The Hellmann–Feynman theorem for approximate wave functions and its application to nonadiabatic coupling matrix elements with the aid of a coupled Hartree–Fock method

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Abstract
Nonadiabatic coupling matrix elements are calculated by means of the Hellmann–Feynman theorem. Thereby the basis set dependence is investigated thoroughly for GTO basis sets. For every occupied AO, at least two polarization functions have to be included, of which the K shell p function have to be taken into special consideration. In this report we will show applications for the calculation of molecular forces on Hartree–Fock level. With a coupled Hartree–Fock method the gradient of orbital energies and nonadiabatic coupling matrix elements between different orbitals will be given. Our computations will deal with the molecules H2, N2, Li2+, and NeO.