Knowledge Bank

The photoionization cross section can be expressed as a particular matrix element of the resolvent of the molecular electronic Hamiltonian. By using a mixture of real and complex Gaussian basis functions to form a matrix representation of the Hamiltonian it is possible to use this expression to compute molecular photoionization cross sections from the results of a matrix diagonalization. This procedure is based on a variational principle for the resolvent matrix element from which the photoionization cross section is calculated, and can be applied in the presence of coupling between ionization channels. The interference between resonance features and the electron-ion scattering background is naturally incorporated by this method, and it is easily implemented for polyatomic systems. Results are reported for valence ionization of $CO2$ at the static exchange level. Agreement with most other calculations is adequate and is especially good with those which compute the photoionization cross section directly from the electron-ion scattering wave function. The complex-basis-function technique is particularly successful in reproducing resonance features in these cross sections. Vibrational averaging over the bending mode, in which the $CO2$ molecule possesses the $C2v$ symmetry, has been studied to further the understanding of the nature of the high energy resonance in the $4\circ g$ ionization channel.