Lynn T. Redmon

Quasidegenerate perturbation theories. A canonical van Vleck formalism and its relationship to other approaches

Three forms of quasidegenerate perturbation theory are discussed and compared in terms of a common general formulation based on a similarity transformation which decouples the model space and complementary space components of the Hamiltonian. The discussion is limited to formal, rather than many‐body (diagrammatic), aspects. Particular attention is focused on a ’’canonical’’ form of van Vleck perturbation theory, for which new and highly compact formulas are obtained. Detailed comparisons are made with the Kirtman–Certain–Hirschfelder form of the van Vleck approach and with the approach based on intermediate normalization which has been used as the basis for most of the diagrammatic formulations of quasidegenerate perturbation theory.

Correlation effects in the isomeric cyanides: HNC↔HCN, LiNC↔gLiCN, and BNC↔gBCN

Correlated values of the isomerization energy and barrier for the HNC→HCN reaction are obtained from many‐body perturbation theory, including the effects of quadruple excitations. Extended basis sets of better‐than‐triple‐zeta plus double‐polarization quality are used, as well as basis sets including counterpoise and bond‐centered orbitals. The best of these basis sets is sufficient to account for 84% of the valence correlation energy of HCN. These studies predict an isomerization energy for the HNC→HCN rearrangement to be −15±2 kcal/mole, in disagreement with a recent experimental value of −10.3±1. kcal/mole. Correlated isomerization energies of LiCN→LiNC and BCN→BNC are obtained in bases of double‐zeta plus polarization quality. In all cases, correlation stabilizes the cyanide isomer more than the isocyanide. Trends in the series R–NC⇄RCN for R=H, Li, and B are discussed.

Multidimensional many‐body theory: Diagrammatic implementation of a canonical van Vleck formalism

A size‐extensive multidimensional many‐body theory is developed from an order‐expanded van Vleck transformation. This provides an effective Hamiltonian in a model space consisting of a set of determinants whose zeroth‐order energies may be nondegenerate. Expressions for the effective Hamiltonian in terms of the perturbation and a set of resolvents generalized from the Rayleigh–Schrodinger form are given. Perturbative evaluation of the resultant formulas via diagrammatic expansion is illustrated and discussed. The diagrams required through second order for a model space consisting of a Hartree–Fock solution plus selected singly and doubly excited determinants are presented, and their relation to those employed in the method of Hose and Kaldor is discussed.

The unimolecular isomerization of methyl isocyanide to methyl cyanide (acetonitrile)

The unimolecular isomerization of CH3NC→[CH3 NC] →CH3CN is studied by many‐body (diagrammatic) perturbation theory. Using double‐zeta plus polarization (DZP) contracted Gaussian basis sets (63 CGTO’s), correlated calculations are made by evaluating all second‐, third‐, and fourth‐order diagrams that occur due to single, double, and quadruple excitations [SDQ–MBPT(4)]. These diagrams involve ∼107 CI type configurations. The SDQ–MBPT(4) model predicts the enthalpy of isomerization to be −22.7 kcal/mole [exp(−23.7 ±0.14)]. The activation barrier is found to be ∼41 kcal/mole (exp 38.4). The inclusion of quadrupole excitation diagrams has little effect on the enthalpy of isomerization but increases the activation barrier by 1 kcal/mole.