Non-hessian method for normal coordinates calculation

Abstract

Normal mode analysis (NMA) plays an essential role in chemistry for a very long time. It is both a key to understanding molecular motions, especially vibration motions, and to identifying characteristic peaks in infrared and Raman spectra. The traditional NMA requires the construction of a Hessian matrix and using harmonic approximation, which is almost impossible when large molecules and quantum mechanics are involved. Usually, NMA serves a complete set of normal coordinates that describes all possible motion modes of a molecule. This work presents a novel methodology to calculate normal coordinates that use only molecular geometries as input by considering a molecule as a ball-and-stick model and using the conservative expansion of angular momentum within the rigid body framework. This method is named Expanded Moment of Inertia Tensor (EMIT) after the way it was created. The considerable advantages of the EMIT methodology are as follows: It can extract a complete set of normal coordinates from molecular geometry at any point in potential energy surface, and it provides normal modes that resemble those obtained from the theoretical calculation. The EMIT reliability was confirmed by calculations of power spectra of NO− 2 and NO− 3 anions in aqueous solutions. This is not only proposing an alternative method to calculate normal coordinates but also showing the way to consider physical worlds differently.