  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.
