Three-center bonding four-electron

Schleyer, P. v. R., Bremer, M., Schotz, K., Kausch, M. Schindler, M. 1987 Four-center two-electron bonding in a tetrahedral topology. Experimental realization of three-dimensional homoaromaticity in the l,3-dehydro-5,7-adamantanediyl dication. Angew. Chem. Int. Ed. Engl. 26, 761 763. 

The energy level diagram shown in Fig. 13 along with the six electrons from the Lewis structure shown earlier shows that the lower three BMO s are filled. These MO s are four-center two-electron bonds and are therefore delocalized over the whole molecule. 

So far, we have looked at different modes of bonding and how Pauli repulsive orbital interactions may either influence them (2c-2e bond) or be an essential part (2c-3e bond). In this section, we examine a different role of Pauli repulsion, namely, the one it plays in the absence of bonding interactions between groups. Here, it is responsible for the fact that such groups, A and B say, repel each other. Or, to put it in another way, steric repulsion between A and B is a pure quantum effect, caused by the Pauli repulsion between same-spin electrons of the different fragments, such as the well-known two-center, four-electron (2c-4e) repulsion (19) or the two-center, two-same-spin-electron (2c-2sse) repulsive component (20) of the three-electron bond. 

The formulas of 37-39 show the substitution of three carbonyls by a conjugated diene. Due to the fact that dienes are four-electron donors, the complexes are electron-deficient species. The electron deficiency is reduced by formation of C—H—Cr three-center, two-electron bonds, previously found for a number of other complexes (43). When 2-methyl-5-isopropyl-l,3-cyclohexadiene is used as a potential ligand, the expected complexes 37r and 39r are not obtained, but instead complexes with the isomeric l-methyl-4-isopropyl-l,3-cyclohexadiene group (37r and 39r ) are formed [Eq. (19)]. Similarly, lk and 11 form not only the corresponding complexes 39k and 391, but also the isomeric complexes with (Z)-l,3-hexadiene (39k ) and with (Z)-2-methyl-1,3-pentadiene (391 ). 

Let us compare the MO descriptions of six and four sep R4E4 tetrahedral clusters. In Figure 2.5 the cluster MO energies for E = C and E = Ga are shown alongside the localized descriptions discussed above. The number of filled and unfilled MOs is equal for E = C a consequence of the two-center-two-electron bond model. Conversely, the number of filled MOs is less than the number of empty MOs for E = Ga a consequence of the three-center-two-electron bond model. Note also that an e symmetry pair of orbitals lies in between lower-energy filled orbitals and... 

Answer. There are a total of 30 orbitals and 26 electrons to be utilized in bonding. The external B-H bonds utihze 12 orbitals and 12 electrons leaving 18 orbitals and 14 electrons for cluster bonding. Four three-center B-B-B and three two-center B-B bonds utilize 12 + 6=18 orbitals and 8 + 6 = 14 electrons. They may be placed on the framework as shown in the diagram above where the top and the bottom of the octahedron are shown separately. By counting you can find that B(l) and B(2) are associated with three three-center-two-electron bonds (and a B-H bond), B(3) and B(4) with two three-center and one two-center bonds (and a B-H), and B(5) and B(6) with one three-center and two two-center bonds (and a B-H), i.e., eight electrons around each B. Notice that one would need to draw a considerable number of resonance structures to give all the boron atoms the same electronic environment. 

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