Diagrammatic coupled-cluster theory

We would like to stress that this chapter is a review of coupled cluster theory. It is not primarily intended to provide an analysis of the numerical performance of the coupled cluster model, and we direct readers in search of such information to several recent publications. " Instead, we offer a detailed explanation of the most important aspects of coupled cluster theory at a level appropriate for the general computational chemistry community. Although many of the topics described here have been discussed by other au-thors, ° this chapter is unique in that it attempts to provide a concise, practical introduction to the mathematical techniques of coupled cluster theory (both algebraic and diagrammatic), as well as a discussion of the efficient... 

Recognition of this relationship between coupled cluster theory and MBPT has inspired research efforts to construct perturbation-based corrections to the CCSD energy to account for higher excitation contributions. Undoubtedly, the most successful and popular of these is the (T) correction first described for closed-shell molecular systems by Raghavachari et al. " In the next section, we will describe the structure of this correction using diagrammatic techniques. 

In Volume 5 of this series, R. J. Bartlett and J. E Stanton authored a popular tutorial on applications of post-Hartree-Fock methods. Here in Chapter 2, Dr. T. Daniel Crawford and Professor Henry F. Schaefer III explore coupled cluster theory in great depth. Despite the depth, the treatment is brilliantly clear. Beginning with fundamental concepts of cluster expansion of the wavefunction, the authors provide the formal theory and the derivation of the coupled cluster equations. This is followed by thorough explanations of diagrammatic representations, the connection to many-bodied perturbation theory, and computer implementation of the method. Directions for future developments are laid out. 

One important property of Eq. (23), which manifests itself very easily in the diagrammatic evaluation of the perturbation expansions, is the linked-diagram theorem (LOT). According to this theorem, only a selected class of terms survives in the perturbation expansion of the wave operator, while all unlinked diagrams cancel in each order of perturbation theory in addition, this theorem ensures the size consistency of MBPT and coupled-cluster theory. Based on LDT, Eq. (23) simplify to... 

Key words Correlation problem - Coupled-cluster theory - Size-entensivity - Many-body theory -Diagrammatic methods... 

The coupled cluster theory may be derived from the many-body perturbation theory which we have presented above. Each coupled cluster approximation can be obtained by summing certain well-defined types of diagrammatic terms through all orders of the perturbation expansion. We shall not present here the details of the relation between coupled cluster and many-body perturbation theories. For a detailed discussion, the reader is referred to the review by Paldus and Li [81], published in 1999, entitled A critical assessment of coupled cluster method in quantum chemistry and the chapter on coupled cluster theory by Paldus [82] in the Handbook of Molecular Physics and Quantum Chemistry. 

Sous J, Goel P, Nooijen M. Similarity transformed equation of motion coupled cluster theory revisited a benchmark study of valence excited states. Mol Phys. 2013 112 616-638. Trofimov AB, Krivdina IL, Weller J, Schimer J. Algebraic-diagrammatic construction propagator approach to molecular response properties. Chem Phys. 2006 329 1-10. 

Many varieties of diagrams have used throughout the chemical physics literature for many years (e.g., see Refs. 1, 2, 80, 117, and 119). The diagrammatic formalism we have chosen here has been frequently used in work by the Bartlett group among others and is particularly straightforward for conventional coupled cluster and many-body perturbation theories. 

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