Variational calculations on many-electron diatomic molecules using Hylleraas-type wavefunctions

Publisher Website
Google Scholar
Abstract
The method of explicitly including the interelectronic distance rij in a variational wavefunction, first proposed by Hylleraas for the helium atom and James and Coolidge for the hydrogen molecule, has been extended to many-electron diatomic molecules for the first time in calculations on He2 + and He2. The configurations in the wavefunctions consist of the product of an rij v variable (v = 0,1) with confocal elliptical orbitals. The correlation of the motion of all pairs of electrons in a molecule is represented explicitly in this way. The 2Σ u + He2 + calculation was carried out at the equilibrium internuclear distance (2·065 bohr) and an energy of -4·98706 hartree was obtained (∼90 per cent of the correlation energy). The 1Σ g + He2 wavefunction, which was computed at the small internuclear distance of 1·0 bohr, yielded an energy of -4·88323 hartree. The energy obtained for the He2 ‘molecule’ is superior to the values reported in all previous calculations including the energy produced in the iterative natural orbital CI calculation of Bender and Davidson. We give a detailed presentation of the formulae and methods used for evaluating the cumbersome many-electron integrals that are required to produce the matrix elements in the secular equations. The possibility of extending the method to more complicated many-electron diatomic molecules is discussed, with particular emphasis being placed upon the computational problems that the technique presents.