TL;DR
This paper provides a comprehensive theoretical overview of molecular normal modes, focusing on internal vibrational degrees of freedom using quantum mechanics and harmonic approximations for simplified analysis.
Contribution
It introduces a general quantum-mechanical framework for molecular vibrations, emphasizing internal degrees of freedom and simplifying the problem to harmonic motion.
Findings
Derivation of a harmonic approximation for internal vibrational modes
Separation of rotational and vibrational motions in molecular systems
Framework for advanced vibrational calculations
Abstract
The aim of this article is a comprehensive description of normal modes of molecular vibrations. The starting point is chosen to be a general molecular system with separated center of mass and an arbitrary embedding of body-fixed axes. This allows to focus on internal degrees of freedom only, leaving the problem of rotational motion behind. Nevertheless, for the sake of completeness we first introduce a general quantum-mechanical Hamiltonian in Eckart-Watson representation, to make a quick leap into a simplified harmonic description for internal motion and rigid rotor for rotational degrees of freedom. This regime constitutes a basis for more sophisticated calculations.
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