Orbital Theories of Electronic Structure. II. Molecularly Invariant Orbitals

Abstract

We express mathematically the question: Do orbitals for localized groups in molecules exist such that they are accurately the same in all molecules containing the same localized electron group? The advantage of giving the question mathematical form is that then the search for such molecularly invariant orbitals requires that accurate Hartree—Fock calculations be carried out only on a set of reference systems. Constructing the Hartree—Fock wavefunction of a molecule from the localized orbitals of subgroups in the reference systems, one can then test the accuracy to which the subgroup orbitals are molecularly invariant orbitals. Based on our quantitative approach, we present arguments and suggest conditions which favor the existence of molecularly invariant orbitals. The conditions favoring their existence are as follows. (a) The subgroup orbitals in general should not be orthogonal to the orbitals of any other subgroup in a molecule. (b) The subgroup orbitals should be well localized, in the sense that they are small in the neighborhood of the nuclei of the other subsystems. (c) The nuclear separations in the molecule from which the localized orbitals are taken, and the nuclear separations in the molecule to which the orbitals are transferred, should be identical. (d) If two molecules differ only through the substitution of one ion for another, the most favorable case will be that in which the two ions have the same net charge. (e) The differences between the eigenvalues of the orbitals of a subsystem in one molecule and those of the same subsystem in another molecule decrease at least as rapidly as the fourth power of the reciprocal of the separation of the subsystem from the rest of the system, for increasing separation.