Physical Review A

Analysis of coupled-cluster methods for first-order static properties

Sourav Pal

Published Apr 1, 1986• 45 citations

Abstract

An analysis of some of the coupled-cluster methods has been undertaken for the calculation of first-order properties. In particular, it has been shown that Arponen's variational extended exp(T) method truncated to the quadratic power in the cluster amplitudes gives a result identical to the average value of the property operator with the linearized coupled-cluster doubles (L-CCD) stationary state truncated to the quadratic power in amplitudes in the model where only two-body excitations have been included in the cluster amplitudes. In the same model it is also shown that Monkhorst's nonvariational method gives results identical to the previously mentioned average value again truncated to the quadratic power in amplitudes with a full CCD stationary-state wave function.

DOI: 10.1103/physreva.33.2240

Related papers

Linearized bivariational coupled-cluster approach: General scheme for derivation of static properties

Sourav Pal

The recently developed bivariational coupled-cluster approach was earlier used for the derivation of equations for first-order properties in a two-body approximation. In this paper we introduce a linearized form of this approach in which the bra vector is linearized. In such a form the bivariational coupled-cluster approach reduces to the nonvariational-response-type approach, and thus it can also be more easily generalized to any higher-order property in a more extended approximation. This also gives us an alternative variational derivation of the original nonvariational-response equations of Monkhorst.

Physical Review AMar 1, 198911 citations

Coupled-cluster singles and doubles for extended systems

So Hirata, Rafał Podeszwa, Motoi Tobita +1 more

Coupled-cluster theory with connected single and double excitation operators (CCSD) and related approximations, such as linearized CCSD, quadratic configuration interaction with single and double excitation operators, coupled-cluster with connected double excitation operator (CCD), linearized CCD, approximate CCD, and second- and third-order many-body perturbation theories, are formulated and implemented for infinitely extended one-dimensional systems (polymers), on the basis of the periodic boundary conditions and distance-based screening of integrals, density matrix elements, and excitation amplitudes. The variation of correlation energies with the truncation radii of short- and long-range lattice sums and with the number of wave vector sampling points in the first Brillouin zone is examined for polyethylene, polyacetylene, and polyyne, and is shown to be a function of the degree of pi-electron conjugation or the fundamental band gaps. The t2 and t1 amplitudes in the atomic orbital (AO) basis are obtained by first computing the t amplitudes in the Bloch-orbital basis and subsequently back-transforming them into the AO basis. The plot of these AO-based t amplitudes as a function of unit cells also indicates that the t2 amplitudes of polyacetylene and polyyne exhibit appreciably slower decay than those of polyethylene, although the asymptotic decay behavior is invariably 1/r3. The AO-based t1 amplitudes appear to correlate strongly with the electronic structure, and they decay seemingly exponentially for polyethylene whereas they stay at a constant magnitude across the seventh nearest neighbors of polyacetylene and polyyne, which attests to far reaching effects of nondynamical electron correlation mediated by orbital rotation. Nonetheless, the unit cell contributions to the correlation energies taper below 10(-6) hartree after 15 A for all three polymers. The basis set dependence of the decay behavior of t2 amplitudes is also examined for linear hydrogen fluoride polymer (HF)infinity and linear beryllium polymer (Be)infinity employing the STO-3G, 6-31G, and 6-31G* basis sets, and proves to be rather small.

The Journal of Chemical PhysicsFeb 4, 2004162 citations

Analysis of coupled-cluster methods for higher-order static properties

Sourav Pal, Keya Basu Ghose

In this paper we present a useful analysis for higher-order static properties involving three different response approaches based on coupled-cluster methods, namely, the nonvariational, the variational and the more recent bivariational methods.

Physical Review AFeb 1, 19929 citations

An Alternative Algebraic Framework for the Simplification of Coupled Cluster Type Expectation Values

Daniel Pape

The Coupled-Cluster (CC) method is one of the most popular and efficient correlation methods in quantum chemistry. \nEspecially the CCSD(T) approximation, which includes single and double excitations by means of the application of the cluster operator \nto a reference determinant and triple excitations via a perturbative treatment, has become a standard tool \nin quantum chemical applications. However, the method is restricted to relatively small system sizes due to its unfavourable scaling (N^7, where N is the number of basis functions applied). \nFor the full treatment of triple excitations the scaling advances to N^8 and every further excitation level increases the exponent by two. \n \nThe goal of this work is to reduce the calculation time for closed shell systems at least by a factor growing with the excitation level for arbitrary truncation levels. \nThis is done by restricting the spatial parts of the spin orbitals and thus treat pairs of spin orbitals on the same footing. The restrictions can be easily constructed \nfor the CCSD model by spin integration. \nThe derivation of the restrictions arising in higher excited case will be done employing \nthe spatial orbital excitation operators E. \n \nIn the first part of this work an algorithm is derived that is capable of the derivation of the energy and amplitude equations for arbitrary excitation levels. In the second part \nan implementation of this algorithm is presented.

Nov 12, 20130 citations

The extended coupled cluster method and the pairing problem

Chris Snape, Niels R. Walet

We study the application of various forms of the coupled cluster method to systems with paired fermions. The novel element of the analysis is the study of the breaking and eventual restoration of particle number in the CCM variants. We specifically include Arponen's extended coupled cluster method, which describes the normal Hartree-Fock-Bogoliubov mean field at lowest level of truncation. We show that all methods converge to the exact results as we increase the order of truncation, but that the breaking of particle number at an intermediate level means that this convergence occurs in a surprising way. We argue that the most straightforward form of the method seems to be the most stable approach to implement for realistic (large number of particles) pairing problems

arXiv:1011.5146Nov 23, 20100 citations

Coupled-cluster response approach: Improved variational strategy

Sourav Pal

In this paper we discuss an improved strategy for variational versions of the coupled-cluster response approach for the study of static properties. This takes care of different truncation levels for the cluster amplitudes and their derivatives required for this calculation.

Physical Review AOct 1, 199022 citations