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The unitary‐group formulation of coupled‐cluster many‐electron theory
Author(s) -
Matsen F. A.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560160831
Subject(s) - unitary group , pauli exclusion principle , atomic orbital , invariant (physics) , mathematics , quantum mechanics , coupled cluster , physics , mathematical physics , unitary state , electron , molecule , political science , law
Coupled‐cluster many‐electron theory (CCMET) has been developed in the second‐quantized formulation with and without spin projection. In this article CCMET is developed in the unitary‐group formulation where the group is U(p) and p is the number of orbitals in the basis set. The zero‐order ground state is the highest‐weight state of an irreducibly invariant subspace of U(p) and the excitation operators are infinitesimal generators. These irreducible spaces are uniquely labeled by Young diagrams which the Pauli principle limits to no more than one column for fermion orbitals and no more than two columns for freeon (spin‐free) orbitals. In the latter case the spin is one‐half the difference in the lengths of the two columns. We employ both the Gel'fand and the generator bases for the irreducible invariant vector spaces. Matrix elements for the former are evaluated by techniques due to Gel'fand, Biedenharn, Louck, Paldus, and Shavitt and for the latter directly by Lie algebraic and diagrammatic techniques as a simple function of the weight components of the highest‐weight state. For freeon or fermion orbitals the results are equivalent to those obtained by the second‐quantized formulation with or without spin projection.