An efficient algorithm for solving the vibronic coupling problem (Q1821496)

The two state coupling problem in wave mechanics is solved in discretized form using the sign changes in the Sturm sequence of the Hamiltonian \(\lambda\)-determinant. The numerical algorithm is simple and fast; precision and accuracy can be separately controlled. The method is applied to the vibronic coupling problem in a diatomic (two closed channels) and the evolution of the adiabatic vibronic levels from the uncoupled (diabatic) states is demonstrated as a function of the strength of coupling. The method can be used for any symmetric pentadiagonal band matrix eigenvalue problem.