Water Dynamics: Vibrational Echo Correlation Spectroscopy and Comparison to Molecular Dynamics Simulations

Hydrogen bonds in liquid water are broken only fleetingly

Although it is widely accepted that the local structure of liquid water has tetrahedral arrangements of molecules ordered by hydrogen bonds, the mechanism by which water molecules switch hydrogen-bonded partners remains unclear. In this mechanism, the role of nonhydrogen-bonded configurations (NHBs) between adjacent molecules is of particular importance. A molecule may switch hydrogen-bonding partners either (i) through thermally activated breaking of a hydrogen bond that creates a dangling hydrogen bond before finding a new partner or (ii) by infrequent but rapid switching events in which the NHB is a transition state. Here, we report a combination of femtosecond 2D IR spectroscopy and molecular dynamics simulations to investigate the stability of NHB species in an isotopically dilute mixture of HOD in D2O. Measured 2D IR spectra reveal that hydrogen-bonded configurations and NHBs undergo qualitatively different relaxation dynamics, with NHBs returning to hydrogen-bonded frequencies on the time scale of water's fastest intermolecular motions. Simulations of an atomistic model for the OH vibrational spectroscopy of water yield qualitatively similar 2D IR spectra to those measured experimentally. Analysis of NHBs in simulations by quenching demonstrates that the vast majority of NHBs are in fact part of a hydrogen-bonded well of attraction and that virtually all molecules return to a hydrogen-bonding partner within 200 fs. The results from experiment and simulation demonstrate that NHBs are intrinsically unstable and that dangling hydrogen bonds are an insignificant species in liquid water.

Polarizable molecules in the vibrational spectroscopy of water

We examine the role of electronic polarizability in water on short (tens of femtoseconds), intermediate (hundreds of femtoseconds), and long (approximately 1 ps) time scales by comparing molecular dynamics results to experimental data for vibrational spectroscopy of HOD in liquid D2O. Because the OH absorption frequency is sensitive to the details of the atomic forces experienced in the liquid, our results provide important quantitative comparisons for several popular empirical water potentials. When compared with their fixed-charge counterparts, the polarizable models give similar slower long time constants for the decay of vibrational correlations and re-orientational motion that is in better agreement with experiments. Polarizable potentials yield qualitatively dissimilar predictions for frequency fluctuations and transition dipole moment fluctuations at equilibrium. Models that confine the polarizability to the plane of the molecule (i.e., TIP4P-FQ) overestimate the width of the distribution describing frequency fluctuations by more than a factor of two. These models also underestimate the amplitude of the hydrogen-bond stretch at 170 cm(-1). A potential that has both an out-of-plane polarization and fluctuating charges, POL5-TZ, compares best with experiments. We interpret our findings in terms of microscopic dynamics and make suggestions that may improve the quality of emerging polarizable force fields for water.

Pronounced non-Condon effects in the ultrafast infrared spectroscopy of water

In the context of vibrational spectroscopy in liquids, non-Condon effects refer to the dependence of the vibrational transition dipole moment of a particular molecule on the rotational and translational coordinates of all the molecules in the liquid. For strongly hydrogen-bonded systems, such as liquid water, non-Condon effects are large. That is, the bond dipole derivative of an OH stretch depends strongly on its hydrogen-bonding environment. Previous calculations of nonlinear vibrational spectroscopy in liquids have not included these non-Condon effects. We find that for water, inclusion of these effects is important for an accurate calculation of, for example, homodyned and heterodyned three-pulse echoes. Such echo experiments have been "inverted" to obtain the OH stretch frequency time-correlation function, but by necessity the Condon and other approximations are made in this inversion procedure. Our conclusion is that for water, primarily because of strong non-Condon effects, this inversion may not lead to the correct frequency time-correlation function. Nevertheless, one can still make comparison between theory and experiment by calculating the experimental echo observables themselves.

Infrared and Raman Line Shapes of Dilute HOD in Liquid H2O and D2O from 10 to 90 °C

A combined electronic structure/molecular dynamics approach was used to calculate infrared and isotropic Raman spectra for the OH or OD stretches of dilute HOD in D2O or H2O, respectively. The quantities needed to compute the infrared and Raman spectra were obtained from density functional theory calculations performed on clusters, generated from liquid-state configurations, containing an HOD molecule along with 4-9 solvent water molecules. The frequency, transition dipole, and isotropic transition polarizability were each empirically related to the electric field due to the solvent along the OH (or OD) bond, calculated on the H (or D) atom of interest. The frequency and transition dipole moment of the OH (or OD) stretch of the HOD molecule were found to be very sensitive to its instantaneous solvent environment, as opposed to the isotropic transition polarizability, which was found to be relatively insensitive to environment. Infrared and isotropic Raman spectra were computed within a molecular dynamics simulation by using the empirical relationships and semiclassical expressions for the line shapes. The line shapes agree well with experiment over a temperature range from 10 to 90 degrees C.

Dynamics of Nanoscopic Water: Vibrational Echo and Infrared Pump−Probe Studies of Reverse Micelles

The dynamics of water in nanoscopic pools 1.7-4.0 nm in diameter in AOT reverse micelles were studied with ultrafast infrared spectrally resolved stimulated vibrational echo and pump-probe spectroscopies. The experiments were conducted on the OD hydroxyl stretch of low-concentration HOD in the H2O, providing a direct examination of the hydrogen-bond network dynamics. Pump-probe experiments show that the vibrational lifetime of the OD stretch mode increases as the size of the reverse micelle decreases. These experiments are also sensitive to hydrogen-bond dissociation and reformation dynamics, which are observed to change with reverse micelle size. Spectrally resolved vibrational echo data were obtained at several frequencies. The vibrational echo data are compared to data taken on bulk water and on a 6 M NaCl solution, which is used to examine the role of ionic strength on the water dynamics in reverse micelles. Two types of vibrational echo measurements are presented: the vibrational echo decays and the vibrational echo peak shifts. As the water nanopool size decreases, the vibrational echo decays become slower. Even the largest nanopool (4 nm, approximately 1000 water molecules) has dynamics that are substantially slower than bulk water. It is demonstrated that the slow dynamics in the reverse micelle water nanopools are a result of confinement rather than ionic strength. The data are fit using time-dependent diagrammatic perturbation theory to obtain the frequency-frequency correlation function (FFCF) for each reverse micelle. The results are compared to the FFCF of water and show that the largest differences are in the slowest time scale dynamics. In bulk water, the slowest time scale dynamics are caused by hydrogen-bond network equilibration, i.e., the making and breaking of hydrogen bonds. For the smallest nanopools, the longest time scale component of the water dynamics is approximately 10 times longer than the dynamics in bulk water. The vibrational echo data for the smallest reverse micelle displays a dependence on the detection wavelength, which may indicate that multiple ensembles of water molecules are being observed.

Energy Transfer in Single Hydrogen-Bonded Water Molecules

We study the structure and dynamics of hydrogen-bonded complexes of H2O/HDO and acetone dissolved in carbon tetrachloride by probing the response of the O-H stretching vibrations with linear mid-infrared spectroscopy and femtosecond mid-infrared pump-probe spectroscopy. We find that the hydrogen bonds in these complexes break and reform with a characteristic time scale of approximately 1 ps. These hydrogen-bond dynamics are observed to play an important role in the equilibration of vibrational energy over the two O-H groups of the H2O molecule. For both H2O and HDO, the O-H stretching vibrational excitation relaxes with a time constant of 6.3+/-0.3 ps, and the molecular reorientation has a time constant of 6+/-1 ps.

Amide I Vibrational Dynamics ofN-Methylacetamide in Polar Solvents: The Role of Electrostatic Interactions

The vibrational frequency of the amide I transition of peptides is known to be sensitive to the strength of its hydrogen bonding interactions. In an effort to account for interactions with hydrogen bonding solvents in terms of electrostatics, we study the vibrational dynamics of the amide I coordinate of N-methylacetamide in prototypical polar solvents: D2O, CDCl3, and DMSO-d6. These three solvents have varying hydrogen bonding strengths, and provide three distinct solvent environments for the amide group. The frequency-frequency correlation function, the orientational correlation function, and the vibrational relaxation rate of the amide I vibration in each solvent are retrieved by using three-pulse vibrational photon echoes, two-dimensional infrared spectroscopy, and pump-probe spectroscopy. Direct comparisons are made to molecular dynamics simulations. We find good quantitative agreement between the experimentally retrieved and simulated correlation functions over all time scales when the solute-solvent interactions are determined from the electrostatic potential between the solvent and the atomic sites of the amide group.

Temperature excursion infrared (TEIR) spectroscopy used to study hydrogen bonding between water and biomolecules

Water is a highly polar molecule that is capable of making four H-bonding linkages. Stability and specificity of folding of water-soluble protein macromolecules are determined by the interplay between water and functional groups of the protein. Yet, under some conditions, water can be replaced with sugar or other polar protic molecules with retention of protein structure. Infrared (IR) spectroscopy allows one to probe groups on the protein that interact with solvent, whether the solvent is water, sugar or glycerol. The basis of the measurement is that IR spectral lines of functional groups involved in H-bonding show characteristic spectral shifts with temperature excursion, reflecting the dipolar nature of the group and its ability to H-bond. For groups involved in H-bonding to water, the stretching mode absorption bands shift to lower frequency, whereas bending mode absorption bands shift to higher frequency as temperature decreases. The results indicate increasing H-bonding and decreasing entropy occurring as a function of temperature, even at cryogenic temperatures. The frequencies of the amide group modes are temperature dependent, showing that as temperature decreases, the amide group H-bonds to water strengthen. These results are relevant to protein stability as a function of temperature. The influence of solvent relaxation is demonstrated for tryptophan fluorescence over the same temperature range where the solvent was examined by infrared spectroscopy.

Vibrational Relaxation of the Bending Mode of HDO in Liquid D2O

The vibrational relaxation of the bending mode of HDO in liquid D2O has been studied using time-resolved mid-infrared pump-probe spectroscopy. At short delays, the transient spectrum clearly shows the v = 1 --> 2 induced absorption and v = 1 --> 0 bleaching and stimulated emission, whereas at long delays, the transient spectrum is dominated by the spectral changes caused by the temperature increase in the sample after vibrational relaxation. From the decay of the v = 1 --> 2 induced absorption, we obtain an estimate of 390 +/- 50 fs for the vibrational lifetime, in surprisingly good agreement with recent theoretical predictions. In the v = 0 --> 1 frequency region, the decay of the absorption change involves a second, slower component, which suggests that after vibrational relaxation the system is not yet in thermal equilibrium.

Quantum corrections in vibrational and electronic condensed phase spectroscopy: line shapes and echoes

Various linear and nonlinear vibrational and electronic spectroscopy experiments in liquids are usually analyzed within the second-cumulant approximation, and therefore the fundamental quantity of interest is the equilibrium time-correlation function of the fluctuating transition frequency. In the usual approach the "bath" variables responsible for the fluctuating frequency are treated classically, leading to a classical time-correlation function. Alternatively, sometimes a quantum correction appropriate for relatively high temperatures is included, which adds an imaginary part to the classical time-correlation function. This approach, although appealing, does not satisfy detailed balance. One can consider a similar correction, but where detailed balance is satisfied, by using the harmonic quantum correction factor. In this article, we compare these approaches for a model system and two realistic examples. Our conclusion is that for linear spectroscopy the classical result is usually adequate, whereas for nonlinear spectroscopy it can be more important to include quantum corrections.

Orientational dynamics of water confined on a nanometer length scale in reverse micelles

The time-resolved orientational anisotropies of the OD hydroxyl stretch of dilute HOD in H(2)O confined on a nanometer length scale in sodium bis(2-ethylhexyl) sulfosuccinate (AOT) reverse micelles are studied using ultrafast infrared polarization and spectrally resolved pump-probe spectroscopy, and the results are compared to the same experiments on bulk water. The orientational anisotropy data for three water nanopool sizes (4.0, 2.4, and 1.7 nm) can be fitted well with biexponential decays. The biexponential decays are analyzed using a wobbling-in-a-cone model that involves fast orientational diffusion within a cone followed by slower, full orientational relaxation. The data provide the cone angles, the diffusion constants for motion within the cones, and the final diffusion constants as a function of the nanopool size. The two processes can be interpreted as a local angular fluctuation of the OD and a global hydrogen bond network rearrangement process. The trend in the relative amplitudes of the long and short exponential decays suggest an increasing rigidity as the nanopool size decreases. The trend in the long decay constants indicates a longer hydrogen bond network rearrangement time with decreasing reverse micelle size. The anisotropy measurements for the reverse micelles studied extrapolate to approximately 0.33 rather than the ideal value of 0.4, suggesting the presence of an initial inertial component in the anisotropy decay that is too fast to resolve. The very fast decay component is consistent with initial inertial orientational motion that is seen in published molecular-dynamics simulations of water in AOT reverse micelles. The angle over which the inertial orientational motion occurs is determined. The results are in semiquantitative agreement with the molecular-dynamics simulations.

Spectrally- and time-resolved vibrational surface spectroscopy: Ultrafast hydrogen-bonding dynamics at D2O/CaF2 interface

Time- and frequency-domain three-wave mixing spectroscopy (IR+visible sum frequency generation) is developed as the lowest-order nonlinear technique that is both surface selective and capable of measuring spectral evolution of vibrational coherences. Using 70 fs infrared and 40 fs visible pulses, we observe ultrafast spectral dynamics of the OD stretch of D2O at the CaF2 surface. Spectral shifts indicative of the hydrogen-bond network rearrangement occur on the 100 fs time scale, within the observation time window determined by the vibrational dephasing. By tuning the IR pulse wavelength to the blue or red side of the OD-stretch transition, we selectively monitor the dynamics of different subensembles in the distribution of the H-bond structures. The blue-side excitation (weaker H-bonding structures) shows monotonic decay and nu(OD) frequency shift to the red on a 100 fs time scale, which is better described by a Gaussian than an exponential frequency correlation function. In contrast, the red-side excitation (stronger H-bonding structures) results in a blue spectral shift and a recursion in the signal at 125+/-10 fs, indicating the presence of an underdamped intermolecular mode of interfacial water.

Ultrafast memory loss and energy redistribution in the hydrogen bond network of liquid H2O

Many of the unusual properties of liquid water are attributed to its unique structure, comprised of a random and fluctuating three-dimensional network of hydrogen bonds that link the highly polar water molecules. One of the most direct probes of the dynamics of this network is the infrared spectrum of the OH stretching vibration, which reflects the distribution of hydrogen-bonded structures and the intermolecular forces controlling the structural dynamics of the liquid. Indeed, water dynamics has been studied in detail, most recently using multi-dimensional nonlinear infrared spectroscopy for acquiring structural and dynamical information on femtosecond timescales. But owing to technical difficulties, only OH stretching vibrations in D2O or OD vibrations in H2O could be monitored. Here we show that using a specially designed, ultrathin sample cell allows us to observe OH stretching vibrations in H2O. Under these fully resonant conditions, we observe hydrogen bond network dynamics more than one order of magnitude faster than seen in earlier studies that include an extremely fast sweep in the OH frequencies on a 50-fs timescale and an equally fast disappearance of the initial inhomogeneous distribution of sites. Our results highlight the efficiency of energy redistribution within the hydrogen-bonded network, and that liquid water essentially loses the memory of persistent correlations in its structure within 50 fs.

Dynamics of confined water molecules

We present femtosecond midinfrared pump-probe measurements of the molecular motion and energy-transfer dynamics of a water molecule that is enclosed by acetone molecules. These confined water molecules show hydrogen-bond and orientational dynamics that are much slower than in bulk liquid water. This behavior is surprising because the hydrogen bonds to the C=O groups of the acetone molecules are weaker than the hydrogen bonds in bulk water. The energy transfer between the O-H groups of the confined water molecules has a time constant of 1.3 +/- 0.2 ps, which is >20 times slower than in bulk water. We find that this energy transfer is governed completely by the rate at which hydrogen bonds are broken and reformed, and we identify the short-lived molecular complex that forms the transition state of this process.

Dynamics of water confined on a nanometer length scale in reverse micelles: ultrafast infrared vibrational echo spectroscopy

The dynamics of water, confined on a nanometer length scale (1.7 to 4.0 nm) in sodium bis-(2-ethylhexyl) sulfosuccinate reverse micelles, is directly investigated using frequency resolved infrared vibrational echo experiments. The data are compared to bulk water and salt solution data. The experimentally determined frequency-frequency correlation functions show that the confined water dynamics is substantially slower than bulk water dynamics and is size dependent. The fastest dynamics (approximately 50 fs) is more similar to bulk water, while the slowest time scale dynamics is much slower than water, and, in analogy to bulk water, reflects the making and breaking of hydrogen bonds.

Local hydrogen bonding dynamics and collective reorganization in water: Ultrafast infrared spectroscopy of HOD/D2O

We present an investigation into hydrogen bonding dynamics and kinetics in water using femtosecond infrared spectroscopy of the OH stretching vibration of HOD in D(2)O. Infrared vibrational echo peak shift and polarization-selective pump-probe experiments were performed with mid-IR pulses short enough to capture all relevant dynamical processes. The experiments are self-consistently analyzed with a nonlinear response function expressed in terms of three dynamical parameters for the OH stretching vibration: the frequency correlation function, the lifetime, and the second Legendre polynomial dipole reorientation correlation function. It also accounts for vibrational-relaxation-induced excitation of intermolecular motion that appears as heating. The long time, picosecond behavior is consistent with previous work, but new dynamics are revealed on the sub-200 fs time scale. The frequency correlation function is characterized by a 50 fs decay and 180 fs beat associated with underdamped intermolecular vibrations of hydrogen bonding partners prior to 1.4 ps exponential relaxation. The reorientational correlation function observes a 50 fs librational decay prior to 3 ps diffusive reorientation. Both of these correlation functions compare favorably with the predictions from classical molecular dynamics simulations. The time-dependent behavior can be separated into short and long time scales by the 340 fs correlation time for OH frequency shifts. The fast time scales arise from dynamics that are mainly local: fluctuations in hydrogen bond distances and angles within relatively fixed intermolecular configurations. On time scales longer than the correlation time, dephasing and reorientations reflect collective reorganization of the liquid structure. Since the OH transition frequency and dipole are only weakly sensitive to these collective coordinates, this is a kinetic regime which gives an effective rate for exchange of intermolecular structures.

Watching Hydrogen Bonds Break: A Transient Absorption Study of Water

Ultrafast infrared transient absorption measurements of the complete hydroxyl OD stretching mode spectrum of HOD in water, from 100 fs to tens of picoseconds, observe hydrogen bond breaking and monitor the equilibration of the hydrogen bond network in water. In addition, the vibrational lifetime, the time constant for hydrogen bond breaking, and the rate of orientational relaxation are determined. The reactant and photoproduct spectra of the hydrogen bond breaking process are identified by decomposing the transient spectra into two components, the initial spectrum associated with vibrational excited states (reactants) and the long-time spectrum associated with broken hydrogen bonds (photoproducts). By properly taking into account the perturbation of the reactant spectrum decay by the growth of the photoproduct spectrum, it is found that the vibrational relaxation (1.45 ps) and orientational relaxation (1.53 ps) are wavelength independent and, therefore, independent of the degree of hydrogen bonding. Energy deposited into water by vibrational relaxation does not immediately break a hydrogen bond by predissociation nor produce a thermally equilibrated hydrogen bond distribution at an elevated temperature. Following deposition of energy by vibrational relaxation, the hydrogen bond breaking time is 800 fs, and there is a transient period of several picoseconds during which the hydrogen bond distribution is not in thermal equilibrium.

Collective Solvent Coordinates for the Infrared Spectrum of HOD in D2O Based on an ab Initio Electrostatic Map

An ab initio MP2 vibrational Hamiltonian of HOD in an external electrostatic potential parametrized by the electric field and its gradient-tensor is constructed. By combining it with the fluctuating electric field induced by the D(2)O solvent obtained from molecular dynamics simulations, we calculate the infrared absorption of the O-H stretch. The resulting solvent shift and infrared line shape for three force fields (TIP4P, SPC/E, and SW) are in good agreement with the experiment. A collective coordinate response for the solvent effect is constructed by identifying the main electrostatic field and gradient components contributing to the line shape. This allows a realistic stochastic Liouville equation simulation of the line shapes which is not restricted to Gaussian frequency fluctuations.

Spectral diffusion in a fluctuating charge model of water

We apply the combined electronic structure/molecular dynamics approach of Corcelli, Lawrence, and Skinner [J. Chem. Phys. 120, 8107 (2004)] to the fluctuating charge (SPC-FQ) model of liquid water developed by Rick, Stuart, and Berne [J. Chem. Phys. 101, 6141 (1994)]. For HOD in H(2)O the time scale for the long-time decay of the OD stretch frequency time-correlation function, which corresponds to the time scale for hydrogen-bond rearrangement in the liquid, is about 1.5 ps. This result is significantly longer than the 0.9 ps decay previously calculated for the nonpolarizable SPC/E water model. Our results for the SPC-FQ model are in better agreement with recent vibrational echo experiments.

Ultrafast vibrational spectroscopy of water and aqueous N-methylacetamide: Comparison of different electronic structure/molecular dynamics approaches

Kwac and Cho [J. Chem. Phys. 119, 2247 (2003)] have recently developed a combined electronic structure/molecular dynamics approach to vibrational spectroscopy in liquids. The method involves fitting ab initio vibrational frequencies for a solute in a cluster of solvent molecules to a linear combination of the electrostatic potentials on the solute atoms due to the charges on the solvent molecules. These authors applied their method to the N-methylacetamide-D/D(2)O system. We (S. A. Corcelli, C. P. Lawrence, and J. L. Skinner, [J. Chem. Phys. 120, 8107 (2004)]) have recently explored a closely related method, where instead of the electrostatic potential, the solute vibrational frequencies are fit to the components of the electric fields on the solute atoms due to the solvent molecules. We applied our method to the HOD/D(2)O and HOD/H(2)O systems. In order to make a direct comparison of these two approaches, in this paper we apply their method to the water system, and our method to the N-methylacetamide system. For the water system we find that the electric field method is superior to the potential approach, as judged by comparison with experiments for the absorption line shape. For the N-methylacetamide system the two methods are comparable.

Interpreting nonlinear vibrational spectroscopy with the classical mechanical analogs of double-sided Feynman diagrams

Observables in coherent, multiple-pulse infrared spectroscopy may be computed from a vibrational nonlinear response function. This response function is conventionally calculated quantum-mechanically, but the challenges in applying quantum mechanics to large, anharmonic systems motivate the examination of classical mechanical vibrational nonlinear response functions. We present an approximate formulation of the classical mechanical third-order vibrational response function for an anharmonic solute oscillator interacting with a harmonic solvent, which establishes a clear connection between classical and quantum mechanical treatments. This formalism permits the identification of the classical mechanical analog of the pure dephasing of a quantum mechanical degree of freedom, and suggests the construction of classical mechanical analogs of the double-sided Feynman diagrams of quantum mechanics, which are widely applied to nonlinear spectroscopy. Application of a rotating wave approximation permits the analytic extraction of signals obeying particular spatial phase matching conditions from a classical-mechanical response function. Calculations of the third-order response function for an anharmonic oscillator coupled to a harmonic solvent are compared to numerically correct classical mechanical results.

Combined electronic structure/molecular dynamics approach for ultrafast infrared spectroscopy of dilute HOD in liquid H2O and D2O

We present a new approach that combines electronic structure methods and molecular dynamics simulations to investigate the infrared spectroscopy of condensed phase systems. This approach is applied to the OH stretch band of dilute HOD in liquid D2O and the OD stretch band of dilute HOD in liquid H2O for two commonly employed models of water, TIP4P and SPC/E. Ab initio OH and OD anharmonic transition frequencies are calculated for 100 HOD x (D2O)n and HOD x(H2O)n (n = 4-9) clusters randomly selected from liquid water simulations. A linear empirical relationship between the ab initio frequencies and the component of the electric field from the solvent along the bond of interest is developed. This relationship is used in a molecular dynamics simulation to compute frequency fluctuation time-correlation functions and infrared absorption line shapes. The normalized frequency fluctuation time-correlation functions are in good agreement with the results of previous theoretical approaches. Their long-time decay times are 0.5 ps for the TIP4P model and 0.9 ps for the SPC/E model, both of which appear to be somewhat too fast compared to recent experiments. The calculated line shapes are in good agreement with experiment, and improve upon the results of previous theoretical approaches. The methods presented are simple, and transferable to more complicated systems.

Nonperturbative vibrational energy relaxation effects on vibrational line shapes

A general formulation of nonperturbative quantum dynamics of solutes in a condensed phase is proposed to calculate linear and nonlinear vibrational line shapes. In the weak solute-solvent interaction limit, the temporal absorption profile can be approximately factorized into the population relaxation profile from the off-diagonal coupling and the pure-dephasing profile from the diagonal coupling. The strength of dissipation and the anharmonicity-induced dephasing rate are derived in Appendix A. The vibrational energy relaxation (VER) rate is negligible for slow solvent fluctuations, yet it does not justify the Markovian treatment of off-diagonal contributions to vibrational line shapes. Non-Markovian VER effects are manifested as asymmetric envelops in the temporal absorption profile, or equivalently as side bands in the frequency domain absorption spectrum. The side bands are solvent-induced multiple-photon effects which are absent in the Markovian VER treatment. Exact path integral calculations yield non-Lorentzian central peaks in absorption spectrum resulting from couplings between population relaxations of different vibrational states. These predictions cannot be reproduced by the perturbative or the Markovian approximations. For anharmonic potentials, the absorption spectrum shows asymmetric central peaks and the asymmetry increases with anharmonicity. At large anharmonicities, all the approximation schemes break down and a full nonperturbative path integral calculation that explicitly accounts for the exact VER effects is needed. A numerical analysis of the O-H stretch of HOD in D(2)O solvent reveals that the non-Markovian VER effects generate a small recurrence of the echo peak shift around 200 fs, which cannot be reproduced with a Markovian VER rate. In general, the nonperturbative and non-Markovian VER contributions have a stronger effect on nonlinear vibrational line shapes than on linear absorption.