Coupled cluster

About: Coupled cluster is a research topic. Over the lifetime, 6280 publications have been published within this topic receiving 301055 citations.

Coupled Cluster Theory

Abstract: The necessity to account for many-electron correlation effects in atomic and molecular electronic structure calculations was realized in the sixties, when the first attempts to compute dissociation or activation energies of simple chemical processes (e. g., Wahl, 1964; Schaefer, 1971, 1972) and various molecular properties (e. g., Huo, 1965) were made. The initial hope that the configuration interaction (CI) approach limited to doubly excited configurations, originating from a single reference state, will provide a satisfactory description of correlation effects soon had to be given up (see, e. g., Bender and Davidson, 1968, 1969; Barr and Davidson, 1970; Davidson, 1974). By that time the basic structure of correlated wavefunctions (Hubbard, 1957, 1958) and the problem of size extensivity (Brueckner, 1955; Goldstone, 1957; Primas, 1965) were well understood [although this term was employed only later (Bartlett and Purvis, 1978)], thanks to the developments in solid state (e. g., Gell-Mann and Brueckner, 1957; Quinn and Ferrell, 1958) and nuclear (e. g., deShalit and Feshbach, 1974; Eisenberg and Greiner, 1972) physics. In particular, the linked cluster theorem of the many-body perturbation theory (MBPT) and the connected cluster structure of the exact wavefunctions (Hubbard, 1958b) were firmly established. The exponential ansatz for the wave operator, implied by Hubbard’s (1958b) work, was exploited in the context of the nuclear correlation problem by Coester (1958) and Coester and Kummel (1960).

Assessment of the single-root multireference Brillouin–Wigner coupled- cluster method: Test calculations on CH2, SiH2, and twisted ethylene

Abstract: Recently developed single-root multireference Brillouin–Wigner coupled-cluster (MR BWCC) theory, which belongs to a broad family of state-selective multireference coupled-cluster methods, has been implemented in the ACES II program package at the CCSD level of approximation. The method represents a new approach to quasidegenerate problems, which is able to continuously switch between the single-reference CC in a nondegenerate situation and the Hilbert-space MRCC in a degenerate case. An assessment of the method has been carried out by means of a comparison with the full configuration interaction (CI) treatments of CH2, SiH2, and twisted ethylene diradicals. The problem of size-extensivity is discussed.

Many‐body methods for excited state potential energy surfaces. I. General theory of energy gradients for the equation‐of‐motion coupled‐cluster method

Abstract: The formal theory is presented for calculating the analytic first derivative of the energy with respect to arbitrary perturbations within the equation‐of‐motion coupled‐cluster (EOM‐CC) approximation. Through use of the Dalgarno–Stewart interchange theorem (Z‐vector method), terms involving derivatives of the ground state cluster amplitudes are eliminated, leading to the definition of a new quasiparticle de‐excitation operator which simplifies the theory and significantly reduces the expected cost associated with studying potential energy surfaces for excited electronic states. For both illustrative and pragmatic reasons, the final equations are cast in a form similar to that developed for ground state CC energy derivatives, involving contraction of effective one‐ and two‐particle density matrices with matrix elements of the differentiated Hamiltonian. Some aspects regarding calculation of the gradient are discussed with particular attention devoted to similarities between the structure of the present formulas and those which have been previously implemented for the ground state problem.

Approximately extensive modifications of the multireference configuration interaction method: A theoretical and practical analysis

Abstract: The extensivity error of configuration interaction (CI) is well understood and unlinked diagram corrections must be applied to get reliable results. Besides the well known a posteriori Davidson‐type corrections, several methods attempt to modify the CI equations a priori to obtain nearly extensive results, while retaining the convenience of working in a configuration space. Such unlinked diagram corrections are particularly important for multireference cases for which coupled‐cluster (CC) calculations, which require a many‐body, integral‐based calculation, are more difficult. Several such multireference methods have been presented recently, ranging from the multireference linearized coupled cluster method (MR‐LCCM), averaged coupled pair functional (MR‐ACPF), through various quasidegenerate variational perturbation theory (QD‐VPT), MR‐coupled electron pair method (MR‐CEPA) to size‐consistent, self‐consistent, selected CI [(SC)2SCI]. We analyze all of these methods theoretically and numerically, paying par...