The ab initio effective dipole operator of CH: Comparisons with semiempirical methods

Matrix elements of the effective valence shell dipole operator μ^v for the CH molecule are computed in the nonorthogonal basis of atomic valence shell self-consistent-field (SCF) orbitals for carbon and hydrogen. Significant contributions emerge from two-center and two-body μ^v matrix elements. The former are generally neglected in semiempirical methods for calculating dipole matrix elements, while the existence of the latter is not acknowledged by these methods but should be averaged into semiempirical dipole matrix elements. The ab initio μ^v matrix elements contain significant correlation contributions, but these are entirely neglected in semiempirical schemes. This neglect of correlation contributions to the semiempirical dipole matrix elements stands in stark contrast to the ``adjustment'' for correlation of semiempirical Hamiltonian matrix elements. An important correlation contribution to the μ^v matrix elements is shown to arise from the usual molecular orbital polarization that is omitted in both semiempirical schemes and theoretical dipole matrix elements in the atomic SCF basis. Thus, the largest correlation contributions to μ^v matrix elements are found to emerge for those matrix elements containing the most polarizable orbitals that are directly involved in bond formation.