Single-random-valley approximation in vibration-transit theory of liquid dynamics.
The first goal of vibration-transit theory is to be able to calculate from a tractable partition function and without adjustable parameters the thermodynamic properties of the elemental monatomic liquids. The key hypothesis is that the random class of potential energy valleys dominates the statistical mechanics of the liquid at temperatures above melting T approximately greater than Tm and that these valleys are macroscopically uniform in the thermodynamic limit. This allows us to use a single random valley to calculate the vibrational contribution to liquid properties, exactly in the thermodynamic limit, and as an approximation at finite number of particles N . This approximation is tested here for liquid Na with a physically realistic potential based on electronic structure theory. Steepest descent quenches were made from the molecular dynamics equilibrium liquid (N=500) at temperatures from 0.90Tm to 3.31Tm, and six potential parameters were calculated for each structure, namely, the potential energy and five principal moments of the vibrational frequency distribution. The results show temperature-independent means and small standard deviations for all potential parameters, consistent with random valley uniformity at N-->infinity, and with finite- N broadening at N=500. The expected error in the single random valley approximation for Na at N=500 and T approximately greater than Tm is 0.1% for the entropy and 0.5% for the internal energy, negligible in the current development of liquid dynamics theory. In related quench studies of recent years, the common finding of nearly temperature-independent means of structural potential energy properties at T approximately greater than Tm suggests that the single random valley approximation might also apply to systems more complicated than the elemental liquids.
De Lorenzi-Venneri
Giulia
G
Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Wallace
Duane C
DC