Boundary condition determined wave functions for the ground states of one-and two-electron homonuclear molecules

Simple analytical wave functions satisfying appropriate boundary conditions are constructed for the ground states of one-and two-electron homonuclear molecules. Both the asymptotic condition when one electron is far away and the cusp condition when the electron coalesces with a nucleus are satisfied by the proposed wave function. For H-2(+), the resulting wave function is almost identical to the Guillemin-Zener wave function which is known to giv e very good energies. For the two electron systems H-2 and He-2(++), the ad ditional electron-electron cusp condition is rigorously accounted for by a simple analytic correlation function which has the correct behavior not onl y for r(12)--> 0 and r(12)-->infinity but also for R --> 0 and R -->infinit y, where r(12) is the interelectronic distance and R, the internuclear dist ance. Energies obtained from these simple wave functions agree within 2 x 1 0(-3) a.u. with the results of the most sophisticated variational calculati ons for all R and for all systems studied. This demonstrates that rather si mple physical considerations can be used to derive very accurate wave funct ions for simple molecules thereby avoiding laborious numerical variational calculations. (C) 1999 American Institute of Physics. [S0021-9606(99)30539- 0].