Application of the many‐body perturbation theory by using localized orbitals

Abstract

The localized and the canonical variants of the many-body perturbation theory are used to calculate the energy corrections through fourth order for C14H14 in Pariser--Parr--Pople approximation, for a wide range of the coupling constant/]. The behaviour of the iocalization terms is examined. It is shown how the nonlocal cont¡ to the correlation energy can be gradually separated. The strictly local contribution left behind is surprisingly large: more than 50% of the total correlation energy. IntrodnctionAs is well known the wavefunctions determined by the Hartree---Fock (HF) method are not suitable to calculate acr values for the energy quantities of the valence shell (elr affinities, ionization and binding energies, etc.). In the last two decades various procedures have been developed which go beyond the independent particle seheme. One of the most straightforward approaches for taking into ar correlation effects is the diagrammatic many-body perturbation theory [1--3]. Ir can be used routinely for small molecules through third order in the energy (including some fourth order temas) [4 6]. Recently, with moderately sized basis sets the evaluation of ail fourth order temas has become feasible [7,8]. Except for some model systems, the calculation of all temas o f a given order lª than the fourth is out of question at present. There exist procedures, however, in which certain types of terms ate summed over to infinite order (CPMET [9,10], CEPA [11,12], and the method of Green's functions [13,14]).Previously it was conjectured that local and nonlocal r can be clr separated and that the former predominate [15]. One.of the authors of the present article (E.K.) developed a perturbation theory whose zeroeth order wavefunction is the APSG ground state [16]

Optimization of orbital-specific virtuals in local Møller-Plesset perturbation theory

“…The first is based on the Kapuy MP2 (KMP2) approximation, [31][32][33] which neglects non-diagonal elements of the occupied block of the Fock matrix (or rather, excludes them from the definition of the zerothorder operator) to give…”

A localized basis that allows fast and accurate second-order Møller-Plesset calculations

“…As stated in the introduction, past work on Kapuy's MPBPT theory in local orbitals have always required the addition of third and higher order perturbative corrections in order to account for the off-diagonal elements of the Fock matrix. In other words, Kapuy et al [12,13,14,18] have focused on computing the quantity…”

“…[12,13,14,15,16,17,18] In particular, Kapuy's approach was to consider the Fock operator in a basis of localized orthonormal occupied and virtual orbitals, and then set the primary Hamiltonian as the diagonal piece of the Fock operator in this basis. Kapuy then treated the off-diagonal elements of the Fock-matrix and the two-electron coulomb term together as the joint perturbation in MBPT.…”

“…In his seminal paper of 1983, Kapuy recognized that in order for his approach to be widely applicable and useful, "Cheap localization procedures should be developed which can satisfy the double requirement: well localized orbitals with small off-diagonal Fock matrix elements." [12] To our knowledge, this idea has not yet been pursued, and is the basic idea behind this paper.…”

Appendix to “Studies in Perturbation Theory”: The Problem of Partitioning

“…Defining just the diagonal part ofF asĤ (0) , one arrives at a partitioning, in which the off-diagonal elements ofF give rise to a new kind of perturbation. This, in connection with using non-canonical MOs in MBPT, was introduced by Davidson [139,140] and extensively used by Kapuy [141][142][143][144][145] (for a review, see [146]). To distinguish this second possibility from MP, we shall refer to it as the Davidson-Kapuy (DK) partitioning.…”