Self-consistent, nonorthogonal group function approximation: An ab initio approach for modelling interacting fragments and environmental effects

Abstract

The reformulation of the single determinantal, closed shell wavefunction into an antisymmetrized product of nonorthogonal group functions (NOGF) is reviewed. It is shown that by introducing the idea of a “reciprocal” group function, i.e. a group function defined as a product of reciprocal orbitals, the resulting expressions for one- and two-electron operators are formally identical with the equations obtained using strong-orthogonal group functions. Orbital equations are given for the NOGF wavefunction which are derived by formulating a variation principle in terms of group energy functionals, where the presence of the other groups is expressed in terms of Coulomb and exchange operators in the group's Hamiltonian, To ensure that the group's orbitals do not violate the Pauli exclusion principle, a coupling or screening operator is introduced into the variational equations. The effectiveness of the coupling operator is discussed and it is demonstrated that it fully screens the group's orbitals from collapsing or distorting into forbidden regions of function space. To provide techniques for modelling and analyzing intermolecular interactions, the procedure for calculating the NGOF wavefunction can be reformulated into a series of steps which allows the components of the interaction energy, i.e. Coulomb, exchange, polarization and charge transfer, to be evaluated. This approach leads to considerable simplification and reduces the computational effort required to determine the wavefunction. The decomposition is used to analyze many-body effects in linear water chains and a model of a helical hydrogen bonding. The basis set superposition error (BSSE) in the NOGF approximation is discussed and methods for its evaluation are given, and it is shown that the BSSE is inherently less in the NOGF wavefunction than in the corresponding HF-SCF wavefunction. In the final parts of the paper, additional methods are given which further reduce computation time when both interacting fragments and their immediate environment must be considered at the quantum chemical level. These techniques are then applied to a study of the effect of environment on ion pair formation and proton transfer. The results of these studies demonstrate the remarkably strong modulating effect of molecules hydrogen bonded to the interacting pair.