Hydrogen Molecule Energy Calculation by Correlated Molecular Orbitals

Abstract

The electronic energy of the hydrogen molecule was calculated using the correlated molecular orbital wave function ψ=(a1+b1)(a2+b2)(1+pr12),where a1, b1, a2, and b2 are 1s atomic wave functions of electrons 1 and 2 about nuclei a and b, and r12 is the interelectronic distance. The p of the above formula together with z, the effective nuclear charge, used in the explicit definition of the atomic orbitals, are two parameters which are varied in minimizing the energy according to the variation method. The energy minimum was found to be 4.11 ev below the value for complete separation of the nuclei. The minimum occurred at an internuclear distance of 0.71A, and the parameters have the values z=1.285 and p=0.28 in atomic units. The energy is far better than Coulson's best molecular orbital calculation and better than any other two-parameter calculation except for that of Gurnee and Magee.