Extracting effective normal modes from equilibrium dynamics at finite temperature

Abstract

A general method for obtaining effective normal modes of a molecular system from molecular dynamics simulations is presented. The method is based on a localization criterion for the Fourier transformed velocity time-correlation functions of the effective modes. For a given choice of the localization function used, the method becomes equivalent to the principal mode analysis (PMA) based on covariance matrix diagonalization. On the other hand, a proper choice of the localization function leads to a novel method with a strong analogy with the usual normal mode analysis of equilibrium structures, where the Hessian system at the minimum energy structure is replaced by the thermal averaged Hessian, although the Hessian itself is never actually calculated. This method does not introduce any extra numerical cost during the simulation and bears the same simplicity as PMA itself. It can thus be readily applied to ab initio molecular dynamics simulations. Three such examples are provided here. First we recover effective normal modes of an isolated formaldehyde molecule computed at 20 K in very good agreement with the results of a normal mode analysis performed at its equilibrium structure. We then illustrate the applicability of the method for liquid phase studies. The effective normal modes of a water molecule in liquid water and of a uracil molecule in aqueous solution can be extracted from ab initio molecular dynamics simulations of these two systems at 300 K.

Vibrational fingerprint of the absorption properties of UiO-type MOF materials

“…The decomposition of VPS into molecular motions is not straightforward for large molecular systems. A principal component analysis (PCA) [45] will be performed to determine the coordinates Q i . PCA is in particular suitable for describing global motions of the system under investigation.…”

Ab initio mass tensor molecular dynamics

“…To the best of our knowledge, relatively little effort has been made [60] to optimize the atomic masses theoretically for finite temperature simulations, although several empirical studies exist [19,23]. To this end, we first introduce the expression for the thermal average of the Hessian [36,55]:…”

“…Nevertheless, there are several possible ways to recover the vibrational spectra of the original system within the harmonic approximation [52][53][54][55]. Most of these methods rely on the covariance matrix of atomic fluctuations,…”

Computational Spectroscopy by Classical Time‐Dependent Approaches

“…Expression 11.3 provides the whole simulated spectrum, while a detailed vibrational analysis requires the unambiguous assignment of each mode contribution. Recently, a number of methods appeared in the literature aimed at the extraction of normal-mode-like analysis from ab initio dynamics [58][59][60][61][62][63]. Some of these [58][59][60] refer to the quasi-harmonic model introduced by Karplus [64,65] in the framework of classical molecular dynamics and individuate normal-mode directions as main components of the nuclear fluctuations in the NVE or NVT ensemble.…”

“…The quasinormal model relies on the equipartition of the kinetic energy among normal modes; thus problems arise when the simulation time required to obtain such a distribution is computationally too expensive, as is often the case for ab initio dynamics. Other approaches [61][62][63] carry out the time evolution analysis in the momenta subspace instead of the configurational space. In these approaches the basic consideration is that, at any temperature, generalized normal modes Q i correspond to uncorrelated momenta such that [61] < _ Q i ðtÞ _ Q j ðtÞ >¼ l i d ij ð11:4Þ…”