Analysis of the velocity autocorrelation function of water (original) (raw)
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Velocity-autocorrelation spectrum of simple classical liquids
Physical Review A, 1978
The velocity-autocorrelation function of a tagged particle moving in a classical liquid is expressed in terms of a characteristic oscillator frequency and a frequency-dependent relaxation kernel. The relaxation spectrum is approximated by calculating the interaction of the tagged particle with current excitations of the liquid. The interaction with the longitudinal modes is shown to be responsible for the observed peak structure of the correlation function. The results of the present theory, in particular the values for the diffusion constant, agree well with the molecular-dynamics experiments on argon and rubidium.
Time correlation functions of simple liquids: A new insight on the underlying dynamical processes
The Journal of Chemical Physics, 2018
Extensive molecular dynamics simulations of liquid sodium have been carried out to evaluate correlation functions of several dynamical quantities. We report the results of a novel analysis of the longitudinal and transverse correlation functions obtained by evaluating directly their self and distinct contributions at different wavevectors k. It is easily recognized that the self-contribution remains close to its k → 0 limit, which turns out to be exactly the autocorrelation function of the single particle velocity. The wavevector dependence of the longitudinal and transverse spectra and their self and distinct parts is also presented. By making use of the decomposition of the velocity autocorrelation spectrum in terms of longitudinal and transverse parts, our analysis is able to recognize the effect of different dynamical processes in different frequency ranges. 1. Introduction. In recent years, the study of dynamical properties of simple monoatomic liquids has received a strong impetus, due to the massive use of new experimental techniques. The large use of X ray [1] and neutron sources [2] along with advanced spectroscopic facilities have allowed the observation of dynamical processes occurring in the terahertz frequency range with surprising good accuracy. Since the seminal works on liquid alkali metals [3], attention has been devoted to other
Molecular hydrodynamic theory of the velocity autocorrelation function
The Journal of Chemical Physics, 2023
The velocity autocorrelation function (VACF) encapsulates extensive information about a fluid's molecular-structural and hydrodynamic properties. We address the following fundamental question: How well can a purely hydrodynamic description recover the molecular features of a fluid as exhibited by the VACF? To this end, we formulate a bona fide hydrodynamic theory of the tagged-particle VACF for simple fluids. Our approach is distinguished from previous efforts in two key ways: collective hydrodynamic modes and tagged-particle self-motion are modeled by linear hydrodynamic equations; the fluid's spatial velocity power spectrum is identified as a necessary initial condition for the momentum current correlation. This formulation leads to a natural physical interpretation of the VACF as a superposition of products of quasinormal hydrodynamic modes weighted commensurately with the spatial velocity power spectrum, the latter of which appears to physically bridge continuum hydrodynamical behavior and discrete-particle kinetics. The methodology yields VACF calculations quantitatively on par with existing approaches for liquid noble gases and alkali metals. Furthermore, we obtain a new, hydrodynamic form of the selfintermediate scattering function whose description has been extended to low densities where the Schmidt number is of order unity; various calculations are performed for gaseous and supercritical argon to support the general validity of the theory. Excellent quantitative agreement is obtained with recent MD calculations for a dense supercritical Lennard-Jones fluid.
Physical Review E, 2015
The velocity autocorrelation function (VAF), a key quantity in the atomic-scale dynamics of fluids, has been the first paradigmatic example of a long-time tail phenomenon, and much work has been devoted to detecting such long-lasting correlations and understanding their nature. There is, however, much more to the VAF than simply the evidence of this long-time dynamics. A unified description of the VAF from very short to long times, and of the way it changes with varying density, is still missing. Here we show that an approach based on very general principles makes such a study possible and opens the way to a detailed quantitative characterization of the dynamical processes involved at all time scales. From the analysis of molecular dynamics simulations for a slightly supercritical Lennard-Jones fluid at various densities, we are able to evidence the presence of distinct fast and slow decay channels for the velocity correlation on the time scale set by the collision rate. The density evolution of these decay processes is also highlighted. The method presented here is very general, and its application to the VAF can be considered as an important example.
Correlated Motions in Simple Classical Liquids
Physical Review, 1968
This paper reports a method for studying correlation functions for simple classical liquids. One atom of the liquid is considered to be an external agent acting on the others, and Liouville' s equation is formally solved to obtain their response. From this solution an equation for the velocity autocorrelation function is derived. The method is also applied to the distinct-particIe part of the density-density correlation function, G~(x, t). The moment relations for Gd(x, t) are in this way made to depend on a hierarchy of equations relating the static correlation functions. When the basic equations derived by this method are approximated further, previously given approximations for G~(x, t) are obtained.
The Journal of Chemical Physics, 2002
A quantum molecular hydrodynamic formalism is developed for the study of dynamical correlations in dense quantum liquids. The approach is based on augmenting an exact closed, self-consistent quantum generalized Langevin equation for the Kubo transform of the dynamical correlation of interest, with a suitable approximation for the memory kernel obtained within the framework of a quantum mode-coupling theory. The solution to the quantum generalized Langevin equation requires as input static equilibrium information which is generated from a path-integral Monte Carlo method. Examples are given for the intermediate and self-intermediate scattering functions, and for the velocity autocorrelation function. The attractive advantages of the present approach are discussed.
Molecular velocity auto-correlation of simple liquids observed by NMR MGSE method
The European Physical Journal B
The velocity auto-correlation spectra of simple liquids obtained by the NMR method of modulated gradient spin echo show features in the low frequency range up to a few kHz, which can be explained reasonably well by a t −3/2 long-time tail decay only for non-polar liquid toluene, while the spectra of polar liquids, such as ethanol, water and glycerol, are more congruent with the model of diffusion of particles temporarily trapped in potential wells created by their neighbors. As the method provides the spectrum averaged over ensemble of particle trajectories, the initial non-exponential decay of spin echoes is attributed to a spatial heterogeneity of molecular motion in a bulk of liquid, reflected in distribution of the echo decays for short spin trajectories. While at longer time intervals, and thus with longer trajectories, heterogeneity is averaged out, giving rise to a spectrum which is explained as a combination of molecular self-diffusion and eddy diffusion within the vortexes of hydrodynamic fluctuations.
Physical Review, 1968
A theory of one-particle and two-particle motions in monatomic classical liquids, which employs the two-particle position-dependent Green' s function in a fundamental way is developed. An equation of motion for the autocorrelation function is derived by assuming that a Brownian particle diffuses in a meantime dependent field. The motion of the atoms which generate the time-dependent field is described by the Green' s function, hi addition, the Green' * function is directly related to the Van Hove scattering function in a simple way. The velocity autocorrelation function and neutron scattering cross sections are computed for liquid argon by assuming a relaxation approximation for the two-particle Green' s function. Comparisons are made with recent experimental results.
Test of molecular mode coupling theory: A first resume
2000
We report recent progress on the test of mode coupling theory for molecular liquids (MMCT) for molecules of arbitrary shape. The MMCT equations in the long time limit are solved for supercooled water including all molecular degrees of freedom. In contrast to our earlier treatment of water as a linear molecule, we find that the glass transition temperature Tc is overestimated by the theory as was found in the case of simple liquids. The nonergodicity parameters are calculated from the "full" set of MMCT-equations truncated at lco = 2. These results are compared (i) with the nonergodicity parameters from MMCT with lco = 2 in the "dipole" approximation n = n ′ = 0 and the diagonalization approximation n = n ′ = 0, l = l ′ and (ii) with the corresponding results from a MD-simulation. This work supports the possibility that a reduction to the most prominent correlators may constitute a valid approximation for solving the MMCT equations for rigid molecules.
Coupling between molecular rotations and OH⋯O motions in liquid water: Theory and experiment
The Journal of Chemical Physics, 2002
A new theory is proposed to describe spectral effects of the coupling between molecular rotations and OH¯O motions in liquid water. The correlation function approach is employed together with a special type of development in which the coupling energy of these two motions is the expansion parameter. The isotropy of the liquid medium plays an essential role in this study. Based on this theory, a new infrared pump-probe experiment is described permitting a visualization of molecular rotations at subpicosecond time scales. Full curves relating the mean squared rotational angle and time, and not only the rotational relaxation time, are measured by this experiment. However, very short times where the incident pulses overlap must be avoided in this analysis. The lifetime of OH¯O bonds in water is rotation-limited.