A genealogical electronic coupling procedure incorporating the Hartree–Fock interacting space and suitable for degenerate point groups. Application to excited states of BH3

The use of Clebsch–Gordan-type coupling coefficients for finite point groups is applied to the problem of constructing symmetrized N-electron wave functions (configurations) for use by the Hartree–Fock SCF and CI methods of determining electronic wave functions for molecular systems. The configurations are eigenfunctions of electronic spin operators, and transform according to a particular irreducible representation of the relevant group of spatial operations which leave the Born–Oppenheimer Hamiltonian invariant. The method proposed for constructing the configurations involves a genealogical coupling procedure. It is particularly useful for studies of molecules which belong to a group which has multiply degenerate irreducible representations. The advantage of the method is that it results in configurations which are real linear combinations of determinants of real symmetry orbitals. This procedure for constructing configurations also allows for the identification of configurations which have no matrix element of the Hamiltonian with a reference configuration. It is therefore possible to construct a Hartree–Fock interacting space of configurations which can speed the convergence of a CI wave function. The coupling method is applied to a study of the ground and two excited electronic states of BH3 in its D3h geometry. The theoretical approach involved Hartree–Fock SCF calculations followed by single and double substitution CI calculations, both of which employed double-zeta plus polarization quality basis sets. The B–H bond length was found to be 1.194 Å for the ground state, 1.26 Å for a 1E″ state lying 6.08 eV above the ground state, and 1.24 Å for a 3E″ state lying 5.48 eV above the ground state. Energies were calculated only for D3h geometries of the molecule, so the excited states may not be stable with respect to C2v distortions. In fact, since both excited states are spatially degenerate, they are expected to exhibit Jahn–Teller distortion. Finally, the effect of including only Hartree–Fock interacting configurations rather than all single and double substitution configurations in the CI calculation is demonstrated to be energetically quite small.