De Lorenzi-Venneri Giulia, Wallace Duane C
Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
J Chem Phys. 2005 Dec 22;123(24):244513. doi: 10.1063/1.2140278.
The first goal of vibration-transit (V-T) theory was to construct a tractable approximate Hamiltonian from which the equilibrium thermodynamic properties of monatomic liquids can be calculated. The Hamiltonian for vibrations in an infinitely extended harmonic random valley, together with the universal multiplicity of such valleys, gives an accurate first-principles account of the measured thermodynamic properties of the elemental liquids at melt. In the present paper, V-T theory is extended to nonequilibrium properties, through an application to the dynamic structure factor S(q,omega). It was previously shown that the vibrational contribution alone accurately accounts for the Brillouin peak dispersion curve for liquid sodium, as compared both with molecular-dynamics (MD) calculations and inelastic x-ray scattering data. Here it is argued that the major effects of transits will be to disrupt correlations within the normal-mode vibrational motion and to provide an additional source of inelastic scattering. We construct a parametrized model for these effects and show that it is capable of fitting MD results for S(q,omega) in liquid sodium. A small discrepancy between model and MD at large q is attributed to multimode vibrational scattering. In comparison, mode coupling theory formulates S(q,omega) in terms of processes through which density fluctuations decay. While mode coupling theory is also capable of modeling S(q,omega) very well, V-T theory is the more universal since it expresses all statistical averages, thermodynamic functions, and time correlation functions alike, in terms of the same motional constituents, vibrations and transits.
振动跃迁（V-T）理论的首要目标是构建一个易于处理的近似哈密顿量，据此可以计算单原子液体的平衡热力学性质。无限延伸的简谐随机势谷中振动的哈密顿量，连同此类势谷的普适多重性，为熔体中元素液体的实测热力学性质提供了准确的第一性原理解释。在本文中，V-T理论通过应用于动态结构因子S(q,ω)扩展到非平衡性质。先前的研究表明，仅振动贡献就准确地解释了液态钠的布里渊峰色散曲线，这与分子动力学（MD）计算结果和非弹性X射线散射数据相比均相符。本文认为，跃迁的主要影响将是破坏简正模式振动运动中的相关性，并提供非弹性散射的额外来源。我们为这些影响构建了一个参数化模型，并表明它能够拟合液态钠中S(q,ω)的MD结果。在大q值时模型与MD之间的小差异归因于多模式振动散射。相比之下，模式耦合理论根据密度涨落衰减的过程来表述S(q,ω)。虽然模式耦合理论也能够很好地对S(q,ω)进行建模，但V-T理论更为通用，因为它用相同的运动成分（振动和跃迁）来表达所有的统计平均值、热力学函数和时间关联函数。
