ISSN:
1432-2234
Keywords:
Stationary perturbation theory
;
Electron correlation
;
Coupled Møller-Plesset (CMP)
;
Uncoupled Møller-Plesset (UCMP)
;
Full CI-Coupled MC-SCF
;
Many-Body-Perturbation theory (MBPT)
;
Brillouin-condition
;
Brillouin
;
Brueckner-condition
;
Brueckner orbitals
;
Hellmann
;
Feynman theorem
Source:
Springer Online Journal Archives 1860-2000
Topics:
Chemistry and Pharmacology
Notes:
Summary After a short recapitulation of the basic concepts of stationary perturbation theory, this is applied to a many-electron Hamiltonian, with or without an external field, given in a Fock space formulation in terms of a finite basis, the exact eigenfunctions of which are the full-CI wave functions. The Lie algebra ℒ c n of the variational group corresponding to this problem is presented. It has an important subalgebra ℒ c (1) of one-particle transformations. Hartree-Fock and coupled Hartree-Fock (also uncoupled Hartree-Fock) as well as MC-SCF and coupled MC-SCF are outlined in this framework. Many-body perturbation theory and Møller-Plesset perturbation theory are derived from the same kind of stationarity condition and a new non-perturbative iteration construction of the full-CI wave function is proposed, the first Newton-Raphson iteration cycle of which is CEPA-0. For the treatment of electron correlation for properties two variants of Møller-Plesset theory referred to as ‘coupled’ (CMP) and ‘uncoupled’ (UCMP) are defined, neither of which is fully satisfactory. While CMP satisfies a Brillouin condition, which implies that first order correlation corrections to first- and second-order properties vanish, it does not satisfy a Hellmann-Feynman theorem, i.e. a first order property isnot the expectation value of the operator associated with the property. Conversely UCMP satisfies a Hellmann-Feynman theorem but no Brillouin theorem. The incompatibility of the two theorems is related to an unbalanced treatment of one-particle- and higher excitations in MP theory. CMP, which is based on coupled Hartree-Fock as uncorrelated reference, appears to have slight advantages over UCMP, but neither variant looks very promising for the evaluation of 2nd order correlation corrections to 2nd-order properties. Then four variants of the perturbation theory of properties with a nonperturbative treatment of electron correlation on CEPA-0 level (but extendable to a higher level) are discussed. While those variants which are the direct counterpart of UCMP and CMP must be discarded, the ‘perturbative CEPA-0’ derived from a perturbative treatment on full-CI level appears to satisfy all important criteria, in particular it satisfies a Brillouin-Brueckner condition and a Hellmann-Feynman theorem. A simplified version, the ‘coupled Brillouin-Brueckner CEPA-0’ appears to have essentially the same qualities. It is important to replace the Brillouin condition of MP theory by the Brillouin-Brueckner condition in non-perturbative approaches, especially if one is interested in properties.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01113515
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