Gaussian cell model for molecular orbitals

Abstract

The convergence of a gaussian basis ø_µ= exp (–α|r–r_µ|²) for molecular orbitals has been examined. One gaussian is located at the centre of each cell in a cubic lattice of spacing λ. The exponent α is the same for all basis functions in order that there shall be many equivalences amongst the molecular integrals. Optimum values of λ and α have been found for several systems.

Convergence to the ground state energy of the hydrogen atom is slow (up to 365 basis functions have been considered) due to a poor representation of the nuclear cusp. Convergence to the dissociation energy and equilibrium bond length of H⁺₂ is more rapid. A 3 × 3 × 4 basis gives D_e within 3 % of the exact value. Calculations on H₂ and HeH⁺ show that the basis is slightly less satisfactory when it has to satisfy the conflicting requirements of electron repulsion and electron nuclear attraction, and for LiH a basis of 36 functions is unable to represent satisfactorily both inner and valence shell orbitals. It is concluded that much larger bases of this type would be necessary for many electron molecules before the results were competitive with those obtained from more flexible conventional gaussian bases.