STATIONARY PERTURBATION-THEORY .2. ELECTRON CORRELATION AND ITS EFFECT ON PROPERTIES

After a short recapitulation of the basic concepts of stationary pertu rbation theory, this is applied to a many-electron Hamiltonian, with o r without an external field, given in a Fock space formulation in term s 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 corr esponding to this problem is presented. It has an important subalgebra L(c)(1) of one-particle transformations. Hartree-Fock and coupled Har tree-Fock (also uncoupled Hartree-Fock) as well as MC-SCF and coupled MC-SCF are outlined in this framework. Many-body perturbation theory a nd Moller-Plesset perturbation theory are derived from the same kind o f stationarity condition and a new non-perturbative iteration construc tion of the full-CI wave function is proposed, the first Newton-Raphso n iteration cycle of which is CEPA-0. For the treatment of electron co rrelation for properties two variants of Moller-Plesset theory referre d to as 'coupled' (CMP) and 'uncoupled' (UCMP) are defined, neither of which is fully satisfactory. While CMP satisfies a Brillouin conditio n, which implies that first order correlation corrections to first- an d second-order properties vanish, it does not satisfy a Hellmann-Feynm an theorem, i.e. a first order property is not the expectation value o f the operator associated with the property. Conversely UCMP satisfies a Hellmann-Feynman theorem but no Brillouin theorem. The incompatibil ity of the two theorems is related to an unbalanced treatment of one-p article- and higher excitations in MP theory. CMP, which is based on c oupled 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 properti es. Then four variants of the perturbation theory of properties with a nonperturbative treatment of electron correlation on CEPA-0 level (bu t extendable to a higher level) are discussed. While those variants wh ich 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 sat isfies a Brillouin-Brueckner condition and a Hellmann-Feynman theorem. A simplified version, the 'coupled Brillouin-Brueckner CEPA-0' appear s to have essentially the same qualities. It is important to replace t he Brillouin condition of MP theory by the Brillouin-Brueckner conditi on in non-perturbative approaches, especially if one is interested in properties.