Explicitly connected expansion for the average value of an observable in the coupled-cluster theory
Article first published online: 19 OCT 2004
Copyright © 1993 John Wiley & Sons, Inc.
International Journal of Quantum Chemistry
Volume 48, Issue 3, pages 161–183, 5 November 1993
How to Cite
Jeziorski, B. and Moszynski, R. (1993), Explicitly connected expansion for the average value of an observable in the coupled-cluster theory. Int. J. Quantum Chem., 48: 161–183. doi: 10.1002/qua.560480303
- Issue published online: 19 OCT 2004
- Article first published online: 19 OCT 2004
- Manuscript Accepted: 13 MAY 1993
- Manuscript Revised: 10 MAY 1993
- Manuscript Received: 9 FEB 1993
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 = eT 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.