Complex-coordinate calculation of matrix elements of the resolvent of the Born-Oppenheimer Hamiltonian

A procedure is outlined for using complex scaling to compute matrix elements of the resolvent of the Born-Oppenheimer Hamiltonian for a molecule with respect to square integrable functions. The method is superficially identical to that used previously for computing atomic photoionization cross sections—even though the molecular Born-Oppenheimer Hamiltonian is ill behaved under the scaling transformation appropriate to the atomic problem. The author gives a heuristic derivation of the method, relating it to Simon's theory of exterior complex scaling, which treats the molecular Born-Oppenheimer problem correctly. Numerical results are presented for ${\mathrm{H}}_2^{+}$ photoionization cross sections for which exact results are available for comparison.