An \emph{ab initio} method for locating characteristic potential energy minima of liquids

It is possible in principle to probe the many--atom potential surface using density functional theory (DFT). This will allow us to apply DFT to the Hamiltonian formulation of atomic motion in monatomic liquids [\textit{Phys. Rev. E} {\bf 56}, 4179 (1997)]. For a monatomic system, analysis of the potential surface is facilitated by the random and symmetric classification of potential energy valleys. Since the random valleys are numerically dominant and uniform in their macroscopic potential properties, only a few quenches are necessary to establish these properties. Here we describe an efficient technique for doing this. Quenches are done from easily generated "stochastic" configurations, in which the nuclei are distributed uniformly within a constraint limiting the closeness of approach. For metallic Na with atomic pair potential interactions, it is shown that quenches from stochastic configurations and quenches from equilibrium liquid Molecular Dynamics (MD) configurations produce statistically identical distributions of the structural potential energy. Again for metallic Na, it is shown that DFT quenches from stochastic configurations provide the parameters which calibrate the Hamiltonian. A statistical mechanical analysis shows how the underlying potential properties can be extracted from the distributions found in quenches from stochastic configurations

Liquid state properties from first principles DFT calculations: Static properties

In order to test the Vibration-Transit (V-T) theory of liquid dynamics, ab initio density functional theory (DFT) calculations of thermodynamic properties of Na and Cu are performed and compared with experimental data. The calculations are done for the crystal at T = 0 and T_m, and for the liquid at T_m. The key theoretical quantities for crystal and liquid are the structural potential and the dynamical matrix, both as function of volume. The theoretical equations are presented, as well as details of the DFT computations. The properties compared with experiment are the equilibrium volume, the isothermal bulk modulus, the internal energy and the entropy. The agreement of theory with experiment is uniformly good. Our primary conclusion is that the application of DFT to V-T theory is feasible, and the resulting liquid calculations achieve the same level of accuracy as does ab initio lattice dynamics for crystals. Moreover, given the well established reliability of DFT, the present results provide a significant confirmation of V-T theory itself.Comment: 9 pages, 3 figures, 5 tables, edited to more closely match published versio

V-T Theory of Self Dynamic Response in a Monatomic Liquid

A new theoretical model for self dynamic response is developed using Vibration-Transit (V-T) theory, and is applied to liquid sodium at all wavevectors q from the hydrodynamic regime to the free particle limit. In this theory the zeroth-order Hamiltonian describes the vibrational motion in a single random valley harmonically extended to infinity. This Hamiltonian is tractable, is evaluated a priori for monatomic liquids, and the same Hamiltonian (the same set of eigenvalues and eigenvectors) is used for equilibrium and nonequlibrium theory. Here, for the self intermediate scattering function Fself(q,t) we find the vibrational contribution is in near perfect agreement with molecular dynamics (MD) through short and intermediate times, at all q. This is direct confirmation that normal mode vibrational correlations are present in the motion of the liquid state. The primary transit effect is diffusive motion of the vibrational equilibrium positions, as the liquid transits rapidly among random valleys. This motion is modeled as a standard random walk, and the resulting theoretical Fself(q,t) is in excellent agreement with MD results at all q and t. In the limit for q to infinity, the theory automatically exhibits the correct approach to the free-particle limit. Also in the limit for q to zero, the hydrodynamic limit emerges as well. In contrast to the benchmark theories of generalized hydrodynamics and mode coupling, the present theory is near a priori, while achieving modestly better accuracy. Therefore, in our view, it constitutes an improvement over the traditional theories.Comment: 16 pages, 11 figures, Journal Paper. Following referee's comments, Section IID has been completely rewritten and a new Section IIE has been adde