The Quartic Centrifugal Distortion Terms In The Effective Hamiltonian For Open-shell Complexes

High-resolution spectroscopy of weakly bound complexes has been widely used to study the nature of intermolecular interactions.Compared with closed-shell complexes,the energy levels and spectra of open-shell complexes are usually more complicated due to the presence of non-zero electron spin and/or electronic orbital angular momentum.A near-rigid rotor model for a nonlinear planar open-shell complex consisting of an open-shell diatomic unit in an electronic state 2S+1A and a closed-shell partner(a rare gas atom or a closed-shell diatomic molecule)has been developed in the literature.Sometimes the quartic centrifugal distortion terms have to be introduced in order to correctly describe experimentally observed energy levels with high J and P quantum numbers.For open-shell complexes with A>0,those terms of quadratic dependence on J and P were omitted in the expression of the quartic centrifugal distortion terms in the literature,which would lead to contaminated rotational constants A,B,C.Consequently,the molecular geometric structure couldn’t be determined reasonably by them.In this thesis,a general expression for the quartic centrifugal distortion terms in the effective Hamiltonian in the Watson S-reduction for open-shell complexes with the open-shell diatomic subunit in an electronic state 2S+1∧(∧>0)iS derived,taking into account all the operators which give matrix elements of quadratic,cubic,and quartic dependence on J and P.Then the non-vanishing matrix elements for the quartic centrifugal distortion terms are derived and listed.In order to check the reliability of our derivation procedure and the consistency with the previous results for open-shell complexes with the open-shell diatomic subunit in the 2S+1∑(∧=0)electronic state,the quartic centrifugal distortion terms and non-vanishing matrix elements for the latter case are also derived.Our results are in good agreement with the previous results.The formula developed in this work is expected to be useful for analyzing and fitting high-resolution spectra of open-shell complexes in which transitions with high J and P quantum numbers are observed.More physically meaningful rotational constants are expected to be determined along with the quartic centrifugal distortion constants.