Independent electron pair approximation

Hartree-Fock with Proper Dissociation Internally Consistent Self Consistent Orbitals Independent Electron Pair Approximation Intermediate Neglect of Differential Overlap Intermediate Retention of Differential Overlap Iterative Natural Orbital Ionization Potential... 

This defines an independent electron pair approximation in terms of extremal pairs, which can be regarded as a generalization of the independent electron pair approximation (IEPA) [4, 8] in terms of pairs (ij) constructed form (preferably) localized orbitals. As in the discussion in Paper I for MP2 [5], one can show that the extremal pairs defined in this section are related to approximate natural geminals corresponding to the coupled-cluster wave function. 

OVC stands for optimum-valence configuration", lEPA for "independent-electron-pair approximation" h) Equilibrium distances (in a. u.)... 

One of us [1] reviewed the situation of electron correlation a quarter of a century ago in a paper with the title electron correlation in the seventies [2]. At that time most quantum chemists did not care about electron correlation, and standard methods for the large scale treatment of electron correlation, like Mpller-Plesset (MP) perturbation theory or coupled-cluster (CC) theory were not yet available. However precursors of these methods such as lEPA (independent electron pair approximation) and CEPA (coupled-electron-pair approximation) had already been developped and were being used, mainly in research groups in Germany [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]. 

Closely related to CC theory (and also to MP-theory) are the lEPA [3, 10, 12] and CEPA [11, 12, 13, 132, 133, 134] methods, that were used in molecular calculations prior even to the large scale studies in terms of MP2. lEPA (independent electron pair approximation) has in common with MP2 that the various electron pairs are decoupled, and MP2 has, in fact, been a first step on the way to lEPA [3,10,12]. Unlike in MP2 the various decoupled pairs are treated exactly (in the limitations due to the use of a finite basis) in lEPA. In CEPA (coupled electron pair approximation) the coupling of the pairs is taken into account, but unlike in CCSD, to which CEPA is closely related, some (generally small) indirect couplings are ignored. Although CEPA can be formulated as an approximation to CCSD [11, 12], in practical applications it has turned out that CEPA performs even better than CCSD (although it is cheaper), because apparently effects of triple substitutions are, to some extent simulated in CEPA [135, 136]. lEPA and CEPA share with MP and CC that they are extensive and not variational. 

F. The Independent Electron-Pair Approximation for Intra and Interpair... 

It can be shown 88) but we are not going to do so here — that starting from the idea of " -representability in the limit one can derive a theory of independent electron pairs that is equivalent to the independent electron-pair approximation (lEPA) which we shall now derive in a more conventional way starting from a Cl expansion. 

The next step in a generalization of the independent electron-pair correlation is to include the interpair correlation contributions as well. The recipe of the general independent electron-pair approximation (lEPA) is hence to calculate independently the correlation-energy contributions Ecorr for any pair of spin orbitals, i. e. the correlation energy accounted for by the wave function... 

There axe two main reasons why this general independent electron-pair approximation (lEPA) has not been too popular for some time. 

There are finally attempts to apply diagrammatic techniques of many-body perturbation theory S ), with the summation of certain diagrams to infinite order, to the correlation problem in atoms and molecules. A close relationship between this kind of approach and the independent electron-pair approximation has been demonstrated >. 

Electron correlation energies for small molecules have been calculated either by the independent electron-pair approximation (lEPA) or by configuration interaction (Cl). Brute force Cl in general did not give too good results Cl calculations gave a substantial part of the correlation energy only where the weakly occupied orbitals had been optimized somehow. Here one must mention the calculations on diatomic molecules by Bender and Davidson ) and by Wahl et.al. >. 

The total correlation energy may be approximated by a sum over pair correlation energies (independent electron-pair approximation lEPA, note that the c s here are not Lagrange multipliers). 

In Section 5.1 we describe the independent electron pair approximation (lEPA). We use an approach that leads quickly to the computational formalism but which may give the misleading impression that lEPA is an approximation to DCI. After showing what is involved in performing pair calculations, we will return to the physical basis of the formalism and show that in fact both lEPA and DCI are different approximations to full Cl. In Subsection 5.1.1 we describe a deficiency of the lEPA, not shared by DCI or the perturbation theory of Chapter 6 namely, that the lEPA is not invariant under unitary transformations of degenerate molecular orbitals. In Subsection 5.1.2 we present some numerical results which show that while the lEPA is reasonably accurate for small atoms, it has serious deficiencies when applied to larger molecules. 

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