Studies of MCSCF optimization and application to many-body techniques for the electronic states of atoms and molecules

Abstract

We develop and review multiconfigurational self-consistent field (MCSCF) procedures based on unitary exponential operators. When the energy functional is expanded through second order in the orbital and state optimization operators, and the variational principle applied, the resulting set of coupled, linear inhomogeneous equations are known as the Newton-Raphson equations. Small eigenvalues of the Hessian may give extremely large step length amplitudes. We discuss two procedures, mode damping and mode controlling, which are used to reduce large step length amplitudes. New calculational results are given for the first excited ('1)(SIGMA)(,g)('+) state of C(,2) and the 2('1)A(,1) state of CH(,2). Generalizations of Newton-Raphson and the multiplicity independent Newton-Raphson (MINR) approaches are discussed. Calculations are presented for the E('3)(SIGMA)(,u)('-) state of O(,2).We utilize the MCSCF wave function to develop multiconfigurational (MC) many-body methods. The first many-body method we review and extend is the multiconfigurational time-dependent Hartree-Fock/multiconfigurational random phase approximation (MCTDHF/MCRPA) technique used to determine excitation energies and various other response properties. The electronic structure of the low-lying valence states of the polyatomic free radical methylene (CH(,2)) is investigated at two different geometries using both MCSCF and MCTDHF/MCRPA techniques. Oscillator strengths and polarizabilities of CH(,2) are also examined with the MCTDHF/MCRPA technique. From calculated MCTDHF/MCRPA energies and oscillator strengths we may apply the Stieltjes-Tchebycheff theory of moments to determine partial channel photoionization cross sections. Calculated photoionization cross section of acetylene (C(,2)H(,2)) are presented and analyzed. Finally, we have developed the many-body multiconfigurational electron propagator (MCEP) technique for the theoretical determination of ionization potentials for general open shell and highly correlated atomic and molecular systems. In order to do this, we have used and extended the generalized spin-symmetry adapted operators of Pickup and Mukhopadhyay. To properly account for correlation effects we have additionally included ionization and electron affinity operators analogous to the (VBAR)(GAMMA)> <O(VBAR) state transfer operators necessary in multiconfigurational linear response. MCEP ionization potentials and ionization process probabilities have been evaluated for both O(,2) and N(,2) and used to carry out detailed examination and interpretation of the respective PES and ESCA spectra.