7 research outputs found
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