Uzi Kaldor

Diagrammatic many-body perturbation theory for general model spaces

Previous formulations, due to Brandow (1977) and subsequent authors, are limited to complete model spaces, including all possible occupations of open-shell orbitals. This definition of the model space may be troublesome for systems with several open shells, such as most molecular excited states, leading to intruder states and slowing or even destroying the convergence of the perturbation series. The formalism presented here applies to any model space, whether complete or incomplete, degenerate, quasi-degenerate or non-degenerate. Certain types of unlinked diagrams may appear for incomplete, quasi-degenerate model spaces. The orbitals are partitioned into two classes (holes and particles) for the purpose of diagram summation instead of Brandows three (core, valence and particles), with the partitioning for a particular element of the effective interaction matrix determined by the ket state of that element.

The Fock space coupled cluster method: theory and application

SummaryThe Fock space coupled cluster method and its application to atomic and molecular systems are described. The importance of conserving size extensivity is demonstrated by the electron affinities of the alkali atoms. Two types of intruder states are discussed, one attributable to the orbital energy spectrum and the other caused by two-electron interactions. They are illustrated by the excited states of Li2 and by1S states of Be, respectively. It is shown how both problems may be solved using incomplete model spaces. The selection of the model space in a moderately dense spectrum is discussed in connection with N2 excited states.

Formulation and implementation of the relativistic Fock-space coupled cluster method for molecules

An implementation of the relativistic multireference Fock-space coupled cluster method is presented which allows simultaneous calculation of potential surfaces for different oxidation states and electronic levels of a molecule, yielding values for spectroscopic constants and transition energies. The method is tested in pilot calculations on the I2 and HgH molecules, and is shown to give a good and balanced description of various electronic states and energies.

Open-shell coupled-cluster theory applied to atomic and molecular systems☆

Abstract The open-shell coupled-cluster method is applied to 21 states of C, O, O 2 and their ions. Only two-electron excitations ( T 2 ) are taken into account. Good agreement with experiment (better than 0.2 eV) is obtained for the ten excitation energies and seven of the eight ionization potentials calculated, the only exception being neutral O. It is conjectured that the omission of T 3 is responsible for this error.

The open‐shell coupled‐cluster method: Excitation energies and ionization potentials of H2O

The open‐shell coupled cluster method is used to calculate directly several electronic excitation energies and ionization potentials of the water molecule. Correlation effects are included by summing single and double virtual excitations to infinite order. Triple excitations are treated approximately, to the lowest order they appear. Their contribution is significant, 0.2–0.4 eV for excitation energies and 0.5–0.7 eV for ionization potentials. The calculated energies are in good agreement (∼0.15 eV) with experiment.

Intermediate Hamiltonian Fock-space coupled-cluster method: Excitation energies of barium and radium

An intermediate Hamiltonian Fock-space coupled cluster method is introduced, based on the formalism developed by Malrieu and co-workers in the context of perturbation theory. The method is designed to make possible the use of large P spaces while avoiding convergence problems traceable to intruder states, which often beset multireference coupled cluster schemes. The essence of the method is the partitioning of P into a main Pm and an intermediate Pi serving as buffer, with concomitant definition of two types of wave and excitation operators. Application to atomic barium and radium yields converged results for a large number of states not accessible by traditional Fock-space coupled cluster. Moreover, states calculated by both methods exhibit better accuracy (by a factor of 2–5) in the intermediate Hamiltonian approach. Energies are given for low-lying states of Ra which have not been observed experimentally.

Three-electron excitation in open-shell coupled-cluster theory

Abstract The three-electron excitation operator T 3 is included approximately in the coupled-cluster method with single and double excitations for open shells (CCSD). The resulting CCSD + T scheme incorporates all energy diagrams up to and including third order in the perturbation. All ten valence-shell energy differences of O and its ions were calculated. They show significant effects of T 3 and are within 0.1 eV of the basis set limit.

LCAO‐SCF Computations for Ethylene

A series of LCAO‐SCF calculations with a minimal Slater basis set were carried out for the ethylene molecule and for its positive and negative monovalent ions in a number of electronic states. These computations, which included configurational mixing of the two low 1A states, were performed for seven values of the twist angle between the two CH2 groups, from 0° to 90°. For planar ethylene four singlet levels, two triplets, and two doublets of each of the ions, were investigated. The two 1Ag states, the triplets, and the ionic doublets were individually computed (with open‐shell SCF procedures where applicable), while their energies, as well as those of the other singlets, were also derived from the data of the closed‐shell calculations. This individual SCF optimization was found to have only limited effect in the case of the neutral molecule, but was more significant for the ions. The energy obtained for the planar ground state, though lower than that of a 40‐function Gaussian calculation, is considerably...

A General-Model-Space Diagrammatic Perturbation Theory

A diagrammatic many-body perturbation theory applicable to arbitrary model spaces is presented. The necessity of having a complete model space (all possible occupancies of the partially-filled shells) is avoided. This requirement may be troublesome for systems with several well-spaced open shells, such as most atomic and molecular excited states, as a complete model space spans a very broad energy range and leaves out states within that range, leading to poor or no convergence of the perturbation series. The method presented here would be particularly useful for such states. The solution of a model problem (He2 excited Σg+ states) is demonstrated.

Theoretical chemistry and physics of heavy and superheavy elements

1 Theoretical Chemistry and Physics of Heavy and Superheavy Elements.- 2 Basic elements of relativistic quantum mechanics.- 3 The Chemistry of the Heaviest Elements.- 4 Core and valence electron distributions in heavy elements by x-ray and electron spectroscopy.- 5 Four-component electronic structure methods for atoms.- 6 Four-component electronic structure methods for molecules.- 7 Relativistic electron correlation theory.- 8 Matrix Approximations to the Dirac Hamiltonian for Molecular Calculations.- 9 Two-component methods.- 10 Relativistic Pseudopotentials.- 11 Relativistic Density Functional Theory.- 12 QED effects in atoms.