A comparative analysis of electron correlation in atomic Be and a momentum space investigation of LiH
In Part I, the electron correlation problem is briefly reviewed and some approaches to its solution are discussed. In Part II, a partitioning technique used previously to examine correlation trends in individual electronic shells for a series of four-electron ions has been extended and applied to a detailed comparison of four well-correlated wavefunctions for the Be atom. The present analysis of a correlated two-particle density, generalized for any N-electron system, retained all contributions from products of all terms in the wavefunction up to and including the pair-correlation effects. For each correlated description of Be, Coulomb holes and shifts have been evaluated and compared for the K(1S), L(1S), KL(1s) and KL(3S) shells. The inverted nature of the intershell holes, relative to the intrashell effects, has been examined and rationalized in terms of the 2s-2p near-degeneracy which exists in Be. The total Coulomb holes for the two energetically best wavefunctions showed a previously unseen structure which was directly attributable to the intershells. The calculation of partial Coulomb holes and shifts, Δg(r12,r1,)vs.r12 & Δg(p12,P1)vs.P12, allowed us to examine changes in the components of correlation as the position r1 or the momentum p1 of a test electron was varied. Selected one- and two-particle radial and momentum expectation values are also reported along with various radial and angular correlation coefficients. In Part III the partitioning technique, discussed in Part II, has been applied to a momentum space study of electron correlation in a molecular system. The correlation effects embedded in a CI wavefunction for LiH has been examined in terms of the intra- and intershell Coulomb shifts and several one- and two-particle expectation values. Finally, in Part IV we present an overview of correlation coefficients as used, quite extensively, in the discussion of electron correlation. We have examined their construction and have reviewed their application towards this subject.