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A coupled‐cluster approach to the many‐body perturbation theory for open‐shell systems
Author(s) -
Lindgren Ingvar
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.560140804
Subject(s) - open shell , diagrammatic reasoning , formalism (music) , physics , classical mechanics , second quantization , perturbation (astronomy) , coupled cluster , mathematical physics , quantum mechanics , quantum , creation and annihilation operators , molecule , art , musical , philosophy , linguistics , visual arts
A new approach to the diagrammatic formulation of many‐body perturbation theory for open‐shell systems is presented. The formalism is based on a generalized form of the Bloch equation that also generates the Rayleigh‐Schrödinger perturbation expansion for a system with several open shells. Second quantization in the particle‐hole formulation is used together with Wick's theorem in order to derive graphical rules in the usual way. The linked‐diagram property of the wave operator and of the effective interaction is shown by expanding the wave operator in terms of normal products of connected diagram clusters, in analogy with the exp(S) formalism of Coester and Kümmel for closed‐shell systems. Self‐consistent “coupled‐cluster” equations are derived for the open‐shell case from the generalized Bloch equation by a straightforward extension of the procedure of Čížek and Paldus. The application of such equations for investigating different properties of open‐shell atoms is discussed.