Static and dynamic quantum effects in molecular liquids: A linearized path integral description of water

Abstract

Structure, transport properties, and IR spectra including quantum effects are calculated for a flexible simple point charge model of liquid water. A recently introduced combination of a variational local harmonic description of the liquid potential surface and the classical Wigner approximation for the dynamics is used. The potential energy and interatomic radial distribution functions are in good agreement with accurate results from the literature and are significantly closer to experiment than predictions found from classical theory. The oxygen and hydrogen velocity correlation functions are also calculated, and the corresponding molecular diffusion coefficient is in good accord with existing theoretical estimates including quantum effects. Of most interest, an ab initio quantum correction factor is obtained to correct the far IR spectrum of water. When corrected, a spectrum based on a classical simulation yields results that agree well with experiment. Combined with internal tests of consistency, these observations indicate that this quite flexible approach will be effective for a variety of molecular problems involving the dynamics of light nuclei.computer simulation ͉ liquid dynamics A lthough the molecular-level description of the structure and dynamics of disordered condensed phases, such as liquids, glasses, and globular proteins, is normally, and generally successfully, described by using classical mechanics, the underlying accurate description is, of course, quantum mechanical. It is simply that the quantum effects can be sufficiently small as to be unimportant in many contexts. Nevertheless, for lower temperatures and lighter masses, quantum effects will become increasingly important. For low-temperature (Ϸ30 K or less) simple liquids, such as liquid helium and molecular hydrogen with low masses, quantum effects associated with positional uncertainty are expected to substantially broaden features in the liquid structure, and the diffusion of these effectively larger but ''softer'' objects is expected to be significantly altered from the classical description, even in the absence of coherent quantum dynamics (1, 2). For a molecular hydrogen-bonded liquid, such as water, the low mass of the hydrogen atom causes the intramolecular vibrations to behave quantum mechanically to quite high temperatures, and the intermolecular vibrational modes, including the relatively high-frequency librational motions (Ϸ250-900 cm Ϫ1 ) resulting from the frustrated rotation of molecules, are significantly quantum mechanical at room temperature, where the available thermal energy, Ϸ200 cm Ϫ1 , is considerably smaller than the librational quantum spacing (3).In recent years, there has been a great deal of progress in our ability to accurately evaluate equilibrium, time-independent properties of liquids, and related materials with complete consideration of quantum mechanics. For the most part, these have been based on simulations implementing discretized path integral forms (3, 4). For dynamics, the problem is far more challe...

Water properties from first principles: Simulations by a general-purpose quantum mechanical polarizable force field

“…The amplitudes are fairly good for OO and HH, but the first OH peak height is overestimated, which is also typical for other models. The quantum MD simulations result in less structured water, giving better overall description of the experiment than classical MD, in agreement with other results (14,18,19). Thus, the amplitude of the first OO peak is decreased from the classical MD value of 3.17 to the quantum MD estimate of 2.87, which approaches the experimental value (21, 22) of 2.8.…”

Quantum diffusion in liquid water from ring polymer molecular dynamics

“…[21][22][23][24][25] We have calculated orientational relaxation times and self-diffusion coefficients that are consistent with those found in a number of earlier approximate quantum-mechanical studies. [15][16][17][18][19][20] In addition, we have FIG. 4.…”

“…16 Several CMD studies of the orientational and translational motions in a rigid-body ͑TIP4P 2 ͒ water model have since appeared, 17,18 and two very recent studies have considered the dynamics of a flexible water model using the Feynman-Kleinert linearized path-integral ͑FK-LPI͒ approach. 19,20 The general conclusion of these papers is that quantummechanical fluctuations tend to increase the diffusion in the ambient liquid, the calculated increase in the self-diffusion coefficient over that obtained in a purely classical simulation varying from a factor of 1.4-2.0 depending on the interaction potential and the approximate quantum dynamical method employed. [15][16][17][18][19][20] This increase in the diffusion coefficient is consistent with the decrease in the structure of the liquid owing to quantum-mechanical effects that was observed in the earlier PIMC calculations.…”

“…19,20 The general conclusion of these papers is that quantummechanical fluctuations tend to increase the diffusion in the ambient liquid, the calculated increase in the self-diffusion coefficient over that obtained in a purely classical simulation varying from a factor of 1.4-2.0 depending on the interaction potential and the approximate quantum dynamical method employed. [15][16][17][18][19][20] This increase in the diffusion coefficient is consistent with the decrease in the structure of the liquid owing to quantum-mechanical effects that was observed in the earlier PIMC calculations. 13,14 Quantum-mechanical fluctuations evidently disrupt the hydrogen-bonding network in ambient water leading to a less structured liquid through which the water molecules diffuse more rapidly.…”

“…13,14 However, it is only comparatively recently that the role of quantummechanical effects in the dynamics of the liquid have been investigated. [15][16][17][18][19][20] The first people to consider these effects were Lobaugh and Voth, 15 who used the centroid molecular-dynamics ͑CMD͒ method to study the dynamics of a flexible simple point-charge ͑SPC/F͒ model of ambient water. This was followed shortly afterwards by a study in which the less sophisticated Feynman-Hibbs effective potential approach was used to calculate the self-diffusion coefficients of light and heavy water over a rather wide temperature range.…”