Fourier analysis of spherically averaged momentum densities for some gaseous molecules

Abstract

The spherically averaged autocorrelation function, B( r), of the position-space wavefunction, ψ( r ), is calculated by numerical Fourier transformation from spherically averaged momentum densities, ϱ( p), obtained from either theoretical wavefunctions or (e,2e) electron-impact ionization experiments. Inspection of B( r) for the π molecular orbitals of C 4 H 6 establishes that autocorrelation function differences, Δ B( r), can be qualitatively related to bond lengths and numbers of bonding interactions. Differences between B( r) functions obtained from different approximate wavefunctions for a given orbital can be qualitatively understood in terms of wavefunction difference,Δψ( r ), maps for these orbitals. Comparison of the B( r) function for the 1 a u orbital of C 4H 6 obtained from (e,2e) momentum densities with that obtained from an ab initio SCF MO wavefunction shows differences consistent with expected correlation effects. Thus, B( r) appears to be a useful quantity for relating spherically averaged momentum distributions to position-space wavefunction differences.