Compact 11S Helium Wave Functions; an 8-Parameter Wave Function and its Sensitivity Analysis

not only satisfies all the cusp conditions (as promised by Hirschfelder) but provides a satisfying variational form for obtaining quite high accuracy predicted energies of the Helium 1S 2-electron ground state. It employs a “to be determined” function g(r1,r2,r12) to correct for all the errors induced by the cusp determined functions (i. e., those functions chosen to make sure that the total Ansatz has no poles and/or singularities). Hirschfelder never comments in his paper why he chose this form, but, serendipitously from our point of view, it works better than the standard e−r12/2 term or variants thereof [3, 4]. In prior work, a 4-parameter expansion of this type gave an average energy of−2.9012 a. u. [2]. The associated wave function for this energy value was [5, 6].