When viewed as a square two-indexed matrix, the array of atomic orbital-based, two-electron integrals (ijlkl) is a positive semidefinite array. Beebe and Linderberg showed, in 1977, that actual or near linear dependencies often exist within the types of atomic orbital basis sets employed in conventional quantum chemical calculations. In fact, large (i.c., higher quality) bases were shown to be substantially more redundant than smaller or more spatially separated bases. In situations where there exists significant basis near redundancy, the rank ( r ) of the (ijlkl) = V,,, matrix of integrals will be significantly smaller than the matrix dimension M . When this occurs, it proves computationally tractable to decompose the M-dimensional matrix V into components L (V = LL') which contain all of the information needed to form the full V matrix. The Cholesky algorithm allows such a decomposition to be carried out and forms the basis of the work described here. The method is found to be highly successful in reducing the number of integrals and integral derivatives that must actually be calculated. In particular, results on the C2 molecule indicate that the algorithm can be superior to traditional methods of integral derivative generation if the orbital basis is large enough to contain appreciable near redundancy. In contrast, results on benzene with a more spatially delocalized basis show that conventional methods are preferred whenever substantial basis (near) redundancy is not present.

By combining the surface walking algorithm of Simons et al. with locally determined forces on an ab initio surface, the reaction paths for the model reactions Be + H2 *-BeH2 -» Be + 2H ('A,) were studied. This represents the first application of this algorithm to an ab initio surface which is generated locally as the walking proceeds.

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Recently we extended our strategy for MRD-CI (multireference double excitation-configuration interaction) calculations based on localizedilocal orbitals and an "effective" CI Hamiltonian for molecular decompositions of large molecules to breaking a chemical bond in a molecule in a crystal or other solid environment. Our technique involves solving a quantum chemical ab-initio SCF explicitly for a system of a reference molecule surrounded by a number of other molecules in the multipole environment of more distant neighbors. The resulting canonical molecular orbitals are then localized and the localized occupied and virtual orbitals in the region of interest are included explicitly in the MRD-CI with the remainder of the occupied localized orbitals being folded into an "effective" CI Hamiltonian. The MRD-CI calculations are carried out for breaking a bond in the reference molecule. This method is completely general. The space treated explicitly quantum chemically and the surrounding space can have voids, defects, deformations. dislocations, impurities, dopants, edges and surfaces, boundaries, etc. We previously applied this procedure successfully to the H,C-N02 bond dissociation of nitromethane in a nitromethane crystal with extensive testing of the number of molecules that have to be included explicitly in the sCF and how many molecules have to be represented by more distant multipoles. The results indicated that it took more energy to dissociate the H3C-NOI bond when the nitromethane molecule was in the crystal than it did to dissociate that bond in the free nitromethane molecule. In this present study we have investigated the effect of voids (both in the nitromethane molecules treated explicitly in the SCF and those in the environment represented by multipoles) on the calculated H3C-NOI bond dissociation energies.

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