Bent-bond representation

Figure 3.19 Bent-bond representation of the double bond in ethene. The overlap of sp3 orbitals on each carbon atom produces to bend bond (r) orbitals.

Figure 2. Bent bond representation of double and triple bonds to carbon in (a) CO2, (b) C2F2 and (c) QHg.

A general equation can be derived that describes the variation in direction of the valence electron density about the nucleus. The distortion from sphericity caused by valence electrons and lone-pair electrons is approximated by this equation, which includes a population parameter, a radial size function, and a spherical harmonic function, equivalent to various lobes (multipoles). In the analysis the core electron density of each atom is assigned a fixed quantity. For example, carbon has 2 core electrons and 4 valence electrons. Hydrogen has no core electrons but 1 valence electron. Experimental X-ray diffraction data are used to deri e the parameters that correspond to this function. The model is now more complicated, but gives a better representation of the true electron density (or so we would like to think). This method is useful for showing lone pair directionalities, and bent bonds in strained molecules. Since a larger number of diffraction data are included, the geometry of the molecular structure is probably better determined. 

As mentioned earlier, oxidative complexation (pattern 3) and reductive decomplexa-tion (pattern 13) are nothing but alternate representations of 7r-complexation (pattern 2) and TT-decomplexation (pattern 12), respectively. It might be useful to note that the -TT-complex formalism and palladacyclopropane formalism correspond to the Walsh model and more commonly used bent o--bond representation of cyclopropanes, respectively. The palladacyclopropane formalism is useful in discussing the formation of larger palladacycles in terms of carbopalladation of palladacyclopropanes and paUadcyclo-propenes (Part IV). 

This conclusion was reinforced by a number of investigations. The title of one publication was Double Bonds Are Bent Equivalent Hybrid (Banana) Bonds. Another study concluded that the GVB description of the double bond in (C2F4) is not the traditional picture of o and n bonds but rather a representation in terms of two bent bonds. Still another paper comparing... 

A drawing may imply as much about the conceptual model used to analyze a problem as it tells about the chemical substance under consideration. A representation of a carbon-carbon double bond may use the cr,n formulation or the bent bond formulation. 

The popularity of HMO theory has helped the cr,7t formulation become the standard pictorial representation of double bonds. The applicability of the bent bond model to benzene was discussed by Schultz, P. A. Messmer, R, P. /. Am. Chem. Soc. 1993, 125,10943. 

Since ethylene oxide has a plane of symmetry bisecting the CC bond [marked by a dotted line in (81)], its MOs must be either symmetric or antisymmetric with respect to reflection in this plane. The MOs in the 7r-complex representation (78) satisfy this criterion but the bent-bond orbitals in (80) do not. We can, however, construct from the two bent-bond orbitals and 02 two linear combinations 0i + 02 02 which is... 

Fig. 4-8.—A representation of the ethylene molecule with the double bond shown as two bent single bonds.

The existence of the agostic bond C-II " M has been firmly established by X-ray and neutron diffraction methods. The symbolic representation C-H M indicates formal donor interaction of a C-H bond with an electron-deficient metal atom M. As in all 3c-2e bridging systems involving only three valence orbitals, the bonded C-II M fragment is bent. The agostic bond will be further discussed in Section 11.5.3. 

Fig. 1. Schematic representation of the essentially nonbonding molecular orbitals in a bent (7 -CjHa),Ti molecule (eu = 30°). For comparison, the corresponding orbitals of a car-bene and their interactions with bonding and antibonding orbitals are traced at the right (hatched orbitals are doubly occupied). Reprinted with permission from Brintzinger and Bar-tell (6), /. Am. Chem. Soc. 92,1106 (1970). Copyright 1970 by the American Chemical Society.

In tetrahedral symmetry the o--bond functions induce a representation AI -j- Tj. The partners px, Py, Pz in T, and the s orbital of Ai type can therefore be used to form the four equivalent bond functions of sp type. The results for other common molecular symmetries are obtained in the same way. Whenever the symmetry of the molecule is lowered, say by bending, then the symmetry restrictions on the content of hybrid orbitals are relaxed and other types of orbitals that have the proper symmetry in the point-group of the bent molecule, may participate. For example, if NOi" becomes nonplanar, the symmetry group becomes Czv, ( 3 ) correlates with A i(Cjr) and since p, transforms like A1, the pz orbital can enter into hybrid bond function can be obtained from symmetry. Let be the ith bond function. Then if Tr is a... 

Figure 4.7 Schematic representation of reievant orbitai interactions in (a) iinear C(BH)j and in (b-d) bent C(BH)2. The boron-carbon a bonding in b and c depicts the same situation, but it uses different starting points.

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