Exponential variational expansion in relative coordinates for highly accurate bound state calculations in four-body systems

Exponential variational expansions in relative coordinates are considered for four-body systems. All matrix elements needed for bound-state calculations are expressed as linear combinations of fifth- and sixth-order derivatives of a basic four-body integral. Computation of the basic four-body integral and its derivatives is performed directly, i.e., without any use of the branch tracking in the complex plane that is required in the Fromm/Hill approach, and by methods that take into account the termwise singularities of the formulas. The final computational procedure is relatively simple, physically transparent, and numerically stable. The methods are illustrated with sample data that show the importance of a singularity-canceling approach and that the increased precision thereby made possible permits more accurate wave function optimization than heretofore.