Energy Computation for Exponentially Correlated Four-Body Wavefunctions

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Formulas are presented for efficient computation of the energy of four-body quantum-mechanical Coulomb systems with wavefunctions consisting of fully correlated exponentials premultiplied by arbitrary integer powers of the interparticle distances. Using the interparticle distances as coordinates, the potential energy is easily expressed in terms of basic integrals involving these wavefunctions. All the contributions to the kinetic energy are also expressible using the same basic integrals, but it is useful to organize the computations in ways that take advantage of the relations between integrals and that illustrate the underlying symmetry of the formulation. The utility of the formulation presented here is illustrated by an “ultra-compact” computation of the ground state of the Li atom.