A new implementation of the full CCSDT model for molecular electronic structure

An Introduction to Coupled Cluster Theory for Computational Chemists

A critical assessment of coupled cluster method in quantum chemistry

Publisher Summary This chapter discusses the developments of the open-shell many-body cluster expansion theories. Interpretation of most of the spectroscopic and dynamical phenomena, involving excited or ionized molecules and molecular fragments require models for open-shell states transcending the simple orbital description. The language of occupation number representation, coupled with the hole-particle description of the operators, the use of Wick's theorem and the attendant diagrammatic depiction of the various terms makes the many-body approach a very attractive alternative to the traditional CI-based theories. The open-shell many-body perturbation theory (MBPT) and the propagator or the Green's function methods have now developed into vast computational technology, generating softwares that are cost-effective and competitive with the CI-based codes. The cluster expansion based open-shell many-body formalisms possess even greater potentiality since they not only share and embed all the desirable features and technical advantages of the open-shell MBPT or propagator theories, but also are inherently non-perturbative in nature. They provide more compact descriptions of the electron correlation and are more flexible. Moreover, the cluster expansion of the open-shell functions provides valuable insight regarding the structure of general many-electron wave-functions.

Use of Cluster Expansion Methods in the Open-Shell Correlation Problem

A new state‐selective multireference (MR) coupled‐cluster (CC) method exploiting the single‐reference (SR) particle‐hole formalism is described. It is an extension of a simple two‐reference formalism, which we presented in our earlier paper [N. Oliphant and L. Adamowicz, J. Chem. Phys. 94, 1229 (1991)], and a rigorous formulation of another method of ours, which we obtained as an approximation of the SRCC approach truncated at triple excitations (SRCCSDT) [N. Oliphant and L. Adamowicz, J. Chem. Phys. 96, 3739 (1992)]. The size extensivity of the resulting correlation energies is achieved by employing a SRCC‐like ansatz for the multideterminantal wave function. General considerations are supplemented by suggesting a hierarchy of approximate schemes, with the MRCCSD approach (MRCC approach truncated at double excitations from the reference determinants) representing the most important one. Our state‐selective MRCCSD theory emerges through a suitable selection of the most essential cluster components appearing in the full SRCCSDTQ method (SRCC method truncated at quadruple excitations), when the latter is applied to quasidegenerate states. The complete set of equations describing our MRCCSD formalism is presented and the possibility of the recursive intermediate factorization [S. A. Kucharski and R. J. Bartlett, Theor. Chim. Acta 80, 387 (1991)] of our approach, leading to an efficient computer algorithm, is discussed.

A state-selective multireference coupled-cluster theory employing the single-reference formalism

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, consistant 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 a computationally viable, size-extensive, high-level description of electron correlation in small polyatomic molecules

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M.R. Hoffmann

Papers

A Full Coupled-Cluster Singles, Doubles, and Triples Model for the Description of Electron Correlation