Complex-basis-function calculations of resolvent matrix elements: Molecular photoionization

Procedures for computing molecular photoabsorption cross sections via finite expansions in sets of $L^2$ complex basis functions are discussed. Two recently proposed schemes for analytically continuing a matrix representation of the Born-Oppenheimer Hamiltonian are investigated. Both of these matrix analytic continuations are used to compute the parallel component of the photoionization cross section for ${\mathrm{H}}_2^{+}$. It is found that to obtain numerically stable results it is necessary to use complex-basis functions which are capable of describing cusps in the molecular wave function at complex values of the coordinates. The application of this technique to larger molecules is also discussed.