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.