Renner-Teller vibronic analysis for a tetra-atomic molecule. I. The effective Hamiltonian and matrix elements

The effective vibronic Hamiltonian for a linear tetra-atomic molecule in a Pi state has been investigated. In addition to the usual vibrational and Renner-Teller coupling terms, the bending mode anharmonicity, spin-orbit coupling, and Fermi resonance interactions have been added to the model. Terms in the Hamiltonian up to the fourth order are given explicitly for molecules of C-infinity upsilon symmetry and simplifications for symmetric D-infinity h molecules are discussed. The matrix elements for the HCCS free radical have been obtained and are used to analyze the observed ground-state levels of HCCS and DCCS in a companion paper. The Sears resonance vibronic interaction that couples levels with the selection rules Delta K=+/- 1, Delta Sigma=-/+ 1, and Delta P=0 has also been studied and the matrix elements derived. The determinable combinations of signs for the major parameters in the model are discussed.