The Computation of the Localised Molecular Orbitals of Formaldehyde

Abstract

The localised molecular orbitals of the formaldehyde molecule are computed using a minimum basis set of Slater atomic orbitals. The method of calculation used obtains localised molecular orbitals (l.m.o.s ) directly at the Hartree-Fock level of approximation, rather than the more usual way of obtaining l.m.o.s from the canonical molecular orbitals.

The major difficulty in implementing this method is found to lie in satisfying orthogonality conditions, required by the l.m.o. theory, prior to an actual calculation. It is not found possible to satisfy these conditions completely for the formaldehyde molecule. Ways of overcoming this difficulty are discussed. L.m.o.s are calculated using Schmidt and Lowdin orthogonalisation of a suitable set of non-orthogonal starting-point functions.

The resulting l.m.o.s are found to give a unique many-electron total wavefunction, which is the same as that obtained by a canonical molecular orbital calculation. The individual l.m.o.s obtained are not unique, their forms depending on the method of orthogonalisation used and on the form of the starting-point functions.

Calculations are also made at several stages of approximation, each stage corresponding to ideas of chemical valence theory.Hence, perfectly localised molecular orbitals are computed directly. The results of calculations in which the operator is truncated to include only contributions from electrons and nuclei in the immediate environment of the l.m.o. being calculated are found to be very similar to those using the full Hartree-Fock operator.

The chemical significance of the l.m.o.s is examined by calculation of various properties including bond-energies. An examination is also made of the effect of making arbitrary changes in the polarity of one bond on some of the properties of other bonds.

Finally, a general study of the electron density given by many l.m.o.s in different molecules is made, and the use of l.m.o.s in describing the formation of a two-electron chemical bond is examined.