Entropy, Dynamics and Instantaneous Normal Modes in a Random Energy Model

It is shown that the fraction f of imaginary frequency instantaneous normal modes (INM) may be defined and calculated in a random energy model(REM) of liquids. The configurational entropy S and the averaged hopping rate among the states R are also obtained and related to f, with the results R~f and S=a+b*ln(f). The proportionality between R and f is the basis of existing INM theories of diffusion, so the REM further confirms their validity. A link to S opens new avenues for introducing INM into dynamical theories. Liquid 'states' are usually defined by assigning a configuration to the minimum to which it will drain, but the REM naturally treats saddle-barriers on the same footing as minima, which may be a better mapping of the continuum of configurations to discrete states. Requirements of a detailed REM description of liquids are discussed

Potential energy landscape-based extended van der Waals equation

The inherent structures ({\it IS}) are the local minima of the potential energy surface or landscape, $U({\bf r})$, of an {\it N} atom system. Stillinger has given an exact {\it IS} formulation of thermodynamics. Here the implications for the equation of state are investigated. It is shown that the van der Waals ({\it vdW}) equation, with density-dependent $a$ and $b$ coefficients, holds on the high-temperature plateau of the averaged {\it IS} energy. However, an additional ``landscape'' contribution to the pressure is found at lower $T$. The resulting extended {\it vdW} equation, unlike the original, is capable of yielding a water-like density anomaly, flat isotherms in the coexistence region {\it vs} {\it vdW} loops, and several other desirable features. The plateau energy, the width of the distribution of {\it IS}, and the ``top of the landscape'' temperature are simulated over a broad reduced density range, $2.0 \ge \rho \ge 0.20$, in the Lennard-Jones fluid. Fits to the data yield an explicit equation of state, which is argued to be useful at high density; it nevertheless reproduces the known values of $a$ and $b$ at the critical point

Instantaneous Normal Mode analysis of liquid HF

We present an Instantaneous Normal Modes analysis of liquid HF aimed to clarify the origin of peculiar dynamical properties which are supposed to stem from the arrangement of molecules in linear hydrogen-bonded network. The present study shows that this approach is an unique tool for the understanding of the spectral features revealed in the analysis of both single molecule and collective quantities. For the system under investigation we demonstrate the relevance of hydrogen-bonding ``stretching'' and fast librational motion in the interpretation of these features.Comment: REVTeX, 7 pages, 5 eps figures included. Minor changes in the text and in a figure. Accepted for publication in Phys. Rev. Let

A 2:1 Co-Crystal of Hydroquinone and 3,5-Bis(2-pyridyl)-1,2,4-triazole

The title compound, 2C₁₂H₉N5₅.C₆H₆O₂, exhibits a three-dimensional hydrogen-bonded network of N-H...N, C-H...N, O-H...N, C-H...O, C-H...π and π...π interactions

Hindered Rotation in Methyl Alcohol with Note on Ethyl Alcohol

The potential barrier to the internal rotation in methyl alcohol is recalculated from the entropy with the aid of new molecular dimensions generously provided by Burkhard and Dennison. The barrier calculation is examined for temperature dependence and checked for reliability by recalculation with the Clapeyron equation substituted for parts of the data. The result is 1600±700 cal./mole, which includes the new spectroscopic barrier of Burkhard and Dennison at 326 cm−1. Within the range covered by the result, a residual entropy up to 0.50 cal./mole deg. is possible, and the retention of 0.46 e.u. by the crystal is consistent with a reasonable simple assumption about the distribution of hydrogen bonds.It is suggested, by analogy, that the barrier to the hydroxyl group rotation in ethyl alcohol should be about 1000 cal./mole.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71293/2/JCPSA6-18-3-361-1.pd

Dynamics and geometric properties of the k-Trigonometric model

We analyze the dynamics and the geometric properties of the Potential Energy Surfaces (PES) of the k-Trigonometric Model (kTM), defined by a fully-connected k-body interaction. This model has no thermodynamic transition for k=1, a second order one for k=2, and a first order one for k>2. In this paper we i) show that the single particle dynamics can be traced back to an effective dynamical system (with only one degree of freedom); ii) compute the diffusion constant analytically; iii) determine analytically several properties of the self correlation functions apart from the relaxation times which we calculate numerically; iv) relate the collective correlation functions to the ones of the effective degree of freedom using an exact Dyson-like equation; v) using two analytical methods, calculate the saddles of the PES that are visited by the system evolving at fixed temperature. On the one hand we minimize |grad V|^2, as usually done in the numerical study of supercooled liquids and, on the other hand, we compute the saddles with minimum distance (in configuration space) from initial equilibrium configurations. We find the same result from the two calculations and we speculate that the coincidence might go beyond the specific model investigated here.Comment: 36 pages, 13 figure

Configurational entropy of hard spheres

We numerically calculate the configurational entropy S_conf of a binary mixture of hard spheres, by using a perturbed Hamiltonian method trapping the system inside a given state, which requires less assumptions than the previous methods [R.J. Speedy, Mol. Phys. 95, 169 (1998)]. We find that S_conf is a decreasing function of packing fraction f and extrapolates to zero at the Kauzmann packing fraction f_K = 0.62, suggesting the possibility of an ideal glass-transition for hard spheres system. Finally, the Adam-Gibbs relation is found to hold.Comment: 10 pages, 6 figure

Saddles in the energy landscape probed by supercooled liquids

We numerically investigate the supercooled dynamics of two simple model liquids exploiting the partition of the multi-dimension configuration space in basins of attraction of the stationary points (inherent saddles) of the potential energy surface. We find that the inherent saddles order and potential energy are well defined functions of the temperature T. Moreover, decreasing T, the saddle order vanishes at the same temperature (T_MCT) where the inverse diffusivity appears to diverge as a power law. This allows a topological interpretation of T_MCT: it marks the transition from a dynamics between basins of saddles (T>T_MCT) to a dynamics between basins of minima (T<T_MCT).Comment: 4 pages, 3 figures, to be published on PR

Instantaneous Normal Mode Analysis of Supercooled Water

We use the instantaneous normal mode approach to provide a description of the local curvature of the potential energy surface of a model for water. We focus on the region of the phase diagram in which the dynamics may be described by the mode-coupling theory. We find, surprisingly, that the diffusion constant depends mainly on the fraction of directions in configuration space connecting different local minima, supporting the conjecture that the dynamics are controlled by the geometric properties of configuration space. Furthermore, we find an unexpected relation between the number of basins accessed in equilibrium and the connectivity between them.Comment: 5 pages, 4 figure