Showing papers on "Coupled cluster published in 1985"
TL;DR: In this article, the effects of single, double, and triple excitation operators on electron correlation were analyzed and an alternate version of the approximate CCSDT•1 method was implemented.
Abstract: Coupled cluster models for electron correlation which include the effects of single, double, and triple excitation operators are analyzed. An alternate version of the approximate CCSDT‐1 method is implemented. In this version, the full CCSDT cluster operator eT1+T2+T3 is preserved in the creation of single and double excitation coefficients, but in calculation of triple excitation coefficients only the T2 operator is used. We also present a theoretical analysis of the simplest improvement for the evaluation of the contribution of triples beyond that obtained with fourth‐order MBPT. In this approximation, an MBPT(4)‐like calculation of the triples energy is evaluated with converged CCSD T2 coefficients. This is found to offer a good approximation to the converged CCSDT‐1 results.
822 citations
TL;DR: In this paper, an augmented coupled cluster scheme was proposed to evaluate the higher order electron correlation effects, which is correct to fourth order in a perturbation expansion and includes significant fifth and higher order terms.
Abstract: An augmented coupled cluster scheme to evaluate the higher order electron correlation effects is proposed. The method is carried out in two steps. First, a coupled cluster calculation with all double substitutions (CCD) is performed. The converged CCD wave function is then used in the evaluation of the contribution of single and triple substitutions. The method is correct to fourth order in a perturbation expansion and includes significant fifth and higher order terms. Illustrative calculations on the excitation and dissociation energies of first‐row homonuclear diatomic molecules are reported. The low‐lying excitation energies of B2 and C2 are accurately calculated. The dissociation energies of B2, C2, N2, O2, and F2 are all uniformly underestimated by 0.1–0.3 eV using large spdf basis sets.
150 citations
130 citations
TL;DR: With the help of a newly developed program for the solution of the coupled-cluster doubles (CCD) equation, the use of localized orbitals has been tested as mentioned in this paper, and the results show that the use can be used to solve the CCD problem.
120 citations
TL;DR: In this paper, the open-shell coupled-cluster method is applied to 21 states of C, O, O 2 and their ions, and 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.
118 citations
TL;DR: The coupled-cluster or exp S formalism, where the wave operator is expressed in exponential form, is treated for a general, multi-Configurational model space in this article.
Abstract: The coupled-cluster or exp S formalism, where the wave operator is expressed in exponential form, is treated for a general, multi-Configurational model space. It is shown that the cluster operator, S, is rigorously connected when the model space is complete or "quasi-complete" in the sense that it contains all configurations that can be formed by distributing the valence electrons within certain groups of valence orbitals with given occupation number in each group. For this class of model spaces also the linked-diagram theorem is valid in the sense that the diagrams of the wave operator and the effective Hamiltonian do not contain any separate, closed part. The diagrams of the effective Hamiltonian are connected, while those of the wave operator may contain disconnected, open parts. For a more general, multi-configurational (incomplete) model space a formal expansion of coupled-cluster type is still possible, but it is found that the cluster operator is no longer necessarily connected, which leads to unlinked diagrams in the expansion of the wave operator and the effective Hamiltonian. A general procedure for generating the cluster operator in this case is described and applied particularly in the pair approximation.
103 citations
TL;DR: In this article, the three-electron excitation operator T 3 was included approximately in the coupled-cluster method with single and double excitations for open shells (CCSD) and the resulting CCSD + T scheme incorporates all energy diagrams up to and including third order in the perturbation.
94 citations
79 citations
73 citations
TL;DR: In this article, the electron affinities of boron, carbon, oxygen, and fluorine atoms have been evaluated by Mo/ller-Plesset perturbation calculations through complete fourth order using several large basis sets.
Abstract: The electron affinities of boron, carbon, oxygen, and fluorine atoms have been evaluated by Mo/ller–Plesset perturbation calculations through complete fourth order using several large basis sets. The convergence of the perturbation series has been evaluated carefully by means of modified coupled cluster methods. Large basis sets and electron correlation effects involving higher substitutions are found to be important in the accurate calculation of electron affinities. Triple substitutions are particularly important in the correlation treatment, contributing more than 0.2 eV to the electron affinities of O and F. The electron affinities of all the systems are calculated to be within 0.1 eV of the corresponding experimental values.
65 citations
TL;DR: In this article, the generalized coupled-cluster (CC) method is cast into the form of the Brueckner-Hartree-Fock (BHF) method.
Abstract: The generalized coupled-cluster (CC) method of the preceding paper is cast into the form of the Brueckner-Hartree-Fock (BHF) method. In this approach the model vacuum \ensuremath{\Phi} is optimized to become the maximum-overlap configuration for the reference eigenfunction \ensuremath{\Psi}. One of the approximation schemes of the preceding paper is applied to derive explicit algebraic equations which can be used for practical calculations of (approximate) energies of several states of a many-fermion system. These include the N-particle ground-state energy, energies of some (N-1)- and (N+1)-particle states, as well as energies of certain N-particle excited states. It is indicated that the numerical effort required in the present approach is comparable to that of the coupled-cluster singles and doubles (CCSD) method of Purvis and Bartlett [J. Chem. Phys. 76, 1910 (1982)].
TL;DR: The first derivatives of the coupled-cluster doubles (CCD) energy have been implemented for the first time in this article, where the Hartree-Fock reference case is considered.
TL;DR: In this paper, the ground and excited state electron affinities of LiH and BeO molecules were calculated using a coupled cluster approach and they were found to have an excited state affinity of 0.0028 and 0.0234 eV, respectively.
Abstract: A recently proposed technique, which combines numerical orbitals for diatomic systems with coupled cluster methods, has been applied to study excited states of negative ions of polar molecules. Computational strategy is presented and calculations of ground and excited state electron affinities are reported for the LiH and BeO molecules. LiH and BeO are found to have excited state electron affinities of 0.0028 and 0.0234 eV. Both excited state affinities should be amendable to experimental determination.
TL;DR: The role of electron correlation effects on the bond-length alternation in linear metallic systems, as modeled by cyclic polyenes CNHN, N = 2n = 4v + 2, v = 1,2,…, is examined using the coupled cluster approach in the localized Wannier basis formalism as discussed by the authors.
Abstract: The role of electron correlation effects on the bond-length alternation in linear metalliclike systems, as modeled by cyclic polyenes CNHN, N = 2n = 4v + 2, v = 1,2,…, is examined using the coupled cluster approach in the localized Wannier basis formalism. A recently developed approximate coupled pair approach which accounts for connected quadruply excited clusters is employed together with various truncation schemes for the localized doubly-excited cluster components. It is found that for the physical value of the coupling constant, the electron correlation has only a very slight effect on the potential energy curves, yielding almost the same values for both the magnitude of the bond-length alternation and for the stabilization energy relative to the symmetric equidistant structures as the restricted Hartree-Fock theory. This is in contrast to a strongly correlated region where the correlation effects stabilize the undistorted non-alternating structures. Different mechanisms of the bond-length alternation or Peierl's distortion as implied by a simple Huckel Hamiltonian and by the Pariser-Parr-Pople Hamiltonian models are also pointed out.
TL;DR: In this paper, Moller-Plesset perturbation theory to finite order in all terms (MP4(SDTQ)) and to infinite order in selected terms (CCD) is used to examine the importance of higher-order excitations in correlation treatments of the nickel atom.
TL;DR: In this paper, the coupled-cluster doubles method for the calculation of the correlation energy in molecular systems is implemented in an ab initio framework, and the use is described.
TL;DR: General procedures for the application of the nonperturbative coupled cluster method (CCM) are described for one-component boson field theories and this procedure is applied to two-dimensional Phi/sup 4/ field theory.
Abstract: General procedures for the application of the nonperturbative coupled cluster method (CCM) are described for one-component boson field theories. The basis set is optimized first by a Hartree-Bogolubov transformation. Then ''correlations'' are added via the CCM. This procedure is applied to two-dimensional Phi/sup 4/ field theory. The results are very stable outside the critical region.
TL;DR: The CCM is helpful to analyze the structure of the vacuum and to make precise statements about the mass spectrum of superrenormalizable quantum field theories.
Abstract: We construct eigenstates of the (phi/sup 4/)/sub 3/ quantum field theory in the framework of the coupled cluster method (CCM). Therefore the principle of coherence is stressed leading to a description of these states by an infinite set of correlation amplitudes. In the standard form of the CCM the amplitudes obey a hierarchy of coupled nonlinear integral equations containing some poorly defined terms because of ultraviolet divergences. We remove these divergences by a systematic transformation to an equivalent set of amplitudes. No expansion in the coupling constant is therefore required to make the hierarchy well defined. It is possible to find truncation schemes for the transformed amplitudes which are compatible with the requirement of renormalizability. We conclude that the CCM is helpful to analyze the structure of the vacuum and to make precise statements about the mass spectrum of superrenormalizable quantum field theories.
TL;DR: In this paper, the authors employ a Slater basis and introduce infinite-order effects of triple excitations with the CCSD + T (CCSD) model. But the results of the triple excitation calculations reveal a large discrepancy between fourth-order and infiniteorder results.
TL;DR: In this article, the authors report the first ab initio molecular applications of linear response theory in the coupled-cluster framework for calculating inner and outer valence ionization potentials (IPs).
TL;DR: In this article, the authors derived the cluster coefficients in a full coupled cluster theory involving single, double, and triple cluster operators with respect to an independent particle reference, expressible as a single determinant of spin-orbitals.
Abstract: Equations for the determination of the cluster coefficients in a full coupled cluster theory involving single, double, and triple cluster operators with respect to an independent particle reference, expressible as a single determinant of spin‐orbitals, are derived. The resulting wave operator is full, or untruncated, consistent with the choice of cluster operator truncation and the requirements of the connected cluster theorem. A time‐independent diagrammatic approach, based on second quantization and the Wick theorem, is employed. Final equations are presented that avoid the construction of rank three intermediary tensors. The model is seen to be computationally viable, size‐extensive, high‐level description of electron correlation in small polyatomic molecules.
TL;DR: In this article, a multireference perturbative-variational method was proposed to compute the molecular energies and wave functions and the importance of the choice of the orbital basis and of the "zeroth order" Hamiltonian on the computed energies was assessed.
Abstract: A multireference perturbative‐variational method, proposed by the authors to compute the molecular energies and wave functions is investigated to assess the importance of the choice of the orbital basis and of the ‘‘zeroth order’’ Hamiltonian on the computed energies A new definition is presented of single particle energy suitable to perform perturbative‐variational computations with any type of orbital sets Test computations performed with various orbital sets for the Be+H2 system at various geometries indicate that the computed energies are not very sensitive to the choice of the single particle energies but they are sensitive to the choice of the orbitals The MCSCF orbitals appear to provide the best starting set of orbitals to perform this type of computation The computed energies are compared to those evaluated by single and multireference coupled cluster, MBPT, and CI methods
TL;DR: In this paper, the algebraic structure of the equations for calculating the first order static properties using several approximate versions of Coupled Cluster (CC) methods is analyzed, in particular, the non-variational and the variational method using a CC wavefunction corresponding to an appropriately defined perturbed Hamiltonian as well as the simple expectation value expression using a CA stationary state are studied under different approximations.
Abstract: In this paper, we analyse the algebraic structure of the equations for calculating the first order static properties using several approximate versions of Coupled Cluster (CC) methods. In particular, the non-variational and the variational method using a CC wavefunction corresponding to an appropriately defined perturbed Hamiltonian as well as the simple expectation value expression using a CC stationary state are studied under different approximations. Two different models are proposed: (a) use of maximum overlap orbitals where the pertinent approximations are T∼T
2, T
(1) ∼T
2
(1), (b) use of Hartree-Fock orbitals and T∼(T
1+T
2), T
(1)∼(T
1
(1)
+T
2
(1)
) approximations. It is analytically shown that in both these models certain approximate versions of the methods under purview yield identical results for first order static properties.
TL;DR: In this article, a general partial summation method for including arbitrary classes of diagrams to all orders in the coupled cluster based size consistent energy functional for closed shell states is developed, where the various reduced density matrices which appear in the energy functional are essentially the time-independent analogues of the corresponding body Green functions, and it is possible to derive Dyson-like equations for these quantities.
Abstract: A general partial summation method for including arbitrary classes of diagrams to all orders in the coupled cluster based size consistent energy functional for closed shell states is developed. Since the various reduced density matrices which appear in the energy functional are essentially the time-independent analogues of the corresponding many body Green functions, it is possible to derive Dyson-like equations for these quantities. By expanding the associated “proper” self energy parts in terms of the T-amplitudes, one can carry out partial summations in the reduced density matrices and thus in energy. At a higher level, higher order terms in a “proper” self energy can also be generated by renormalizing the internal propagators in it, and considering only the “irreducible” self-energy terms.
TL;DR: In this paper, the authors define the correlation potential as the error potential linked to an uncorrelated function in configurational space, and derive a range of O.lu for the forces.
Abstract: We define the correlation potential as the error potential linked to an uncorrelated function. The problem of complete interaction of configurations is solved through successive perturbations. The obtained expression can be identified to that of a coupled cluster expansion. This method is enhanced by the results of the error potential theory. The correlation potential is expressed in configurational space. Yet it can be compared to the correlation forces we have defined in physical space. A numerical experiment on H+3 in minimal base lead us to propose a range of O.lu.a. for the forces.
TL;DR: A diagrammatic perturbation-theory method for direct calculation of spin-density matrix of open-shell N-electron systems described by the restricted Hartree-Fock one-particle functions is formulated in this paper.
Abstract: A diagrammatic perturbation-theory method for direct calculation of spin-density matrix of open-shellN-electron systems described by the restricted Hartree-Fock one-particle functions is formulated. The formulae correct up to the second order of perturbation theory (second order in correlation effects) are presented. Their generalization to account for infinite summations of dominant correlation effects is simple, realized by making use of the so-called coupled cluster approach.
TL;DR: In this article, the Hartree approximation for the quantum soliton was improved by utilizing the high-precision coupled cluster method with arbitrary accuracy, and a preliminary test indicates the necessity for further investigations, as the used truncation scheme which ignored all continuum excitations, becomes unreliable when approaching the critical region.
Abstract: The recently developed Hartree approximation for the\(\varphi _2^4 \) quantum soliton is reviwed. Higher-order corrections to the soliton mass can be worked out by utilizing the high-precision coupled cluster method with arbitrary accuracy. A preliminary test indicates the necessity for further investigations, as the used truncation scheme, which ignored all continuum excitations, becomes unreliable when approaching the critical region.
TL;DR: In this article, the derivation of an explicit form of the coupled cluster equations using the time independent formalism and its various aspects are discussed in view of a recent derivation given by Dabrowski.
Abstract: The derivation of an explicit form of the coupled cluster equations using the time-independent formalism and its various aspects are discussed in view of a recent derivation given by Dabrowski. Var...