Response to “Comment on a critique of the instantaneous normal mode (INM) approach to diffusion” [J. Chem. Phys. 109, 4693 (1998)]

Brownian motion with time-dependent friction and single-particle dynamics in liquids

A microscopic theory of molecular motion in classical monatomic liquids, proposed by Glass and Rice [Phys. Rev. 176, 239 (1968)10.1103/PhysRev.176.239], is revisited and extended to incorporate the dynamic friction in the Brownian description of the atomic diffusion in a mean-time-dependent harmonic force field. A modified, non-Markovian Langevin equation is utilized to derive an equation of motion for the velocity autocorrelation function with time-dependent friction coefficient. Numerical solution of the equation gives an excellent account of the velocity autocorrelation function in Lennard-Jones liquids, liquid alkali, and transition metals over a broad range of density and temperature. Derivation of the equation of motion leads to a self-consistent expression for the time dependence of friction coefficient. Our results demonstrate that the nature of time dependence of the friction coefficient changes dramatically with the liquid density. At low and moderate densities, the dynamic friction decays exponentially whereas it increases exponentially at high liquid densities. Our findings provide an opportunity for a different outlook of the Brownian description of atomic dynamics in liquids.

Localization-delocalization transition of the instantaneous normal modes of liquid water

Despite the fact that the localization-delocalization transition (LDT) widely exists in wave systems, quantitative studies on its critical and multifractal properties are mainly focused on solids. In this work, these properties are investigated on the vibrational motions of liquid water. Simulations of up to 18000 molecules on the flexible extended simple point charge water model provide nearly 10(6) instantaneous normal modes. They are shown to undergo an LDT close to the translational transition and exhibit multifractal fluctuations while approaching the LDT. In combination with finite-size scaling, multifractal analysis predicts the critical frequency Im(ω(c))≈-131.6 cm(-1) for unstable modes at room temperature. The estimated critical exponent ν≈1.60 is close to those of other calculated systems in the same Wigner-Dyson class. At the LDT, the fractal spectrum f(α) and the most probable local vibrational intensity α(mc)≈4.04 coincide with those of the Anderson model, which might be additional universal properties of LDT in more general wave systems. The results extend the validity of the multifractal scaling approach beyond Andersonian systems to a Hessian system.

Modeling velocity autocorrelation functions for confined fluids using γ distributions

We propose a model for the short-time dynamics of fluids confined in slit-shaped pores. The model has been developed from the observation that the real lobe of the instantaneous normal mode density of states (INM DOS) closely follows a gamma distribution. By proposing that the density of states of the confined fluid can be represented by a gamma distribution, the resulting velocity autocorrelation function (VACF) is constructed such that it is accurate upto the fourth frequency moment. The proposed model results in an analytical expression for the VACF and relaxation times. The VACFs obtained from the model have been compared with the VACFs obtained from molecular dynamic simulations and INM analysis for fluids confined in slit-shaped pores over a wide range of confinement and temperatures. The model is seen to capture the short-time behavior of the VACF extremely accurately and in this region is superior to the predictions of the VACF obtained from the real lobe of the INM DOS. Although the model predicts a zero self-diffusivity, the predicted relaxation times are in better agreement with the molecular dynamics results when compared with those obtained from the INM theory.

Relative pair dynamics in simple supercooled liquids: longitudinal contributions

The pair dynamics of simulated argon samples is investigated at the melting (85 K), supercooled (55 K), and quenched (20 K) liquid states, and in the crystal (20 K) state. Tagged pairs, initially lying in a given shell, were divided into incoming and outgoing groups and followed along simulated trajectories. Over them, specific correlation functions deltaB(r(0);t), involving the pair separation vector projected along its initial value r(0) (longitudinal dynamics), have been evaluated. More or less pronounced oscillations are detected according to the temperature of the thermodynamic states (and, obviously, their solid or liquid nature); for each state, they depend on the initial pair distance r(0), too. The oscillations vanish after few picoseconds (fast dynamics) in the case of crystal, whereas in the supercooled liquid they decay towards a plateau, whose height increases with the temperature. It is shown that the power spectrum of deltaB(r(0);t) practically yields the same density of states (DOS) produced by the pair velocity correlation function. The deltaB(r(0);t) functions obtained from the argon crystal at 20 K produce DOS curves dominated by two main frequency contributions, at about 40 and 60 cm(-1) (Einstein and Debye frequency, respectively). Their shape is quite well reproduced by damped harmonic oscillator-like (DHO) functions vibrating at that frequencies. In liquid states, the deltaB(r(0);t) plateau, that forms after the fast DHO dynamics, accounts for the system diffusivity. The relaxation towards the plateau is modeled by an exponential function whose decay time is comparable with the average vibration period. Evidence that the liquid states conserve a certain memory of the vibrational modes of the crystal is obtained. In these states, the DHO functions at the Einstein and Debye frequencies plus an exponential function cannot reproduce the deltaB(r(0);t) shape. A pronounced shoulder, that forms around 0.5 ps, requires the contribution of a third DHO. In the DOS, it yields a band centered below 20 cm(-1) that produces low frequency DOS excess in comparison with the DOS of the crystal. This contribution is present in liquid and supercooled high temperature states and survives near the temperature of the glass transition whereas the diffusion practically vanishes.

On the Debye-Waller factor of hexagonal ice: a computer simulation study

We investigate by molecular dynamics (MD) simulations the temperature dependence of the Debye-Waller (DW) factor of hexagonal ice with 25 different proton-disordered configurations. Each initial configuration is composed of 288 water molecules with no net dipole moment. The intermolecular interaction of water is described by TIP4P potential. Each production run of the simulation is 15 ns or longer. We observe a change in slope of the DW factor around 200 K, which cannot be explained within the framework of either classical or quantum harmonic approximation. Configurations generated by MD simulations are subjected to the steepest descent energy minimization. Analysis of the local energy minimum structures reveals that water molecules above 200 K jump to other lattice sites via some local energy minimum structures which contain some water molecules sitting on the locations other than the lattice sites. As time evolves, these defect molecules move back and forth to the lattice sites yielding defect-free structures. Those motions are responsible for the unusual increase in the DW factor at high temperatures. In making a transition from an energy-minimum structure to another one, a small number of water molecules are involved in a highly cooperative fashion. The larger DW factor at higher temperature arises from jump-like motions of water molecules among these locally stable configurations which may or may not be a family of the proton-disordered ice forms satisfying the "ice rule".

Mean-atom-trajectory model for the velocity autocorrelation function of monatomic liquids

We present a model for the motion of an average atom in a liquid or supercooled liquid state and apply it to calculations of the velocity autocorrelation function Z(t) and diffusion coefficient D. The model trajectory consists of oscillations at a distribution of frequencies characteristic of the normal modes of a single potential valley, interspersed with position- and velocity-conserving transits to similar adjacent valleys. The resulting predictions for Z(t) and D agree remarkably well with molecular dynamics simulations of Na at up to almost three times its melting temperature. Two independent processes in the model relax velocity autocorrelations: (a) dephasing due to the presence of many frequency components, which operates at all temperatures but which produces no diffusion, and (b) the transit process, which increases with increasing temperature and which produces diffusion. Because the model provides a single-atom trajectory in real space and time, including transits, it may be used to calculate all single-atom correlation functions.