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n ‐Electron problem and its formulation in terms of k ‐particle density cumulants
Author(s) -
Kutzelnigg Werner
Publication year - 2003
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.10751
Subject(s) - cumulant , hierarchy , unitary state , coupled cluster , fock space , mathematics , order (exchange) , space (punctuation) , physics , particle (ecology) , quantum mechanics , statistical physics , mathematical physics , computer science , molecule , statistics , oceanography , finance , political science , economics , law , market economy , geology , operating system
Approaches to the solution of the n ‐electron problem in terms of the reduced k ‐particle density matrices γ k or their cumulants λ k are critically reviewed. The advantages of a cumulant‐based theory are outlined, especially its extensivity, which implies a connected‐diagram theorem. A perturbative analysis of the hierarchy of k ‐particle approximations, based on the irreducible contracted Schrödinger equations (ICSE k ) (which are conditions for the stationarity of the energy), reveals that the three‐particle approximation is necessary to obtain the energy correct to the MP2 (second‐order Møller–Plesset) level. This disqualifies the naive use of the k ‐particle hierarchy, in a linearly converging iterative scheme, as ineffective (compared, e.g., to coupled‐cluster theory). A promising alternative is, however, a quadratically convergent iterative scheme based on successive unitary transformations in Fock space. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003