On the determination of radial coupling matrix elements for non-adiabatic transitions

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Abstract
Methods for the determination of radial coupling matrix elements, which arise in electronic non-adiabatic processes such as charge transfer, are examined. The Hellmann-Feyman formula, valid for exact Born-Oppenheimer eigenstates, is modified so as to incorporate dipole and velocity transition matrix elements. The Sidis expression (1971) is rederived without use of a specific coordinate system, and is extended to systems with more than two nuclear centres. In addition, a simple expression is derived for delta / delta R matrix elements involving large-scale configuration interaction wavefunctions at two closely spaced values of internuclear separation in terms of the trace of the product of the mixed transition density matrix and the molecular orbital overlap matrix.