Systematic ab initio calculation of spectroscopic constants for A-reduced rotational effective Hamiltonians of asymmetric top molecules using normal ordering of cylindrical angular momentum operators.

This research paper presents a new fundamental approach for evaluating accurate ab initio quartic, sextic, and octic centrifugal distortion parameters of A-reduced rotational effective Hamiltonians of asymmetric top molecules. In this framework, the original Watson Hamiltonian, expanded up to sextic terms of kinetic and potential energies, is subjected to a series of vibrational and rotational operator unitary transformations, leading to reduced Watson effective Hamiltonians for the equilibrium configuration, ground state, and weakly perturbed vibrationally excited states. The proposed scheme is based on a numerical-analytic implementation of the sixth-order Van Vleck operator perturbation theory with the systematic normal ordering of vibrational rising and lowering operators (a†, a) and cylindrical angular momentum operators (Jz, J+, J-).

Normal ordering of the angular momentum cylindrical ladder operators and their products with Wigner D functions.

The operator canonical perturbation theory (CPT) is an efficient tool for solving the molecular vibration-rotation Schrödinger equation. The corresponding Watson Hamiltonian can be written using angular momentum cylindrical ladder operators (J, J = J ∓ iJ) possessing the Lie algebra su(2) commutation relations [J, J] = 2J, [J, J] = ±J. The reduced effective Hamiltonians suitable for fitting to observed spectra are traditionally based on Hermitian basis sets, e.