of ∼1000◦ C, practical solution-phase applications are im-

possible. First generation ILs were synthesized with the goal of developing lower

temperature molten salts based on eutectic mixtures of chloroaluminates. These ILs

were able to operate at a lower temperature, however their extremely hygroscopic

nature resulted in an overproduction of HCl which limited their applicability. The

second generation ILs use ammonium, phosphonium, and most commonly imida-

zolium cations paired with discrete anions which offer more air and water stable

operable conditions[20] and ushered in a new era of intense IL research.

The cations examined in this dissertation, 1-butyl-3-methyl imidazolium, [bmim],

1-ethyl-3-methyl imidazolium, [emim], offer certain complexities that separate them

from inorganic cations K+ and Na+ (Figure 1.1). Their larger size and thus increased

charge delocalization decreases the lattice energy allowing these compounds to remain

liquid below 100◦ C. While studies examining the dependence of certain properties

on the alkyl-chain length have found changes in the viscosity[21, 22], solubility of

gases[23], and structural heterogeneity,[24, 25] the choice of the anion offers greater

control over the physicochemical properties. The favored IL 1-ethyl-3-methyl imi-

dazolium tetrafluoroborate [emim][BF4] was first introduced in 1992[26] followed by

the addition of another highly fluorinated anion, hexafluorophosphate [emim][PF6]

in 1994[27]. Unfortunately the melting point ∼ 58-60◦ C made [emim][PF6] cumber-

some until the introduction of [bmim][PF6] and [bmim][BF4] the following year.[28]

These cation/

anion pairs dominated the IL literature for a decade, however concerns

3

[emim]

[bmim]

Cations Anions

[BF4] [PF6]

[DCA] [TfO]

Figure 1.1. The structures of imidazolium cations and inorganic anionsstudied here. These geometries were calculated with density functionaltheory (DFT) with a B3LYP functional and the aug-cc-pVDZ basis set.The cations are 1-butyl-3-methyl imidazolium, [bmim], 1-ethyl-3-methyl

imidazolium, [emim], while the anions are tetrafluoroborate, [BF4],dicyanamide, [DCA], trifluoromethanesulfonate, [TfO],

hexafluorophosphate, [PF6].

4

over their aptitude to form HF gas[29] prompted the appearance of alternative an-

ions. Trifluoromethanesulfonate, [TfO], anions emerged as interesting ILs given their

relatively lower viscosities and stability.[30] The only non-fluorinated anion surveyed

in this dissertation, dicyanamide [DCA], relies on the highly electronegative carbon-

nitrogen triple bond to delocalize the charge resulting in some unique properties.

Presenting some of the lowest viscosities and highest conductivities for all ILs[31],

DCA based ILs are often considered in solar cell applications.[32, 33]

1.1.1 Polarity of ILs

The polarity of a solvent is informative regarding its solvating capability. A

common empirical measure of the polarity relies on the sensitivity of solvatochromic

probes reporting on various interactions in the solvent commonly reported on the

Reichardt’s solvent polarity parameter E(30)T scale. Representative E

(30)T values range

from 63.1 kcal/mol for water and 30.7 kcal/mol for tetramethylsilane, the least polar

compound. Despite large variations in the different structural motifs that comprise

the classes of ILs, the E(30)T values fall within a very narrow window around 47-49

kcal/mol.[34–36] This suggests ILs are more polar than acetonitrile (E(30)T of 45.6

kcal/mol) and less polar than methanol (E(30)T of 55.6 kcal/mol), more similar to

medium chain alcohols (butanol = E(30)T of 49.1 kcal/mol).[34]

Another descriptor of the solvent polarity is the dielectric constant, ε, which

characterizes the loss of intermolecular Coulombic interaction energy in the condensed

phase relative to vacuum. A large ε found in water or formaldehyde, ε = 80 and 84

respectively, is a reflection the ability of the solvent to efficiently shield the solute

charges, thus enabling effective solvation of polar or charged species. With that

definition is is reasonable to speculate that a system composed entirely of charged

species would have a larger ε than water. However, experimental measurements

on a range of ILs indicate ε for these systems are in the range of 8–15, similar

5

to pentanol (ε=15.1) and octanol(ε=8.8).[37] The modest ε is an indication of the

diverse environment of structured charge density and modulated screening efficiency

presented by these systems. Most notable, however, is the appreciable range that the

polarity can be altered solely by differing the components of the liquid.

1.2 Solvation Dynamics

Solvation dynamics refers to molecular reorganizations in response to a perturba-

tion in the geometric or electronic structure of a solute and are particularly important

for charge-transfer reactions whose kinetic rates are determined almost exclusively

by solvent reorganization. Solvent reorganization also influences the kinetic rates

and mechanisms of other classes of chemical reactions that involve polar transition

states.[38] Solvation dynamics are measured in time-dependent fluorescence Stokes

shift (TDSS) experiments. TDSS experiments employ fluorescent probe molecules to

measure the response of the environment to a sudden perturbation of the charge dis-

tribution of the probe molecule.[39–41] In brief, the experiment begins with an initial

laser pulse, v(0) that electronically excites the probe molecule. This excitation occurs

effectively instantaneously, such that the molecular geometry of the probe molecule is

unchanged, but its charge distribution is significantly altered. After the initial exci-

tation, the solvent environment begins to reorganize to accommodate the new charge

distribution. The reorganization stabilizes the excited electronic state of the probe

relative to its ground electronic state, and subsequent fluorescence, v(t), is redshifted

with respect to the initial fluorescence, v(0). The time scales of the environment

reorganization are typically characterized by a solvation response function,

S(t) =v(t)− v(∞)

v(0)− v(∞)(1.1)

where v(∞) is the emission frequency after the environment has completely responded

6

to the excited state charge distribution of the dye.

A suitable fluorescent probe molecule that can capture the dynamics of the solva-

tion environment over the necessary timescales while being minimally perturbative to

the system is tantamount to the success of solvation dynamics measurements. Often

fluorescent molecules that are sensitive to environmental polarities have been used

to shed insight into a variety of physicochemical properties. Typically these probes

possess an electron donating group, often an amino group, and an electron withdraw-

ing group that is positioned at a maximal distance from the amino group to achieve

a transfer of electron density that produces the large excited state dipole moment.

There are two classes of probe molecules depending on their ability to hydrogen bond

with the solvent.

Hydrogen bonding probes can complicate interpretations of the solvation timescales

because these interactions can destabilize the Franck-Condon excited state and can

potentially cause a blue shift in the absorption spectrum. Common hydrogen bond-

ing probes such as 6-propionyl-2-(N,N,-dimethylamino) naphthalene (PRODAN) and

4-aminophthalimide (4-AP) have been used to examine the solvation properties of

ILs, however the kinetics of their excited state are complex and debated. Differing

theoretical studies disagree on the existence of a twisted intramolecular or planar

intramolecular charge transfer state, thus impeding a straightforward interpretation

of the spectra.[42–46] Additionally, measurements utilizing 4-AP are extremely sen-

sitive to the degree of hydrogen bonding present in the solvation environment, and

in the present context introduce an additional complexity when describing solvation

dynamics.[47–50]. Because of these complications, rigid 7-aminocoumarins are typi-

cally used as solvatochromic laser dyes. Coumarin 153 (C153), the probe of choice for

this study, is a dye within the class of 7-aminocoumarins that possess a highly dipolar

excited state whose fluorescence is strongly sensitive to the solvent environment pro-

viding exceptional quantum yield. Theoretical investigations determined the HOMO

7

Figure 1.2. The structure coumarin 153 (C153) with the differences incharge density, ∆q, predicted upon excitation as calculated and validated

by Cinacchi et al.[1]

→ LUMO excitation corresponds to a π − π∗ transition with a substantial change

in the partial charges (Figure 1.2), and thus the dipole moment. Since intersystem

crossing is strongly forbidden in C153 its transition to ground electronic state is by

fluorescence exclusively, with a lifetime of 3–5 ns.[51]

Probe dependency remains an unresolved issue. An extensive examination by

Maroncelli et al. revealed significant differences in solvation relaxation time scales

independent of the quality and experimental conditions.[52] The assumption that

solvation dynamics is an inherent property of the media is invalid given the differences

in relaxation times for different probe molecules within the same IL.[53] Examining

the solvation dynamics of ILs is entirely dependent on the quality and location of

the probe molecule. Given the heterogeneous nature of these systems[54–64] it is

conceivable a degree of preferential solvation persists, a topic explored further in

Chapters 2 and 3.

1.2.1 Solvation Dynamics in ILs

The majority of the solvation dynamics measurements on ILs employ the time-

correlated single photon counting (TCSPC) technique to measure the TDSS following

8

optical excitation of the probe molecule.[34–36, 52, 65–72] TCSPC has a time resolu-

tion of approximately 20 ps, therefore any solvation dynamics occurring faster than

20 ps are left largely unresolved. Since the TDSS often persists to ∼10 ns in ILs,

TCSPC is an ideal technique to capture these relatively long time scales. In practice,

though, TCSPC will miss about half of the total solvation response.[71] Several in-

vestigators have utilized fluorescence upconversion spectroscopy with sub-100 fs time

resolution[73, 74] to measure faster portions of the TDSS in ILs.[75–79] By combining

the two measurement techniques, the full solvation response from ∼10 fs to ∼10 ns

is elucidated.[75, 76, 78, 79] Recently, Maroncelli, Ernsting, and coworkers have mea-

sured the TDSS of coumarin 153 (C153) in a series of ILs from 50 fs to 20 ns.[2, 3]

Immediately apparent in their results is a complex, highly nonexponential kinetic

profile with a noticeable plateau in the region between 1 and 10 ps, where the TDSS

slows appreciably. Trends with respect to varying the identity of the cations and

anions are not immediately apparent, although the slowest time scales do correlate

with viscosity (Figure 1.3).[2, 65, 69, 80]

There have been numerous experimental measurements [2, 3, 34–36, 52, 65–72, 75–

80] in addition to a number of theoretical and simulation studies[81–93] of solvation

dynamics in ILs. Kim and coworkers have examined important aspects IL dynamics,

including solvation dynamics, with both united and all-atom fully-flexible models.[84–

86, 91] For the united atom studies, solvation responses were computed to time scales

as long as 1 ns, whereas shorter time scales of 10 ps were considered for the all-atom

simulations. In these studies, the solute was modeled either as a diatomic or with

a benzene-like structure. Kobrak and coworkers performed simulations of solvation

dynamics that closely mimic experiment in so much as the all-atom, fully-flexible

liquids contain a realistically modeled C153 solute.[87, 88] The solvation response

was computed to 10 ps, and a number of decomposition strategies were employed to

understand the factors responsible for the onset of solvation dynamics in ILs. In par-

9

Figure 1.3. The experimental solvation relaxation time as a function of thesolvent viscosity[2]

10

ticular, Kobrak emphasizes the importance of the translations of the ions to the early

solvation response.[88] This is in stark contrast to conventional polar liquids, whose

short-time solvation dynamics are dominated by rotations.[41] Kobrak encountered

some difficulties in applying certain decomposition strategies to his calculated sol-

vation response functions because of the non-pairwise additive nature of the Ewald

summation technique.[94–96] Roy and Maroncelli performed extensive equilibrium

and nonequilibrium simulations of a variety of model solutes, as well as a fully atom-

istic C153 probe, in a coarse grained IL model.[82] For the C153 solute the computed

solvation response was in generally good agreement with experiment with the am-

plitude of the short time response being slightly overestimated. Roy and Maroncelli

also noted the importance of translational motions of the IL molecules to the in-

ertial solvation response, as well as reasonable agreement between the equilibrium

and nonequilibrium solvation response functions implying the validity of the linear

response approximation. Most recently, Schmollngruber, Schrder, and Steinhauser

investigated with the solvation dynamics of C153 in three imidazolium-based ILs.[81]

Their simulations utilized an electronically polarizable force field, and their results

for the solvation response functions agree well with experiment, although the long

time decay was slightly too slow. Once again, translational motions of the molecules

were implicated as being particularly important to the solvation response. By de-

composing the total response in terms of auto- and cross-correlation functions for the

anions and cations, Schmollngruber, Schrder, and Steinhauser found that the anion

and cation auto-correlation functions were similar, and the cross-correlation functions

were highly anti-correlated.

1.3 Vibrational Spectroscopy

Complementing measurements of solvation dynamics, ultrafast vibrational spec-

troscopy is an effective tool for probing the structure and dynamics in condensed

11

phase systems. Vibrational frequencies are susceptible to subtle changes in the sur-

rounding electric field, shifting in frequency relative to the magnitude and direction

of the oncoming electric field relative to the transition dipole of the vibration. This

information is experimentally captured in the line shape of the IR absorption spec-

trum and can reflect the distribution of electric fields surrounding the probe. This

simplified perspective can result in motional narrowing, where the line shape appears

to be more narrow than the actual distribution of frequencies, yet is informative re-

garding the dynamics of the surrounding solvent. For example, if the dynamics of

the surrounding solvent are slower than the vibrational frequency of interest the line

shape will be a Gaussian distribution identical to the distribution of the frequencies.

However if self averaging occurs resulting in motional narrowing, the line shape is

Lorentzian, the direct result of a Fourier transformation of an exponential decay.

The linear vibrational spectrum can be in principle be obtained by performing a

Fourier transformation of the quantum mechanical dipole moment time correlation

function (TCF)

I(ω) =

∫ ∞−∞

dt exp−iωt 〈µ(t) · µ(0)〉 (1.2)

where µ is the fully quantum mechanical dipole operator. While this approach is

exact, it is computationally intractable to determine the quantum mechanical TCF. A

common approximation is to treat the translational degrees of freedom classically and

replace the quantum mechanical dipole operator with the classical dipole moment.

This oversimplification can result in large errors when calculating relevant frequencies

of interest, when ~ω > kT , or when the Born-Oppenheimer potential deviates from a

harmonic approximation. Alternatively, the IR absorption spectra can be computed

from knowledge of the frequency and transition dipole moment trajectories using the

semiclassical fluctuating frequency approximation (FFA),[97]

12

I(ω) =

∫ ∞0

dteiωt⟨~µ(t) · ~µ(0)e−i

∫ t0 dτδω(τ)

⟩e−t/2T1 , (1.3)

where 〈· · ·〉 represents a classical ensemble average, δω(t) = ω(t)− 〈ω〉 is the fluctu-

ation of the frequency from its average value, 〈ω〉, and ~µ(t) is the transition dipole

moment vector. The FFA expression, 1.3, approximately captures the effects of

inhomogeneous broadening, motional narrowing, rotational broadening, and non-

Condon transition dipole moments on the vibrational line shape. The quality of the

resulting spectrum then solely depends on the method of acquiring the frequency

trajectory and transition dipole moment. As further discussed in Chapter 4, the vi-

brational frequencies for the IR spectra of water in ILs were obtained by connecting

solvent configurations to vibrational frequencies via an empirical relationship. Al-

ternatively, mixed quantum mechanics/molecular mechanics simulations employing

the self-consistent-charge density functional tight binding (SCC-DFTB) were used to

generate the frequencies in Chapter 6 for a tangential project that focused on proton

transfer in aqueous solution.

1.3.1 Spectroscopic Studies in ILs

1.3.1.1 Spectroscopic Characterization of ILs

Typical imidazolium-based ILs have weak absorption in the 250–400 nm region

and slight fluorescence around 300–600 nm. Most interesting however, is the shift of

the emission maximum to longer wavelengths when increasing the excitation wave-

length [98] inconsistent with Kasha’s rule resulting from the large degree of spa-

tial heterogeneity similarly observed in highly viscous media such as glasses and

polymers.[99] The absorption and fluorescent properties of ILs are extremely depen-

dent on the purity of the mixtures, as spurious spectroscopic signatures can result

from contaminants.[100] In the context of solvation dynamics, C153 has an absorp-

13

tion and emission fluorescence maximum that is orders of magnitude more intense

than the absorption and fluorescence behavior of imidazolium ILs, so convolution of

the spectrum is not observed.

1.3.1.2 Vibrational Reporters in ILs

X-ray spectroscopy, NMR, and vibrational spectroscopy have been used to char-

acterize the structure in bulk ILs.[25, 101–104] Ultrafast two-dimensional infrared

(2D IR) spectroscopy measurements of ILs have the potential to elucidate impor-

tant dynamical motifs that differ from conventional solvents. 2D IR spectroscopy

has already proven itself as a powerful technique for investigating the structure and

dynamics of liquids by monitoring the response of a vibration to the evolution of its

local environment, a process called spectral diffusion. The frequencies of vibrational

reporters are exquisitely sensitive to changes in their local environment, particularly

to changes in electrostatics, hydrogen bonding, and chemical processes. For example,

the OH and OD stretch frequencies of HOD are known to depend hydrogen bonding:

an increase in hydrogen-bond strength red-shifts the OH and OD stretch vibrational

frequencies. The inhomogeneous IR absorption line shape of liquid water reflects the

range of different hydrogen bonding environments present. [105–107] The spectral

diffusion time scales revealed by 2D IR have been shown to directly relate to hydrogen

bond rearrangement processes in liquid water.[108–111]

Previous work examining isolated water in ILs determined a water molecule is

bridged by two anions in an IL, existing in a A· · ·HOH· · ·A complex. As a result

of this proximity, the anions are most responsible for influencing the OH stretch

frequency.[112–114] Investigations varying the lengths of the cation alkyl chains in

imidazolium-based ILs suggest the chains do not have an influence on the OH stretch-

ing frequency.[112, 115] Recently, the dynamics of HOD isolated in an IL was in-

vestigated with vibrational spectroscopy.[116] The linear IR absorption spectrum

14

of the OD stretch frequency of dilute HOD in 1-butyl-3-methyl imidazolium hex-

afluorophosphate, [bmim][PF6], revealed a blue-shifted and a significantly narrowed

vibrational line shape compared to the spectrum of HOD in water. The blue-shift

suggests weaker OD interactions with the ionic environment and is characteristic

of a relatively isolated OD stretch, for example the free OD stretches at a liquid

D2O/vacuum interface.[117–119] The 2D IR measurements monitored spectral dif-

fusion of the OD stretch of HOD in the IL. An important quantity accessible by

both simulation and experiment is the frequency fluctuation time correlation func-

tion (FFCF), C(t) = 〈δω(t)δω(0)〉, where δω(t) is the deviation of the frequency

from its equilibrium value, δω(t) = ω(t)−〈ω〉. As a water molecule samples different

molecular environments, the FFCF decays to zero. This can be approximately related

to the spectral diffusion measurements quantified experimentally using the center line

slope (CLS) method.[120, 121] Measurements of the amplitudes and timescales of the

FFCF thus give information about the dynamics of the environment surrounding the

HOD molecule. Two times scales were found: 6.9 ± 2.1 ps and 72 ± 20 ps. The

faster of the two relaxation timescales was attributed to changes in the local structure

of the anions bridged by the water and the subsequent motions of the cations. The

slower relaxation time was assigned to orientational relaxation, though a discrepancy

of approximately one order of magnitude exists between the 72 ps timescale and

the 2.3 ns response in optical heterodyne detected optical Kerr effect experiments in

[bmim][PF6].[122]

15

CHAPTER 2

THE MECHANISM OF SOLVATION DYNAMICS IN [emim][BF4]

2.1 Introduction

Recall from Chapter 1, that solvation dynamics are measured in time-dependent

fluorescence Stokes shift (TDSS) experiments which employ fluorescent probe molecules

to measure the response of the environment to an instantaneous perturbation of the

charge distribution of the probe molecule.[39–41] The experiment begins with an ini-

tial laser pulse, v(0) that electronically excites the probe molecule. This excitation

occurs effectively instantaneously, such that the molecular geometry of the probe

molecule is unchanged, but its charge distribution is significantly altered. After the

initial excitation, the solvent environment begins to reorganize to accommodate the

new charge distribution. The reorganization stabilizes the excited electronic state of

the probe relative to its ground electronic state, and subsequent fluorescence, v(t), is

red shifted with respect to the initial fluorescence, v(0). The time scales of the envi-

ronment reorganization are typically characterized by a solvation response function,

S(t) =v(t)− v(∞)

v(0)− v(∞)(2.1)


to the excited state charge distribution of the dye, achieving an equilibrium solvation

structure around the newly formed charges.

Experimental studies of solvation dynamics in imidazolium-based ionic liquids

(ILs) have revealed complex kinetics over a broad range of time scales from fem-

16

toseconds to tens of nanoseconds. This chapter presents calculations of the solvation

response over the full range of time scales (from 10 fs to 10 ns) accessed in mea-

surements of C153 in 1-ethyl-3-methyl imidazolium ([emim]) and tetrafluoroborate

([BF4]). These calculations utilized microsecond-length molecular dynamics (MD)

simulations with the C153 and IL molecules modeled in full atomistic detail neces-

sary to capture the highly nonexponential kinetic profile, including the plateau in

the region between 1 and 10 ps. The calculated response is compared directly with

experiment, and analysis of the simulations with decomposition strategies developed

previously to understand solvation dynamics in complex biological systems[123–126]

provide insights into the mechanism of solvation dynamics in this imidazolium-based

IL.

2.2 Theoretical Methodology

2.2.1 Solvation Response Calculations

The solvation response of C153 in [emim][BF4] was computed using methodology

that has been utilized and validated extensively in previous MD studies of solvation

dynamics.[127–129] The central quantity in this approach is ∆E(t) = Ee(t)− Eg(t),

which represents the difference in the interaction energy of the probe molecule with

its environment for its excited (Ee) and ground (Eg) electronic states. The elec-

tronic states are modeled classically as two different distributions of atomic-centered

charges, which have been derived and validated previously from density functional

theory calculations.[1] This allows for the calculation of the equilibrium time corre-

lation function for the fluctuations in the solvation energy differences within a MD

simulation,

C(t) =〈δ∆E(t)δ∆E(0)〉〈(δ∆E)2〉

, (2.2)

17

where δ∆E(t) = ∆E(t)− 〈∆E〉 and 〈· · ·〉 is an ensemble average in the ground elec-

tronic state of the probe. Within linear response theory, which will be specifically

examined in Chapter 4, in addition to previous studies have generally found to be ap-

plicable to solvation dynamics in ILs at early times in the response,[89] C(t) is equal

to S(t), thus allowing direct comparisons with experiment.[129, 130] During calcula-

tions of ∆E(t), the long–ranged electrostatic interactions between C153 and the IL

molecules were computed with the damped shifted force (DSF) method.[131] The DSF

method is used as an alternative to the traditional Ewald summation technique,[94–

96] and facilitates decomposition of the solvation response (see 2.2.2) because it is

based explicitly on a pairwise sum.

2.2.2 Decomposition of the Solvation Response by Solvent Component

The total solvation response can be decomposed into contributions from the dif-

ferent constituents present in the liquid. Such decompositions are made possible

because of the additive nature of the solute interaction energy, ∆E(t) =∑

α∆Eα(t),

where ∆Eα(t) is the solute interaction energy with solvent component α, in this case

the anions, cations, and intramolecular electrostatic interactions within the probe

itself. Unfortunately, there is not a unique decomposition of Eq. (2.1) simply based

on expressing ∆Eα(t) as a sum. However, one decomposition strategy is formally

compatible with linear response theory,[90, 124, 132]

Cα(t) =〈δ∆Eα(t)δ∆E(0)〉〈(δ∆E)2〉

, (2.3)

where superscript α signifies the solvent component of interest. Previous investi-

gations have confirmed empirically that, when linear response theory holds, C(t)

corresponds to the contributions to S(t) from the solvent components (note that S(t)

does uniquely decompose due to the additive property ∆E(t)).[132, 133] Kobrak and

18

Znamenskiy[90] were the first to employ Eq.(2.3) in the context of solvation dynamics

in ILs. They decomposed the solvation response of the solute betaine-30 in 1-butyl-

3-methyl imidazolium ([bmim]) and hexafluorophosphate ([PF6]) over the range from

1 to 5 ps and found that the anion dominates the response on this timescale.

2.2.3 Decomposition of the Solvation Response by Translations and Rovibrations

The solvation response functions for the anions and cations of the IL can be further

decomposed into contributions from their respective translational and rovibrational

motions. The translational contribution, ∆Eαtrans, to ∆Eα for the cations and anions

are computed by regarding each relevant IL molecule as a single point charge located

at its center of charge. The rovibrational contribution, ∆Eαrovib, to ∆Eα is then just

obtained as the difference, ∆Eαrovib = ∆Eα − ∆Eα

trans. With these definitions, the

correlation functions for the cations and anions decompose into translational and

rovibrational contributions,

Cα(t) = Cαtrans(t) + Cα

rovib(t) (2.4)

where the functions Cαtrans(t) and Cα

rovib(t) are computed with Eq.(2.3) using ∆Eαtrans(t)

and ∆Eαrovib(t) in place of ∆Eα(t).

2.2.4 Molecular Dynamics Simulations

The MD simulations were performed using the Large-scale Atomic/Molecular

Massively Parallel Simulator (LAMMPS)[134] program with periodic boundary con-

ditions and a cubic simulation box containing 256 [emim] cations, 256 [BF4] anions,

and one C153 molecule. All of the molecules were modeled as fully flexible, except

for covalent bonds containing hydrogen which were fixed at equilibrium lengths using

the SHAKE algorithm.[135] For the C153 and [emim] molecules force-field parame-

19

ters for the bonds, bends, dihedrals, and atomic-centered Lennard-Jones sites were

adopted from the generalized Amber force field (GAFF).[136] Parameters for [BF4]

are not available in the GAFF, so these parameters were obtained from Liu et al.[137]

Atomic-centered partial charges for the IL molecules and the ground state of C153

were calculated via the Merz-Singh-Kollman[138] analysis of the electron density of

the optimized geometry of the molecules obtained with density functional theory

(DFT) with a B3LYP functional and the aug-cc-pVDZ basis set. The change in

the partial charges for C153 upon electronic excitation were calculated and validated

previously by Cinacchi et al.[1] thus the excited state partial charges for C153 are

obtained by simply adding these changes to the computed ground state charges. In

the MD simulations the long-ranged electrostatic interactions were computed with

the particle-mesh Ewald summation method with a 15 A real-space cutoff.[94, 139]

This same cutoff distance was utilized when computing interactions between Lennard-

Jones sites.

Since imidazolium-based ILs are known to exhibit slow (nanosecond) relaxation

dynamics, we employed a rigorous equilibration protocol before performing the pro-

duction run simulations from which the solvation response function was calculated.

Following an initial period of minimization, the temperature was slowly raised from

0 K to 300 K over a period of 200 ps. This was followed by a 4 ns simulation in the

NPT ensemble (300 K and 1 atm) using a Nose-Hoover thermostat and barostat.[140]

The size of the simulation box was isotropically scaled to reflect the average density

and was then simulated in the NVT ensemble for 1 ns at 300 K, the temperature

was raised to 600 K over 1 ns to destroy any pseudo-stable ionic cages that may

have formed. Next, the temperature was reduced back to 300 K in 1 ns, followed by

the NVT simulation for 1 ns at constant temperature of 300 K. The final velocities

were scaled to 300 K and a pre-production NVE simulation was performed for 11

ns. Production-runs (comprising a total of 5.015 µs) were performed in the NVE

20

ensemble with a 2 fs integration time step and a collection resolution of 10 fs.

A 100 ns control simulation of pure [emim][BF4] was performed to validate the

IL force-field. The average density of the liquid was found to be 1.19 g/cc, which

compares reasonably well to experiment (1.28 g/cc).[141] It is important to note

that the partial charges for [emim] and [BF4] were empirically scaled by a factor of

0.80, guided by DFT calculations,[142] to achieve better agreement with experiments

where dynamic properties are of interest. Charge scaling has become a fairly com-

mon practice in IL MD simulations and a valid means of increasing diffusion.[143]

The scaling factor is further addressed in Chapter 3, though, in brief, it can be re-

garded as an additional force-field parameter whose physical role is to account, in an

approximate and empirical fashion, for the effects of electronic polarizability. This

adjustment decreases the calculated density from 1.27 g/cc in a simulation with full

charges[137] to 1.19 g/cc with scaled charges. However, the computed self-diffusion

constants, 8.1× 10−11 m2/s for [emim] and 5.5× 10−11 m2/s for [BF4], compare more

favorably with experiment (5.0 × 10−11 m2/s and 4.2 × 10−11 m2/s) than diffusion

constants reported for simulations with full charges (1.1×10−11 m2/s and 0.9×10−11

m2/s).[137]

2.3 Results and Discussion

The calculated solvation response for C153 in [emim][BF4] is shown in Figure 2.1

along with the experimental measurement[2, 3] for direct comparison. The simulated

solvation response is in good overall agreement with experiment and it reproduces

the complex non-exponential decay, including the plateau in the ∼1 – 10 ps regime

reminiscent of dynamics in supercooled liquids. The pronounced oscillations in the

calculated response at times less than 10 ps are due to internal motions of the C153

probe molecule and will be discussed in more detail below. While the calculated re-

sponse is qualitatively similar to experiment over all timescales, it decays too quickly

21

in the regime beyond 10 ps. To quantify the differences in the long-time decay be-

tween experiment and theory, both solvation response curves were fit with a stretched

exponential function, Aexp(−(t/τ)β), in the range from 10 ps to 1 ns (Table 2.1 and

Figure 2.2). A stretched exponential is ideal over this range as it captures the su-

perposition of an indefinite number of single exponential decays all weighted by a

distribution of relaxation times.[144]

The time constant, τ , is shorter in the theoretical result (81.4 ps) than in the

experiment (115.7 ps). It has been empirically established that the long-time decay of

the solvation response in imidazolium-based ILs is viscosity dependent.[7, 65, 69, 80]

Thus, the slightly too large self-diffusion constants for the molecules in the neat

[emim][BF4] simulation Section 2.2.4 are a likely culprit for the slightly too fast long-

time decay of the solvation response. While it is beyond the scope of the present study,

it might be possible to utilize the experimental solvation response data to further

refine the dynamical properties of the IL force-field via the empirical charge scaling

factor discussed in Section 2.2.4 and Chapter 3. While modest discrepancies in the

long-time decay exist, the calculated solvation response captures the complex kinetic

behavior of the experimental measurement, thus validating the simulations directly

with experiment, and we will now proceed to further analyze the simulations to

uncover the molecular mechanisms responsible for solvation dynamics in [emim][BF4].

Figure 2.3 shows the decomposition of the total calculated solvation response of

C153 in [emim][BF4] into contributions from the anions, cations, and internal motions

of the C153 solute. It is immediately apparent that the anions dominate the solvation

response. Not only is the anion contribution substantially larger than that of the

cations or C153 for all time scales, it also mimics closely the characteristic shape of

the total response curve. The internal motions of the C153 solute do not contribute

to the decay of the solvation response (i.e. the C153 component of the response

22

Figure 2.1. Calculated (black) and experimental[2, 3] (green) solvationresponse functions in the range from 50 fs to 1 ns.

23

Figure 2.2. Fits of the calculated (black) and experimental (green) solvationresponses of C153 in the IL [emim][BF4] to a stretched exponential

function, Aexp(−(t/τ)β), in the time range between 10 ps and 1 ns. Thedata are shown as filled circles, while the fits are lines. The quality of thefits in terms of the correlation coefficient, r2, are excellent: r2 = 0.9987 for

the theoretical data and r2 = 0.9983 for the experimental data.

24

Figure 2.3. The calculated total simulated solvation response (black) isdecomposed using the methodology described in Section 2.2.2 into

contributions from the anions (red), the cations (blue), and the internalmotions of the C153 solute (purple).

25

TABLE 2.1

PARAMETERS FOR A STRETCHED EXPONENTIAL FIT

Experiment Theory

A 0.38 0.32

τ(ps) 115.7 81.4

β 0.55 0.74

Parameters for a stretched exponential, A exp(−(t/τ)β), fit to the calculated and ex-perimental solvation response functions in the range from 10 ps to 1 ns.

is generally flat). However, these motions do engender pronounced oscillations in

the total response function. Such oscillations in the solvation response have been

observed in high temporal resolution measurements in solution[145] and for a dye

molecule (Hoechst 33258) bound to DNA.[146] For H33258 bound to DNA an analysis

of the oscillations computed with theoretical methodology similar to that employed

in the present work yielded reasonably good agreement with experiment.[125] The

decomposition in Figure 2.3, which is formally consistent with the linear response

approximation, results in a less ambiguous interpretation than the analysis in terms

of auto- and cross-correlation functions presented most recently by Schmollngruber,

Schrder, and Steinhauser,[81] where it is not clear that the anions are the dominant

contributor to the solvation response over all timescales.

The results shown in Figure 2.3 suggest that the [BF4] anions play a particularly

important role in determining the solvation response. To begin to understand the role

of the anions in the solvation response, we first focused on the structure of the IL in

the vicinity of the C153 probe. Shown in Figure 2.4 are radial distribution functions,

26

g(r), for the center-of-mass of the cations and anions relative to the center-of-mass

of the C153 solute. The most striking feature is the dramatic enhancement of [emim]

cations in the vicinity of the C153 molecule, represented by the pronounced peak near

4 A and the corresponding depletion of [BF4] anions close to C153. The preferential

solvation of C153 by [emim] is perhaps not surprising, since the molecules can align

their flat surfaces and take advantage of favorable π–π stacking interactions. While

the radial distribution function shown in Figure 2.4 does not give a full characteriza-

tion of the three-dimensional solvent structure around the non-spherical C153 solute,

it does indicate that the [emim] cations are, on average, more proximal to the C153

solute than the [BF4] anions. This observation is consistent with previous studies of

the three-dimensional solvent structure around aromatic compounds in imidazolium

ILs.[147, 148] The observation of preferential solvation creates a conundrum for un-

derstanding solvation dynamics in [emim][BF4]. Conventionally, solvation dynamics

is dominated by molecules close to the fluorescent dye molecule. In this case, how-

ever, the anions, which have been implicated as the dominant player in the response

dynamics (Figure 2.3), are generally further away from the C153 dye molecule than

the cations. Before we resolve this issue, it is worth noting that the observation of

preferential solvation has broader implications. In most experiments that employ an

exogenous spectroscopic probe molecule, the general assumption is that the presence

of the solute does not greatly alter the native structure and dynamics of interest.

In this case, the C153 molecule is apparently inducing structure in the IL. This im-

plies that there is some ambiguity as to whether the experiment is really measuring

dynamics that are native to the neat IL. Preferential solvation effects could also be

relevant to the interpretations of other experiments on IL structure and dynamics.

To determine which specific motions of the [emim] and [BF4] molecules are most

relevant to solvation dynamics, we further decomposed the anion and cation sol-

vation responses into contributions from translations and rovibrations (Figure 2.5).

27

Figure 2.4. The radial distribution function, g(r), for C153-[emim] andC153-[BF4] pairs, where r is defined as the distance between the

center-of-mass positions of the relevant pair of molecules.

28

Focusing first on the [BF4] anions the results are unambiguous: translational mo-

tions of the anions dominate the total response, whereas [BF4] rovibrational motions

are negligible. Note that the shape of the anion translational decomposition nearly

perfectly mimics the total solvation response. Since the [BF4] molecule is symmetric

and possesses no permanent dipole moment it is not surprising that its rovibrational

motions do not affect the solvation dynamics. However, since solvation dynamics in

conventional polar liquids is governed mostly by rotational motions of the solvent,

the central importance of the translational motions of [BF4] to the solvation response

of C153 in [emim][BF4] is unusual and warrants further investigation. The cations

also exhibit unusual and interesting behavior in Figure 2.5. The translations of the

cations are also a significant contributor to the total solvation response (but still sig-

nificantly less than the anion translations), however these contributions are largely

offset by the cation rotations, which are uniformly negative in sign on all time scales.

Negative values of the cation rotational contribution to the total solvation response

indicate that these motions are actually counterproductive, on average, to stabilizing

the excited state charge distribution of the C153 solute.

The final unresolved issue for obtaining a complete view of the mechanism of

solvation dynamics in the [emim][BF4] IL is to determine which specific translational

motions of the [BF4] anion are relevant. For this we computed the residence-time

correlation function (RTCF) for the anions and cations in the first solvation shell of

the C153 solute, 〈n(0)n(t)〉, where n(t) = 1 if the molecule of interest is in the first

solvation shell and n(t) = 0 if it is not (Figure 2.6). For the purposes of the RTCF

calculation the first solvation shell was defined as any molecule whose center-of-mass

lies within 5.6 A of the center-of-mass of the C153 probe. 5.6 A was chosen because

it is the first minimum of the C153-[emim] radial distribution function. The RTCF

describes the time scales for molecules, either anions or cations, to enter or leave the

first solvation shell of the solute. The RTCF for the anion is generally similar to

29

Figure 2.5. The solvation responses of [emim] (blue) and [BF4] (red)decomposed into contributions from translational (solid) and rovibrational

(dashed) motions. For reference, the total solvation response minus thecontribution from the internal motions of the C153 solute is also shown

(black).

30

Figure 2.6. The residence-time correlation function (RTCF) for the anionsand cations in the first solvation shell of the C153 solute. The first

solvation shell was defined as any molecule whose center-of-mass lies within5.6 A of the center-of-mass of the C153 probe.

31

the solvation response. It appears to exhibit the same unusual kinetic profile as the

solvation response, which is suggestive that these anionic translational motions are

relevant for the response. In contrast, the RTCF for the cations is significantly slower

than the anions and its shape is qualitatively different from the solvation response.

The time scales for the decay of the anion RTCF are similar, although clearly slower,

than the solvation response. However, the difference in the times scales is likely due to

the somewhat arbitrary definition of the solvation shell. Changing the cutoff distance

for the solvation shell alters the time scales for the RTCF decay of both anions and

cations, but the qualitative profiles are unchanged (data not shown). The results in

Figures (2.4–2.6) support a solvation dynamics mechanism in [emim][BF4] where the

translational motion of the anions into and out of the first solvation shell of the C153

probe molecule potentially play an important role.

2.4 Summary

Extensive MD simulations have revealed the detailed molecular motions responsi-

ble for solvation dynamics of C153 in the imidazolium-based IL [emim][BF4] (Figure

2.7). Solvation dynamics in liquids generally involves collective motions of the solvent

environment in the vicinity of the fluorescence probe molecule. In this case, however,

we have identified a particular molecular motion that appears to be especially rele-

vant to solvation dynamics in [emim][BF4], namely the translational motion of the

[BF4] anion into and out of the first solvation shell of C153. This proposed mecha-

nism is consistent with a number of previous simulation studies that have implicated

translational motions and/or motions of the anions as being especially relevant to

solvation dynamics in imidazolium-based ILs.[82, 86, 88–90] The MD simulations

have also revealed that the IL forms a specialized structure around the C153 solute,

in which the first solvation shell is enriched in [emim] while the second solvation

shell is enriched in [BF4]. An important question remains for future studies: how

32

Figure 2.7. A schematic depiction of the mechanism of solvation dynamicsin C153/[emim][BF4].

33

general is this anion-translation mechanism? It seems likely that other imidazolium-

based ILs, whose cations can preferentially solvate dyes with fused ring structures,

will exhibit this mechanism. However, as one deviates from the structural motifs

of the C153/[emim][BF4] system, new solvation dynamics mechanisms could emerge.

This presents both challenges and opportunities for the theoretical and experimental

communities interested in designing ILs with properties selectively tuned for specific

applications.

34

CHAPTER 3

SIMULATIONS OF THE SOLVATION RESPONSE IN A SERIES OF IONIC

LIQUIDS

3.1 Introduction

In the previous chapter microsecond-length molecular dynamics (MD) simula-

tions of coumarin 153 (C153) in 1-ethyl-3-methyl imidazolium tetrafluoroborate,

[emim][BF4], were performed to reveal the molecular-level mechanism for solvation

dynamics. In that particular system it was the translational motion of the [BF4] anion

into and out of the first solvation shell of C153 that dominated the solvation response.

Given the sensitivity of certain properties to variations in the cation and anion con-

stituents in the IL[9, 21–25], it is necessary to understand if this anion-translation

mechanism can be generalized to other imidazolium-based ILs. This chapter presents

calculations of the solvation response of C153 in a series of imidazolium-based ILs

comprised of cations and anions seen in Figure 3.1. Two cations, 1-butyl-3-methyl im-

idazolium, [bmim], and 1-ethyl-3-methyl imidazolium, [emim], were paired with four

different anions, tetrafluoroborate, [BF4], dicyanamide, [DCA], trifluoromethanesul-

fonate, [TfO], hexafluorophosphate, [PF6], to create five unique systems, [emim][BF4],

[bmim][BF4], [bmim][DCA], [bmim][PF6], and [emim][TfO] allowing a direct compar-

ison to experiment. Studying this series where size, shape, and charge distribution of

the cations and anions varies is helpful to determine if any trends or generalizations

regarding the solvation mechanism are present.

Additionally, this chapter investigates the effects of charge scaling. Transport

properties such as the mean-square displacement (MSD), diffusion coefficients, and

35

[emim]

[bmim]

Cations Anions

[BF4] [PF6]

[DCA] [TfO]

Figure 3.1. Optimized structures of imidazolium cations and inorganicanions studied in this chapter. The cations are 1-butyl-3-methyl

imidazolium, [bmim], 1-ethyl-3-methyl imidazolium, [emim], while theanions are tetrafluoroborate, [BF4], dicyanamide, [DCA],

trifluoromethanesulfonate, [TfO], hexafluorophosphate, [PF6].

36

viscosity are all affected by modifications to the charges. The accuracy of a molecular

dynamics simulation is dependent on the proper selection of the force field parame-

ters. Force fields are an approximation to the intra- and inter-molecular interactions

that attempt to capture the properties of molecules accurately and efficiently over a

range of conditions. A force field contains three kids of parameters that determine

bonded interactions, electrostatics, and short range interactions. Bonded parame-

ters are generally calculated from quantum mechanics, whereas electrostatics and

short-range interactions are more difficult to parametrize. Accurately representing

this interplay between long-range and short-range interactions is key to achieving a

correct description of the system, and it truly matters how the force field deals with

charge transfer and polarization. Some force fields are more general, such as OPLS,

GAFF, or CHARMM, meant to be transferable over a range of molecules and tem-

peratures while others are created and parameterized to match specific experimental

properties.

Classical, or non-polarizable, force fields use static partial charges for each atomic

site to model the electrostatic interactions. In IL systems, non-polarizable force

fields typically underestimate dynamic and transport properties due to a neglect

of the electronic polarization and charge transfer effects present in the condensed

phase. Ideally using a fully polarizable force field would adequately capture the

movement of electron densities, and various studies have examined the inclusion of

polarizability.[81, 143, 149–151] Polarizable models consistently show faster transla-

tional and rotational relaxations, higher self-diffusion and conductivity, and lower

shear viscosity when compared to non polarized models. This is a consequence of

a weakening of the long-range interactions caused by enhanced screening. However,

due to the sluggish dynamics and the the long timescales required for accurate de-

scriptions of solvation dynamics calculations, simulating hundreds of molecules in a

fully polarizable model for microseconds is computationally prohibitive.

37

Utilizing fixed charges in a non-polarizable force field requires careful insight into

how one deals with charge transfer and polarization. While not modeling the atomic

sites as being explicitly responsive to their local environment, fixed-charge force fields

accomplish an effective representation by scaling the charges of the molecules and

using existing generalized force fields, or undergo a complete reparameterization of the

short-range interactions and keep the unit charges ±1. Adopting the latter method,

Koddermann et al.[152] showed that through reparameterization and matching the

experimentally derived observables (density, self-diffusion coefficients, and rotational

correlation dynamics) they were able to reproduce viscosity, the heats of vaporization

and dynamic properties maintaining full unit charges on all molecules. While this

force field is transferable to imidazolium cations with various alkyl chain lengths, it

requires dynamical properties as inputs to fit these short range parameters, which

presents a difficulty as these experiments for a range of cation and anion pairs are

sparse.

Reducing the net charges, entertainingly referred as ‘Poor man’s polarization,’[143]

is grounded in electronic structure calculations. A number of studies performing ab

initio calculations of non-isolated IL ions revealed the net charges are reduced due to

charge transfer and polarization.[153–158] In principle, charge transfer occurs when

the charge density is shifted from one ion to another ion via orbital overlap. Quanti-

fying this effect was carried out when a systematic study involving XPS, NMR, and

corroborating evidence from DFT calculations determined significant charge transfer

and polarization are present in these ILs.[103] Taken together, a reduced point charge

is representative of this screened partial charge. In Section 3.4 the effects of varying

the overall scaled charges on the dynamics in ILs are discussed.

38

3.2 Methodology

3.2.1 Decomposition of the Solvation Response

Recall the total solvation response can be decomposed into contributions from the

different constituents present in the liquid. Such decompositions are made possible

because of the additive nature of the solute interaction energy, ∆E(t) = Σα∆Eα(t),

where ∆Eα(t) is the solute interaction energy with solvent component α, in this case

the anions, cations, and intramolecular electrostatic interactions within the probe

itself. Unfortunately, there is not a unique decomposition of C(t) simply based on

expressing ∆Eα(t) as a sum. However, one decomposition strategy is formally com-

patible with linear response theory,[90, 124, 132]

Cα(t) =〈δ∆Eα(t)δ∆E(0)〉〈(δ∆E)2〉

, (3.1)

where superscript α signifies the solvent component of interest. Note that α could

also correspond to other components such as rotations and translations of cations

and anions, thus allowing further insight.


Similar to [emim][BF4] in Chapter 2, cubic simulation boxes were created contain-

ing 256 cations, 256 anions, and one C153 molecule for each of the following systems:

[bmim][BF4], [bmim][DCA], [bmim][PF6], and [emim][TfO]. The solvation dynamics

calculations presented in Section 3.3 employed a charge scaling parameter, λ, of 0.80

and 0.84, respectively, based on DFT calculations and simulations of [emim][BF4]

and [bmim][BF4] which found the ideal scaling parameter for these systems.[142]

Lacking an exhaustive investigation into the appropriate scaling parameter for these

systems, λ was assumed to be cation dependent where the [emim] cation-based sys-

tems, [emim][BF4] and [emim][TfO], λ = 0.80, while for [bmim] cation-based systems,

39

[bmim][BF4],[bmim][PF6], and [bmim][DCA], λ = 0.84. The validity of this assump-

tion is examined below in Section 3.4.1. For the analysis of charge scaling, identical

systems were created however the net charge was scaled appropriately. All of the

molecules were modeled as fully flexible, except for covalent bonds containing hydro-

gen which were fixed at equilibrium lengths using the SHAKE algorithm.[135] The

force field parameters for the bonds, bends, dihedrals, and atomic-centered Lennard-

Jones sites for [BF4] and [PF6] were obtained from Liu et al.[137], while the parame-

ters for [DCA] were taken from Lopes et al.[159] For C153, [emim], [bmim], and [TfO],

parameters were adopted from the generalized Amber force field (GAFF).[136] All

atomic-centered partial charges for the IL molecules and the ground state of C153

were derived using the Merz-Singh-Kollman[138] scheme to interpret the electron

density of the optimized geometry of the molecules obtained with density functional

theory (DFT) with a B3LYP functional and the aug-cc-pVDZ basis set. The change

in the partial charges for C153 upon electronic excitation were calculated identical

to Chapter 2. In the MD simulations the long-ranged electrostatic interactions were

computed with the particle-mesh Ewald summation method with a 15 A real-space

cutoff.[94, 139] This same cutoff distance was utilized when computing interactions

between Lennard-Jones sites. The equivalent equilibration protocol was employed

whereby each system undergoes a total of 22 ns of minimization, NPT, NVT, and

NVE ensemble simulations explicitly laid out in Chapter 2. All production-runs were

performed in the NVE ensemble with a 2 fs integration time step and a collection

resolution of 10 fs for trajectories 2.0 µs long.

Simulations of the pure ILs were performed for 100 ns to validate our force field

and charge scaling parameter. Determining a reliable a self-diffusion coefficient re-

quires considerable amounts of simulation time, though to ensure sufficient conver-

gence, multiple checkpoints from the trajectory were used as starting points in the

calculation. Using the Einstein relation, limt→∞MSD = 6Dt, in the linear range of

40

TABLE 3.1

SELF-DIFFUSION COEFFICIENTS FROM MD SIMULATIONS

System λ D+[sim] D

[sim]− D

[lit]+ D

[lit]− Ref

[bmim][BF4] 0.84 1.7 1.2 1.4 1.3 [161]

[bmim][DCA] 0.84 1.7 2.0 0.4 0.5 [160]a

[bmim][PF6] 0.84 0.6 0.3 0.8 0.6 [162]

[emim][TfO]0.80 3.0 1.3 1.1 1.6 [81]a

0.84 1.9 0.9

[emim][BF4]

0.80 8.1 5.5 5.0 4.2 [163]

1.0 0.3 0.2

0.80ring 6.8 4.9

a Polarizable MD simulation results. The ion self-diffusion coefficients D+/− (in unitsof 10−11 m2/s) from MD simulations along with literature values for the IL systems.The net unit charge of the cations and anions is given by λ.

0.1 – 1000 ps, self-diffusion coefficients were calculated (Table 3.1). In all cases the

simulated ILs compare favorably with experiment, albeit predicting faster dynamics.

In the absence of experimental data for [bmim][DCA] and [emim][TfO], transport

properties calculated using parameters from polarizable force fields [81, 160] indi-

cate our MD simulations are in reasonable agreement. See Section 3.4, in particular

Subsection 3.4.1, for a discussion regarding the implications of charge scaling on the

dynamic properties.

41

3.3 Solvation Dynamics Results

Shown in Figure 3.2 are the calculated solvation responses for C153 in [emim][BF4],

[bmim][BF4], [bmim][DCA], [emim][TfO], and [bmim][PF6], along with the exper-

imental measurements[2, 3] for direct comparison. The experimental results were

scaled by a multiplicative constant to bring the results into maximum coincidence

for comparative purposes (Appendix A). The simulated solvation response is able to

capture the complex non-exponential decay, including the plateau in the ∼ 1− 10 ps

regime, and agrees well with experiment. For all the ILs systems studied here, the

decay response is qualitatively similar to experiment over the entire range, however

it consistently predicts a more rapid decay than experimental measurements, with

the exception of [bmim][DCA]. The calculated response function for [bmim][DCA]

predicts faster short-time and slower long-time dynamics than experimental observa-

tions, most likely due to inaccurate approximations in the force field parameters for

this anion.

To facilitate comparison to experiment, the solvation response functions were fit

with a single exponential, Aexp(−(t/τ)), in the range from 50 ps to 400 ps seen

in Appendix A. The theoretical time constants are lower than those measured by

experiment (Figure 3.3), however it appears to be a systematic underestimation due

to overscaling the charges that led to slightly larger self-diffusion constants reported

in Table 3.1. This phenomena is examined in greater detail in Section 3.4 where varied

charge scaling parameters are used to refine the the dynamical properties of the IL

force field to improve the ability of the simulation to reproduce the experimental

solvation response data. Although the simulations report response functions that are

faster than experimental measurements, the calculated solvation response captures

the non-exponential kinetic behavior, thereby validating the simulations directly with

experiment. Figures 3.4-3.7 shows the decomposition of the total calculated solvation

response of C153 in [bmim][BF4], [bmim][DCA], [bmim][PF6], and [emim][TfO] into

42

Figure 3.2. The calculated (dashed) and experimental (solid) solvationresponse functions for [emim][BF4] (black), [bmim][BF4] (red),

[bmim][DCA](green), [emim][TfO](blue), and [bmim][PF6] (brown) over therange 50 fs to 1 ns.

43

Figure 3.3. Time constants for experiment and calculated responsefunctions derived from a fit to a single exponential, Aexp(−(t/τ)), in the

range from 50 ps to 400 ps.

44

contributions from the anions (red), cations (blue), and internal motions of the C153

solute (purple). In all cases the anions dominate the solvation response. Not only is

the anion contribution substantially larger than that of the cations or C153 for all

time scales, the anions are responsible for the the characteristic shape of the total

response curve. The internal motions of the C153 solute do not contribute to the

decay of the solvation response (i.e. the C153 component of the response is generally

flat).

The decomposition results indicate the anions play a particularly important role

in determining the solvation response. Further insight regarding the role of the anions

in the solvation response, is gained by analyzing the structure of the IL in the vicin-

ity of the C153 probe. Shown in Figure 3.8 are radial distribution functions, g(r),

for the center-of-mass of the cations and anions relative to the center-of-mass of the

C153 solute, including the results from [emim][BF4] reported in Chapter 2. Imme-

diately apparent is the proximity at which the relatively larger imidazolium cations

are to the C153 molecule compared to the smaller, mostly spherical anions. The

non-spherical anion, [DCA], shows a small enhancement near 4 A before mimicking

similar charge ordering seen in the other ILs. While the radial distribution function

shown in Figure 3.8 does not give a full characterization of the three-dimensional sol-

vent structure around the non-spherical C153 solute, it does indicate that the cations

are, on average, closer to the C153 solute than the anions. This observation is consis-

tent with previous studies of the three-dimensional solvent structure around aromatic

compounds in imidazolium-based ILs,[147, 148] though confirms that despite the di-

versity of the molecular environments in these ILs, preferential solvation of C153 by

the imidazolium-based cations is persistent. Given the favorable π–π stacking in-

teractions between C153 and the imidazolium ring and the heterogeneous nature of

these systems,[54–64] it is conceivable a degree of preferential solvation is present.

Preferential solvation as first understood in mixtures of polar and non-polar solvents

45

Figure 3.4. The calculated total solvation response (black) is decomposedinto contributions from the [BF4] anions (red), the [bmim] cations (blue),

and the internal motions of the C153 solute (purple).

46

Figure 3.5. The calculated total solvation response (black) is decomposedinto contributions from the [DCA] anions (red), the [bmim] cations (blue),


47

Figure 3.6. The calculated total solvation response (black) is decomposedinto contributions from the [PF6] anions (red), the [bmim] cations (blue),


48

Figure 3.7. The calculated total solvation response (black) is decomposedinto contributions from the [TfO] anions (red), the [emim] cations (blue),


49

Cations

Anions

Figure 3.8. The radial distribution function, g(r), for C153-[cation] andC153-[anion] pairs, where r is defined as the distance between the

center-of-mass positions of the relevant pair of molecules.

50

was first described in terms of ‘dielectric enrichment’[164, 165] where the solute is

surrounded by solvent molecules to form an associated complex in thermodynamic

equilibrium. Studies examining the effects of preferential solvation of C153 in toluene-

acetonitrile and toluene-methanol mixtures[166] and more recently in IL-surfactant

solutions[167] have highlighted the implications of these non-ideal systems. In most

experiments that employ a spectroscopic probe molecule, the general assumption is

that the presence of the solute does not alter the native structure and dynamics of

interest. Figure 3.8 reveals the C153 molecule is apparently inducing structure in

the ILs. This suggests that there is some ambiguity as to whether the experiment is

really measuring dynamics that are native to the neat IL.

Further decomposition of the component solvation responses in Figures 3.9-3.12

identifies specific motions, translations and rovibrations, of the cation and anion

molecules necessary for effective charge accommodation. The results are unambigu-

ous: translational motions of the anions (solid red) dominate the total response for

all imidazolium-based ILs studeied here, whereas anion rovibrational motions (red

dashed) are negligible, or slightly negative in the case of [bmim][DCA]. The transla-

tions of the cations (solid blue) are also a significant contributor to the total solva-

tion response, however these contributions are offset by the cation rotations, which

are negligible or negative in sign on all time scales. Negative values of the [DCA]

and cation rotational contribution to the total solvation response indicate that these

motions are actually counterproductive to stabilizing the excited state charge distri-

bution of the C153 solute.

Solvation dynamics in conventional polar liquids is governed mostly by libra-

tional and rotational motions of the solvent molecules proximal to the fluorescent

dye molecule. The results of the solvation response decomposition presented in Fig-

ures 3.4-3.12 indicate the translational motions of the anions are essential to the

solvation response of C153 in imidazolium-based ILs. To determine which specific

51

Figure 3.9. The solvation responses of [bmim] (blue) and [BF4] (red)decomposed into contributions from translational (solid) and rovibrational(dashed) motions. For reference, the total solvation response is also shown

(black).

52

Figure 3.10. The solvation responses of [bmim] (blue) and [DCA] (red)decomposed into contributions from translational (solid) and rovibrational(dashed) motions. For reference, the total solvation response is also shown

(black).

53

Figure 3.11. The solvation responses of [bmim] (blue) and [PF6] (red)decomposed into contributions from translational (solid) and rovibrational(dashed) motions. For reference, the total solvation response is also shown

(black).

54

Figure 3.12. The solvation responses of [emim] (blue) and [TfO] (red)decomposed into contributions from translational (solid) and rovibrational(dashed) motions. For reference, the total solvation response is also shown

(black).

55

Figure 3.13. The residence-time correlation function (RTCF) for the anionsand cations in the first solvation shell of the C153 solute. The first solvationshell was defined as any molecule whose center-of-mass lies within the first

solvation shell, defined as the first minimum of the cation-C153 g(r).

56

translational motions of the anions are relevant we computed the residence-time cor-

relation function (RTCF) for the anions and cations in the first solvation shell of

the C153 solute, 〈n(0)n(t)〉, where n(t) = 1 if the molecule of interest is in the first

solvation shell and n(t) = 0 if it is not (Figure 3.13). For the purposes of the RTCF

calculation the first solvation shell was defined as any molecule whose center-of-mass

lies within the first solvation shell, defined as the first minimum of the cation-C153

g(r) (top panel in Figure 3.8). The RTCF reports on the time scales for molecules,

either anions or cations, that enter or leave the first solvation shell of the solute. The

RTCF for the anions share the characteristic shape of the solvation response, which

is suggestive that these anionic translational motions are relevant for the response.

In contrast, the RTCF for the cations is significantly slower than the anions and

its shape is qualitatively different from the solvation response. The time scales for

the decay of the anion RTCF are similar, although clearly slower, than the solvation

response. However, the difference in the times scales is likely due to the somewhat

arbitrary definition of the solvation shell. The results in Figures (3.8–3.13) support

a solvation dynamics mechanism in ILs where the translational motion of the anions

into and out of the first solvation shell of the C153 probe molecule potentially play

an important role.

3.4 Charge Scaling

3.4.1 Self-Diffusion Coefficients

Force fields inherently contain a variety of approximations to model intra- and

inter-molecular interactions and rely on extensive parameterization and analytic ex-

pressions to describe the potential energy. Traditional non-polarizable force fields

utilize force constants, reference angles, Lennard-Jones parameters and static unit

charges to describe the molecular interactions. The charge scaling parameter, λ, can

57

Figure 3.14. Calculated self-diffusion coefficients for [emim] (blue) and[BF4] (red) for varied unit charges. Experimental measurements (dashed)self-diffusion coefficients for this IL in the range of 298-303 K are reportedto vary from 4.4− 5.4× 10−11 m2/s for [emim] and 3.6− 4.2× 10−11 m2/s

for [BF4].[4]

58

be thought of as an additional mutable parameter set on improving the accuracy of

the force field. MD Simulations employing ions with a static net charge of ±1 dras-

tically underestimate the dynamics of the system, thus requiring the simulations to

either be performed at elevated temperatures,[168] or reducing the overall charge on

the ions by introducing a scaling parameter. As discussed above, 100 ns simulations

of each IL were performed to determine the self-diffusion coefficients (Table 3.1) for

a given charge scaling parameter, λ.

Modifying λ for identical systems results in dramatic changes to the self-diffusion

constant. For example, six systems of pure [emim][BF4] were simulated for 100 ns

with λ ranging from 0.80-0.85 to calculate the self-diffusion coefficient (Figure 3.14).

Included in Figure 3.14 are experimental measurements (dashed) of the self-diffusion

coefficients for [emim][BF4] in the range of 298-303 K are reported to vary from

4.4−5.4×10−11 m2/s for [emim] and 3.6−4.2×10−11 m2/s for [BF4].[4] Particularly

interesting is the linear dependence of the diffusion on λ, predicting unit charges

scaled by 82.5% as being most appropriate for both the cation and anion to reproduce

the transport properties observed experimentally.

To examine whether λ is an inherent characteristic of the cation, the scaling pa-

rameter appropriate for [emim][BF4], 0.80, and for [bmim][BF4], 0.84, were applied

to [emim][TfO] to calculate the self-diffusion coefficient. Polarizable MD simulations,

which in the absence of any experimental evidence represent the most accurate de-

termination for the self-diffusion coefficients, reports D+ = 1.1 × 10−11 m2/s and

D− = 1.6 × 10−11 m2/s, indicating λ = 0.84 (D+ = 1.9 × 10−11 m2/s and D− =

0.9 × 10−11 m2/s) as being more representative of the dynamics of the system than

when λ = 0.80. When λ = 0.80, excessive reduction of the charges results in D+ that

is almost triple the reported literature value 3.0× 10−11 m2/s and 1.1× 10−11 m2/s,

respectively.[81]

For [emim][BF4] the atomic partial charges were scaled by a factor of 0.80, which

59

increased the self-diffusion coefficients from 0.3×10−11 m2/s for [emim] and 0.2×10−11

m2/s for [BF4] with full unit charges to 8.1× 10−11 m2/s for [emim] and 5.5× 10−11

m2/s for [BF4]. It is conceivable that the alkyl chain of the cation will play a minor

role in the polar regions of increased charge density, and applying a uniform charge

scaling factor to the entire molecule is too drastic. In fact, if the atomic partial

charges on the imidazolium ring are scaled while the charge density on the alkyl chain

is unchanged the computed self-diffusion coefficients, 6.8×10−11 m2/s for [emim] and

4.9 × 10−11 m2/s for [BF4], compare more favorably with experiment (5.0 × 10−11

m2/s and 4.2× 10−11 m2/s).[163]

3.4.2 Charge Scaling Effects on Solvation Dynamics

Response functions characterizing the solvation dynamics are a excellent measure

of the validity of a force field. The decay profile contains a wealth of information

regarding the temporal evolution of collective dynamics over a broad range (fs to ns).

The consequences of altering the electrostatic interactions of the molecules results in

pronounced changes in the timescales of solvation. Figure 3.15 highlights the striking

differences in the solvation response brought about by modifying the Coulombic in-

teractions. As expected, from the dramatic reduction in the self-diffusion, simulations

using full unit charges (λ = 1) for the IL molecules results in a solvation response

that overestimates the decay timescale. The response function in a simulation where

the partial charges for the IL molecules were scaled by 0.80 (as reported in Chapter

2) is in good qualitative agreement with experiment (filled black circles), though it

decays too quickly in the regime beyond 10 ps. Reducing the partial charges only on

the imidazolium ring (turquoise) improves the translational dynamics (see Section

3.4.1), though also decays too quickly beyond 10 ps. Examining the dependence of

the self-diffusion coefficient on λ suggested partial charges reduced by 0.825 (Figure

3.14) are necessary to reflect the dynamics observed experimentally. However the

60

Figure 3.15. The calculated (solid) solvation response functions for[emim][BF4] where the charge scaling parameter λ was varied from 1.0

(orange), 0.825 applied to the entire [emim] cation(red) 0.80 applied to theentire [emim] cation (black), or 0.80 applied to the imidazolium ring

(turquoise), along with experimental measurements (black filled circles)over the range 50 fs to 1 ns.

61

solvation response utilizing the scaled charges of 0.825 only modestly improves the

long time dynamics, relative to experiment.

The unsophisticated approach of tuning the partial charges of the molecules as

a means to improve agreement with experimental measurements of the solvation

response is not ideal. To be thoroughly correct, a full reparameterization of the force

field is necessary to adequately describe the complicated combination of molecular

interactions observed in solvation dynamics.

3.5 Summary

The calculated solvation response of C153 in a series of imidazolium-based ILs,

[emim][BF4], [bmim][BF4], [bmim][DCA], [emim][TfO], and [bmim][PF6] identify a

general solvation mechanism. The particular molecular motion that appears to be

especially relevant to solvation dynamics in imidazolium-based ILs are the the transla-

tional motions of the anions into and out of the first solvation shell of C153, regardless

of the composition of the IL. It is conceivable postulate that as one deviates from the

structural motifs whereby the cations cannot preferentially solvate dyes with favorable

aromatic interactions, new solvation dynamics mechanisms will emerge. Investigat-

ing the impacts of charge scaling revealed the linear dependence of the self-diffusion

coefficient on the effective scaling parameter. Charge-scaled models are able to re-

produce the complexities of the solvation response function, and are ideally suited to

reproduce collective properties where the use of polarizable models is impractical.

62

CHAPTER 4

REGARDING THE VALIDITY OF LINEAR RESPONSE THEORY IN

SOLVATION DYNAMICS SIMULATIONS OF IONIC LIQUIDS

4.1 Introduction

Observing the evolution of solvent reorganization in the vicinity of an excited

probe molecule provides unique insight into molecular interactions responsible for

accommodating a charge perturbation. In particular, discerning these molecular

mechanisms is important to understanding the role of solvents in charge-transfer

reactions whose kinetic rates are influenced by solvent reorganization.[38] Central

to the study of solvation dynamics is linear response, which makes the assumption

that the dynamics of a system responding to a nonequilibrium state are equivalent

to the response to thermal fluctuations identical in amplitude and frequency in an

equilibrium system.

Time dependent fluorescence Stokes-shift (TDSS) measurements investigating

these solvation dynamics rely on an ultrafast laser pulse with energy hv(0), that

electronically excites a fluorescent probe molecule such as Coumarin-153 (C153),

4-aminophthalamide (4-AP), or PRODAN. This excitation is essentially occurring

instantaneously following the Franck-Condon principle, where the molecular geome-

try of the probe molecule is unchanged, but the charge distribution is significantly

altered such that a large change in the dipole is achieved. The subsequent fluorescent

emission of the probe, v(t), is continuously shifted to longer wavelengths over time,

as the solvent molecules reorganize to establish new equilibrium positions relative

63

to the new charge distribution. TDSS experiments monitor this temporal evolution

with a time dependent solvent response function,

S(t) =v(t)− v(∞)

v(0)− v(∞)(4.1)


to the excited state charge distribution of the probe.[39–41] Linear response theory

equates the nonequilibrium response function S(t) to the equilibrium time correlation

function (TCF), C0(1)(t), of the fluctuations in the solvent effect on the electronic

energy gap,[129, 169]

S(t) ∼= C0(1)(t) =〈δ∆E(0)δ∆E(t)〉0(1)〈(δ∆E)2〉0(1)

(4.2)

where δ∆E(t) = ∆E(t) − 〈∆E〉0(1) and 〈...〉0(1) is an ensemble average with the

probe molecule modeled in the ground or excited electronic state, respectively. Here

∆E(t) = Ee(t)−Eg(t) the difference in the interaction energy of the probe molecule

with its environment for the excited (Ee) and ground (Eg) electronic states. An

important criteria for the validity of linear response theory is that the time-dependent

distribution of ∆E(t) be adequately described by a Gaussian distribution.[130, 170]

Deviations from linear response occur when the electronic transition of the probe

molecule undergoes significant change in magnitude, size, or when the excitation

alters the solvation structure in such a way that it is no longer similar to ground

state fluctuations, e.g. altering the hydrogen bonding capabilities.[41, 128]

In Chapters 2 and 3, we postulated the solvation mechanism in imidazolium-

based ILs is dominated by translational movements of anions into and out of the

first solvation shell surrounding the probe molecule.[171] Our calculations compare

favorably with experiment, though they rely on the validity of linear response in order

to appropriately characterize the system. A study using all-atom molecular dynamics

64

simulations which included polarization effects calculated C0(t) and C1(t) for three

ILs over the entire duration of the response, however no direct comparison to S(t)

was achieved due to the significant computational costs.[81] Simulations explicitly

comparing the nonequilibrium response S(t) and C(t) in ILs were performed by Shim

et al. using a diatomic and benzene-like probes and united-atom representations of

the IL molecules, where they found sufficient similarity between S(t) and C(t).[89]

While their findings have been used as justification for applying linear response theory

in solvation dynamics simulations of ILs, due to computational limitations at that

time, the simulations only calculated the solvation response out to 2 ps. Given

experimental evidence that the solvation response is known to persist for nanoseconds

in ILs[2, 3], examining the applicability of linear response theory over the entire

relaxation timescale is warranted.

4.2 Computational Methods

The simulation box was constructed and equilibrated using an identical protocol

as in our previous study of [emim][BF4], as discussed in Chapter 2. In brief, a total

of 256 [emim] cations, 256 [BF4] anions, and one C153 molecule comprised the three

systems. All of the molecules were modeled as fully flexible, except for covalent bonds

containing hydrogen which were fixed using the SHAKE algorithm.[135] For C153 and

the [emim] molecules force-field parameters were obtained from the generalized Am-

ber force field (GAFF).[136] Parameters for [BF4] were adopted from Liu et al.[137]

Partial charges for the IL molecules and the ground state of C153 were calculated via

the Merz-Singh-Kollman[138] analysis of the electron density of the optimized geom-

etry of the molecules obtained with density functional theory (DFT) with a B3LYP

functional and the aug-cc-pVDZ basis set. The partial charges for [emim] and [BF4]

were empirically scaled by a factor of 0.80, guided by DFT calculations,[142] to

achieve better agreement with experiments where dynamic properties are of interest.

65

In the MD simulations the long-ranged electrostatic interactions were computed with

the particle-mesh Ewald summation method with a 15 A real-space cutoff.[94, 139]

This same cutoff distance was utilized when computing interactions between Lennard-

Jones sites. The the long–ranged electrostatic interactions between C153 and the IL

molecules calculated for ∆E(t), were computed with the damped shifted force (DSF)

method.[131] The DSF method is a useful alternative to the traditional Ewald sum-

mation techniques,[94–96] and provides a straightforward description based explicitly

on a pairwise sum.

Simulations of C0(t) were calculated using identical methods described earlier

(Chapter 2). Similar conditions were employed for the calculation of C1(t), however

the cations and anions were equilibrated in the presence of an excited C153 molecule.

Note, the excited state partial charges for C153 were calculated and validated previ-

ously by Cinacchi et al.,[1] thus the excited state partial charges for C153 are obtained

by simply adding these changes to the computed ground state charges. Indepen-

dent trajectories generated from the ground state equilibrium simulation were used

as starting configurations for the nonequilibrium calculations, whereby the partial

charges of C153 were abruptly switched to reflect the excited state charge distribu-

tion. Production-runs (comprising a total of 5.015 µs for C0(t), 2.0 µs for C1(t),

and 5.0 µs for S(t)) were performed using the large-scale atomic/molecular massively

parallel simulator (LAMMPS).[134]


As seen in Figure 4.1, the ground and excited state equilibrium TCFs C0(t) and

C1(t), results are nearly identical and fully compatible with the nonequilibrium S(t)

response function. The inset contains the total solvation response including the

oscillations due to internal motions of the C153 probe molecule. These oscillations in

the solvation response have been observed in high temporal resolution measurements

66

in solution[145] and for a dye molecule (Hoechst 33258) bound to DNA.[146] To

facilitate comparison, these oscillations can be subtracted from the total response,

which is shown in the main panel of Figure 4.1. The calculated response functions

all include an ultrafast inertial relaxation followed by a complex non-exponential

decay, which is known to be viscosity dependent.[7, 65, 69, 80] The equilibrium C0(t)

(green) better reproduces the short-time inertial component of S(t) (black) than C1(t)

(red), a consequence of the similar solvent configurations explored in C0(t) and S(t)

simulations at early time.

Certain systems exist where S(t) is equal to C(t), though this is due entirely

to coincidental timescales of certain motions, and not because the linear response

approximation is valid.[172, 173] Decomposition of the total solvation response into

contributions arising from the different constituents present in the liquid is necessary

to rule out any accidental timescale correlations. Taking advantage of the additive

nature of the solute interaction energy, ∆E(t) =∑

α∆Eα(t), where ∆Eα(t) is the

solute interaction energy with solvent component α, i.e. the anions, cations, and

intramolecular electrostatic interactions within the probe itself. The decomposition

of S(t) is uncomplicated such that

Sα(t) =∆Eα(t)− 〈∆Eα(∞)〉1〈∆Eα(0)〉0 − 〈∆Eα(∞)〉1

(4.3)

where the overbar represents an average over nonequilibrium trajectories and the

superscript α signifies the solvent component of interest. Calculating the component

contributions to Cα(t) in a way that is formally compatible with linear response

theory is given as,[124, 126, 132, 169]

Cα(t) =〈δ∆Eα(t)δ∆E(0)〉〈(δ∆E)2〉

. (4.4)

This formalism importantly retains the same amount of information without invoking

67

Figure 4.1. The normalized solvation response without the contribution ofthe dye for the nonequilibrium S(t) (black) and equilibrium C1(t) (red),and C0(t) (green) from 50 fs to 1 ns. The inset is the identical responseincluding intramolecular interactions of the dye molecule responsible for

the large oscillations below 10 ps.

68

any cross-correlations that are often incapable of providing a clear molecular mech-

anism for solvation dynamics. Unfortunately, a commonly reported decomposition

scheme utilizes binomial multiplication providing auto- and cross-correlation terms

that are inadequate at identifying distinct components responsible for solvation.

The two alternative decomposition schemes applied to C0(t) are shown in Figure

4.2. The top panel contains the auto- and cross-correlation functions contrasted with

the proper decomposition for a complex perturbation in the bottom panel. The auto-

correlation of the anion-anion component in top panel shows the dominance of the

anion-anion contribution (red) followed by the cation-cation (blue) auto-correlation

term. The dashed lines represent the cross-correlation terms (anion-cation, anion-

dye, and cation-dye), which are mostly negligible, with exception to the anion-cation

cross-correlation contribution. While this does contain interesting information about

the interactions between components, this unnecessarily complicates the interpreta-

tion of the solvation mechanism by indicating there is a degree of anti-correlation

between the constituents, without exposing the exact intricacies necessary to un-

derstand solvation. It is possible to remove the ambiguity by employing Eq. 4.4 to

determine the contribution from each component relative to the total response, as

seen in the bottom panel of Figure 4.2. It is then straightforward to understand

the importance of the anions in solvating C153 without any obscure cross-correlation

terms. Using the latter decomposition scheme, Figure 4.3 presents the component

solvation response for anion (top) and cation (bottom) contributions for nonequilib-

rium S(t) (black) and equilibrium C1(t) (red), and C0(t) (green). The decompositions

for Cα0(1)(t) that are consistent with Sα(t), fitting with linear response theory.

The solvation response functions for the anions and cations can be further de-

composed into contributions resulting from their respective translational and rovi-

brational motions. The translational contribution, ∆Eαtrans, to ∆Eα for the cations

and anions are computed by regarding each relevant IL molecule as a single point

69

Figure 4.2. A comparison of two decomposition strategies as applied toC0(t) showing auto- and cross-correlation decomposition (top), to the

alternative method defined in Eq. 4.4 that calculates the contribution ofthe relevant component relative to the total response.

70

Figure 4.3. The normalized solvation response decomposed into anion (top)and cation (bottom) contributions for nonequilibrium S(t) (black) and

equilibrium C1(t) (red), and C0(t) (green) from 50 fs to 1 ns.

71

Figure 4.4. The normalized solvation responses of S(t) (black), C1(t) (red),and C0(t) (green) decomposed into contributions due to translational

(solid) and rovibrational (dashed) motions.

72

charge located at its respective center of charge. The rovibrational contribution,

∆Eαrovib, to ∆Eα is then obtained as the difference, ∆Eα

rovib = ∆Eα−∆Eαtrans. With

these definitions, the correlation functions for the cations and anions decompose into

translational and rovibrational contributions,

Cα(t) = Cαtrans(t) + Cα

rovib(t) (4.5)

where the functions Cαtrans(t) and Cα

rovib(t) are computed with Eq. 4.4 using ∆Eαtrans(t)

and ∆Eαrovib(t) in place of ∆Eα(t).

The translational and rovibrational contributions originating from the anions

(top) and the cations (bottom) are displayed in Figure 4.4, where the translational

component (solid) and rovibrational component (dashed) lines are presented for S(t)

(black), C1(t) (red), and C0(t) (green). In agreement with our previous study, trans-

lations of the anion are the dominant contributor to the solvation response with a

negligible rovibrational contribution.[171] Because the anion possesses a lack of sym-

metry and therefore no permanent dipole, the contributions arising from rovibrational

motions are expected to be trivial. The translational motion of cations also contribute

to the total solvation response, albeit to a lesser degree than the translational move-

ments of the anions, however these contributions are largely negated by rotational

motion of the cations. In this sense the anti-correlation effect can be understood as

the rotations of cation molecules as being counterproductive in stabilizing the excited

state charge distribution of the C153 solute.

Using the appropriate decomposition strategy that unambiguously identifies the

respective motion of the constituents in the IL responsible for accommodating the

charge perturbation, we are able to confidently identify the solvation mechanism in

[emim][BF4]. Given the level of agreement between the component decomposition and

translational/rovibrational analysis of S(t), C1(t), and C0(t), we do not anticipate

any breakdown in linear response theory and thus validates the use of linear response

73

theory in simulating solvation dynamics of ILs.

74

CHAPTER 5

A MOLECULAR DYNAMICS INVESTIGATION OF THE VIBRATIONAL

SPECTROSCOPY OF ISOLATED WATER IN AN IONIC LIQUID

5.1 Introduction

Our understanding of water-ion interactions is derived primarily from studies of

dilute aqueous salt solutions in which the ions are fully hydrated and water-water

interactions are perturbed but still prevalent. Studying water at dilute concentrations

in an ionic liquid (IL) reverses this scenario; the water is isolated in a sea of ions and

the water-water interactions are negated. The water/IL system provides a unique

opportunity to investigate the dynamics of water in a highly electrolytic environment.

Moreover, the isolated water molecule can serve as a reporter of the structure and

dynamics of the IL.

Despite their promise as environmentally friendly solvents and in clean and re-

newable energy applications,[7, 10–17] widespread industrial adoption of many ILs

is plagued by their large viscosities.[174] While impurities such as water are known

to alter the physical properties and chemical reaction rates in hygroscopic ILs,[20,

175, 176] the addition of this cosolvent is gaining in popularity as a means to reduce

viscosity.[177] Thus, understanding the behavior of water in ILs and how water alters

the properties of ILs has important practical implications.

Many ILs are hygroscopic and complete removal of water is nearly impossible.[178–

180] A variety of experimental[54–58] and computational[59–64] studies have aimed to

understand the influence of water on the properties of ILs. These studies suggest that

75

some ILs have nanoscale structuring with polar and nonpolar regions.[60, 61, 181–

186] As the water concentration in these ILs increase, the polar domains collapse with

the formation of larger water clusters stabilized by a hydrogen-bond network.[60, 187]

Previous work examining isolated water in ILs determined a water molecule is bridged

by two anions in an IL, existing in an A· · ·HOH· · ·A complex. As a result of

this proximity, the anions were assumed to be most responsible for influencing the

OH stretch frequency.[112–114] Investigations varying the lengths of the cation alkyl

chains in imidazolium-based ILs suggest the chains do not have an influence on the

OH stretching frequency.[112, 115]

X-ray spectroscopy, NMR, and vibrational spectroscopy have been used to un-

derstand structure in bulk ILs. [25, 101, 102, 104] Ultrafast two-dimensional infrared

(2D IR) spectroscopy measurements of ILs have the potential to elucidate impor-

tant dynamical motifs that differ from conventional solvents. 2D IR spectroscopy

has already proven itself as a powerful technique for investigating the structure and

dynamics of liquids by monitoring the response of a vibration to the evolution of its

local environment, a process called spectral diffusion. The frequencies of vibrational

reporters are exquisitely sensitive to changes in their local environment, particularly

to changes in electrostatics, hydrogen bonding, and chemical processes. For exam-

ple, the OH and OD stretch frequencies of HOD are known to depend on hydrogen

bonding: an increase in hydrogen-bond strength red-shifts the OH and OD stretch

vibrational frequencies. The inhomogeneous IR absorption line shape of liquid water

reflects the range of different hydrogen bonding environments present. [105–107] The

spectral diffusion time scales revealed by 2D IR have been shown to directly relate

to hydrogen bond rearrangement processes in liquid water.[108–111]

Recently, the dynamics of HOD isolated in an IL was investigated with vibrational

spectroscopy.[116] The linear IR absorption spectrum of the OD stretch frequency

of dilute HOD in 1-butyl-3-methyl imidazolium hexafluorophosphate, [bmim][PF6],

76

revealed a blue-shifted and a significantly narrowed vibrational line shape compared

to the spectrum of HOD in water. The blue-shift suggests weaker OD interactions

with the ionic environment and is characteristic of a relatively isolated OD stretch,

for example the free OD stretches at a liquid D2O/vacuum interface.[117–119] The 2D

IR measurements monitored spectral diffusion of the OD stretch of HOD in the IL.

An important quantity accessible by both simulation and experiment is the frequency

fluctuation time correlation function (FFCF), C(t) = 〈δω(t)δω(0)〉, where δω(t) is

the deviation of the frequency from its equilibrium value, δω(t) = ω(t) − 〈ω〉. As a

water molecule samples different molecular environments, the FFCF decays to zero.

This can be approximately related to the spectral diffusion measurements quantified

experimentally using the center line slope (CLS) method.[120, 121] Measurements of

the amplitudes and timescales of the FFCF thus give information about the dynamics

of the environment surrounding the HOD molecule. Two times scales were found: 6.9

± 2.1 ps and 72 ± 20 ps. The faster of the two relaxation timescales was attributed to

changes in the local structure of the anions bridged by the water and the subsequent

motions of the cations. The slower relaxation time was assigned to orientational

relaxation, though a discrepancy of approximately one order of magnitude exists

between the 72 ps timescale and the 2.3 ns response in optical heterodyne detected

optical Kerr effect experiments in [bmim][PF6].[122]

The objective of this chapter is to utilize molecular simulation to understand

the factors responsible for the spectral diffusion timescales for HOD isolated in the

[bmim][PF6] IL. In Section 5.2 the theoretical methodology necessary to compute

the linear IR absorption spectrum of HOD in [bmim][PF6], as well as the FFCF, is

discussed. In addition, approaches to decompose the FFCF into contributions from

specific motions of the anions and cations are presented. In Section 5.3 results for the

IR absorption spectrum, the FFCF, and its decompositions are shown and discussed.

Finally, some concluding remarks can be found in Section 5.4.

77

5.2 Theoretical Methodology

5.2.1 Spectroscopic Maps

In order to calculate the IR absorption spectrum and the spectral diffusion dy-

namics of the OD stretch of isolated HOD in [bmim][PF6] within an MD simulation,

one must have a model for relating the OD vibrational frequency and its transition

dipole moment to the instantaneous solvent environment of the HOD molecule. We

will adopt an approach that has shown considerable success in describing the vi-

brational spectroscopy of HOD in water[188–191] and in electrolyte solutions,[192]

whereby the relevant spectroscopic quantities (i.e. the OD vibrational frequency and

transition dipole moment) are empirically related to the electric field of the environ-

ment projected along the OD bond of interest. The motions of the environment cause

the projected electric field, and thus the OD vibrational frequency, to fluctuate. From

the vibrational frequency and transition dipole moment dynamics the IR spectrum

and FFCF can be calculated.

The projection of the electric field along the OD bond axis, EOD, due to a collec-

tion of N solvent point-charges, {qi}, is given in atomic units by

EOD = rOD ·N∑i=1

qiriDr2iD

(5.1)

where rOD is the unit vector along the OD bond, riD is the distance between charge i

and the D atom, and riD is a unit vector between site i and the D atom. For calcula-

tions of EOD the long-range electrostatic interactions were corrected with the damped

shifted force (DSF) method.[131] One motivation for utilizing the DSF method rather

than traditional Ewald summation techniques[94–96] is that DSF treats the interac-

tions as a pairwise sum, thus lending itself to straightforward decomposition in terms

of the contributions of the anions and cations in the IL.

The empirical relationship that relates the OD vibrational stretch frequency,

78

ωOD, to EOD was developed by Lin, Auer, and Skinner in HOD for aqueous NaBr

solutions[192]

ωOD = 2762.6 cm−1 −(

3640.8cm−1

au

)Eeff −

(56641

cm−1

au2

)E2eff . (5.2)

Here an effective electric field, Eeff , was introduced to account for the blue-shifts in

the OD stretch frequency observed experimentally with increasing salt concentrations,

Eeff = EH2O + aEcat + bEan , (5.3)

where a and b are empirical parameters, 0.81379 and 0.92017, respectively. EH2O,

Ecat, and Ean are contributions to EOD from water, cations, and anions, respec-

tively. This spectroscopic map was designed to be applicable for all aqueous salt

concentrations, and when no ions are present the map is conveniently appropriate for

HOD in H2O. The unequal weighting of the contributions for the cations and anions

reproduces the smaller OD frequency shifts observed in electrolyte solutions.

Because non-Condon effects are known to be important in the vibrational spec-

troscopy of water,[191] calculations of the IR absorption spectrum of HOD also re-

quires a spectroscopic map for the magnitude of transition dipole moment, µ′, for the

OD stretch relative to its value in the gas phase, µ′g,

µ′

µ′g= 0.71116 + 75.591Eeff (5.4)

It is important to emphasize that the spectroscopic maps given by Eqs. (5.3) and

(5.4) were developed in the context of aqueous alkali halide salt solutions, and not

specifically for water in ILs. Comparisons of the results for the IR absorption spec-

trum and the FFCF for isolated HOD in [bmim][PF6] directly with experiment will

79

both provide validation and reveal the extent to which the spectroscopic maps are

transferable.

5.2.2 Infrared Absorption Spectrum

The IR absorption spectra were computed from knowledge of the frequency and

transition dipole moment trajectories using the semiclassical fluctuating frequency

approximation (FFA),[97]

I(ω) =

∫ ∞0

dteiωt⟨~µ(t) · ~µ(0)e−i

∫ t0 dτδω(τ)

⟩e−t/2T1 , (5.5)

where 〈· · ·〉 represents a classical ensemble average, δω(t) = ω(t)− 〈ω〉 is the fluctu-

ation of the frequency from its average value, 〈ω〉, and ~µ(t) is the transition dipole

moment vector,

~µ(t) = µ′x10rOD , (5.6)

assumed to be in the direction of the OD bond, rOD . In Eq. (5.6), x10 = 〈1 |x| 0〉

is the matrix element of the position operator computed assuming Morse oscillator

ground, |0〉, and first excited-state, |1〉, vibrational wavefunctions. For convenience,

x10 can also be related, empirically, to the OD stretch frequency,

x10 = 0.0880 A −(

1.105× 10−5A

cm−1

)ωOD . (5.7)

The FFA expression, Eq. (5.5), approximately captures the effects of inhomoge-

neous broadening, motional narrowing, rotational broadening, and non-Condon tran-

sition dipole moments on the vibrational line shape. The effects of lifetime broaden-

ing are captured empirically via the exp(−t/

2T1) factor, where T1 is the vibrational

population lifetime, 1.8 ps for the OD stretch of HOD in water.[193] T1 has not

been determined for HOD in [bmim][PF6]. For the calculation of the IR absorption

80

spectrum of HOD in [bmim][PF6] the value 1.8 ps was assumed to be qualitatively

representative of the population lifetime.

5.2.3 Spectral Diffusion and Decomposition of the FFCF

Spectral diffusion of the OD stretch vibrational frequency of HOD is a sensitive

reporter of the dynamics of its local solvation environment. These dynamics are often

quantified in terms of the normalized FFCF,

Cω(t) =〈δω(t)δω(0)〉

Cω(0). (5.8)

Cω(t) is accessible experimentally and can be computed from frequency trajectories

obtained during MD simulations using, for example, the spectroscopic maps described

in Subsection 5.2.1. The FFCF has been measured for HOD in water[191] and in

the [bmim][PF6] IL.[116] For HOD in water, the long-time (∼1.5 ps) decay of the

FFCF have been attributed to hydrogen bond rearrangements. FFCFs computed

using the spectroscopic maps developed by Skinner and coworkers generally have the

same long-time decay rate as the hydrogen-bond time correlation function for a given

empirical water model.[111] The quantitative agreement of the long-time FFCF decay

with experiment, however, varies by water model. Water models without electronic

polarizability generally have FFCFs and hydrogen-bond time correlation functions

that decay too quickly.[188]

For a multicomponent solution, like the [bmim][PF6] IL, it would be physically

insightful to decompose the FFCF into contributions from the respective components

(i.e. from the anions and the cations). A straightforward decomposition is somewhat

hindered by the quadratic form of the empirical frequency map, Eq. (5.2), where the

total frequency shift, δω, is not a simple sum of contributions from anions, δωan,

and cations, δωcat : δω 6= δωan + δωcat. However, the effective electric field, Eeff ,

81

from which the frequencies are computed is naturally a sum of contributions from the

anions and cations, Eq. (5.3). Note that, for isolated water in an IL, the contribution

to the effective electric field from other water molecules can be ignored. Fortuitously,

the normalized time correlation function of the electric field fluctuations,

CE(t) =〈δE(t)δE(0)〉

CE(0), (5.9)

where δE(t) = Eeff − 〈Eeff〉 is the fluctuation of the effective electric field from its

average value, is an excellent surrogate for Cω(t) . For a linear relationship between

the electric field and the vibrational frequency, the two normalized correlation func-

tions are identical. For a quadratic relationship between the field and the frequency,

the functions can differ. However, for HOD in [bmim][PF6] the normalized correla-

tion functions are almost quantitatively identical (vide infra). Thus, we will proceed

to decompose CE(t) and assume that the qualitative insights are relevant for Cω(t) .

Since δE(t) can be expressed as a linear sum, Eq. (5.3), CE(t) can be decomposed

into contributions from anions and cations using the same approach that has proven

successful in unraveling the factors that influence solvation response functions in

ILs,[90, 171] proteins,[132] and DNA,[123–126, 194]

CE(t) =∑α

CαE(t)

CE(0)=∑α

〈δEα(t)δE(0)〉CE(0)

, (5.10)

where α represents the solvent component of interest. This method of decompos-

ing, CαE(t), and Cω(t) by proxy, is rigorously consistent with the linear response

approximation, and has not previously been applied in the context of understanding

vibrational spectral diffusion in multicomponent liquids.

Each of the solvent component correlation functions, CαE(t), in Eq. (5.10) can also

be further separated into contributions that arise from their respective translational

and rotational motions. The translational contribution to Eα, Eα,trans, is calculated

82

by regarding each relevant IL molecule as a single point charge located at its center

of charge. The rovibrational contribution to Eα is then just the difference Eα,rovib =

Eα − Eα,trans. These definitions allow the solvent component correlation functions

for the cations and anions to be decomposed into their respective translational and

rovibrational contributions,

CαE(t) = Cα,trans

E (t) + Cα,rovibE (t) , (5.11)

where the functions Cα,transE (t) and Cα,rovib

E (t) are computed with Eq. (5.10), but

with δEα,trans(t) and δEα,rovib(t) in place of δEα(t).


For our control calculations on dilute HOD in water, a cubic simulation box of 512

H2O molecules was constructed with periodic boundary conditions. The vibrational

spectroscopy of neat water is complicated by intra- and inter-molecular coupling, of

the OH stretches. Considering dilute HOD in H2O is preferable because the OD

stretch is spectrally isolated from all other vibrational modes and limits intra- and

inter-molecular vibrational coupling. For our calculations of the vibrational spec-

troscopy of dilute HOD in H2O, we can regard each bond as the OD vibration of

interest. Here we are taking advantage of the fact that a single HOD molecule

in H2O is indistinguishable from a neat H2O simulation.[188] The atomic-centered

partial charges and other force-field parameters for the H2O molecule are from the

SPC/E model.[195]

The cubic simulation box of ILs was constructed with 256 [bmim] cations, 256

[PF6] anions, and one D2O molecule with periodic boundary conditions. A D2O

molecule was used because its dynamics are not particularly different from HOD, and

both OD bonds could be considered the vibration of interest, thus providing a twofold

83

increase of our statistics. The MD simulations were performed using the Large-

scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) program.[134] All

molecules were modeled as fully flexible, except for covalent bonds containing hy-

drogen or deuterium which were fixed at equilibrium lengths using the SHAKE

algorithm.[135, 196] For the [bmim] molecules force-field parameters for the bonds,

bends, dihedrals, and atomic-centered Lennard-Jones sites were adopted from the

generalized Amber force field (GAFF).[136] Minor dihedral angle modifications were

made to better match density functional theory calculations carried out with a B3LYP

functional and the aug-cc-pVDZ basis set. Parameters for [PF6] are not available in

the GAFF and were obtained from Liu et al.[137] Atomic-centered partial charges

for the IL molecules were calculated via the Merz-Singh-Kollman[138] analysis of the

electron density of the optimized geometry of the molecules obtained with DFT with

a B3LYP functional and the aug-cc-pVDZ basis set. In an attempt to more accurately

model the dynamics of the system, the partial charges were empirically scaled by a

factor of 0.84, as suggested by DFT calculations for a similar IL, [bmim][BF4].[142]

Treating the charge scaling factor as a tunable force field parameter to approximately

describe the effects of electronic polarizability is commonly used as a means to more

accurately capture diffusion in ILs.[143] The long-ranged electrostatic interactions

in the simulations were computed with the particle-mesh Ewald summation method

with a 15 A real-space cutoff.[94, 139]

Out of concern for the long relaxation dynamics, we rely on a rigorous equilibra-

tion procedure identical to our previous work simulating ILs. In brief, the molecules

are allowed to relax during a minimization procedure after which the temperature

is slowly raised from 0 K to 300 K and maintained at 300 K for 4 ns in the NPT

ensemble controlled by a Nose-Hoover thermostat and barostat.[140] The size of the

simulation box was isotropically scaled to reflect the average density and was then

simulated in the NVT ensemble for 1 ns at 300 K, the temperature was slowly raised

84

to 600 K over 1 ns to destroy any pseudo-stable ionic cages that may have formed.

Next, the temperature was reduced back to 300 K in 1 ns, followed by an NVT sim-

ulation for 1 ns at constant temperature of 300 K. The final velocities were scaled to

300 K and a pre-production NVE simulation was performed for 11 ns. A total of 50

ns of continuous dynamics for the D2O:IL system and 5 ns for the neat H2O systems

were collected in the NVE ensemble with a 2 fs integration time step and a collection

resolution of 4 fs.

As a preliminary validation of the simulations and force-fields, we calculated the

orientational time correlation function for an OD bond in neat H2O and in the

[bmim][PF6] IL, given as 〈P2(rOD(0) · rOD(t))〉, where P2(x) is the second-order Leg-

endre polynomial (Figure 5.1). The oscillations below 1 ps are indicative of water

librational motion and will be discussed in more detail in Subsection 5.3.1. The re-

orientational dynamics are clearly much faster in H2O than in the IL. Experimental

measurements of the OD anisotropy decay in [bmim][PF6] were collected out to 40

ps, and a biexponential fit revealed two time constants: 2.4 and 24.7 ps.[116] The cal-

culated rotational correlation function was fit to a tri-exponential function for t ≥ 1

ps (Figure 5.1). The three time constants were 3.5 ps, 19.4 ps, and 85.6 ps. The

first two time constants agree fairly well with experiment and serve as a validation

of the simulations. The longer time decay (85.6 ps) would not be resolvable in the

experiment because of the population lifetime of the OD vibrational reporter.


5.3.1 IR Absorption

The calculated IR absorption spectra for the OD stretch of dilute HOD in H2O

and in [bmim][PF6] are shown in Figure 5.2. It is immediately apparent that the

line width is narrowed dramatically in the IL by 128 cm−1 and is blue-shifted by

85

0.01 0.1 1 10 100t (ps)

0.1

1

Rota

tiona

l Cor

rela

tion

ILH2O

Figure 5.1. The orientational time-correlation function for an OD bond inH2O (black) and in the [bmim][PF6] IL (turquoise).

86

Figure 5.2. Vibrational line shapes for the OD stretch of dilute HOD inH2O and in the [bmim][PF6] IL. The spectra were arbitrarily scaled to have

the same maximum intensity.

87

TABLE 5.1

IR ABSORPTION DATA

ωmax (cm−1) FWHM (cm−1)

HOD in H2OTheory 2548 148

Expa 2510 170

HOD in [bmim][PF6]Theory 2712 20

Expa 2678 21

a Ref. [116]. Summary of the theoretical and experimental IR absorption line shapes forthe OD stretch of HOD in H2O and in [bmim][PF6]. ωmax is the frequency of maximumabsorption and FWHM is the full-width at half the maximum absorption.

164 cm−1 (Table 5.1). Experimentally, the spectrum shifts by 168 cm−1 and narrows

by 149 cm−1. The agreement between theory and experiment for the differences

in the line shapes between the aqueous and IL environments are excellent, which

validates both the simulations and the spectroscopic maps. Consistent with previous

studies[112, 113, 115] the peak of the OD stretch spectrum of HOD in water is to the

blue of experiment and the spectrum is slightly too narrow. In the IL the peak in the

spectrum is again to the blue of experiment, but its width is almost exactly correct.

As discussed previously, there is some ambiguity about the vibrational lifetime of

HOD in the IL, and the spectrum in Figure 5.2 assumes T1 = 1.8 ps, the same value

as HOD in H2O. However, the lifetime is likely longer because the HOD molecule is

not hydrogen bonding and the 2D IR spectrum were collected out to 40 ps implying a

T1 longer than 1.8 ps. Therefore, the 20 cm−1 width of the spectrum can be regarded

as an upper-bound. Taking T1 = ∞ provides a lower bound of 16 cm−1. The

significant narrowing of the spectrum in the IL solvent relative to aqueous solution

88

is a reflection of the absence of hydrogen bonding sites on the IL molecules and a

reduction in the diversity of solvent environments to inhomogeneously broaden the

line shape.

Examining the distribution of electric fields present in water and in the IL is phys-

ically insightful for understanding the contributions to the IR absorption spectrum

of HOD in these two liquids. Figure 5.3 shows distribution functions, F (E), for the

projection of the electric field along the OD bond of HOD in H2O and in [bmim][PF6].

In the IL the electric field of interest is Eeff , as defined in Eq. (5.3). The electric

field distribution for HOD in water exhibits a characteristic shoulder on the low-field

side of F (E). These small values of the field correspond to frequencies on the blue

side of the IR absorption spectrum, which have been attributed in previous studies

to HOD molecules whose OD bond is not engaged as a hydrogen-bond donor. The

electric field distribution for HOD in the IL is significantly narrowed and is centered

almost exactly at the same location of the shoulder in the water distribution. The

difference in widths between the two distributions is consistent with the calculated

and experimentally observed narrowing in the IR absorption spectrum, and suggests

that the origin of the change in width is mostly inhomogeneous in nature. Figure 5.3

also shows distribution functions for the effective electric fields from the cations and

anions. Note that the distribution for the total effective field should not be a sum of

the contributions from the cations and anions. Interestingly, the distribution of fields

from the anions mimics the total, whereas the distribution function for the cations is

narrow and centered almost at zero. These results confirm that the anions interacts

more strongly with the HOD molecule and are the dominant contributor to the IR

absorption spectrum.

89

-0.02 0 0.02 0.04 0.06 0.08E (au)

F(E)

ILCationAnionH2O

Figure 5.3. Distribution functions, F (E), for the projection of the electricfield projected along the OD of HOD in H2O (black) and in the

[bmim][PF6] IL (turquoise). The distribution of electric fields in the ILresulting from cations (blue) and anions (red) are also shown. The

distribution functions have all been scaled to have the same value at theirmaximum.

90

Figure 5.4. Normalized CE(t) for HOD in H2O and HOD in the[bmim][PF6] IL. Also shown is a comparison between Cω(t) (red) and CE(t)

for HOD in the IL.

91

5.3.2 Spectral Diffusion

Figure 5.4 shows the normalized electric field correlation function, CE(t), for

the OD stretch of dilute HOD in H2O and isolated HOD in [bmim][PF6]. Also

shown in Figure 5.3 is the FFCF, Cω(t), which is nearly identical to CE(t) at all

times, particularly for t > 1 ps. While the FFCF is directly related to spectral

diffusion measurements, CE(t) serves as an exemplary surrogate and the two functions

will be regarded as interchangeable for the remainder of the paper. As discussed

in Subsection 5.2.2, CE(t) is amenable to decomposition strategies that can offer

additional physical insight regarding the physical motions responsible for spectral

diffusion.

Immediately apparent in Figure 5.3 is a dramatic difference in the long-time decay

of the FFCF for HOD in the aqueous environment, where the decay is complete in un-

der 5 ps, versus in the IL solvent, where the function persists beyond 100 ps. For HOD

in water, CE(t) was fit to a tri-exponential function, which revealed three timescales:

37 fs, 297 fs, and 0.86 ps. In previous studies the faster timescales were attributed

to hydrogen bond fluctuations, while the slowest time was related to hydrogen-bond

rearrangement processes.[197, 198] Given that the viscosity of the [bmim][PF6] IL

is ∼450 times larger than the viscosity of water,[199] it is not surprising that more

large-scale rearrangement of solvent structures takes considerably longer in the IL

than in aqueous solution, though the specific motions cannot be assigned until we

consider physical decompositions of CE(t) below.

A similar tri-exponential fit of CE(t) for HOD in the IL revealed time constants

of 54 fs, 1.6 ps, and 38 ps. Experimentally, two timescales were identified for spectral

diffusion: 6.9 ± 2.1 ps and 72 ± 20 ps.[116] Spectral diffusion occurring on a ∼50

fs timescale, as predicted in our calculations, would be difficult to resolve experi-

mentally, so we cannot make a direct comparison. The other two calculated time

constants are too fast compared to experiment by about a factor of 4 for the 1.6 ps

92

time and a factor of two for the longest, 38 ps timescale. For HOD in water it has

been established that spectral diffusion occurs too quickly in non-polarizable water

models, by about a factor of approximately 1.5–2.[200] It is therefore likely that quan-

titatively reproducing the spectral diffusion timescales for HOD isolated in ILs would

also require electronically polarizable force fields. Nonetheless, the qualitative agree-

ment between experiment and theory is reasonable enough to proceed to decompose

CE(t) for HOD in the IL to achieve additional physical insight. Already, the simple

absence of nanosecond timescales in both simulation and experiment demonstrate

that the OD vibrational reporter is insensitive to longer-time rearrangements that

have been observed in both theoretical and experimental investigations of solvation

dynamics in [bmim][PF6].[2, 79, 88, 90, 201, 202]

Before progressing to decompositions of CE(t) for HOD in the IL, it is important

to discuss the sub-picosecond damped oscillation that is evident in the electric field

correlation function for both HOD in water and HOD in the IL. Such oscillations

have been experimentally verified for spectral diffusion of HOD in liquid water and

assigned to a oscillatory stretching motion of the hydrogen bond between the OD

vibrational reporter and a neighboring water molecule.[203] The peak in the oscil-

lation occurs at 120 fs for HOD in water, but at 280 fs for HOD in [bmim][PF6].

Also, the oscillation is considerably more pronounced in the IL. The decompositions

discussed below will reveal that the oscillation is related to translational motion of

the water relative to the anions. Thus, the physical interpretation is similar in the IL,

only now it is an oscillatory stretch within a [PF6] · · · HOD · · · [PF6] complex. Ex-

perimentally, significant oscillations were observed for the spectral diffusion of D2O

in the [bmim][PF6] IL having a period of 0.3 ps. However, these oscillations were

assigned as quantum mechanical coherence oscillations due to anharmonic coupling

between the symmetric and asymmetric stretches of D2O (i.e. the same oscillations

were observed in the center-line-slope of the diagonal and cross peaks of the symmet-

93

ric and asymmetric stretches of D2O in the 2D IR spectra). Here, the OH and OD

vibrational frequencies of HOD are too far out of resonance to support oscillations

due to coherent energy transfer. Moreover, such an effect would also not be captured

using the theoretical approach utilized in this paper.

Figure 5.5 shows results for decomposing CE(t) for the OD stretch of HOD in

the IL in terms of contributions from the [PF6] anions and the [bmim] cations. It

is immediately apparent that the anions are the dominant contributor to spectral

diffusion over all timescales; the cations never contribute more than ∼10% to CE(t).

The long time decay of both the anion and cation correlation functions are similar to

the 38 ps decay of the total correlation function (36 ps for the anions and 43 ps for

the cations). This suggest that the long-time decay is a collective process involving

reorganization of both the anions and cations. The pronounced 280 fs oscillation in

CE(t) is clearly visible only in the anion component, however both the anion and

cation correlation functions have smaller amplitude vibrations superimposed upon

the decay at short times. Additional physical insight can be obtained by further

decomposing the anion and cation contributions to the spectral diffusion process into

contributions from translational and rovibrational motions of these molecules relative

to the OD bond of interest (Figure 5.6). From this analysis it is clear that the long-

time spectral diffusion dynamics are dominated by translational motions of the anion

relative to the OD bond. Translational and rotational motions are nearly equal

contributors to the cation portion of the correlation function. The pronounced 280

fs oscillation in CE(t) is only present in the anion translational correlation function.

Thus, we can now assign this feature to a vibrational motion between the HOD

molecule and a neighboring [PF6] anion. A much smaller amplitude and higher

frequency oscillation is also present in the total correlation function, which can now

clearly be assigned to rovibrational motions of the anions.

94

0.01 0.1 1 10 100t (ps)

0

0.2

0.4

0.6

0.8

1

C(t)

ILCationAnion

Figure 5.5. Decomposition of normalized CE(t) for the OD stretch of HODisolated in the [bmim][PF6] IL in terms of the contributions from the

cations (blue) and anions (red).

95

0.01 0.1 1 10 100t (ps)

-0.2

0

0.2

0.4

0.6

0.8

1

C(t)

ILCation-TransCation-RovibAnion-TransAnion-Rovib

Figure 5.6. Decomposition of normalized CE(t) for the OD stretch of HODisolated in the [bmim][PF6] IL in terms of the contributions from the

translational (solid) and rovibrational (dashed) components from cations(blue) and anions (red).

96

5.4 Concluding Remarks

A combined MD simulation and spectroscopic map approach has been utilized to

investigate the vibrational spectroscopy and spectral diffusion dynamics of the OD

stretch of HOD isolated in the [bmim][PF6] IL. Excellent agreement between exper-

iment and theory was achieved for the dramatic shift and change in width of the

IR absorption spectrum for the OD stretch of HOD in the IL relative to in aqueous

solution. This result served to validate the spectroscopic maps that were originally

developed for aqueous electrolyte solutions. The spectral diffusion dynamics were

calculated and the agreement with experiment was more modest. The theoretical

timescales were too fast compared to experiment, which is perhaps expected for the

non-polarizable force fields used in the MD simulations. Decompositions of the total

spectral diffusion dynamics in terms of contributions from anions and cations revealed

that the anions dominate the response at all times. Further decompositions revealed

that translational motions of the anions relative to the OD bond of interest was, by

far, the most important component of the spectral diffusion dynamics. The decom-

positions also allowed us to assign a pronounced oscillation in the calculated FTCF

to a OD· · ·[PF6] vibrational motion. Overall, the results of this paper demonstrate

the utility of the MD/spectroscopic map approach for determining unambiguously

the signature of specific physical motions in complex heterogeneous solvents in linear

and 2D IR experiments.

97

CHAPTER 6

MONITORING INTRAMOLECULAR PROTON TRANSFER WITH

TWO-DIMENSIONAL INFRARED SPECTROSCOPY

6.1 Introduction

Proton transfer (PT) plays a critical role in many chemical, photochemical, cat-

alytic, and biomolecular processes.[204, 205] It remains an important challenge to

elucidate the factors that affect the kinetic rates and mechanisms of PT in realistic

contexts. Novel spectroscopic approaches for monitoring PT processes in real time

are therefore essential. Because of its sub-picosecond time resolution and superb

sensitivity of infrared reporters to their local environments, chemical exchange two-

dimensional infrared (2D IR) spectroscopy[206, 207] has the ability to offer tremen-

dous insight regarding the dynamics of thermally activated PT. Chemical exchange

2D IR spectroscopy requires a suitable IR active mode whose vibrational frequency is

sensitive, i.e. strongly coupled, to the PT reaction coordinate. A potential strategy

is to monitor directly the bonds in which the transferring proton participates. While

such an approach is necessarily completely non-perturbative, a likely drawback is the

complexity of the resulting spectra because of tunneling and nonadiabatic effects.[208]

An alternative approach is to introduce a spectroscopic reporter whose vibrational

frequency is sensitive to the PT process, but whose presence is minimally perturbative

to the motion (e.g. mechanism and kinetics) of the transferring proton of interest.

Selective deuteration of carbon atoms in the vicinity of the PT event can potentially

offer a means to monitor the reaction with minimal perturbation. Site-specific C-D

98

Figure 6.1. Proton transfer reaction coordinate in malonaldehyde.

bonds generally absorb between 2100-2300 cm−1, a region of the IR spectrum that

is mostly absent of other vibrational transitions in biomolecular contexts, and are

known to be excellent reporters of their chemical environment.[209, 210] Moreover,

since carbon is rarely the donor or acceptor in most PT processes of interest, C-D

vibrations will be adiabatically decoupled from the PT reaction.

The use of C–D to monitor the kinetics of PT processes using chemical exchange

2D IR spectroscopy was demonstrated and analyzed computationally for the model

compound malonaldehyde (3-hydroxy-2-propenal, Figure 6.1). Malonaldehyde con-

tains an intramolecular hydrogen bond across which a proton can transfer between

symmetric donor and acceptor oxygen atoms (OA–H· · ·OB), a process that has been

studied extensively by both theory[211–214] and experiment.[215–218] In this study,

one of the carbonyl/enol carbon atoms, a direct neighbor to the proton transfer event,

is deuterated. This particular C–D vibrational reporter is likely to be exquisitely

sensitive to the PT event because of (1) its spatial proximity, (2) the known sensi-

tivity of C–D vibrational frequencies to the movement of charge via the vibrational

Stark effect,[219] and, most importantly, (3) the coupling of the C–D bond to the

dramatic change in the electronic structure of the malonaldehyde molecule upon

99

intramolecular PT. The chemical environment of the carbon-atom to which the deu-

terium probe is attached changes markedly from HOA–CD=C to OA=CD–C when

the proton transfers. In essence, this change in the electronic structure of the malon-

aldehyde molecule results in a substantial alteration of the force constant of the C–D

bond. In the gas phase, density functional theory (DFT) at the B3LYP/6-311+G(d,

p) level of theory/basis set predicts a 179 cm−1 shift in the harmonic vibrational

frequency of C–D vibrational probe. This large shift contrasts significantly with the

< 10 cm−1 shifts observed due to the vibrational Stark effect in previous experimen-

tal studies,[209, 210, 219] which provides a qualitative indication of the importance

of the electronic structure change to the C–D vibrational frequency as well as an

important experimental design principle. Classically, labeling the carbonyl/enol car-

bon atoms in malonaldehyde with a deuterium should have a negligible effect on the

kinetic rate of intramolecular PT because the free energy profile for the PT process

will be unchanged and there is more than a 1000 cm−1 mismatch between the O-H

and C–D vibrational frequencies. Quantum mechanically, however, there could be an

indirect effect due to altering the zero-point-energy of the proton on the labeled side

of the molecule relative to the unlabeled side of the molecule. Also, nonadiabatic

coupling of nuclear motions to the electronic structure of the molecule could be rel-

evant. These potentially interesting quantum mechanical effects will be ignored for

the purposes of the present proof-of-concept study.

6.2 Methodology

2D IR spectroscopy has been utilized to investigate complexation reactions in

solution,[206, 207, 220] including hydrogen-bond formation and dissociation pro-

cesses. In particular, Nydegger, Rock, and Cheatum have used 2D IR spectroscopy to

investigate C–D labeled formic acid dimmer in hexane solution.[220] Unfortunately,

the interpretation of the spectra was complicated by the presence of an accidental

100

Fermi resonance so the kinetics of the intermolecular double PT process could not

be elucidated. The technique requires that the reactant (A) and product (B) species

have well-defined spectral signatures. At zero waiting time, peaks appear along the

diagonal that correspond to A and B. As the waiting time is increased, off-diagonal

peaks appear that correspond to the formation of A from B and B from A. Kinetic

rate constants for both the forward and back reactions, as well as the equilibrium

constant between A and B can then be extracted from the growth of the off-diagonal

peaks and the decay of the diagonal peaks (the effects of vibrational population re-

laxation must also be taken into account). In this study, the 2D IR spectra of C–D

labeled malonaldehyde in aqueous solution will be calculated to demonstrate how

the technique is applicable to the study of thermally-induced PT reactions. Because

the intramolecular PT reaction is symmetric in malonaldehyde, the resulting 2D IR

spectra will be symmetric and the diagonal peaks should decay at the same rate as

the off-diagonal peaks grow (neglecting vibrational population relaxation).

In order to calculate the 2D IR spectrum of C–D labeled malonaldehyde it is first

necessary to map the instantaneous C–D vibrational frequency to the PT reaction

coordinate,

ρ =R(OAH) · cosθ(OBOAH)

R(OAOB)(6.1)

where R(OAH) is the distance from the transferring proton to the donor oxygen

atom, R(OAOB) is the distance between the donor and acceptor oxygen atoms, and

θ(OBOAH) is the angle between the OAH and OAOB bonds (see Figure 6.1). The

transition state for the intramolecular PT is located at a value of ρ = 0.5. Using DFT

with the B3LYP functional and a 6-311+G(d, p) basis set, optimized geometries of

malonaldehyde in the gas-phase were obtained for 40 values of ρ constrained between

0.1 and 0.9. All gas-phase electronic structure calculations were performed in Gaus-

sian 09.[221] The energies of the optimized geometries are plotted in the top panel

101

Figure 6.2. (top) Potential energy curves for the intramolecular protontransfer in malonaldehyde generated with DFT and SCC–DFTB. The DFT

barrier height is 3.2 kcal/mol while SCC–DFTB predicts a barrier of 2.6kcal/mol. (middle) Free energy profile from a QM/MM simulation of

malonaldehyde in water with a barrier height of 4.1 kcal/mol. (bottom)Anharmonic C–D vibrational frequencies as a function of the protontransfer reaction coordinate for malonaldehyde in the gas-phase. The

frequencies were fit to Eq. 6.2, where A0 = 1534.0, A1 = 91.5, A2 = 11.8,A3 = 2106.5, A4 = 42.7, and A5 = 7.0.

102

of Figure 6.2. DFT predicts a barrier to PT of 3.2 kcal/mol, which agrees well with

higher level quantum chemistry calculations (e.g., MP2/cc-pVTZ and CCSD(T)/cc-

pVDZ predict barriers of 2.8 and 3.9 kcal/mol, respectively).[222, 223] For each of

the geometries (i.e. values of ρ), the anharmonic C–D vibrational frequency of in-

terest was calculated using previous methodology.[224–227] Briefly, the C–D bond is

stretched from 0.88 to 1.44 A in 0.08 A increments, holding the rest of the molecule

fixed. At each increment, the molecular energy is calculated with B3LYP/6-311+G(d,

p) yielding the Born-Oppenheimer potential energy curve for the C–D stretch, which

is fit to a Morse oscillator. The Morse parameters are sufficient to determine the 0–1

vibrational frequency, since the energy levels are known analytically for a Morse os-

cillator. The C–D vibrational frequencies are shown as a function of ρ in the bottom

panel of Figure 6.2. Note the extraordinary sensitivity of the C–D stretch to the PT

reaction coordinate. The mapping of the C–D stretch frequency to ρ is completed by

utilizing an appropriately flexible fitting function,

ω(ρ) = A0 exp [−A1ρ exp [−A2ρ]] + A3 + A4ρ+ (A5ρ)2 (6.2)

Next, the malonaldehyde molecule was simulated in aqueous solution using a

mixed quantum mechanics/molecular mechanics (QM/MM) approach in which the

malonaldehyde molecule was modeled using self-consistent-charge density functional

tight binding (SCC–DFTB)[228, 229] methodology and the water was modeled with

SPC/E.[195] DFTB is a computationally efficient semi-empirical quantum chemistry

method that is parameterized against local density approximation (LDA) DFT cal-

culations for atoms and pairs of atoms within a tight binding framework. The SCC

correction improves the accuracy of DFTB by incorporating electronic polarization

effects.[230] In the top panel of Figure 6.2, the SCC–DFTB method was used to cal-

culate the potential energy curve for the intramolecular PT in malonaldehyde. To

facilitate a direct comparison with the DFT result, the molecular geometries opti-

103

mized with DFT were utilized for the SCC–DFTB energy calculations. The DFT

and SCC–DFTB potential energy curves are qualitatively similar. The two primary

differences are in the barrier region (SCC–DFTB predicts a 1.5 kcal/mol lower barrier

than DFT) and in the repulsive parts of the potential.

The SCC–DFTB-based QM/MM molecular dynamics (MD) simulations of mal-

onaldehyde solvated by 2932 water molecules were performed in AMBER 10.[231]

The simulations employed periodic boundary conditions with a cubic simulation box,

and the long-ranged electrostatic interactions were treated with the particle mesh

Ewald (PME) method.[139] The SHAKE[196] algorithm was used to constrain the

geometry of the rigid SPC/E water molecules. Our equilibration protocol involved

(1) 500 steps of steepest descent minimization, (2) 500 steps of conjugate gradient

minimization, (3) a gradual defrost from 0 K to 300 K over 200 ps of simulation in

the NVT ensemble with a Langevin thermostat and a 1 fs time step, (4) 200 ps of

simulation in the NPT ensemble, (5) rescaling the simulation box size to the average

of the last 50 ps of the NPT simulation (∼45 A), (6) 100 ps of NVT simulation,

(7) rescaling the velocities to 300 K, and (8) 100 ps of NVE simulation. A 105 ns

trajectory in the NVE ensemble was then collected for analysis.

For each snapshot in the production run trajectory, the instantaneous value of

the PT reaction coordinate, Eq. (6.1), was calculated. A histogram of ρ(t) was

constructed, P (ρ), from which the free energy, F , of the intramolecular PT reaction

in malonaldehyde could be calculated using the relationship F = kBT ln(P ) (middle

panel of Figure 6.2). The free energy barrier height for the PT reaction in aqueous

solution in solution was 4.3 kcal/mol, which is in excellent agreement with a previous

SCC–DFTB simulation of malonaldehyde in water (4.2 kcal/mol).[232] From the

time dependence of ρ, a trajectory of the C–D stretch vibrational frequency, ω(t),

was constructed via the relationship in Eq. (6.2).

As described in Chapter 1, knowledge of ω(t) is sufficient to calculate linear IR

104

Figure 6.3. (a) C–D stretch IR absorption spectrum of labeledmalonaldehyde in aqueous solution. (b-d) Chemical exchange 2D IR

spectra for waiting times of 0, 15, and 50 ps.

105

absorption using Eq. 1.3 within a semiclassical framework with well-characterized

approximations. For the calculations of the 2D IR spectra of the C–D stretch of

labeled malonaldehyde in aqueous solution, it is assumed that the instantaneous C–

D stretch frequency is solely determined by the value of ρ. In reality, fluctuations

of the solvent will also affect the C–D stretch frequency. However, from previous

studies of solvatochromic shifts of C–D stretch frequencies,[210] the magnitude of the

solvent effects are approximately an order of magnitude smaller than the effects of

intramolecular PT.

In 2D IR spectroscopy, three separate femtosecond IR pulses interact with the

sample, and the subsequent response is measured. The three pulses have specific wave

vectors labeled k1, k2, and k3 corresponding to the their sequence. The rephasing

signal is observed in the kRP = -k1 + k2 + k3 direction, while the non-rephasing signal

is described as kNR = k1 k2 + k3 direction. Within the Condon approximation and

assuming that only two vibrational states are relevant, the three-pulse echo response

functions are given by[191]

RRP (t3, t2, t1) = exp(−i 〈ω10〉 t3 + i 〈ω10〉 t1)φRP (t3, t2, t1)

RNR(t3, t2, t1) = exp(−i 〈ω10〉 t3 − i 〈ω10〉 t1)φNR(t3, t2, t1)

(6.3)

where

φRP (t3, t2, t1) = exp

[i

∫ t1

0

dτδω10(τ)− i∫ t1+t2+t3

t1+t2

dτδω10(τ)

]φNP (t3, t2, t1) = exp

[−i∫ t1

0

dτδω10(τ)− i∫ t1+t2+t3

t1+t2

dτδω10(τ)

] (6.4)

where RRP and RNP are the rephasing and non-rephasing responses, respectively.

The waiting time, Tw, is synonymous with t2 in the equations above. The 2D IR

signal S(ω3, t2, ω1) is given by the sum of the rephasing and non-rephasing signals,

106

S(ω3, t2, ω1) ∼ Re [SRP (ω3, t2, ω1) + SNP (ω3, t2, ω1)] (6.5)

where

SRP (ω3, t2, ω1) =

∫ ∞0

dt1

∫ ∞0

dt3 exp(iω3t3 − iω1t1)RRP (t3, t2, t1)

SNP (ω3, t2, ω1) =

∫ ∞0

dt1

∫ ∞0

dt3 exp(iω3t3 + iω1t1)RNP (t3, t2, t1)

(6.6)

where SRP and SNP are the rephasing and non-rephasing signals, respectively.


Shown in the Figure 6.4(a) is the IR absorption spectrum for the C–D stretch

of labeled malonaldehyde. As expected, the spectrum exhibits a pair of sharp ab-

sorbances, which are separated by 153 cm−1. The peak near 2150 cm−1 corresponds

to when the transferable proton is proximal to the C–D label, and the peak near

2300 cm−1 is when the proton is distal relative to the label. A total of 18 chemical

exchange 2D IR spectra with waiting times spanning 0-500 ps were also calculated.

In Figure 6.4 (b-d) the 2D IR spectra for three representative waiting times, 0, 15,

and 50 ps, are reported (additional spectra for Tw over the range 0 to 500 ps can be

found in Appendix B). Analogously to the 1D IR absorption spectrum, the 2D IR

spectra all exhibit peaks on the diagonal separated by approximately 153 cm−1 (note

that at infinite waiting time that a diagonal slice through the 2D IR spectrum should

yield the 1D spectrum). As the waiting time increases, the intensity of the diagonal

peaks decrease and the off-diagonal peaks grow into the spectra. The off-diagonal

peaks correspond to circumstances where the transferable proton was initially on the

side of the malonaldehyde containing the C–D reporter and it transfers to the other

side of the molecule within the waiting time, or vice versa. By monitoring the decay

of the diagonal peaks and the growth of the cross peaks as function of the waiting

107

time, the kinetics of the PT process should be elucidated.

To quantify that the kinetics observed in the 2D IR spectra corresponded to the

time scale of intramolecular PT in malonaldehyde, the time correlation function of

the fluctuations of the PT reaction coordinate was computed (top panel of Figure

6.4). The time correlation function was fit reasonably by a single exponential with a

time constant of 28.8 ps, which is in reasonable agreement with previous theoretical

investigations in the gas-phase.[213] Next, the normalized volumes of the diagonal and

off-diagonal peaks were calculated as a function of the waiting time (bottom panel

of Figure 6.4). The decay and growth in volume of the diagonal and off-diagonal

peaks were also reasonably well-described by single exponentials with time constants

of 29.7 and 28.3 ps, respectively. The congruity of the PT lifetime and the kinetics

for the decay and growth of the diagonal and off-diagonal peaks on the computed 2D

IR spectra demonstrates the potential utility of the peripheral C–D labeling strategy

and the use of chemical exchange 2D IR spectroscopy to monitor intramolecular PT.

The use of chemical exchange 2D IR spectroscopy of a peripheral (and minimally

perturbative) C–D vibrational reporter to monitor PT processes in real-time has been

demonstrated computationally. While C–D vibrations have notoriously low absorp-

tivity that may make 2D IR measurements difficult (but not impossible),[220, 233]

the strategy of monitoring site-specific vibrational labels, rather than the transferring

proton itself, has general applicability in a broad range of contexts. Other kinds of

vibrational reporters (e.g. nitrile, azido, etc.) with substantially better absorptiv-

ity are also viable because they would be sensitive to the redistribution of charge

that occurs in proton and electron transfer processes via the vibrational Stark effect.

Finally, this work demonstrates how theory and computation can be used to guide

the development of new experiments by directly computing the relevant experimental

observables.

108

Figure 6.4. (top) Reaction coordinate time correlation function along witha fit to a single exponential with a time constant of 28.8 ps. (bottom)

Evolution of the normalized volumes of the diagonal and off-diagonal peaksin the 2D IR spectra as a function of the waiting time. Both curves were fitto a single exponential yielding time constants of 29.7 and 28.3 ps for the

diagonal and off-diagonal peaks, respectively.

109

CHAPTER 7

SUMMARY

The challenges and opportunities presented when characterizing the structure

and dynamics of condensed phased reactions are considerable. Utilizing theory and

computational techniques are necessary complements to the interpretation of experi-

mental observables. Comprehending the magnitude of precise solvent movements are

important for understanding electron and proton transfer reactions in the condensed

phase, as it is these dynamics that often determines the kinetics of solution-phase re-

actions. In particular, the decay of a solvation response function, S(t) yields a wealth

of information about reorganizational rates relevant to these charge-transfer reactions

in addition to developing our intuition regarding solute-solvent and solvent-solvent

interactions. An understanding of solvation dynamics has dramatically influenced

our understanding of the rates of chemical reactions in conventional dipolar media,

as solvation dynamics are known to govern the reaction rates of electron or proton

transfer.[39, 41] At the very minimum ILs are binary systems with heterogenous

regions of diverse dynamics with the ability to participate and influence chemical re-

actions. With the excellent thermal and chemical stability, superior solvating ability,

and controllable physicochemical properties, ILs represent a fascinating class of sol-

vents poised to take on important challenges in energy research. Given the immense

undertaking to synthesize a fraction of the estimated 1018 possible combinations, ac-

curate theoretical simulations are necessary to elucidate the complex, many-bodied

interactions responsible for certain macroscopic properties. This dissertation ad-

dresses the need for a fundamental understanding of the complex intermolecular

110

interactions in ILs that are responsible for microscopic structures and dynamics that

ultimately manifest in macroscopic physical properties.

In Chapters 2 and 3, we identified the persistence of preferential solvation, where

the cations are, on average, closer to the the aromatic solute than the anions. While

presenting some ambiguity in the interpretation of simulations and experiments that

depend on a spectroscopic probe to be a passive observer of the local environment,

scientists and engineers can utilize this knowledge to selectively tune solubility of

compounds by choosing the right combination of cation and anion constituents.

The mechanism of solvation in ILs is distinctly different from conventional dipolar

solvents, where collective dipole-dipole interactions in the vicinity of the fluorescence

probe molecule are the most dominant interaction. In ILs, the media is no longer

a single component liquid, rather a heterogeneous mixture, and because of their

different shapes, sizes, and charge distributions the ions respond differently to the

charge perturbation. However, extensive MD simulations in a series of imidazolium-

based ILs, [emim][BF4], [bmim][BF4], [bmim][DCA], [emim][TfO], and [bmim][PF6]

revealed a general solvation dynamics mechanism despite these differences in ions.

Consistently, the translational motion of the anions into and out of the first solvation

shell of C153 are most responsible for the solvation response. While initially this

mechanism appears distinct from polar solvents, if considering particular cation-anion

pairs form a molecule with a fictitious dipole moment, it is the rotation of these

‘fictitious’ molecules that dominate the response (Figure 7.1). The concept of the

fictitious dipole molecule is a proof-of-concept, with the current definition identifying

any anions with 7.75 A of the center-of-mass of the cations. The distance 7.75 A was

identified as the first minimum in the radial distribution function of the center-of-

mass of the cations relative to the center-of-mass of the anions.

Analogous to experimental observations that the solvation relaxation is correlated

with viscosity (Chapter 1), a comparable resemblance is found when relating the

111

Figure 7.1. The simulated solvation response (black) is decomposed usingthe methodology described in Chapter 2 into contributions from the

rovibrational (dashed pink) and the translational motions of the fictitiousdipole molecule (solid blue).

112

Figure 7.2. The calculated solvation relaxation time as a function of theinverse cube root of the molecular volume.

113

theoretical solvation time to the inverse of the cube root of the molecular volume

(Figure 7.2). Predicting relevant solvation time scales is beyond the scope of this

study, though a survey of additional ILs would be beneficial.

One of the most daunting scientific challenges facing our society today is the

production of environmentally clean and renewable energy. Chemists and engineers

are no longer dependent on varying the reaction conditions as a means for control over

rates and products; now selectivity over the reaction media represents a paradigm

shift in our approach to chemical reactions in the condensed phase. This research

which characterized the structure and dynamics in ILs in unprecedented detail, will

benefit other scientists and engineers who are seeking to control the properties of ILs

for advanced applications in energy research.

7.1 Alternative Systems of Interest

This dissertation considers only binary compositions of common ILs, though

ternary mixtures and beyond are achievable and would present a more complicated

solvation mechanism. Previous studies have found that consistent with imidazolium-

based ILs, the solvation dynamics are extremely slow however ILs using ammonium

and phosphonium cations do not display an ultrafast component, suggesting an alter-

native solvation mechanism is in effect.[67–69, 234] Beyond relatively planar cations

and spherical anions, preliminary investigations including planar anions and approx-

imately spherical cations challenge the validity of the mechanism suggested in Chap-

ters 2 and 3.

Four different cations 1-butyl-3-methyl imidazolium, [bmim], 1-ethyl-3-methyl im-

idazolium, [emim], triethyl sulfonium, [S222], and tri(methoxymethyl)-methyl phos-

phonium, [Tmet] were paired with five anions tetrafluoroborate, [BF4], trifluoro-

methane sulfonate, [TfO], 1-pyrazolide, [Pyrazo], 1,2,3,-triazolium, [Triazo], and bistri-

fluoromethylsulfonylimide, [Tf2N] to create seven unique systems (Figure 7.3). The

114

cation [Tmet] is preferred over the non-ether containing counterpart tributyl-methyl

phosphonium, [P3331], because recent studies have identified the introduction of ether-

bonds significantly improves transport properties.[235–237] Shown in Figures 7.4-

7.10 are the solvation response and decomposition for [bmim][TfO], [emim][Pyrazo],

[emim][Tf2N], [emim][Triazo], [S222][[BF4], [Tmet][BF4], and [Tmet][Pyrazo]. Consis-

tent with the imidazolium-based ILs and spherical anions presented in Chapter 3, the

anion contribution is substantially larger than that of the cations or C153 for all time

scales of the solvation response. Decompositions of the individual ion components

into translational and rovibrational contributions have not been performed, so it is

unclear if the mechanism of solvation where the translational motion of the anions

into and out of the first solvation shell of C153 is present. This represents an exciting

avenue for future study.

115

[emim]

[bmim]

Cations Anions

[Tmet]

[S222]

[BF4]

[Pyrazo]

[Triazo]

[TfO]

[Tf2N]

Figure 7.3. The optimized structures of cations and anions. The cations are1-butyl-3-methyl imidazolium, [bmim], 1-ethyl-3-methyl imidazolium,

[emim], triethyl sulfonium, [S222], and tri(methoxymethyl)-methylphosphonium, and [Tmet]. The anions are tetrafluoroborate, [BF4],

trifluoro-methane sulfonate, [TfO], 1-pyrazolide, [Pyrazo], 1,2,3,-triazolium,[Triazo], and bistrifluoromethylsulfonylimide, [Tf2N]

116

Figure 7.4. The calculated total solvation response (black) is decomposedinto contributions from the [TfO] anions (red), the [bmim] cations (blue),


117

Figure 7.5. The calculated total solvation response (black) is decomposedinto contributions from the [Pyrazo] anions (red), the [emim] cations

(blue), and the internal motions of the C153 solute (purple).

118

Figure 7.6. The calculated total solvation response (black) is decomposedinto contributions from the [Tf2N] anions (red), the [emim] cations (blue),


119

Figure 7.7. The calculated total solvation response (black) is decomposedinto contributions from the [Triazo] anions (red), the [emim] cations (blue),


120

Figure 7.8. The calculated total solvation response (black) is decomposedinto contributions from the [BF4] anions (red), the [S222] cations (blue),


121

Figure 7.9. The calculated total solvation response (black) is decomposedinto contributions from the [BF4] anions (red), the [Tmet] cations (blue),


122

Figure 7.10. The calculated total solvation response (black) is decomposedinto contributions from the [Pyrazo] anions (red), the [Tmet] cations

(blue), and the internal motions of the C153 solute (purple).

123

APPENDIX A

SOLVATION RESPONSE FUNCTION FITS

As mentioned in Chapter 3, the experimental results observed in Figure 3.2 were

scaled by a multiplicative constant to bring the results into maximum coincidence for

comparative purposes. A systematic analysis identified the ideal multiplicative con-

stant, k, by minimizing the root-mean-square deviation (RMSD) of the experimental

measurements to the normalized simulated response (Table A.1).

Also shown in this appendix are the solvation response functions fit to a single

exponential A exp(−(t/τ)) in the range from 50 to 400 ps as referred to in Chapter

3.

124

Figure A.1. Fits of the calculated (black) and experimental (red) solvationresponses of C153 in the IL [emim][BF4] to a single exponential function in

the time range between 50 ps and 400 ns. The data are shown as filledcircles, while the fits are lines.

125



126



127



128



129

TABLE A.1

IDEAL MULTIPLICATIVE CONSTANTS

k RMSD (10−2)

[emim][BF4] 1.17 3.9

[bmim][BF4] 0.78 3.2

[bmim][DCA] 0.945 2.7

[emim][TfO] 0.79 6.1

[bmim][PF6] 0.71 8.0

Ideal multiplicative constants, k, for experimental solvation response data that mini-mized the root-mean-square deviation (RMSD) for each IL system.

130

APPENDIX B

MALONALDEHYDE TWO-DIMENSIONAL INFRARED SPECTRA

Shown in this appendix are chemical exchange two-dimensional infrared (2D IR)

spectra for the CD stretch of labeled malonaldehyde in aqueous solution for waiting

times, Tw in the range 0 to 500 ps referred to in Chapter 6.

131

Figure B.1. Chemical exchange 2D IR spectra for waiting times of 0 ps.

132


133


134


135


136


137


138


139


140


141


142


143


144

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