Scattered-Wave Theory of the Chemical Bond

Publisher Summary The limitations of applying an ab initio linear combination of atomic orbitals (LCAO) methods to complex molecules and solids are the size of the basis sets and the number of multicenter integrals or equivalent Hartree-Fock matrix elements. In the self-consistent field (SCF)-Xα scattered-wave model that is also a first-principle technique, there is no basis-set problem because Schrodinger's equation for an Xα potential is numerically integrated. There are no multicenter integrals and the model is practicable in both spin-restricted and spin-unrestricted forms for polyatomic systems of considerable stereochemical complexity. The SCF-Xα scattered-wave technique uses only a small fraction of the computer time required by an ab initio Hartree–Fock LCAO method. The applications of the scattered-wave method to polyatomic molecules and crystals are concerned with the generation of one-electron energy and wave functions. While an SCF-Xα one-electron analysis leads to an accurate quantitative description of many chemical and physical properties, it is also very important to determine the total many-electron energy. As the present method leads to a rapidly convergent numerical representation of the orbital wave functions, the accuracy of the theoretical model can easily be improved via perturbation theory, when necessary. Finally, the original theoretical formalism can be extended to more general forms of superposed-atom Xα potentials by means of the generalized scattered-wave theory.