RAYLEIGH-SCHRODINGER PERTURBATION-THEORY FOR COUPLED OSCILLATORS .3. CURVE-CROSSING PROBLEMS

The Rayleigh-Schrodinger perturbation theory approach developed previo usly for evaluating nonadiabatic corrections to the adiabatic energy l evels of a system of two coupled oscillators is generalized to the cas e of the so-called ''mixed'' representations which arise from the diab atic representation of a given problem by performing a unitary transfo rmation on the diabatic potential energy matrix (the adiabatic represe ntation is obtained as a special case with a purely diagonal potential energy matrix). Different representations provide different coupling conditions and, consequently, different bases for evaluation of the pe rturbation corrections, This is reflected, quite generally, in the con vergence and summability properties of the perturbation series and can thus be used to improve the accuracy and stability of the perturbatio n calculations, The latter possibility is especially important in the case of closely coinciding levels. Model calculations have revealed th at changing representations may allow the determination of the energie s of these levels to a high degree of accuracy even in the case of str ong perturbation resonances, (C) 1997 American Institute of Physics.