Showing papers on "Coupled cluster published in 1980"

Molecular Applications of Coupled Cluster and Many-Body Perturbation Methods

Abstract: A series of molecular applications of many-body perturbation theory (MBPT) and the coupled-cluster doubles (CCD) model are described. Even though these methods have been available for sometime, only recently have large scale, MBPT molecular calculations become available. In the case of CCD, the results presented here are among the first obtained from a general purpose ab initio program. The intention of this paper is to present an overview of the current state of the many-body approach to ground state properties of molecules. The properties studied are correlation energies, including contributions from single, double, and quadruple excitations diagrams in fourth-and higher-order; dissociation energies; potential energy surfaces; and molecular polarizabilities and hyperpolarizabilities. Examples are taken from studies of a variety of molecules including HF, H2O, HCO, C6H6, B2H6, CO2, and N2. In many cases, it is found that quantitatively accurate dissociation energies, geometries, and force constants can be obtained. In an illustration of the X1Σg+ potential energy curve of N2, it is shown that a single UHF or RHF reference function MBPT/CCD approach is inadequate at some internuclear separation.

Coupled Cluster Approach

Abstract: A brief overview concerning the motivations and the development of the coupled cluster approach to the many-electron correlation problem for both closed and open shell systems is given. The basic characteristics and applications of this approach are briefly summarized as well as its relationship to other approaches.

A Numerical Coupled-Cluster Procedure Applied to the Closed-Shell Atoms Be and Ne

Abstract: A coupled-cluster procedure, applicable to closed-shell as well as open-shell atoms, is described, and results from calculations on the closed-shell atoms Be and Ne are presented. The procedure is based on numerical solution of coupled radial pair equations, which can be iterated to self-consistency. The coupling between different pair excitations is considered in two steps. The first step, called intra-shell coupling, includes the interaction between excitations differing in the final states as well as in the mlms values of the electrons being excited. In the second step, the inter-shell coupling, also the residual interaction between excitations involving different nl shells is considered. While the former coupling is quite important, it has been found that the latter contributes only about 1% to the correlation energy. Single and triple excitations are neglected in the present work, but quadrupole excitations are included by means of the exponential ansatz of the coupled-cluster procedure. According to our results for Be, 98.6% of the experimental correlation energy is obtained with complete pair-pair coupling, which is consistent with the estimated value of about 1.5% for the contribution of single and triple excitations. With only intra-shell coupling the result is in almost exact agreement with the experimental value due to cancellations between single/triple excitations and inter-shell couplings. Similar results are obtained for Ne. The results of the present work are compared and discussed in relation to earlier many-body calculations on these systems.

Molecular polarons and valence fluctuations in Fe3O4

Abstract: We propose a ‘molecular polaron’ model which describes the properties of valance fluctuations in Fe3O4 above the Verwey transition temperature. The molecular polaron is dynamically coupled cluster, or a vibronic state associated with two electrons in four-site molecular orbitals coupled to local vibrational modes with T2g symmetry. The lifetime of a molecular polaron is assumed to be long enough to induce a strain field around it. That is, each molecular polaron is considered to be ‘dressed’ by an instantaneous strain field. Based on this model, neutron Huang scattering due to the strain field around independent molecular polarons has been calculated. The observed patterns of neutron diffuse scatteringagree quite well with the calculated patterns, which seems to ensure the validity of the proposed model.

Application of linear response function theory in a coupled-cluster framework

Abstract: (1980). Application of linear response function theory in a coupled-cluster framework. Molecular Physics: Vol. 39, No. 2, pp. 519-524.

An alternative definition of the electron propagator in the superoperator form and its relation to linear response theory in a coupled-cluster framework

Abstract: In this paper it is shown that (i) there exists an alternative definition of the superoperator resolvent for calculation of difference energy satisfying linked cluster theorem for a coupled-cluster choice of the ground-state function which may even be approximate; (ii) the pole-structure of this propagator-like function in superoperator form is shown to contain information similar to that contained in the conventional propagator. (iii) It is demonstrated that suitable “Killer conditions” and completeness of the “operator manifold”—essential for understanding the pole-structure of the propagator—can be established both for an exact and an approximate ground state function in a coupled-cluster form. (iv) It is also demonstrated that difference energies calculated with these propagator-like functions are identical to those obtained from a linear response theory in a coupled-cluster form put forward recently by Mukherjeeet al and Monkhorst.

The Unitary Group Formulation of the Many-Electron Problem

Abstract: The unitary group formulation is a viable alternative to the Slater determinant and second quantized methods when the Hamiltonian is spinfree. Here the Hamiltonian is expressed as a second degree polynomial in the infinitesimal generators of U(ρ) where p is the number of spatial (spin-free) orbitals. Each irreducible space of U(ρ) is invariant under this Hamiltonian and is uniquely characterized by a Young diagram which, for the Pauli allowed spaces, supplies both particle and spin quantum numbers. Each irreducible space is spanned by a set of orthonormal Gel’fand states and the Hamiltonian matrix elements are conveniently calculated by the graphical unitary approach (GUGA). The many-body approximation theories (single and multiconfiguration restricted Hartree Fock, RPA, perturbation, coupled cluster and effective Hamiltonian theories) have been given a unitary group formulation