Many-electron correlation problems

J. Paldus, (1994) Many-Electron Correlation Problem, and Lie Algebras. In Contemporary Mathematics, Vol. 160. (American Mathematical Society, Providence, RI, 1994), pp. 209-236 and references therein. 

Jiri Cizek s research program centers on the quantum theory of molecular electronic structure and related developments in quantum chemical methodology, coupled-cluster approaches to many-electron correlation problems,105 large-order perturbation theory,106 dynamical groups and exactly solvable models, lower bounds, and the use of symbolic computation language in physics and in chemistry. 

Since his appointment at the University of Waterloo, Paldus has fully devoted himself to theoretical and methodological aspects of atomic and molecular electronic structure, while keeping in close contact with actual applications of these methods in computational quantum chemistry. His contributions include the examination of stability conditions and symmetry breaking in the independent particle models,109 many-body perturbation theory and Green s function approaches to the many-electron correlation problem,110 the development of graphical methods for the time-independent many-fermion problem,111 and the development of various algebraic approaches and an exploration of convergence properties of perturbative methods. His most important... 

X. Li, Q. Zhang, Int. J. Quant. Chem. XXXVI, 599 (1989). Bonded Tableau Unitary Group Approach to the Many-Electron Correlation Problem. 

J. Paldus, Many-Electron Correlation Problem. A Group Theoretical Approach, in Theoretical Chemistry Advances and Perspectives, H. Eyring and D. J. Henderson (eds.) Academic, New York 1976, pp 131-297. 

This article is divided into seven parts. The many-body perturbation theory is discussed in the next section. The algebraic approximation is discussed in some detail in section 3 since this approximation is fundamental to most molecular applications. In the fourth section, the truncation of the many-body perturbation series is discussed, and, since other approaches to the many-electron correlation problem may be regarded as different ways of truncating the many-body perturbation expansion, we briefly discuss the relation to other approaches. Computational aspects of many-body perturbative calculations are considered in section 5. In section 6, some typical applications to molecules are given. In the final section, some other aspects of the many-body perturbation theory of molecules are briefly discussed and possible directions for future investigations are outlined. 

Congress of Quantum Chemistry, P.-O. Lowdin and B. Pullman, Eds., D. Reidel, Dordrecht, 1983, pp. 31-60. Coupled Cluster Approaches to the Many-Electron Correlation Problem. 

Keywords many-electron correlation problem, post-Hartree-Fock methods, coupled cluster approaches, configuration interaction, externally corrected coupled cluster methods, reduced multireference coupled cluster method... 

In the context of atomic and molecular electronic stmcture, it was Hugh Kelly [63] who first applied Goldston s MBPT to closed-sheU-type atoms by developing several very successful approximation schemes. In the molecular context, the handling of the many-electron correlation problem was very much influenced by the work of Sinanoglu... 

J. Paldus, Many-electron correlation problem. A group theoretical approach, in H. Eyring, D. Henderson (Eds.), Theoretical chemistry Advances and perspectives, Vol. 2, Academic P, New York, 1976, pp. 131-290. 

Unitary group approach to the many-electron correlation problem spin-dependent operators... 

In the domain of Cl methodology, our close interaction followed the formulation of the unitary group approach (UGA) to the many-electron correlation problem by one of us [2-5]. Professor Shavitt soon fell in love with this formalism and designed an ingenious graphical representation [6-8] of the electronic Gel fand-Tsetlin (G-T) basis as described in terms of the so-called ABC or Paldus tableaux (see below). This development ultimately resulted in his graphical UGA (GUGA) version of UGA (for most recent overviews of these approaches see [4, 9-13]). 

Paldus J (1976) Many-electron correlation problem a group theoretical approach. In Eyring H, Henderson DJ (eds) Theoretical chemistry advances and perspectives, vol 2. Academic, New York, pp 131-290... 

Shavitt I (1977) Graph theoretical concepts for the unitary group approach to the many-electron correlation problem. Int J Quantum Chem 12(S11) 131-148... 

Group Approach to the Many-Electron Correlation Problem. 

We have overviewed the new approach to the many-electron correlation problem in atoms and molecules, termed the method of moments of coupled-cluster equations (MMCC). The main idea of the MMCC theory is that of the noniterative energy corrections which, when added to the ground- and excited-state energies obtained in approximate CC calculations, recover the exeict energies. We have demonstrated that the MMCC formalism leads to a number of useful approximations, including the renormalized and completely renormalized CCSD(T), CCSD(TQ), and CCSDT(Q) methods for... 

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