HAMILTONIANS IN OBLIQUE BODY-FRAME: A GEOMETRIC ALGEBRA APPROACH

Abstract

In this work, I present a practical way to obtain the vibration-rotation kinetic energy operator for an N-atomic molecule in an arbitrary body-frame [Formula: see text]. The body-frame need not be orthogonal or rigid. In practice, I derive the explicit form of the measuring vectors associated with the body-frame components of the internal angular momentum. Their inner products with the vector derivatives of the shape coordinates give the "Coriolis" part of the metric tensor appearing in the Hamiltonian, and their inner products among themselves give the "rotational" part. As a simple example, the measuring vectors are explicitly derived in an oblique bond-vector body-frame. The metric tensor elements are also derived for a tetra-atomic pyramidal molecule, whose shape is parametrized in bond-angle coordinates.