The development and application of multiconfigurational self-consistent field states to study the electronic structure of atoms and molecules

Abstract

We develop and review complete second-order Newton-Raphson type multiconfigurational self-consistent field (MCSCF) iterative procedures based on unitary exponential operators. We discuss characteristics that an MCSCF stationary point should possess to be a proper representation of the exact Nth state in energy of a certain symmetry. We derive an MCSCF iterative scheme that invokes some of these characteristics directly as conditions on the iterative algorithm. Numerical examples demonstrate that convergence is obtained rapidly and reliably. Combining this new MCSCF procedure with a modified surface walking algorithm, we examine an MCSCF energy hypersurface at fixed geometry in detail. Calculational examples show that several near-lying MCSCF stationary points which fulfill all or some of the characteristics we require of an MCSCF state exist on the hypersurface. Considering these results, we discuss the importance of examining the characteristics of an MCSCF stationary point before assigning it as an appropriate representation for the desired state. We employ the MCSCF wavefunction to develop and extend multiconfigurational (MC) many-body methods. We review MC linear response (MCTDHF/MCRPA) which determines excitation energies and other response properties. We combine this explicitly correlated Green's function approach with Stieltjes-Tchebycheff moment theory for the first time to calculate outer valence photoionization cross-sections for N2 and O2. In both cases our results are in overall agreement with static exchange results. A few significant differences in the partial and total photoionization cross-sections are discussed. We develop an MC spin-tensor electron propagator technique for the theoretical determination of vertical ionization potentials for general open-shell and highly correlated atomic and molecular systems. To do this, we use and extend the spin-tensor operators of Rowe and Ngo-Trong. To properly account for correlation effects, we include ionization potential and electron affinity operators analogous to the state transfer operators necessary in MC linear response. Comparison calculations with other large scale methods, i.e. 螖SCF, 螖MCSCF, perturbative-type Green's function, and 螖multi-reference CI using the same basis set are presented...