The usual building blocks of molecular orbital theory are one-center atomic orbitals. If we instead use two-center orbitals derived from the exact solution for H-2(-), a simple calculation of the H-2 binding energy yields 4.5 eV, with a Hylleraas correlation factor having no adjustable parameters. Variational minimization with respect to a couple of parameters in our trial function then shifts the binding energy to 4.7 eV, very near the experimental value. The approach is also applicable to heteronuclear molecules; e.g., HeH-, whose ground state energy we calculate to be -2.96 hartree with no adjustable parameters. This is to be compared with -2.98 hartree previously calculated using a wavefunction with 83 terms. (C) 2004 Elsevier B.V. All rights reserved.