Spectral distributions in a model N-electron Hamiltonian

A study on the energy-level distribution of the Pariser-Parr-Pople Hamiltonian has been performed. In particular, relations between the values of the electron interaction parameters, the symmetry of the core potential, and the form of the secular distribution of the energy-level density have been investigated. The density is shown to be Gaussian in the physically significant range of the parameter values. However, very strong deviations from the Gaussian behavior have been observed at the limit of the very weak electron-core interaction. The secular density distribution functions have been used to predict the Hamiltonian spectra in very good agreement with the results of the matrix diagonalization. Spacings of the nearest-neighbor levels behave mainly in a Poisson-like form, showing the existence of approximate hidden symmetries even in the case of highly nonsymmetric core potentials.