Separated electron pair, theory

In the separated electron pairs theory the eight electrons may be grouped in four distinct pairs as follows ... 

We must now address a fundamental question. Are there C-H bonds in methane The answer from MO theory is clearly no. Population of the four bonding molecular orbitals with four pairs of electrons leads to a bonding interaction among the carbon atom and all of the hydrogen atoms (not just between carbon and the individual hydrogens). Thus, we should say that there is bonding in MO theory, but there are not distinct bonds formed by separate electron pairs localized between two atoms. 

A tentative application of this idea has been made by using the same molecular wave function which is used in the so-called theory of the separated electron pairs , developed mainly by Lennard-Jonesi and, more recently, by Parks and Parr. ... 

Now, in the theory of the separated electron pairs as formulated by Parks and Parr it is possible to show that by separating the contributions due to the two nuclei A and B, relative to the... 

In the future work on interactions between groups in a molecule, the McWeeny s theory of the separated electron groups will very probably assume a very important r61e. This theory, which is a particular formulation of the general theory of the density matrix, may also be considered as a generalization of the electron pairs theory. 

Primas, H. Separability in many-electron systems. In Modem quantum chemistry. Istanbul lectures. Sinanoglu, O. (ed.). New York Academic Press 1965 s°) Paldus, J., Ctzek, J. Relation of coupled-pair theory, Cl and some other many-body approaches. In Energy, Structure, and Reactivity. Proceedings of the 1972 Boulder Summer Research Conference on Theoretical Chemistry. Smith, D. W., McRae, W. B. (eds.). New York Wiley 1973, pp. 198-212... 

Improta et studied large molecules with a well-separated electron donor and electron acceptor pair. In this case, the electron-transfer process may lead to a dissociation of the molecule. Improta et al. applied the Marcus theory to obtain an expression for the electron transfer rate constant. Subsequently, the values of the parameters entering this expression were calculated using a density-functional approach for the solute together with the polarizable continuum model for the solvent. They applied their approach for a specific system (for the present purpose, the details are less important) and found the results of Table 24. Here, three different... 

The Fermi hole for the reference electron at a bonded maxima in the VSCC of the carbon atom has the appearance of the density of a directed sp hybrid orbital of valence bond theory or of the density of a localized bonding orbital of molecular orbital theory. Luken (1982, 1984) has also discussed and illustrated the properties of the Fermi hole and noted the similarity in appearance of the density of a Fermi hole to that for a corresponding localized molecular orbital. We emphasize here again that localized orbitals like the Fermi holes shown above for valence electrons are, in general, not sufficiently localized to separate regions of space to correspond to physically localized or distinct electron pairs. The fact that the Fermi hole resembles localized orbitals in systems where physical localization of pairs is not found further illustrates this point. 

VSEPR theory predicts that four valence shell electron pairs are directed toward the corners of a regular tetrahedron. That shape gives the maximum separation for four electron pairs around one atom. Thus, VSEPR theory predicts tetrahedral electronic geometry for an AB molecule that has no unshared electrons on A. There are no lone pairs of electrons on the central atom, so another atom is at each corner of the tetrahedron. VSEPR theory predicts a tetrahedral molecular geometry for each of these molecules. 

In an SFg molecule we have six valence shell electron pairs and six F atoms surrounding one S atom. Because the valence shell of sulfur contains no lone pairs, the electronic and molecular geometries in SFg are identical. The maximum separation possible for six electron pairs around one S atom is achieved when the electron pairs are at the comers and the S atom is at the center of a regular octahedron. Thus, VSEPR theory is consistent with the observation that SFg molecules are octahedral. 

The extent to which individual electron pairs are localized in distinct spatial regions has been carefully analyzed by Bader and Stephens (1975) using the minimum fluctuation criterion. These authors arrive at the conclusion that the model of spatially localized pairs is appropriate for LiH, BeH2, BH3, and BH-r, it is borderline for CH4, but in NHj, OH2, FH, Ne, N2, and F2, the motions of the valence electrons are so strongly inter-correlated, the localized pair model ceases to afford a suitable description. Moreover, their results provide no physical basis for the view that there are two separately localized pairs of nonbonded electrons in H20. This clearly shows the limit of the Lewis electron pair concept which otherwise has practically disappeared in Linnett s theory. 

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