Beyond Born-Oppenheimer theory for spectroscopic and scattering processes

We review our development on beyond Born?Oppenheimer (BBO) theory and its implementation on various models and realistic molecular processes as carried out over the last 15 years. The theoretical formulation leading to the BBO equations are thoroughly discussed with ab initio calculations. We have employed first principle based BBO theory not only to formulate single surface extended Born?Oppenheimer equation to understand the nature of nonadiabatic effect but also to construct accurate diabatic potential energy surfaces (PESs) for important spectroscopic systems, namely, NO radical, Na and K clusters, NO radical, benzene and 1,3,5-trifluorobenzene radical cations ( and ) as well as triatomic reactive scattering systems like and . The nonadiabatic phenomena like Jahn?Teller (JT), Renner?Teller, pseudo Jahn?Teller effects and the accidental conical intersections are the key players in dictating spectroscopic and reactive scattering profiles. The nature of diabatic coupling elements derived from ab initio data with BBO theory for molecular processes in Franck-Condon region has been analysed in the context of linearly and bilinearly coupled JT model Hamiltonian. The results obtained from quantum dynamical calculations on BBO based diabatic PESs of the above molecular systems are found to be in accord with available experimental outcomes.