Renner–Teller effect in linear tetra-atomic molecules. I.Variational method including couplings between all degreesof freedom on six-dimensional potential energy surfaces

摘要

For electronically degenerate states of linear tetra-atomic molecules, a new method is developed forthe variational treatment of the Renner–Teller and spin-orbit couplings. The approach takes intoaccount all rotational and vibrational degrees of freedom, the dominant couplings between the corresponding angular momenta as well as the couplings with the electronic and electron spinangular momenta. The complete rovibrational kinetic energy operator is expressed in Jacobicoordinates, where the rovibrational angular momenta JN have been replaced by J–LeZ–S and thespin-orbit coupling has been described by the perturbative term A_(SO) X L_(ez)·S_z·Attention has beenpaid on the electronic wave functions, which require additional phase for linear tetra-atomic molecules. Our implemented rovibrational basis functions and the integration of the different partsof the total Hamiltonian operator are described. This new variational approach is tested on the electronic ground state X~2Π_Uof HCCH~+for which new six-dimensional potential energy surfaceshave been computed using the internally contracted multireference configuration interaction methodand the cc-pV5Z basis set. The calculated rovibronic energies and their comparisons with previous theoretical and experimental works are presented in the next paper.