Independent electron-pair approach

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. 

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. 

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 >. 

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. 

The most widely used qualitative model for the explanation of the shapes of molecules is the Valence Shell Electron Pair Repulsion (VSEPR) model of Gillespie and Nyholm (25). The orbital correlation diagrams of Walsh (26) are also used for simple systems for which the qualitative form of the MOs may be deduced from symmetry considerations. Attempts have been made to prove that these two approaches are equivalent (27). But this is impossible since Walsh s Rules refer explicitly to (and only have meaning within) the MO model while the VSEPR method does not refer to (is not confined by) any explicitly-stated model of molecular electronic structure. Thus, any proof that the two approaches are equivalent can only prove, at best, that the two are equivalent at the MO level i.e. that Walsh s Rules are contained in the VSEPR model. Of course, the transformation to localised orbitals of an MO determinant provides a convenient picture of VSEPR rules but the VSEPR method itself depends not on the independent-particle model but on the possibility of separating the total electronic structure of a molecule into more or less autonomous electron pairs which interact as separate entities (28). The localised MO description is merely the simplest such separation the general case is our Eq. (6)... 

An approach to quantifying the interaction between solute and solvent and hence to solvent effects on redox potentials is that developed by Gutmann.41 Interactions between solvent and solute are treated as donor-acceptor interactions, with each solvent being characterized by two independent parameters which attempt to quantify the electron pair donor properties (donor number)... 

Here, every bonded electron pair, in atomic or hybrid orbitals, contributes every pair of bonds (or bonds involving nonbonded atoms) with spin-independent electrons contributes — every electron pair with parallel spins contributes — Jy-. This expression tells us that bonding lowers the energy, and nonbonded atoms or nonpaired electrons raise the energy. Increased stability will therefore be found when the negative terms in (9) approach zero, as they must when the relevant atoms or electrons move apart. 

The frozen-core (fc) approach is not restricted to spin-independent electronic interactions the spin-orbit (SO) interaction between core and valence electrons can be expressed by a sum of Coulomb- and exchange-type operators. The matrix element formulas can be derived in a similar way as the Sla-ter-Condon rules.27 Here, it is not important whether the Breit-Pauli spin-orbit operators or their no-pair analogs are employed as these are structurally equivalent. Differences with respect to the Slater-Condon rules occur due to the symmetry properties of the angular momentum operators and because of the presence of the spin-other-orbit interaction. It is easily shown by partial integration that the linear momentum operator p is antisymmetric with respect to orbital exchange, and the same applies to t = r x p. Therefore, spin-orbit... 

An alternative method, named internally contracted Cl, was suggested by Meyer and was applied by Werner and Reinsch in the MCSCF self-consistent electron-pair (SCEP) approach. Here only one reference state is used, the entire MCSCF wavefunction. The Cl expansion is then in principle independent of the number of configurations used to build the MCSCF wavefunction. In practice, however, the complexity of the calculation also strongly depends on the size of the MCSCF expansion. A general configuration-interaction scheme which uses, for example, a CASSCF reference state, therefore still awaits development. Such a Cl wavefunction could preferably be used on the first-order interacting space, which for a CASSCF wavefunction can be obtained from single and double substitutions of the form ... 

Often symmetry operations cannot be used in a simple way to classify chiral forms because, e.g., the molecule consists of a number of conformations. Therefore, independent of the symmetry considerations, a chemical approach to describe chiral molecules has been introduced by the use of structural elements such as chiral centers, chiral axis, and chiral planes. Examples for a chiral center are the asymmetric carbon atom, i.e., a carbon atom with four different substituents or the asymmetric nitrogen atom where a free electron pair can be one of the four different substituents. A chiral axis exists with a biphenyl (Figure 3.2) and chiral planes are found with cyclo-phane structures [17]. Chiral elements were introduced originally to classify the absolute configuration of molecules within the R, S nomenclature [16]. In cases where the molecules are chiral as a whole, so-called inherent dissymmetric molecules, special names have often been introduced atropiso-mers, i.e., molecules with hindered rotation about a helical molecules [18], calixarenes, cyclophanes [17], dendrimers [19], and others [20]. 

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