De Lorenzi-Venneri Giulia, Wallace Duane C
Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Oct;76(4 Pt 1):041203. doi: 10.1103/PhysRevE.76.041203. Epub 2007 Oct 18.
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.
振动输运理论的首要目标是能够从一个易于处理的配分函数出发，且无需可调参数，来计算元素单原子液体的热力学性质。关键假设是，在温度高于熔点T（约大于Tm）时，势能谷的随机类主导液体的统计力学，并且在热力学极限下这些谷在宏观上是均匀的。这使我们能够使用单个随机谷来计算对液体性质的振动贡献，在热力学极限下是精确的，在有限粒子数N时是一种近似。本文基于电子结构理论，用一个物理上现实的势对液态钠测试了这种近似。在温度从0.90Tm到3.31Tm的条件下，从分子动力学平衡液体（N = 500）进行最速下降淬火，并为每个结构计算六个势参数，即势能和振动频率分布的五个主矩。结果表明，所有势参数的均值与温度无关且标准偏差较小，这与N趋于无穷时随机谷的均匀性一致，以及在N = 500时有限N的展宽一致。对于N = 500且T约大于Tm的钠，单随机谷近似中熵的预期误差为0.1%，内能的预期误差为0.5%，在当前液体动力学理论的发展中可忽略不计。在近年来相关的淬火研究中，在T约大于Tm时结构势能性质的均值几乎与温度无关这一常见发现表明，单随机谷近似可能也适用于比元素液体更复杂的系统。
