Treatment of non-adiabatic Hamiltonians by matrix continued fractions. I. Electronic two-level system coupled to a single vibrational mode

The eigensolutions of an electronic two-level system coupled to a single vibration mode via diplacive and transitive couplings are determined using continued-fraction methods. In the case of vanishing displacive coupling a scalar continued fraction has to be calculated, whereas in the general case the solution of the eigenvalue problem involves matrix continued fractions. It is shown that the first step of the continued-fraction method yields analytical approximations published recently by Friesner and Silbey (1981). The convergence behaviour of the matrix continued fractions is discussed on the basis of a theorem derived by Denk and Riederle (1982).