Electron-pair Approach

The simplest way to take correlation effects into account is to treat explicitly only two electrons at a time and keep the others in their SCF orbitals. 

This approach is called the independent electron-pair approach (lEPA), since electron pairs are treated completely independently of each other. The lEPA has been developed and discussed extensively by Sinanoglu and by Nesbet, although in different contexts and in variants which differ slightly from the one sketched above. 

The lEPA is obviously size-extensive. A simple justification of the lEPA may be given by using a transition energy formula for . Let 

In other words, the lEPA is accurate up to second order of perturbation theory based on the Hartree-Fock (HF) model as zeroth-order approximation. The exact third-order contribution involves—besides the terms which are properly included—the interaction between different pair correlation functions 

These terms are nowhere included within the lEPA, which is the major drawback of this procedure. As a consequence, one finds that evaluated according to Eqs. (5) and (6) depends crucially on the actual choice of occupied molecular orbitals (MOs), i.e. is not invariant with respect to a unitary transformation of occupied MOs. lEPA correlation energies may either overshoot or undershoot the exact E dejiending on the chosen. This deficiency may be rectified by an inclusion of (9) in in the lowest order of perturbation theory,but this approach will not been pursued further. 

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Parallel to these endeavors, work started in Germany on new concepts to account for electron correlation. The independent electron pair approach (lEPA) was developed by Ahlrichs and Kutzelnigg, followed a few years later by the CEPA (coupled electron pair approach).The relation of these methods to contemporary Moller-Plesset second order (MP2) and coupled cluster treatments is discussed in Ref. 60. Work on circular dichroism by Ruch and on the chemical shift by Voitlander showed the variety of ab initio problems treated. The special priority program of the DFG from 1966-1970 demonstrated the intended impact. 

Table 3. Summary of duster valence electron counts from the Polyhedral Skeletal Electron Pair approach...

CEPA Coupled electron pair approach N Slight underestimate of bonding... 

Neese, R, Wennmohs, E, and Hansen, A. (2009). Efficient and accurate local approximations to coupled-electron pair approaches An attempt to revive the pair natural orbital method, / Chem. Phys. 130, p. 114108, doi 10.1063/l.3086717. 

IIL THEORY OF PAIR APPROACHES A. The Ori nal Coupled Electron-pair Approach... 

Wan-Vaacob Ahmad and Mat B. Zakaria, Drawing Lewis Structures from Lewis Symt)ols A Direct Electron Pairing Approach, /. Chem. Educ.. Vol. 76,1999, 329-331. 

The polyhedral skeletal electron pair approach retains the condition that each metal atom uses its nine valence atomic orbitals. However it does not consider all the electron in the system but only those involved in the metal network. This approach is fundamentally grounded on the analogy existing between metal clusters and boron hydrides and carboranes. 

Mingos DMP (1984) Polyhedral skeletal electron pair approach. Acc Chem Res 17 311-319... 

Gabriel et al. [60] reported ab initio coupled electron pair approach (CEPA) DMSs of SiH2 for X Ai and states represented with polynomials. Absorption intensities T = 300 K) were computed and plotted. 

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