On the Theory of Radiationless Electronic Transitions. II. The Morse Oscillator Model for Arbitrary Values of the Parameter Z

Abstract

Abstract In a previous paper1 it has been shown that the harmonic oscillator model is incapable of providing sufficiently large Franck-Condon factors F(E) if realistic parameter values are to be used. In consequence the calculated rate constants v=i/τ of radiationless electronic transitions at E ∼ 3 ev do not agree with those obtained experimentally. It has further been shown that this problem can be solved by using the Morse oscillator model. The calculations, however, were confined to a specific, though frequently encountered, case of the general expression for the Franck-Condon factor of a Morse oscillator, viz., the case of a small parameter =, where δω1-ω, ω1 and ω being vibrational frequencies in a higher and lower electronic states respectively, Δr = rei - re is the difference of coordinates of oscillator equilibrium positions in the respective electronic states mentioned, and α is a parameter of the Morse curve for the lower electronic state.