Sigma-pi separation

Santos, J. C., Tiznado, W., Contreras, R, Fuentealba, P. (2000). Sigma-pi Separation of the Electron Localization Frmction and Aromaticy,J. Chem. Phys. 120,1670-1673. Savin, A., Jepsen, J., Andersen, O. K., Preuss, H., von Schnering, H. G. (1992). Electron localization in the solid-state structures of the elements The diamond structure. Angew. Chem., Int. Ed. Engl. 31,187-188. 

Santos, J. C. Tiznado, W. Contreras, R. Fuentealba, P. Sigma-pi separation of the electron localization function and aromaticity. J. Chem. Phys. 2004,120,1670. 

J ug, K., Hiberty, P. C., and Shaik, S. "Sigma-Pi Energy Separation in Modern Electronic Theory for Ground States of Conjugated Systems." Chem. Rev., 101,1477 (2001). 

An approximate treatment of tt electron systems was introduced in 1931 by Erich Huckel (Figure 15.17) and is called the Huckel approximation of tt orbitals. The first step in a Huckel approximation is to treat the sigma bonds separately from the pi bonds. Therefore, in a Huckel approximation of a molecule, only the tt bonds are considered. The usual assumption is that the <7 bonds are understood in terms of regular molecular orbital theory. The <7 bonds form the overall structure of the molecule, and the tt bonds spread out over, or span, the available carbon atoms. Such 77 bonds are formed from the side-on overlap of the carbon 2p orbitals. If we are assuming that the tt bonds are independent of the cr bonds, then we can assume that the 77 molecular orbitals are linear combinations of only the 2p orbitals of the various carbon atoms. [This is a natural consequence of our earlier linear combination of atomic orbitals—molecular orbitals (LCAO-MO) discussion.] Consider the molecule 1,3-butadiene (Figure 15.18). The tt orbitals are assumed to be combinations of the 2p atomic orbitals of the four carbon atoms involved in the conjugated double bonds ... 

If a compound is to absorb in die region above 200 nm, the energy separation between its HOMO and LUMO must be smaller than in the case of alkanes. The bonding and antibonding MOs for pi bonds, which are weaker than sigma bonds, are closer... 

A triple bond is composed of one sigma bond and two pi bonds. Since the two pi bonds are perpendicular to each other, they are treated as two separate, noninteracting pi bonds. Perpendicular orbitals do not interact. The triple bond is linear, and atoms bonded to it lie in a straight line (Fig. 1.13). Organic chemists tend to draw skinny p orbitals (see Fig. 1.8) the triple bond is overall cylindrically symmetrical. 

Accordiug to valeuce boud theory, the C atom is described as sp hybridized, aud it forms oue sigma boud with each of the three O atoms. This leaves one unhybridized 2p atomic orbital on the C atom, say the 2p orbital. This orbital is capable of overlapping and mixing with the 2p orbital of any of the three O atoms. The sharing of two electrons in the resulting localized pi orbital would form a pi bond. Thus, three equivalent resonance structures can be drawn in valence bond terms (Figure 9-10b). We emphasize that there is no evidence for the existence of these separate resonance structures. 

Fig. 9 Electronic localization function (ELF) for benzene. Left. ELF = 0.85 iso-surface. Right. ELF = 0.66 iso-surfaces. The right iso-surface is cut on the front side for showing the complex topology the Carbon core basins sharply separate from the scalar ELF field. The aromatic ELF basin is clearly defined. Both in the high or lower ELF value iso-surface, no separation between Sigma and Pi basins can be found, which is a characteristic of delocalized bonds, similar to that shown in Fig. 11. All the molecular plots reporting ELF iso-surfaces or MPD are performed using the Xcrysden program [44]...

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