Momentum distributions for two-electron systems: the Coulomb shift and correlation coefficients for the HeH+molecular ion

Abstract

With the objective of gaining further insight into the effects of correlation on the electronic momentum distribution in small molecules, the authors have calculated the Coulomb shift Delta f(p12) for HeH+ in its ground state. For comparison, the Coulomb hole in position space Delta f(r12) has been reported at the theoretical bond length RTh approximately=1.4. By introducing the distribution function Delta g(p12, p1, theta 1) the authors have been able to examine the effects of correlation with respect to the magnitude and orientation of the momentum p1 for the 'test' electron 1; theta 1 is measured relative to the internuclear axis. Various 'radial' and 'angular' correlation coefficients were determined by evaluating several one- and two-particle expectation quantities, and they also obtained results for the spherically averaged Compton profile. The variations of the radial and angular components of correlation are examined as a function of the internuclear separation R. A brief discussion is also presented concerning the effects of correlation and bond formation on the molecular momentum density rho (p) at RTh approximately=1.4. The authors' results have revealed, once again, that momentum space is especially advantageous for an analysis of electron correlation into its radial and angular contributions.