Maurice G. Sheppard

Analysis of abinitio effective valence shell Hamiltonian calculations using third order quasidegenerate many‐body perturbation theory

A generalization of quasidegenerate many‐body perturbation theory is provided which enables the calculation of the Hermitian effective valence shell Hamiltonian Hv along with the individual one‐ , two‐ , three‐ , and the never‐before‐calculated four‐electron effective integrals of Hv. Emphasis is placed upon the problems encountered by the use of large valence spaces and the desire to use the same Hv for all valence states of a given system and all its ions. These stringent requirements, motivated by a desire to investigate the theoretical foundations of semiempirical quantum chemistry, introduce severe difficulties with the quasidegeneracy constraints of the theory. A detailed analysis is presented of methods to handle these problems within a third order formulation which in its simplest form reduces to a symmetrized version of Brandow’s diagrammatic linked‐cluster (size consistent) perturbation expansion. An outline of practical ab initio third order Hv calculations is discussed here and systematically ...

Convergence studies of the effective valence shell Hamiltonian for correlation energies of the fluorine atom and its ions using third order quasidegenerate many‐body perturbation theory

The effective valence shell Hamiltonian Hv, is evaluated through third order quasidegenerate many‐body perturbation theory (QDMBPT) for all 46 [2s,2p] valence states of F+7 through F−. The effects of independently varying the orbital basis set, the unperturbed Hamiltonian, and the definition of the valence shell are studied. A generalized of QDMBPT allows the separate evaluation of the many‐electron effective integrals which are independent of the number and configuration of valence electrons; hence, one Hv calculation yields all 46 state energies simultaneously. Methods for dealing wih quasidegeneracy problems associated with large valence shells are numerically tested and proven effective. Guidelines for Hv calculations on more complicated systems are presented.

Abinitio third order effective valence shell Hamiltonian calculations for first row diatomic hydrides

Ab initio effective valence shell Hamiltonian Hv calculations are presented through third order for the correlation energies of CH, NH, and OH at their equilibrium internuclear distance. The valence shell consists of the 2σ, 3σ, 1π, and 4σ orbitals. This represents the first quasidegenerate third order many‐body perturbation calculation of Hv for molecules with more than two valence electrons. As in the atomic case, a single Hv calculation provides correlation energies for all neutral valence states as well as for the positive and negative ion valence states of the hydrides. Calculated vertical excitation energies are in good agreement with those obtained from large configuration interaction calculations. Four‐electron effective interactions, present in the third order expansion of Hv, are evaluated. These four‐electron terms make significant contributions to the energies of many states. Technical difficulties are discussed which are related to Hv calculations with large valence spaces that violate the qu...

Generalized perturbation theory of effective valence shell hamiltonians

Abstract The second quantized effective valence shell hamiltonian of Iwata and Freed is generalized to incorporate valence orbital energies into the perturbative (matrix) energy denominators, eliminating convergence difficulties in calculations of atomic valence shell hamiltonians. When the matrix energy denominators are taken to be the simplest form our generalized effective hamiltonian reduces to Brandow quasi-degenerate theory.

Abinitio effective valence Hamiltonian description of electron correlation for the neutral and ion valence states of transition metal atoms

Results of second order ab initio effective valence shell. Hamiltonian calculations are reported, where all the valence states of Ti through Ti t+4 are computed simultaneously. The correlation energies of higher lying 4S23dn, 4S3dn+1 and 3dn+2 states and the ground state of Ti are reported. (AIP)

Ab initio effective valence shell Hamiltonian calculations of Li2 potential curves

Potential curves are calculated for the lithium molecule using an effective valence shell Hamiltonian formulation of quasidegenerate many‐body perturbation theory and two different sets of molecular orbitals. One set utilizes the low lying valence molecular orbitals which are optimized for particular valence states, while the other set is simply taken as the union of the atomic valence sets. The shapes of the potential curves for the lowest four states (1Σ+g,3Σ+u,3Πu, and 1Σ+u) are in excellent agreement with those obtained by Olson and Konowalow from extensive MCSCF calculations and hence with experiments. The total energies are high by about 0.1 a.u. because our basis set does not describe the core electrons as well. The perturbation expansion is found to display excellent convergence properties between the second and third order calculations. A future paper will compare the bond length dependence of the effective matrix elements with those customarily assumed in semiempirical theories of bonding.

First principles test of transferability hypothesis of semi-empirical theories using correlated ab initio effective valence shell hamiltonian methods

Abstract Ab initio effective valence shell hamiltonian ( v ) calculations for CH, NH and OH are utilized to test the transferability of one-center v integrals between the hydrides and the C, N and O atoms as well as to investigate the transferability hypothesis of traditional semi-empirical theories which introduce model hamiltoruans v to mimic v .

Effective many-body interactions in exact valence-shell hamiltonians

Abstract The theoretical many-body structure of the exact effective valence-shell hamiltonian ( H V ) is analyzed to derive experimentally observable values of many-electron effective interactions for the [2s, 2p] H V of N, O, and F, and the [2p] H V of F. Unique experimental values are presented for four-, five-, and six-electron effective integrals.