A One-Center Wave Function for the Hydrogen Molecule

Slater atomic orbitals, s, p, d, etc., centered at the molecular midpoint and having variable orbital exponents and variable principal quantum numbers, are used to construct a seven-term wave function for the ground state of the hydrogen molecule of the form Ψ=C1(ssI)+C2(sIIsIII)+C3(sIVd0)+C4(sVg0)+C5(p0p0)+C6(p+1p−1)+C7(p0′f0). Values for the seven linear coefficients, the twelve orbital exponents and the twelve principal quantum numbers are determined by the variational method. The total molecular energy obtained is — 1.15883 a.u., or 31.53 ev (exptl. 31.96 ev), corresponding to a binding energy of 4.32 ev (exptl. 4.75 ev). A ten-term function of similar form is constructed which gives a binding energy of 4.34 ev.