Theoretical studies in photoelectron spectroscopy: Use of angular distribution data to deduce molecular orbital parameters

We present formulas for the differential cross section for ejection of energetic molecular photoelectrons. The cross section has been factorized into a radial and angular part. The angular part has been evaluated by use of standard angular momentum algebra, while the radial part requires explicit expressions for each partial wave component of the initial molecular orbital (which must be in the form of a single‐center partial wave expansion) and for each partial wave of the photoelectron. We assume a parametrized form for the initial molecular orbital, and we calculate the photoelectron wavefunction by consecutive use of the distorted‐wave‐Born and Coulomb‐Born approximations. This is a perturbative form, valid to O(k⁻²) in the asymptotic region of the wavefunction, where in atomic units k is the velocity of the photoelectron. The theory provides the means to invert angular distribution data, if available, to determine the parameters of the initial molecular orbital. Or, if this orbital is known, the theory provides an accurate high energy limit to test low energy theories or to normalize relative cross section measurements. We calculate the cross section for photoionization of ${\mathrm{H}}_2^{+}$ from states of different symmetries as a function of internuclear distance. We indicate how the method can be extended to more complicated molecules.