Use of the normal coordinates in variational and perturbative ab initio handling of the vibronic and spin-orbit couplings in Π electronic states of linear tetra-atomic molecules

Abstract

A variational and a perturbative approach are developed to handle the combined effect of the vibronic and spin-orbit couplings in Π electronic states of tetra-atomic molecules with linear equilibrium geometry. Both of them are based on the use of the normal vibrational bending coordinates. The perturbative treatment is carried out via two schemes for partition of the model Hamiltonian: In the first, the spin-orbit coupling term is treated as a perturbation; in the second, it is included in the zeroth-order Hamiltonian. It is demonstrated that both perturbative approaches lead to the same second-order formulae when the spin-orbit coupling constant is small compared to the bending frequency, but much larger than the splitting of potential surfaces upon bending. These approaches are used to calculate the vibronic and spin-orbit structure in the X 2 Π electronic state of HCCS by employing the ab initio-computed potential energy surfaces. Complete numerical equivalence of the results obtained with the present variational approach and those generated by the algorithms employing internal vibrational coordinates is demonstrated. The restrictions concerning the applicability of the perturbative approaches are discussed in terms of the agreement between the results obtained by means of them with those generated in the corresponding variational computations. The general reliability of the model employed is checked by comparing the theoretical results with the available experimental data.