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Extended Born-Oppenheimer equation for tri-state system

Biplab Sarkar·Satrajit Adhikari
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Abstract

We present explicit form of non-adiabatic coupling (NAC) elements of nuclear Schroedinger equation (SE) for a coupled tri-state electronic manifold in terms of mixing angles of real electronic basis functions. If the adiabatic-diabatic transformation (ADT) angles are the mixing angles of electronic basis, ADT matrix transforms NAC terms to exactly zeros and brings diabatic form of SE. ADT and NAC matrices satisfy a curl condition and find a novel relation among the mixing angles for irrotational case. We also find that extended Born-Oppenheimer (EBO) equations have meaningful solution and can reproduce numerically exact results only when the equations are gauge invariant.

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Biplab Sarkar, Satrajit Adhikari. 2004-10-02. Extended Born-Oppenheimer equation for tri-state system. https://arxiv.org/abs/physics/0410015

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