Construction of Diabatic Hamiltonian Matrix from ab Initio Calculated Molecular Symmetry Adapted Nonadiabatic Coupling Terms and Nuclear Dynamics for the Excited States of Na₃ Cluster

We present the molecular symmetry (MS) adapted treatment of nonadiabatic coupling terms (NACTs) for the excited electronic states (2²E′ and 1²A₁^′) of Na₃ cluster, where the adiabatic potential energy surfaces (PESs) and the NACTs are calculated at the MRCI level by using an ab initio quantum chemistry package (MOLPRO). The signs of the NACTs at each point of the configuration space (CS) are determined by employing appropriate irreducible representations (IREPs) arising due to MS group, and such terms are incorporated into the adiabatic to diabatic transformation (ADT) equations to obtain the ADT angles. Since those sign corrected NACTs and the corresponding ADT angles demonstrate the validity of curl condition for the existence of three-state (2²E′ and 1²A₁^′) sub-Hilbert space, it becomes possible to construct the continuous, single-valued, symmetric, and smooth 3 × 3 diabatic Hamiltonian matrix. Finally, nuclear dynamics has been carried out on such diabatic surfaces to explore whether our MS-based treatment of diabatization can reproduce the pattern of the experimental spectrum for system <b>B</b> of Na₃ cluster