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Explicitly connected expansion for the average value of an observable in the coupled‐cluster theory
Author(s) -
Jeziorski Bogumił,
Moszynski Robert
Publication year - 1993
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.560480303
Subject(s) - commutator , observable , operator (biology) , perturbation theory (quantum mechanics) , cluster expansion , coupled cluster , physics , mathematical physics , ansatz , mathematics , quantum mechanics , biochemistry , chemistry , lie conformal algebra , repressor , lie algebra , molecule , transcription factor , gene
Abstract An explicitly connected commutator expansion for the average value of an observable in the coupled‐cluster theory is derived. Specifically, it is shown that the expectation value of an operator for the state Ψ, related to the Fermi vacuum Φ by the exponential Ansatz ψ = e T Φ, is expressed as a finite commutator series containing the cluster operator T and an auxiliary operator S , defined by a linear equation involving again a finite commutator series in T . The above result is applied to derive the explicitly connected commutator form of the order‐by‐order many‐body perturbation theory (MBPT) expansion for the expectation values and density matrices. We also show how the commutator expansion derived by us can be used as a basis for size‐extensive infinite‐order summation techniques. An operator technique of eliminating the nonlocal , “off‐energy shell” denominators from MBPT expressions is proposed and applied to obtain compact commutator formulas for the expectation values of one‐ and two‐electron operators through the fourth and third order, respectively, and for the correlation energy through the fifth order of perturbation theory. © 1993 John Wiley & Sons, Inc.