Department of Physics "A. Pontremoli," University of Milan, 20133 Milan, Italy;
Department of Chemical Engineering and Biotechnology, University of Cambridge, CB3 0AS Cambridge, United Kingdom.
Proc Natl Acad Sci U S A. 2021 Feb 2;118(5). doi: 10.1073/pnas.2022303118.
An analytical derivation of the vibrational density of states (DOS) of liquids, and, in particular, of its characteristic linear in frequency low-energy regime, has always been elusive because of the presence of an infinite set of purely imaginary modes-the instantaneous normal modes (INMs). By combining an analytic continuation of the Plemelj identity to the complex plane with the overdamped dynamics of the INMs, we derive a closed-form analytic expression for the low-frequency DOS of liquids. The obtained result explains, from first principles, the widely observed linear in frequency term of the DOS in liquids, whose slope appears to increase with the average lifetime of the INMs. The analytic results are robustly confirmed by fitting simulations data for Lennard-Jones liquids, and they also recover the Arrhenius law for the average relaxation time of the INMs, as expected.
一直以来，由于存在无限多的纯虚模式——瞬时法线模式（INMs），液体振动态密度（DOS）的解析推导，特别是其特征频率线性的低能区的解析推导，一直难以实现。通过将普莱梅利身份的解析延拓到复平面与 INMs 的过阻尼动力学相结合，我们推导出了液体低频率 DOS 的封闭形式解析表达式。所得到的结果从第一性原理上解释了液体 DOS 中广泛观察到的频率线性项，其斜率似乎随 INMs 的平均寿命而增加。解析结果通过拟合 Lennard-Jones 液体的模拟数据得到了稳健的验证，并且它们还恢复了 INMs 的平均弛豫时间的阿伦尼乌斯定律，这是预期的。
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