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

Abstract

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−). The efficiency of the developed theoretical model is demonstrated by the juxtaposition of predicted centrifugal distortion parameters for several three to eight atomic molecules, including H2S, CH2O, C2H4, CH2D2, CH2F2, CH2Cl2, and B2H6, using the coupled-cluster single double triple/quadruple-ζ level of quantum chemistry. In comparison with the values derived using the customary analytic expressions, the calculated quartic and sextic parameters may improve by an order of magnitude in the fourth and sixth orders, respectively, reaching an accuracy of about 1%. Predicted octic constants can serve as an excellent starting point for fitting to experimental spectra.