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Ab initio self-consistent field (SCF) calculations are performed with the standard 6-31G* basis set for all-trans conjugated oligomers C2n+2H2n+4. The canonical occupied and virtual molecular orbitals (MOs) are separately localized by unitary transformations. Due to the localization, the perturbation operator is partitioned into two-particle and into single-particle terms; the MBPT is, therefore, a double-perturbation expansion in this case. By using the localized representation of the MBPT, the correlation energy contributions can be partitioned into local and nonlocal effects. It can be shown that the local effects are very important and well transferable, which makes possible the calculation of the correlation energy of larger molecules if the localized molecular orbitals (occupied and virtual) of smaller related molecules are known. © 1994 John Wiley & Sons, Inc.

Supermolecular model of the intermolecular interaction energy is studied. The correlation energy components are calculated by using the many-body perturbation theory (MBPT) in the canonical representation as well as in the localized one. The components of the corrections of the different order are analyzed individually. The effects of the localization procedure and the basis set are also investigated. An H2O trimer is used to study the two- and three-body components of the interaction energy. © 1993 John Wiley & Sons, Inc.

Diagrammatic formulation of the MBPT is applied when the occupied and the virtual canonical orbitals are separately localized by unitary transformations. In this localized representation, due to the off-diagonal Fock matrix elements, the perturbation operator contains extra terms generating the so-called localization corrections. These corrections enter the perturbation energy in third and higher orders. Their magnitude depends on the type of localization, but they represent only a small fraction of the canonical corrections. The calculation of the localization corrections, however, does not need a significant amount of extra computer time. It is shown that by introducing an “order of neighborhood” local and nonlocal effects of the electron correlation can be separated and the contribution of the nonlocal effects can be neglected to a good approximation. Ab initio calculations have been carried out for the normal saturated hydrocarbons: C2n+1H4n+4 and for the all-trans conjugated polyenes C2n+2H2n+4. As to the ratio of the local and nonlocal corrections, it is shown that there is only a quantitative difference for these two kinds of systems (strongly or weakly localizable). Neglecting nonlocal effects, considerable amount of computer time can be saved.

The application of the MBPT in the localized representation requires that both the occupied and the virtual orbitals obtained by the canonical HF equation should be localized. The localization of the occupied orbitals is straightforward in general by any localization method. It is shown that by using Boys' method the localized virtual orbitals are spatially well separated and transferable not only in minimal basis sets.

Ab initio double-zeta quality molecular orbital calculations have been carried out on an extensive series of ten-electron hydrides. The Edmiston–Ruedenberg energy-localized molecular orbitals were calculated and the total molecular and localized orbital densities analyzed in terms of dipole moments, contour plots, and a simplified model for the orbital density involving analysis of the first and second moments. The simplified moment analysis model may be easily visualized in terms of threedimensional geometric objects, spheres, and ellipsoids. The model summarizes the information on the effective functional distribution inherent in the more detailed orbital contour plots in a clear and concise manner.