Ab initio calculations on the excited states of Na₃ cluster to explore beyond Born-Oppenheimer theories: Adiabatic to diabatic potential energy surfaces and nuclear dynamics

Abstract

We perform ab initio calculation using quantum chemistry package (MOLPRO) on the excited states of Na₃ cluster and present the adiabatic PESs for the electronic states 2²E' and 1²A'₂ and the non-adiabatic coupling (NAC) terms among those states. Since the ab initio calculated NAC elements for the states 2²E' and 1²A'₂ demonstrate the numerical validity of so called "Curl Condition," such states closely form a sub-Hilbert space. For this subspace, we employ the NAC terms to solve the "adiabatic-diabatic transformation (ADT)" equations to obtain the functional form of the transformation angles and pave the way to construct the continuous and single valued diabatic potential energy surface matrix by exploiting the existing first principle based theoretical means on beyond Born-Oppenheimer treatment. Nuclear dynamics has been carried out on those diabatic surfaces to reproduce the experimental spectrum for system B of Na₃ cluster and thereby, to explore the numerical validity of the theoretical development on beyond Born-Oppenheimer approach for adiabatic to diabatic transformation.