Energy eigenvalues of the spin-1/2system with linear vibronic coupling: different static and adiabatic approximations in comparison with a numerically accurate treatment

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Abstract
A spin-1/2 system with transitive and displacive couplings to one vibrational mode is considered. It represents a simple model for radiationless multiphonon transitions, for example, in dimers or at point defects in crystals. The numerically calculated energy eigenvalues of the system are discussed and compared with different static and adiabatic approximations. For the static approach the optimum electronic base functions are derived. They refer to the nuclear configuration which belongs to the absolute minimum of the adiabatic potential. The adiabatic approximation is treated accurately by means of a numerical diagonalisation. For its validity two criteria are presented which are shown to be consistent with the authors' numerical results.