Journal of Physics B Atomic Molecular and Optical Physics

On the generalized multi-reference Brillouin-Wigner coupled cluster theory

Ivan Hubač, Stephen S. Wilson

Published Oct 31, 2001• 24 citations

Abstract

The generalized multireference Brillouin-Wigner coupled cluster theory is presented for the case of a single root function. The Bloch-like equation and the Lippmann-Schwinger-like equation for the generalized multireference Brillouin-Wigner perturbation theory are obtained. These equations are then applied to the solution of the multireference coupled cluster equations for the case in which a single root function is required.

DOI: 10.1088/0953-4075/34/21/314

Related papers

Size-consistent Brillouin-Wigner perturbation theory with an exponentially parametrized wave function: Brillouin-Wigner coupled-cluster theory

Ivan Hubač, Pavel Neogrády

Size consistency of the Brillouin-Wigner perturbation theory is studied using the Lippmann-Schwinger equation and an exponential ansatz for the wave function. Relation of this theory to the coupled cluster method is studied and a comparison through the effective Hamiltonian method is also provided.

Physical Review ADec 1, 199483 citations

Brillouin–Wigner coupled cluster theory. Fock-space approach

Nicholas D. K. Petraco, Ľuboš Horný, Henry F. Schaefer +1 more

The generalization of coupled cluster (CC) theory is far from being a standard method to account for correlation effects of ubiquitous open-shell systems. This dilemma is largely due to three problems. The first concerns the incorporation of multiple reference “guess” wave functions into nonvariational theories. Next is the size-extensivity issue. Finally, and perhaps most importantly is the notorious intruder state problem. Brillouin–Wigner (BW) and generalized Brillouin–Wigner (gBW) perturbation theories are used to aid in the development of new Fock-space coupled cluster theories in an attempt to alleviate some of these problems. Bloch equations are derived which can be used to formulate BWCC and gBWCC theories of arbitrary dimension in all sectors of Fock space. Since this is our first study of Brillouin–Wigner coupled cluster theories in Fock space we have chosen to keep our approach very simple. Explicit effective Hamiltonian and amplitude equations for up to two-body S-amplitudes in the (0,1) and (1,0) sectors are given for the single reference case. Aspects concerning the connectivity of the amplitude equations are addressed.

The Journal of Chemical PhysicsNov 14, 200219 citations

Many‐body Brillouin–Wigner second‐order perturbation theory: A robust and efficient approach to the multireference correlation problem

Péter Papp, P. Mach, Ivan Hubač +1 more

Abstract The multireference, state‐specific, second‐order, Brillouin–Wigner perturbation theory is presented as a robust approach to the electron correlation problem for systems demanding the use of a multireference function. A posteriori modifications are made which, in the case of a single reference function, recover the well known formula of second‐order many‐body perturbation theory (MBPT2), i.e. Møller–Plesset (MP2) theory, and in the multireference case can be shown to be equivalent to state‐specific multireference Rayleigh–Schrödinger‐like perturbation theory. It is shown that multireference many‐body Brillouin–Wigner perturbation theory when restricted to second‐order is a true many‐body theory, that is, it is a theory, which has the property of extensivity. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

International Journal of Quantum ChemistryJan 1, 200715 citations

Multireference Brillouin-Wigner coupled-cluster theory Hilbert space formulation

Jozef Mášik, Ivan Hubač

Jan 1, 19960 citations

Coupled-cluster method for multideterminantal reference states

Bogumił Jeziorski, Hendrik J. Monkhorst

A general coupled-cluster method valid for arbitrary multideterminantal reference states is formulated. The resulting cluster expansion for the wave function is a generalization of that introduced by Silverstone and Sinano\ifmmode \check{g}\else \v{g}\fi{}lu and applied by Sinano\ifmmode \check{g}\else \v{g}\fi{}lu and collaborators. The connected nature of the cluster operators and the effective interaction is proven in the case when the reference space is complete, i.e., is invariant under unitary transformations of partly occupied orbitals. For incomplete reference spaces the disconnected terms appearing in the effective interaction are properly generated by the coupled-cluster theory. Approximate schemes for solving coupled-cluster equations are proposed and their relation with perturbation theory is briefly discussed.

Physical Review AOct 1, 1981873 citations

Coupled-cluster approach to the many-body perturbation theory for open-shell systems. [Bloch equation]

Ingvar Lindgren

A new approach to the diagrammatic formulation of many-body perturbation theory for open-shell systems is presented. The formalism is based on a generalized form of the Bloch equation that also generates the Rayleigh--Schroedinger perturbation expansion for a system with several open shells. Second quantization in the particle-hole formulation is used together with Wick's theorem in order to derive graphical rules in the usual way. The linked-diagram property of the wave operator and of the effective interaction is shown by expanding the wave operator in terms of normal products of connected diagram clusters, in analogy with the exp(S) formalism of Coester and Kuemmel for closed-shell systems. Self-consistent coupled-cluster equations are derived for the open-shell case from the generalized Bloch equation by a straightforward extension of the procedure of Cizek and Paldus. The application of such equations for investigating different properties of open-shell atoms is discussed. 56 references.

Mar 1, 19780 citations