Four simple three-electron systems

In this chapter we describe four rather different three-electron systems the it system ofthe allyl radical, the HeJ ionic molecule, the valence orbitals ofthe BeHmolecule, and the Li atom. In line with the intent of Chapter 4, these treatments are included to introduce the reader to systems that are more complicated than those of Chapters 2 and 3, but simple enough to give detailed illustrations of the methods of Chapter 5. In each case we will examine MCVB results as an example of localized orbital treatments and SCVB results as an example of delocalized treatments. Of course, for Li this distinction is obscured because there is only a single nucleus, but there are, nevertheless, noteworthy points to be made for that system. The reader should refer back to Chapter 4 for a specific discussion of the three-electron spin problem, but we will nevertheless use the general notation developed in Chapter 5 to describe the results because it is more efficient. 

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Four simple three-electron systems Table 10.1. C2v characters. 

The electronics behind the insertion reaction is generally explained in terms of a simple three-orbitals four-electrons scheme. Hoffmann and Lauher early recognized that this is an easy reaction for d° complexes, and the relevant role played by the olefin n orbital in determining the insertion barrier [26], According to them, the empty Jt orbital of the olefin can stabilize high energy occupied d orbitals of the metal in the olefin complex, but this stabilization is lost as the insertion reaction approaches the transition state. The net effect is an energy increase of the metal d orbitals involved in the d-7t back-donation to the olefin n orbital. Since for d° systems this back-donation does not occur, d° systems were predicted to be barrierless, whereas a substantial barrier was predicted for dn (n > 0) systems [26],... 

The yellow to orange compounds 804(118207)2, 864(84 013)2, and 8e4(8b2Fii)2 have been prepared. Crystallographic studies on 804(118207)2 have shown that the cation 8c4 + has square-planar D h) geometry. The structure can be described by valence bond theory in terms of four resonance structures equivalent to (la), or by simple molecular orbital theory in which three of the four n molecular orbitals are filled. " The 8e4 + ions are examples of six-jr-electron systems, and they are thus examples of inorganic aromatic compounds (lb). 

Bimolecular nucleophilic substitution reactions (Sn2) involve pentacoordinate carbon in their transition state. Whereas pentacoordinate CHs -like intermediates of Se2 reactions represent only an eight-electron system around the carbocationic center involving 3c-2c bonding (octet rule is obeyed), an Sn2 reaction intermediate would represents a 10-electron system involving three-center, four electron (3c-4e) bonding (a lO-C-5 species). This, however, is an unstable situation since carbon cannot accommodate 10 electrons in its valence shell. A simple picture of typical molecular orbitals in 3c-4c bonding is shown in Figure 6.9. 

A corresponding example in a simple molecular system would be the multielectron excitation of Li2 la la 2a S+, where three or four of the electrons in the subshells could be excited to relatively low-lying states labeled... 

A rigorous description of electron hopping in the presence of other unpaired electrons can be written down for the simple model system defined in Fig. 6.4. The two electrons in the ai and b orbitals provide a static background of unpaired electrons for the mobile electron in the 02 b2 channel. Choosing Ms = there are 24 ways to distribute the three electrons over the four orbitals, but only six of them... 

Craig, D. P., Proc. Roy. Soc. [London) A202, 498, Electronic levels in simple conjugated systems. I. Configuration interaction in cyclobutadiene. (ii) All the interelectron repulsion integrals, three- and four-centered atomic integrals, are included. 

In this chapter, we develop a model of bonding that can be applied to molecules as simple as H2 or as complex as chlorophyll. We begin with a description of bonding based on the idea of overlapping atomic orbitals. We then extend the model to include the molecular shapes described in Chapter 9. Next we apply the model to molecules with double and triple bonds. Then we present variations on the orbital overlap model that encompass electrons distributed across three, four, or more atoms, including the extended systems of molecules such as chlorophyll. Finally, we show how to generalize the model to describe the electronic structures of metals and semiconductors. 

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