On the determination of the unperturbed energy levels and the interaction matrix elements leading to a complex vibronic analogue of the Fermi resonance

A noniterative solution to the problem of determination of the unperturbed energy levels a _i and interaction matrix elements b _i describing a complex vibronic analogue of the Fermi resonance (the number of interacting states n > 2) is found. It is assumed that a _i and b _i can be determined on the basis of experimental data known for the resonance region, namely, the transition energies e _k and intensities I _k . The source of the intensity of observed transitions is assumed to be only one perturbed transition (the S ₀ → S ₂ transition of the 0-0 type or its vibronic sideband). The algorithm uses algebraic methods based on finding eigenvectors of real matrices of a particular form, whose elements are constructed from combinations of e _k and I _k .