Multi-center bond

To be more exact, every bond is a multi-center bond with contributions of the wave functions of all atoms. However, due to the charge concentration in the region between two atoms and because of the inferior contributions %H2, Xm> and Xh4> the bond can be taken to a good approximation to be a two-center-two-electron bond (2c2e bond) between the atoms C and HI. From the mathematical point of view the hybridization is not necessary for the calculation, and in the usual molecular orbital calculations it is not performed. It is, however, a helpful mathematical trick for adapting the wave functions to a chemist s mental picture. 

Hypervalent 10—E f (C2X2) compounds are widely studied.10a,b Furukawa and co-workers studied the 10-E-4 (C2X2) of the types 30 and 31, together with the related compounds, such as 32.10b,15<3,35,55 The interactions are established by the X-ray analysis and NMR.15d,3S Adducts 33 and 34 are also detected by NMR. If the X and Te atoms in 33 and 34 align linearly, the multi-center bonds are expected to form the extended hypervalent bonds, which will be discussed later. 

Aside from tert- mty cation, where the experimental X-ray structure is clearly suspect, and aside from semi-empirical methods applied to cations with multi-center bonding, all models perform quite well for all systems. Subtle (and not so subtle) effects such as the alternation in bond distances in benzyl and in heptamethylbenzenium cations, or the greatly elongated carbon-carbon bonds in the derivative of adamantyl cation are generally well reproduced. In fact, except for systems capable of multi-center bonding, the differences among the various methods are fairly modest. (Of course, this is due in part to "lack of precision" in the experimental data.)... 

It is important to point out that the covalent bond has many faces. They can range from simple s, p, d, bonds to sp- or spd- hybridization bonds which may result in a and ji bonds that form the building block for single, double, and triple bonds. In more complex cases they can be resonance bonds or multi-centered bonds that are often observed in metals and alloys. 

Fig. 16.17. Mechanism of the carbocupration of acetylene (R = H) or terminal alkynes (R H) with a saturated Gilman cuprate. The unsaturated Gilman cuprate I is obtained via the cuprolithiation product E and the resulting carbolithiation product F in several steps—and stereoselectively. Iodolysis of I leads to the formation of the iodoalkenes J with complete retention of configuration. Note The last step but one in this figure does not only afford I, but again the initial Gilman cuprate A B, too. The latter reenters the reaction chain "at the top" so that in the end the entire saturated (and more reactive) initial cuprate is incorporated into the unsaturated (and less reactive) cuprate (I). - Caution The organometallic compounds depicted here contain two-electron, multi-center bonds. Other than in "normal" cases, i.e., those with two-electron, two-center bonds, the lines cannot be automatically equated with the number of electron pairs. This is why only three electron shift arrows can be used to illustrate the reaction process. The fourth red arrow—in boldface— is not an electron shift arrow, but only indicates the site where the lithium atom binds next.

The fourth paper in this volume is devoted to some extensions and generalizations of the algebra of the be- and r-matrices. The latter is only valid for the chemistry of molecular systems that are representable by integer bond orders and thus is not applicable to the great variety of molecules with multi-center bonds and delocalized electron systems. This deficiency is overcome by the introduction of the so-called extended be- and r-matrices the xbe- and xr-matrices. They contain additional rows/columns which refer to the delocalized electron systems. Some corresponding data structures are presented that also account for stereochemical aspects. 

In order to estimate multi-center bonds in the rhombic (Rh) and tetrahedral (Td) AM and AE tetramers, we mapped the charge density distributions of the metal clusters. This analysis compensates for a shortcoming of the Mulliken population analysis, where the analysis estimates only one- and two- center charge distributions. We therefore examined the charge redistribution on the formation of the chemical bonds. We used the differential charge density Ap defined as... 

NMR. If the X and Te atoms in 33 and 34 align linearly, the multi-center bonds are expected to form the extended hypervalent bonds, which will be discussed later. 

The 2s electrons are uncoupled and one is promoted to the 2p orbital to form three equivalent s[P- hybrid orbitals with three axes located in the same plane, each directed to the comers of an equilateral triangle and separated by the same angle of 120°. The covalent radius is not well defined and is estimated to be 0.085-0.090 nm. Since boron has four orbitals available for bonding and only three electrons, it is an electron-pair accq)tor and it tends to form multi-center bonds. 

We are just beginning to explore the fascinating area of hypercoordination, but a global picture with three classes of hypercoordination already emerges from the curve crossing model. The species of the different classes share one common feature, they all possess delocalized electrons and multi-center bonding . The three classes differ though in the manners by which this electronic delocalization is stabilized or not with respect to the normal-coordinated constituents. STATEMENT 6 summarizes the main features of these classes. 

Compare the multi-center bonds in Xep2 with the ones in B2H6. 

One of the major reasons for an increased interest in boron nanostructures is that boron itself has some attractive properties it has a very low density of 2.340 g/cm it has a high melting point (2076°C) and a Mohs hardness of 9.3 (diamond = 10.0). These should be reflected in boron s nanomaterials. Chemically it is of interest in that it has more valence orbitals (4) than valence electrons (3). Therefore, it tends to form so-called electron-deficient compounds having delocalized multi-centered bonds. 

One way to visualize the reaction is to realize that the twelve cage electrons can be accommodated into five 2c-2e bonds plus one multi-center bond. In a planar transition state, this bond would be formed by the in-phase overlap of the five r-orbitals. As the C-C and B-B distances increase from the 1,2-isomer to the transition state (Figure 9), the bonding becomes more dominated by five 2c-2e interactions and the unique 5c-2e (pseudo-jr) interaction. As the reaction proceeds to the 1,5-isomer, stabilizing interactions begin through the opposite lobe of one carbon p-orbital with the indicated boron p-orbitals and with the same lobe of the other carbon and the two indicated boron p-orbitals. 

Tesfaye AA et al. Prediction of a multi-center bonded solid boron hydride for hydrogen storage. Accepted PRB available at http //arxiv.org/PS cache/arxiv/pdf/1003/1003.0492vl. pdf. Accessed 3 Mar. 2011... 

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