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Exploring Electrostatic Effects on the Hydrogen Bond Network of Liquid Water through Many-Body Molecular Dynamics Shelby C Straight, and Francesco Paesani J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b02366 • Publication Date (Web): 24 Apr 2016 Downloaded from http://pubs.acs.org on April 28, 2016

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The Journal of Physical Chemistry

Exploring Electrostatic Effects on the Hydrogen Bond Network of Liquid Water through Many-Body Molecular Dynamics Shelby C. Straight and Francesco Paesani* Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, California 92093, USA

ABSTRACT To probe the dynamic nature of the hydrogen bond network in water, linear and nonlinear infrared spectra of dilute HOD in H2O are computed from many-body molecular dynamics simulations with the MB-pol potential, which have been shown to accurately predict the properties of water from the gas to the condensed phase. The effects of various approximations to the many-body expansion of the dipole moment surface on the OD-stretch absorption lineshapes are analyzed at different levels of theory. The interplay between effects associated with the variation of the HOD dipole moment and instantaneous nuclear configurations causes qualitative differences in the absorption profiles, which are traced back to how induction contributions are treated within the many-body formalism. Further analysis of the multidimensional infrared spectra demonstrates that the spectral diffusion of the OD stretching 1 ACS Paragon Plus Environment


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frequencies depends explicitly on the level of truncation in the many-body expansion of the dipole moment in the short-time regime that is associated with intact hydrogen-bond dynamics. In contrast, the long-time evolution of spectral diffusion, describing collective rearrangements of the hydrogen-bond network, is effectively independent of the details with which many-body contributions to the dipole moment are represented.

1. INTRODUCTION In the past twenty years, ultrafast spectroscopies have emerged as powerful tools for probing molecular interactions, providing insight into the dynamics of fundamental chemical processes.14

Originally designed for probing a sample through the use of successive Raman laser pulses,1

nonlinear vibrational spectroscopy has since been appropriated by infrared (IR) implementations targeted at disentangling the dynamics of dipole-allowed vibrational transitions, overcoming some technical limitations associated with Raman probes.5-7 It should be noted that recent experimental developments8 have renewed interest in higher-order nonlinear Raman and mixed Raman-IR responses.9-11 Given its ubiquity,12 water has been extensively studied by nonlinear vibrational spectroscopy.2-3, 13-15 In most of these experiments, dilute solutions of HOD molecules in H2O (D2O) are prepared to probe the dynamics of the hydrogen bond network of the liquid by interrogating the OD (OH) stretching vibrations of the HOD molecules.2 Due to the different reduced mass, the OD (OH) vibrational dynamics are effectively decoupled from all other vibrational degrees of freedom of the D2O (H2O) solvent, thus providing an ideal probe of the instantaneous local structure of the hydrogen-bond network of the liquid.14, 16-17 In principle, molecular dynamics (MD) simulations can provide direct, molecular-level insights into the origin of all spectral features measured for liquid water.18-19 However, as 2 ACS Paragon Plus Environment

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discussed in detail in Ref. 20, the accuracy of vibrational spectra calculated from computer simulations of liquid water is directly related to the accuracy with which the underlying multidimensional potential energy and dipole moment or polarizability surfaces as well as nuclear dynamics are treated.21-22 Among the innumerable simulation approaches reported in the literature, many-body molecular dynamics (MB-MD) has recently emerged as a unique theoretical and computational methodology that consistently enables highly accurate molecularlevel simulations of water from the gas to the condensed phase.20-21,

23-27

MB-MD combines

many-body representations of the potential energy (MB-pol), dipole moment (MB-µ), and polarizability (MB-α) surfaces, derived entirely from correlated electronic structure calculations, with either classical or quantum-mechanical descriptions of the nuclear dynamics.20 In this study, we investigate the dependence of the OD lineshape of HOD in H2O with respect to the various terms in the many-body expansion of the water dipole moment. Beginning with the IR spectroscopic predictions, the structure of the liquid is characterized from the analysis of the lineshapes computed using various approximations to the dipole moment. The differences in the dynamics corresponding to different representations of the dipole moment surface (DMS) are then examined from calculations of two-dimensional infrared (2D-IR) spectra. Finally, the interpretation of these spectra metrics is given with respect to the dynamics of the hydrogen bond network of liquid water. The article is organized as follows: in section 2, the computational methods detailing the simulation protocol and the calculation of (non)linear response functions are given. In section 3, both IR and 2D-IR spectra are presented and discussed. Section 4 is dedicated to concluding statements and closing remarks.

2. COMPUTATIONAL METHODS

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2.1 Simulation protocol Both 1D-IR and 2D-IR spectra were calculated by averaging the relevant response functions (see Section 2.2) over 46 independent centroid molecular dynamics (CMD)28 trajectories carried out at 298.15 K for a simulation box containing 215 H2O molecules and one HOD molecule in periodic boundary conditions. The box side was kept fixed at a length of 18.64258 Å corresponding to a liquid density of 0.997 g / cm3 as predicted by path-integral molecular dynamics (PIMD) simulations using the MB-pol water potential.25 The initial conditions for all CMD trajectories were generated from PIMD simulations in which each atom was represented by a ring-polymer with P = 32 beads, while the temperature was controlled through the use of Nosé-Hoover thermostat chains attached to every degree of freedom. Following our previous studies,20-21 the centroid dynamics were propagated through a normal-mode representation, and the centroid and nozero frequency normal modes were decoupled by adjusting the adiabaticity parameter, γ, to 0.1.29 A time step of 0.02 fs was used, as this has been determined to be adequeate for energy conservation. Each CMD trajectory was simulated for 25 ps.

2.2 Response functions Within linear response theory, the OD infrared absorption spectrum of HOD in H2O can be determined from the Fourier transform of the quantum dipole autocorrelation function,30

~ < 0 ∙ >

(1)

where is the dipole moment operator,31 which is approximated here by the analogous CMD quantity.28 Focusing on the 0-1 transition of the OD stretching vibration, Eq. (1) can be recast in the semiclassical (SC) limit and ignoring lifetime effects as32

~ < 0 >

(2)


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where and are the instantaneous transition dipole moment and frequencies between the ground and first excited vibrational states of the OD stretch, respectively, and = − < >, with < > being the average 0-1 transition frequency. Different approximations to Eq. (2) can be formulated depending on the treatment of the time correlation function of the transition dipole moment. Briefly, starting from the semiclassical expression, the non-Condon lineshape can be derived by neglecting the orientational motion of the transition dipole moment,

~ < μ 0μ >

(3)

where here µ is the magnitude of the transition dipole moment vector. The Condon lineshape is then be obtained by further neglecting the time-dependence of the transition dipole moment,

~ < >.

(4)

Last, the expression for the Condon lineshape can be expanded using cumulants of the frequency distribution, which, truncating the expansion after the second term, results in the second-order cumulant approximation to the lineshape,32-33

~ #

(5)

where

$ = % − %&%

(6)

and & is the frequency autocorrelation function (FTCF), & = < 0 > .

(7)

In the limit of Gaussian frequency fluctuations about < >, the cumulant lineshape is exact.31-33 It should be noted that Eqs. 1 – 5 are normalized so as to only compare the OD lineshapes, which implies that information about relative intensities between the different levels 5 ACS Paragon Plus Environment


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of theory is therefore lost. Although we have previously shown how the differences in the expansion of the dipole moment modulate the intensity of IR spectrum of liquid water,20 an analysis of the infrared intensity as a function of the different approximations to the OD lineshape is beyond the scope of this study. Analogous expressions to Eqs. 1 – 5 can be derived for the third-order rephasing, Rr(t1, t2, t3), and nonrephasing, Rnr(t1, t2, t3), nonlinear response functions which, upon double FourierLaplace transformation, result in the 2D-IR spectrum,

, ( , ) ≡ + ) , - . . +/ ) , ( , + - . . +1/ ) , ( , 2 (8) where t1 is the time delay between the first and second laser pulses, and t2 is the time delay between the second and third laser pulses. The 2D-IR signal, which directly reports on the time evolution of the OD stretching frequency of HOD in H2O,14, 16, 22, 33-39 is then detected at time t3 after the third laser pulse in the background-free directions kr = -k1 + k2 + k3 (rephasing signal) and knr = k1 - k2 + k3 (nonrephasing signal), with k1, k2, and k3 being the wave vectors of the three laser pulses. In addition to the 0-1 transition, both Rr(t1, t2, t3) and Rnr(t1, t2, t3) include pathways involving transitions between the first and second excited vibrational states which are associated with instantaneous frequencies ( .32 Specific details on the calculation of the response functions are given in the Supporting Information. Since the OD stretching vibration of the HOD molecule is, to a good approximation, decoupled from all other H2O degrees of freedom, the vibrational wavefunctions describing the OD instantaneous transition frequencies are effectively localized on the OD bond vector. Within this approximation, both and ( were calculated along the CMD trajectories from the numerical solution of the one-dimensional Schrödinger equation associated with the OD oscillator. To obtain these quantities, the OD Born-Oppenheimer potential energy surface was


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computed by stretching the OD bond while keeping the positions of all other atoms fixed for each instantaneous configuration of HOD in H2O-following the procedure described in Ref. 40. The corresponding vibrational frequencies and wavefunctions of the ground and first two excited states were then computed from the resultant potential curve by way of the iterative Numerov method. To obtain the vibrational transition moments, numerical integration was employed by projecting the appropriate dipole moment surface over the appropriate wavefunctions. As previously reported,27 within MB-MD, the water DMS is accurately represented by a multidimensional many-body function (MB-µ), including explicit one-body (1B) and two-body (2B) terms, with all higher-order (NB) terms being described by a classical many-body induction term built upon the TTM4-F Thole-type polarizable model.41 The specific functional form of MB-µ was derived from a systematic analysis of the many-body convergence of the electrostatic properties of water.20, 27 To investigate the modulation of both IR and 2D-IR spectra of HOD in H2O with respect to the DMS, the response functions in Eq. 3 and Eq. 8 were calculated using different terms of MB-µ, corresponding to different approximations to many-body effects on the water dipole moment. Specifically, the infrared lineshapes were computed using the gas-phase (1B) term, the 1B+NB representation in which explicit short-range 2B effects are neglected, and the full (1B+2B+NB) MB-µ DMS. Given the importance of accounting for quantum dynamics in the calculation of 2D-IR spectra,42-43 the anharmonicity and zero point energy of the vibrational energy levels must be explicitly accounted for in MD simulations used for the computation of multidimensional signals, accomplished here through the use of CMD. The present simulations represent a systematic improvement over previous studies by consistently applying Semiclassical dynamics (CMD) to a near-perfect Born-Oppenheimer potential energy surface to obtain parameters for a



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quantum noise correlation function, rather than attempting to map classical MD trajectories onto these quantum TCF’s. Many approaches to this problem have utilized ab initio based maps in conjunction with Molecular Dynamics simulations in order to compute the relevant physical quantities associated with the expressions for vibrational signals in equations 3 and 8. While such techniques can, in principle, reproduce the effect of population transfer through the incorporation of vibrational coupling to the chromophore of interest, the computed spectroscopic signatures are in a sense phenomenological given that the dynamics inferred from these Infrared signals only partially reflect the dynamics of the underlying MD simulation. Building upon the pioneering approaches developed by Skinner and co-workers,32 the present study, which employs accurate many-body representations of both potential energy and dipole moment surfaces, represents a step towards predictive accuracy in MD simulations through the use of self-consistent calculations of physical quantities within a robust computational framework.

3. RESULTS AND DISCUSSION 3.1 CMD IR spectrum


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Figure 1. IR spectra of HOD in H2O calculated from CMD MB-MD simulations. In red is the spectrum computed using the 1B (gas phase) DMS, in green is the spectrum computed using the 1B+NB (gas phase and classical induction effects) DMS, and in blue is the spectrum computed using the full MB-µ (1B+2B+NB) DMS,20 which includes an explicit short-range 2B term to account for the overlap between electron densities. The HOD IR spectra computed directly from the CMD trajectories (Eq. 1) using different approximations to the DMS are shown in Figure 1. It can be seen that the 1B IR spectrum predicts the HOD bending vibration to have the greatest intensity. Since this vibration is fairly localized,19, 44-45 it is not surprising that the 1B dipole moment is more strongly modulated by this motion. When the effects of classical induction are included (1B+NB), the OH vibrational motion of the surrounding water molecules become the most prominent modulators of the HOD dipole moment. These results thus demonstrate that the representation of many-body effects on



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the HOD dipole moment through classical induction correctly captures the more delocalized nature of the HOD stretching vibrations.46 In addition, the small feature near 1620 cm-1 indicates that the HOD dipole autocorrelation function effectively reports on the H2O bending vibrations. The explicit inclusion of the short-range 2B term in the many-body expansion of the HOD dipole moment20 causes the intensity of both OD and OH stretching peaks to grow, while leaving the peak associated with the H2O bending vibration essentially unchanged. This indicates that the 1B+NB representation of the DMS is sufficient to correctly describe the infrared response of the bending vibrations, providing support for the localized nature of these motions in liquid water. Due to their more delocalized nature, both peaks associated with the OD and OH stretch vibrations grow appreciably when the short-range 2B term, which more accurately describe interactions between hydrogen-bonded pairs, are explicitly included in the DMS. This analysis clearly demonstrates that the HOD stretching vibrations are more strongly coupled to the surrounding water molecules than the corresponding bending vibration. The ratio between the intensities of the HOD bend and the OH stretch peaks with respect to the DMS used in the calculations of the corresponding spectra (Eq. 1) is indicative of the importance of many-body polarization effects on the IR response functions. Such an analysis thus predicts that when the gas-phase (1B) dipole is sufficient to describe the electric field felt by a water molecule, the bending intensity should surpass that of the stretch. Experimental infrared studies of water at low concentration in inert matrices indeed show a greater intensity for bending than for stretching vibrations.47-48 For studies of water at higher concentrations48 and in matrices that actively interact with individual water molecules,49 electrical induction is non-negligible, and, consequently, the intensity of the stretching peaks is comparable to that of the bending vibrations.


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3.2 OD stretch IR lineshape The non-Condon approximation to the IR lineshape contains explicit information on the time dependence of the transition dipole moment, which alters the lineshape in different ways for different representations of the DMS. Since MB-pol predicts intramolecular stretching vibrations which are approximately 57 cm-1 blueshifted compared to experiment,20 all MB-MD results shown in Figure 2a are redshifted by the same amount to facilitate the comparison with the experimental results. Despite this adjustment, the non-Condon lineshape computed with the 1B DMS is still blueshifted by ~30 cm-1 due to the lack of electrostatic correlations with the surrounding water molecules. In contrast, the non-Condon lineshapes calculated with DMSs that include many-body induction effects (1B+NB and 1B+2B+NB) correctly reproduce the overall absorption profile although they predict slightly higher intensity at lower frequency. In addition, the 1B+2B+NB noncondon lineshape is marginally wider than the 1B+NB noncondon spectra, as can be seen in Table 1; this is likely due to a high degree of 2B electrostatic correlation for strongly hydrogen-bonded configurations. These results provide further support to the analysis reported in Ref. 26 which highlights the importance of a rigorous description of many-body electrostatic effects to correctly capture the infrared signatures of the hydrogen-bond dynamics in liquid water. Nearly quantitative agreement with the experimental results is provided by the CMD lineshape (upon accounting for the 57 cm-1 blue shift). Considering the accuracy of the MB-pol potential energy surface and MB-µ dipole moment surface for water, the comparison between CMD and semiclassical lineshapes suggests that semiclassical response functions may provide an



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incomplete description of vibrational dynamics of HOD in H2O, possibly associated with the underestimation of motional narrowing and lifetime effects.

Figure 2. a) Non-Condon (Eq. 3), Condon (Eq. 4), and CMD (Eq. 1) approximations to the OD stretch lineshape compared to experiment. Red: non-Condon lineshape computed using the 1B DMS; green: non-Condon lineshape computed using the 1B+NB DMS; blue: non-Condon lineshape computed using the full MB-µ (1B+2B+NB) DMS. Dotted violet: Condon lineshape computed using the full MB-µ (1B+2B+NB) DMS. Dashed Blue: CMD lineshape computed using the full MB-µ (1B+2B+NB) DMS. Black: experimental lineshape.18 All simulated lineshapes are redshifted by 57 cm-1 to facilitate comparison with the experimental results. b) 1B (red), 1B+NB (green), and 1B+2B+NB (blue) OD transition dipole moment (µ10) computed along a representative CMD trajectory.


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Table 1: FWHM and Peak Frequencies for MB-pol and Experimental OD Stretch Lineshapes. FWHM (cm-1)

Frequency of Max Absorbance (cm-1)*

Experimental

157

2508

1B+2B+NB CMD spectrum

153

2514

1B+2B+NB non-Condon

176

2509

1B+NB non-Condon

163

2512

1B non-Condon

184

2531

Condon

184

2531

Lineshape

* Max absorbance frequencies correspond to the identified spectra in figure 2a after having shifted by 57 cm-1 to better facilitate comparison with experiment.

Interestingly, Figure 2a also shows that the expansion of the 1B DMS yields a lineshape almost identical to that obtained within the Condon approximation. Due to the lack of electrostatic coupling with the surrounding water molecules, the 1B (gas phase) dipole moment of the HOD molecule can only fluctuate in response to intramolecular distortions. While both stretching and bending vibrations are always occurring, the magnitude of their effects are relatively smaller than those associated with induction interactions as shown in Figure 2b. As a result, within the 1B representation of the DMS, the 1-0 transition dipole is approximately constant (i.e. non-Condon effects are negligible), which make the Condon and non-Condon approximations to the lineshape virtually identical when the 1B DMS is used in Eqs. 3 and 4. Some discussion concerning the comparison of the presented 1D-IR signals and the isotropic Raman spectrum is warranted; specifically regarding the presence of a pronounced shoulder on the blue side of the Raman spectrum which is not present in these infrared signals. Previous studies32, 50 have attributed this feature to the underlying frequency distribution dictated by the absence or participation of the OD oscillator in hydrogen-bond donation. The dependence of



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transition dipole moment on hydrogen bonding topology was assumed to “wash out” this highfrequency shoulder, whereas the independence of the isotropic polarizability tensor on molecular environment is assumed to preserve the bimodal transition frequency distribution. However, given the lack of the feature in the Condon lineshape in the MB-pol spectra (but the presence of this shoulder in both the Raman and Condon IR lineshapes computed using the SPC/FQ model combined with the ES/MD technique used in the previously mentioned studies), we believe the appearance of this feature is an artifact of either the dynamic frequency mapping technique or the inaccurate description of the SPC/FQ and BYLYP models of the PES of the liquid.25 Further investigation into the MB-pol prediction of the Raman lineshape of HOD in H2O is left for future study.

3.3 OD stretch 2D-IR spectra


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Figure 3: From top to bottom are the 2D-IR spectra computed within the non-Condon approximation using the full MB-µ (1B+2B+NB), 1B+NB, and 1B DMSs. Warm (red) colors correspond to the 1-0 transition and cool (blue) colors correspond to the 2-1 transition. Each spectrum is normalized with respect to the largest 1-0 transition intensity. As in Figure 2, all 2DIR spectra are redshifted by 57 cm-1 to facilitate comparison with the experimental results. Following Refs. 40 and 51, the 2D-IR spectra were modeled within the non-Condon approximation using Eq. 8. These spectra, shown in Figure 3 for different waiting times (t2), contain information about the timescales of lineshape broadening,1,

52-55

which reports on the

dynamics of the local hydrogen-bond network probed by the OD oscillator.2, 14, 18, 35, 56 At t2 = 0 15 ACS Paragon Plus Environment


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ps, both peaks associated with the 1-0 (warm colors) and 2-1 (cold colors) transitions are elongated along the diagonal. As discussed extensively in the literature.14,

16-17

this elongation

progressively disappears, reflecting the loss of correlation of the OD vibrational frequencies calculated at later delay times, in agreement with the experimental observations. Similar to the IR lineshapes shown in Figure 2a, the 2D-IR spectra calculated using the 1B DMS are consistently shifted by ~30 cm-1 relative to those obtained including many-body electrostatic contributions.

Figure 4. a) 1-0 frequency time correlation function (FTCF) defined in Eq. 7. The Fourier transform of this signal is given in the inset. b) Slope of the nodal line (SNL) derived from the 2D-IR spectra (Figure 3) calculated using the 1B DMS (red), the 1B+NB DMS (green), and the full MB-µ (1B+2B+NB) DMS (blue). The experimental SNL is shown in black.57 Within the Condon (and subsequent second-order Cumulant) approximations to the nonlinear response functions, quantities such as the slope of the nodal line (SNL), ellipticity, center line slope (CLS), and inhomogeneity index, extracted from 2D-IR spectra, are all linearly proportional to the frequency time correlation function (FTCF),58-59 and can be used interchangeably to characterize spectral diffusion and vibrational dephasing in liquid water.58-61 16 ACS Paragon Plus Environment

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Since the non-Condon 2D-IR spectra calculated from Eq. 4 depends on how the underlying DMS is represented, the time evolution of the 1-0 and 2-1 lineshapes in Figure 3 can still be used to gain insights into the dynamic electrostatic coupling between the OD oscillator and the surrounding water molecules, even if the Condon and subsequent second-order cumulant approximations are not explicitly made. The FTCF calculated from MB-MD simulations (Figure 4a) shows that OD spectral diffusion is characterized by two different decay times, indicative of long- and short-lived processes modulating the dynamics of the hydrogen-bond network surrounding the HOD molecule. These decay times have been associated with the dynamics of fast fluctuating configurations of intact hydrogen bonds and slower collective rearrangements of the hydrogen bond network, respectively.18, 57 At short time, the SNL (figure 4b) decays faster when explicit short-range 2B contributions are included in the representation of the DMS, in agreement with the time evolution of the FTCF. The high-frequency, small-amplitude oscillations in the computationally derived FTCF occur with period ~20fs, the oscillation time of the HOD bending motion; a Fourier transform of this signal (shown in the inset of figure 4a) reveals the OD frequency timecorrelation function to be modulated by the intramolecular bend, low-frequency hindered rotations and translations, and low-frequency h-bond vibrations. The similar time dependence of the SNL and FTCF further highlights the importance of accounting for short-range electrostatic interactions between hydrogen-bonded molecules when modeling the structural and dynamical properties of liquid water.62 Since at short distance the interactions between water molecules arise from the overlap of the monomer electron densities, they are intrinsically quantum-mechanical in nature and cannot be described quantitatively by dipole representations such as the 1B+NB DMS in which many-body effects are solely



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represented by classical induction. In contrast, the long-time decay of the FTCF is mirrored in the SNL independently of the DMS used in the calculation of the 2D-IR spectra. A comparison between the FTCF extracted from MB-pol simulations and the temperaturedependent experimentally obtained FTCF’s from the Tokmakoff group63 shows qualitatively similar short and long-time decay of HOD vibrational frequency correlation. Experimentally, the mono-exponential decay of the FTCF ranges from ~0.5ps to ~2ps, with colder conditions giving rise to slower decay. Although the MB-pol prediction offers qualitative agreement with these experiments, the non-negligible effects of finite pulse-widths (as opposed to the impulsive limit assumed in the simulations) indicate that simulation and experiment are not directly comparable. This neglect of pulse-width, in addition to the different melting points between MB-pol and liquid water, suggests that quantitative comparison between these simulations and experiment is inaccessible at this time.

4. CONCLUSIONS In this work, we have applied many-body molecular dynamics to the study of the linear and nonlinear infrared spectroscopy of HOD in H2O. Particular emphasis has been placed on the analysis of the vibrational lineshapes of the OD stretch using different approximations to the many-body expansion of the dipole moment surface. The calculated linear spectra show that the HOD bending motion is highly localized and is only weakly electrostatically coupled to the surrounding water molecules. In addition, the appearance of a peak near 1620 cm-1 demonstrates that the HOD molecule reports on nearby H2O bending frequencies, an effect which is completely captured by classical electrostatics. Interestingly, the Condon approximation to the


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OD lineshape using the 1B DMS is virtually identical to the corresponding non-Condon results, as expected for systems in which many-body inductive effects are absent. The calculated 2D-IR spectra provide further insight into the molecular origin of the spectral diffusion and vibrational dephasing in liquid water. It is found that the time-evolution of these multidimensional signals is qualitatively similar between the 1B and 1B+NB approximation to the DMS, which suggests that the differences in the corresponding linear OD stretch absorption spectra are due to the lack of intermolecular electrostatic correlation in the 1B DMS. Furthermore, while the long-time contributions to spectral diffusion are the same regardless of the approximation to the many-body DMS, the short-time components (corresponding to intact hydrogen-bond dynamics) are qualitatively different when short-range 2B effects are explicitly included. These differences emphasize the importance of accounting for short-range electrostatic interactions in the description of hydrogen-bonded water molecules. Since these interactions arise from the overlap of the monomer electron densities, their quantum-mechanical nature cannot be correctly captured by dipole representations in which many-body effects are solely represented by classical expressions (e.g. polarizable force fields). Although the effects of vibrational coupling and exchange induced relaxation are outside the scope of this work, questions related to these phenomena can be addressed through the use of nonequilibrium molecular dynamics64-66 and have been successfully applied to the interrogation of low-frequency intermolecular motions of liquid water.67 While such simulations are computationally expensive, they are worthwhile topics of investigation for future study with MB-pol, given the numerically predictive capability of this fully ab-initio many-body potential energy function.25



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ASSOCIATED CONTENT Supporting Information. Further detail is provided for the derivation of the various theoretical formulations of the nonlinear response functions. In addition, the 2D-IR spectra within the Condon and cumulant approximations to the nonlinear response functions are presented for completeness. AUTHOR INFORMATION Corresponding Author *[email protected], 858-822-3383 Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding Sources National Science Foundation, award numbers CHE-1453204 and ACI-1053575. ACKNOWLEDGMENT This research was supported by the National Science Foundation through grant number CHE1453204. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by the National Science Foundation grant number ACI-1053575 (allocation TG-CHE110009). REFERENCES 1. Tanimura, Y.; Mukamel, S. Two‐Dimensional Femtosecond Vibrational Spectroscopy of Liquids. J. Chem. Phys. 1993, 99 (12), 9496-9511.


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