Chapter 1 - Fully Correlated Wavefunctions for Three- and Four-Body Systems

Abstract

Abstract There is particular value in having wavefunctions for few-body systems that are compact but nevertheless have the features needed to capture the essence of the correlation effects. These desiderata are inherently in conflict and cannot be simultaneously reconciled when the wavefunction is described in terms of orbitals. However, explicit use of the interparticle distances leads to more efficient expansions; when all these distances are included as exponentials it is found that the expansions converge extremely rapidly, but only when the nonlinear parameters occurring therein are very carefully optimized. The present contribution reports the use of such expansions. For typical three-body systems (the He isoelectric series), with wavefunctions containing four terms (configurations), ground-state energies are obtained with errors between 32 and 38 microhartrees, and other properties, including those arising entirely from electron correlation, are given with very small errors. For a four-body system (the Li atom), a four-term wavefunction yields a ground-state energy within 350 microhartrees of the correct value.