ASSESSMENT OF GAUSSIAN-WEIGHTED ANGULAR RESOLUTION FUNCTIONS IN THE COMPARISON OF QUANTUM-MECHANICALLY CALCULATED ELECTRON MOMENTUM DISTRIBUTIONS WITH EXPERIMENT

A critical assessment is made of the recently proposed momentum-averaged Gaussian-weighted (MAGW) method {[}A.O. Bawagan and C.E. Brion. Chem. Phys. 144 (1990) 167] of incorporating angular (or momentum) resolution into quantum-mechanically calculated momentum distributions for comparison with EMS measurements. In particular, the general efficacy of the proposed, semi-empirically based Gaussian angular (theta and phi) resolution functions as dimensioned in the MAGW method is tested by systematic application to high-level (essentially Hartree-Fock limit and/or configuration interaction) calculations of the momentum distributions of the outermost orbitals of a wide range of target species including Ne, Ar, Kr, He, H2O, and H2-S. The folded calculations are compared with recent measurements. New highly accurate analytical mathematical procedures have been developed and confirm the adequacy of the previous Monte Carlo method for resolution folding. However, the new procedures result in substantial improvements over use of the Monte Carlo method for the graphical representation of the variation of the momentum resolution function with azimuthal angle. The respective merits of comparing folded theory and experiment as a function of nominal relative azimuthal angle (phi(0)) or of momentum are discussed. In the momentum representation, the question of whether it is preferable to use average or nominal momentum is further considered. Either choice is found to afford a reasonable basis for detailed comparison of folded theory and experiment. In all cases, the folded theory is found to be in good agreement with experiment when the Gaussian-weighted angular resolution functions are used. whereas less satisfactory overall agreement is obtained when the calculations are folded with earlier types of resolution-folding procedure. It is concluded that the Gaussian-weighted angular resolution functions, appropriately dimensioned, provide a satisfactory accounting for the experimental angular (or momentum) resolution effects and that they can be used with reasonable confidence in future studies for the evaluation of molecular wavefunctions.