The molecular Hamiltonian with two-rotational-angle embedding

Abstract

Our approach for the derivation of the exact (non-relativistic) translational-rovibronic Hamiltonian, based on the Hamiltonian operator in tensor form, is now extended to cases in which a body-fixed frame is defined via the introduction of two Euler angles (two-rotationalangle embedding). Diatomic molecules and diatom-diatom systems are considered as examples for this general formulation. For comparison, the three-rotational-angle embedding version of the diatom-diatom Hamiltonian is also derived.

A general rigorous quantum dynamics algorithm to calculate vibrational energy levels of pentaatomic molecules

“…That is, the resulting Hamiltonian is very compact with a partitioned structure, and has a common formulation except for the mass-dependent prefactors regardless of types of orthogonal vectors [11,13,25,34,36,49,[66][67][68]. Otherwise, if non-orthogonal coordinates [25, [69][70][71][72][73][74][75][76] are used, the kinetic energy operators obtained are rather complicated. The complicated Hamiltonian will make calculations difficult, especially for polyatomic molecules, although the basis size can be somewhat reduced for rigid or semi-rigid molecules.…”