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Special Issue on Recent Advances in Coupled Cluster Theory

by Sourav Pal

Int. J. Mol. Sci. 2002, 3(5), 445-446; https://doi.org/10.3390/i3050445 - 31 May 2002

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Abstract

The Coupled-cluster (CC) theory has emerged as the most accurate method to describe the electron correlation problem and thus the state-of-the-art electronic structure tool.[...] Full article

(This article belongs to the Special Issue Recent Advances in Coupled Cluster Theory)

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On the Estimation of the Remainder Term in Møller-Plesset MP2 Theory from Limited Configuration Interaction

by I. Hubac and S. Wilson

Int. J. Mol. Sci. 2002, 3(5), 570-578; https://doi.org/10.3390/i3050570 - 31 May 2002

Cited by 1 | Viewed by 6926

Abstract

In a previous paper, we have avoided an infinite order perturbation expansion and obtained a closed expression which consists of the second-order Møller-Plesset energy component together with a remainder term. The applicabilty of second-order many-body perturbation theory with a Møller-Plesset reference hamiltonian then [...] Read more.

In a previous paper, we have avoided an infinite order perturbation expansion and obtained a closed expression which consists of the second-order Møller-Plesset energy component together with a remainder term. The applicabilty of second-order many-body perturbation theory with a Møller-Plesset reference hamiltonian then rests upon the magnitude of this remainder term rather than the behaviour of the higher order terms on the perturbation series. In the present work, we show how this remainder term can be estimated by limited configuration interaction. Full article

(This article belongs to the Special Issue Recent Advances in Coupled Cluster Theory)

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Use of a New Cluster Ansatz to Treat Strong Relaxation and Correlation Effects: A Direct Method for Energy Differences

by Debasis Jana, Uttam Sinha Mahapatra and Debashis Mukherjee

Int. J. Mol. Sci. 2002, 3(5), 550-569; https://doi.org/10.3390/i3050550 - 31 May 2002

Cited by 5 | Viewed by 8439

Abstract

We have presented in this paper a new cluster Ansatz for the wave operator for open-shell and/or quasidegenerate states, which takes care of strong relaxation and correlation effects in a compact and efficient manner. This Ansatz allows contraction among the various cluster operators [...] Read more.

We have presented in this paper a new cluster Ansatz for the wave operator for open-shell and/or quasidegenerate states, which takes care of strong relaxation and correlation effects in a compact and efficient manner. This Ansatz allows contraction among the various cluster operators via spectator orbitals, accompanied by suitable combinatorial factors. Since both the orbital and the correlation relaxations are treated on the same footing, it allows us to develop a very useful direct method for energy differences for open shell states relative to a closed-shell ground state, where the total charge for the two states may differ. We have discussed a new spin-free coupled cluster (CC) based direct method and illustrated its performance by evaluating electron affinity of a neutral doublet radical. We have also indicated how the scope of the theory can be extended to compute the state energies of simple open shell configurations as well. In that case, the CC equations terminate after the quartic power of cluster operators – exactly as in the closed-shell situation, which is not the case for the current methods. Full article

(This article belongs to the Special Issue Recent Advances in Coupled Cluster Theory)

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Alternative Multi–reference State–specific Coupled Cluster Wave Functions

by Ludwik Adamowicz, Jean–Paul Malrieu and Vladimir V. Ivanov

Int. J. Mol. Sci. 2002, 3(5), 522-549; https://doi.org/10.3390/i3050522 - 31 May 2002

Cited by 12 | Viewed by 8194

Abstract

An analysis of alternative expressions of the state–specific (SS) multi–reference (MR) coupled cluster (CC) wave functions is presented. The approach utilizes the CASSCF (complete active space self consistent field) wave function as the reference. It is designed specifically for calculating excited electronic states. [...] Read more.

An analysis of alternative expressions of the state–specific (SS) multi–reference (MR) coupled cluster (CC) wave functions is presented. The approach utilizes the CASSCF (complete active space self consistent field) wave function as the reference. It is designed specifically for calculating excited electronic states. The cluster structure of the CC wave operator and the origin(s) for the cluster expansion(s) are the key features of the development. Test calculations reveal some interesting features of the SMRCC approaches. Full article

(This article belongs to the Special Issue Recent Advances in Coupled Cluster Theory)

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On the Use of Connected Moments Expansion with Coupled Cluster Reference

by Jozef Noga, Agnes Szabados and Péter R. Surján

Int. J. Mol. Sci. 2002, 3(5), 508-521; https://doi.org/10.3390/i3050508 - 31 May 2002

Cited by 8 | Viewed by 7382

Abstract

We examine the possibility of introducing a new class of so called noniterative corrections to coupled cluster energies, based on the connected moments expansion (CMX). Approximate Coupled Cluster (CC) wave functions are used as reference states and then the “improved energies” can be [...] Read more.

We examine the possibility of introducing a new class of so called noniterative corrections to coupled cluster energies, based on the connected moments expansion (CMX). Approximate Coupled Cluster (CC) wave functions are used as reference states and then the “improved energies” can be formally obtained either by CMX in terms of the moments of CC similarity transformed Hamiltonian, or in CMX of the usual Hamiltonian. Numerical results are given for some model systems that show the superiority of the latter approach. Full article

(This article belongs to the Special Issue Recent Advances in Coupled Cluster Theory)

102 KiB

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Potential Functions of Al2 by the Relativistic Fock-Space Coupled Cluster Method

by Arie Landau, Ephraim Eliav, Lucas Visscher and Uzi Kaldor

Int. J. Mol. Sci. 2002, 3(5), 498-507; https://doi.org/10.3390/i3050498 - 31 May 2002

Cited by 2 | Viewed by 9227

Abstract

Potential functions of the ground and low excited states of Al₂ are calculated by the relativistic Fock-space coupled cluster method in the framework of the projected Dirac-Coulomb Hamiltonian. A moderate-size basis [16s11p3d3f/6s6p3d2f] is used. ³Π_u is confirmed as the ground [...] Read more.

Potential functions of the ground and low excited states of Al₂ are calculated by the relativistic Fock-space coupled cluster method in the framework of the projected Dirac-Coulomb Hamiltonian. A moderate-size basis [16s11p3d3f/6s6p3d2f] is used. ³Π_u is confirmed as the ground state of the system. Its spin orbit splittings are reproduced well, with the Λ = 1, 2 states lying 32.5 and 66.1 cm⁻¹, respectively, above the Λ = 0 minimum (experimental values are 30.4 and 63.4 cm⁻¹). The bond is somewhat too weak, with D_e 0.14 eV below experiment, R_e too high by 0.08 ˚A, and ω_e 21 cm⁻¹ too low. It is speculated that the better agreement obtained in earlier calculations may be due to neglect of basis set superposition errors. The description of bonding in the molecule may be improved by the use of a better basis and the inclusion of more correlation by the intermediate Hamiltonian coupled cluster method, which makes it possible to handle larger P spaces and extend the potential functions to the whole range of internuclear separations. Full article

(This article belongs to the Special Issue Recent Advances in Coupled Cluster Theory)

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153 KiB

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Method of Moments of Coupled-Cluster Equations: Externally Corrected Approaches Employing Configuration Interaction Wave Functions

by Piotr Piecuch, Karol Kowalski and Ian S.O. Pimienta

Int. J. Mol. Sci. 2002, 3(5), 475-497; https://doi.org/10.3390/i3050475 - 31 May 2002

Cited by 28 | Viewed by 8402

Abstract

A new approach to the many-electron correlation problem, termed the method of moments of coupled-cluster equations (MMCC), is further developed and tested. The main idea of the MMCC theory is that of the noniterative energy corrections which, when added to the energies obtained [...] Read more.

A new approach to the many-electron correlation problem, termed the method of moments of coupled-cluster equations (MMCC), is further developed and tested. The main idea of the MMCC theory is that of the noniterative energy corrections which, when added to the energies obtained in the standard coupled-cluster calculations, recover the exact (full configuration interaction) energy. The MMCC approximations require that a guess is provided for the electronic wave function of interest. The idea of using simple estimates of the wave function, provided by the inexpensive configuration interaction (CI) methods employing small sets of active orbitals to define higher–than–double excitations, is tested in this work. The CI-corrected MMCC methods are used to study the single bond breaking in HF and the simultaneous breaking of both O–H bonds in H₂O. Full article

(This article belongs to the Special Issue Recent Advances in Coupled Cluster Theory)

166 KiB

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by Seiichiro Ten-no and Osamu Hino

Int. J. Mol. Sci. 2002, 3(5), 459-474; https://doi.org/10.3390/i3050459 - 31 May 2002

Cited by 19 | Viewed by 7904

Abstract

We recently developed an explicitly correlated method using the transcorrelated Hamiltonian, which is preliminarily parameterized in such a way that the Coulomb repulsion is compensated at short inter-electronic distances. The extra part of the effective Hamiltonian features short-ranged, size-consistent, and state-universal. The localized [...] Read more.

We recently developed an explicitly correlated method using the transcorrelated Hamiltonian, which is preliminarily parameterized in such a way that the Coulomb repulsion is compensated at short inter-electronic distances. The extra part of the effective Hamiltonian features short-ranged, size-consistent, and state-universal. The localized and frozen nature of the correlation factor makes the enormous three-body interaction less important and enables us to bypass the complex nonlinear optimization. We review the basic strategy of the method mainly focusing on the applications to single-reference many electron theories using modified Møller-Plesset partitioning and biorthogonal orbitals. Benchmark calculations are performed for 10-electron systems with a series of basis sets. Full article

(This article belongs to the Special Issue Recent Advances in Coupled Cluster Theory)

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66 KiB

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Time Dependent Coupled Cluster Approach to Resonance Raman Excitation Profiles from General Anharmonic Surfaces

by M. Durga Prasad

Int. J. Mol. Sci. 2002, 3(5), 447-458; https://doi.org/10.3390/i3050447 - 31 May 2002

Cited by 9 | Viewed by 7175

Abstract

A time dependent coupled cluster approach to the calculation of Resonance Raman excitation profiles on general anharmonic surfaces is presented. The vibrational wave functions on the ground electronic surface are obtained by the coupled cluster method (CCM). It is shown that the propagation [...] Read more.

A time dependent coupled cluster approach to the calculation of Resonance Raman excitation profiles on general anharmonic surfaces is presented. The vibrational wave functions on the ground electronic surface are obtained by the coupled cluster method (CCM). It is shown that the propagation of the vibrational ground state on the upper surface is equivalent to propagation of the vacuum state by an effective hamiltonian generated by the similarity transformation of the vibrational hamiltonian of that surface by the CCM wave operator of the lower surface up to a normalization constant. This time propagation is carried out by the time-dependent coupled cluster method in a time dependent frame. Numerical studies are presented to asses the validity of the approach. Full article

(This article belongs to the Special Issue Recent Advances in Coupled Cluster Theory)

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