Computation of the SCF Molecular Orbital Wavefunction in Terms of Localized Orbitals

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Abstract
The Hartree—Fock—Roothaan equations are written down and solved for the localized molecular orbitals which describe the chemical bonds and lone pairs of many molecules. The work involves the formulation of a local operator which is concerned with the physical situation in and around the bond in question and which is largely independent of the rest of the molecule. The matrix elements of this operator over the atomic orbitals of the molecule are known, but the explicit form of the operator itself has not been obtained so far. The theory is applied to two simple examples, the He2 molecule and the BH molecule. The known wave‐functions and energies of these two examples are obtained again in a novel way which should be applicable to molecules of any size. These two examples illustrate some, but not all, of the points which arise in the general case. If it does prove possible to use this method in large molecules, then there is no upper limit to the size of the molecule which can be dealt with at the Hartree—Fock—Roothaan SCF level of approximation.

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