Highly compact wavefunctions for two-electron systems

There is particular value in having wavefunctions for multielectron systems which are compact but nevertheless have the features needed to capture the essence of electron correlation effects. For few-electron systems, explicit use of the interelectron distances has proved to be an indispensible component of highly accurate wavefunctions, but such wavefunctions contain hundreds or thousands of terms (configurations). We show here that for two-electron systems (the He isoelectronic series), expansions in which all the interparticle distances occur exponentially converge extremely rapidly if the nonlinear parameters occurring therein are very carefully optimized. Compact expansions of this kind give excellent values of the total energy (four-configuration functions exhibiting energy errors between 32 and 38 microhartree), and give other properties, including those arising entirely from electron correlation, with very small errors. These functions are highly suitable for visualizing the wavefunctions and for performing other analyses.