Michael F. Herman

Abinitio effective valence shell Hamiltonian for the neutral and ionic valence states of N, O, F, Si, P, and S

The effective valence shell Hamiltonian, Hv, which acts within a finite valence space and exactly describes all the valence state energies, is applied to several atomic systems. The n=2 (L shell) Hv of the first row atoms, N, O, and F and n=3 (M shell) s and p orbital Hv of the second row atoms, Si, P, and S, are evaluated through second order using STO 5s4p2d and 6s5p3d basis sets, respectively. The calculations are equivalent to a (perturbative) Bk approximation which incorporates all excited configurations and which chooses the primary (valence) space as all the valence K2(2s)m(2p)n and K2L6(3s)m(3p)n configurations, respectively. Using the calculated matrix elements of Hv, the energies of all the valence states of the neutrals and ions are simultaneously determined from a single ab initio calculation on only one charge state of each of these atomic systems. To understand the dependence of Hv on the choice of core and valence orbitals, several sets of orbitals, obtained within the same primitive orbita...

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.

Shake-up peak positions and intensities by many-body theory methods

Abstract The valence shell X-ray photoelectron spectrum of N 2 is calculated using the equations-of-motion—Greens function method. The inclusion of shake-up basis operator configurations in the primary operator space along with the simple ionization operator configurations allows for the calculation of shake-up peak positions on an equal footing with the simple ionization energies. The important shake-up basis operator configurations are identified using configuration selection techniques similar to those which have been successfully employed in large scale configuration interaction problems, thus minimizing the size of the matrices to be diagonalized. The relative peak intensities are calculated within the plane wave approximation. The intensity equations are analyzed indicating that the relative peak intensities are more sensitive to ground state correlation effects than the peak positions. Modifications of the theory to improve the calculations of shake-up energies are discussed.

Critical analysis of equations-of-motion—Green's function method: Ionization potentials of N2

The X ^2Σ^+_g, B ^2Σ^+_u and A ^2Π_u ionization potentials of N_2 are evaluated with the equations-of-motion (EOM)—Greens function method using four different basis sets and various forms of symmetrization. The importance of the inclusion of polarization functions is demonstrated as well as the necessity for having a basis which strikes a balance between those optimal for the neutral and ion states. With our best basis the calculated ionization potentials are within 0.35 eV of experimental values, and the results are of comparable accuracy to those obtained by Ermler with the same basis in a configuration interaction calculation with all singles and doubles with respect to the principal configuration for both the neutral and ion states.

Ab initio calculation of the effective valence shell hamiltonian of carbon: Simultaneous treatment of neutral and ion states

Abstract The n = 2 effective valence shell hamiltonian, H v , of carbon is evaluated through second order using 3 P Hartree—Fock orbitals (5s4p) with added d functions to provide results within a few percent of the spd convergence limits. The calculated H v is employed to evaluate the n = 2 valence states of C, C − , C + , C 2+ and C 3+ with an average deviation of the 21 excitation energies, ionization potentials and electron affinity from experimental values of 0.32 eV. Three-electron parts of H v contribute substantially to a number of these excitation energies.

Critical test of equation‐of‐motion–Green’s function methods. II. Comparison with configuration interaction results

A detailed comparison is presented between calculated equation‐of‐motion (EOM) ionization potentials and electron affinities and highly converged configuration interaction (Cl) results for a variety of atomic and molecular systems. Since an exact EOM calculation and a full Cl calculation within the same orbital basis set must yield identical results, this type of study allows for the separation of errors due to the approximations employed in solving the EOM equations from those errors arising from the use of an incomplete orbital basis set. The convergence of the EOM calculations at different levels of approximation is also investigated for these same systems. Important EOM basis operators, involving ionization and excitation (shakeup operators) or ionization and de‐excitation, are numerically identified by configuration selection routines and are diagonalized rather than treated perturbatively. Terms involving second order couplings (arising from ground state correlation) between these shakeup states are...

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 .

Critical test of equation‐of‐motion–Green’s function methods. I. Theory of higher order terms

The equation‐of‐motion–Green’s function method for calculating ionization potentials is analyzed within the framework of a linear matrix eigenvalue representation, and an extended form of the theory is developed. The utility of the modifications presented in this paper is strongly suggested by recent numerical studies which successfully employ a generalized definition of the primary operator space in analogy with configuration selection procedures that have proven useful in configuration interaction calculations. The basic theoretical questions are associated with the choice of the basis operators for the primary space and the approximations to be employed in the evaluation of the individual matrix elements. This extended form of the theory incorporates the lowest order effects of ground state correlation on matrix elements between the shakeup basis operators in the primary operator space. A first approximation to the contributions of basis operators involving ionization and double excitation or ionizatio...

Analysis of approximations and errors in equations of motion method calculations

Abstract We analyze a number of fundamental questions associated with the use of a finite one-particle orbital basis in equations of motion (EOM) method calculations of excitation energies etc., of atomic and molecular systems. This approximation yields an approximate n e -electron ground state and say, N excited states, while there are ( N + 1) 2 different possible basis operators for EOM calculations. We show that sets of at most 2 N basis operators can contribute to the EOM calculations. Any set of 2 N basis operators, satisfying certain conditions, provides the exact EOM energies which are equivalent to complete configuration interaction results within the same orbital basis. We investigate the use of particle-particle shifting operators which are not employed in EOM calculations in model calculations on He with operator bases smaller than the complete 2V to consider the convergence of the expansion. The dependence of EOM calculations on the quality of the approximate ground state wavefunction is studied through calculations for Be where additional support is provided for the frequent need for multiconfigurational zeroth order reference functions (as corrected perturbatively). Excited state EOM wavefunctions from EOM calculations are shown to not necessarily be orthogonal to either the exact or approximate ground state wavefunction, suggesting implications in the use of EOM methods to evaluate excited state properties. The He and Be examples and a simple two-level problem are also utilized to illustrate questions concerning the use of the EOM equations to obtain an iteratively improved ground state wavefunction.

Critical Comparison Between Equation of Motion-Green's Function Methods and Configuration Interaction Methods: Analysis of Methods and Applications

A description is provided of the common conceptual origins of many-body equations of motion and Greens function methods in Liouville operator formulations of the quantum mechanics of atomic and molecular electronic structure. Numerical evidence is provided to show the inadequacies of the traditional strictly perturbative approaches to these methods. Nonperturbative methods are introduced by analogy with techniques developed for handling large configuration interaction calculations and by evaluating individual matrix elements to higher accuracy. The important role of higher excitations is exhibited by the numerical calculations, and explicit comparisons are made between converged equations of motion and configuration interaction calculations for systems where a fundamental theorem requires the equality of the energy differences produced by these different approaches.