Exact matrix elements for general two-body central-force interactions, expressed as sums of products.

In a manner similar to but distinct from concurrent tensor efforts in electronic structure, it is shown that the Laplace transform can serve as a generator for a sum-of-products (SOP) form that allows one to write essentially any function of distance between two particles (i.e. any central force potential) as an exact two-body matrix. In particular, exact expressions for the Coulomb, Yukawa and long-range Ewald two-body operators are evaluated in a band-limited (Sinc function) basis. The resultant exact, full-basis, SOP representations for these interaction potentials – acting in conjunction with an external harmonic confining field – are validated via comparison with energy eigenstate solutions obtained via an independent calculation based on separation of variables. The new two-body matrix representations may have substantial impact in any of the many disciplines in which pair-wise central force interactions are relevant – especially, electronic structure and dynamics. [ABSTRACT FROM AUTHOR]