Description of Ethene

Let s review how the tt molecular orbitals of ethene are constructed. An MO description of ethene is shown in Figure 7.8. The twop orbitals can be either in-phase or out-of-phase. (The different phases are indicated by different colors.) Notice that the number of orbitals is conserved—the number of molecular orbitals equals the number of atomic orbitals that produced them. Thus, the two atomic p orbitals of ethene overlap to produce two molecular orbitals. Side-to-side overlap of in-phase p orbitals (lobes of the same color) produces a bonding molecular orbital designated i/ i (the Greek letter psi). The bonding molecular orbital is lower in energy than the p atomic orbitals, and it encompasses both carbons. In other words, each electron in the bonding molecular orbital spreads over both carbon atoms. 

A much older description of ethene is known as the bent bond formulation. The double bond is described as the result of overlap of two sp hybrid orbitals on each of the two carbon atoms, as shown in Figure 1.29. This model also predicts that ethene should be a planar molecule, but it predicts H-C-H bond angles of 109.5°— which is even further from the observed 117° than was the prediction based on sp hybridization. Furthermore, except for cyclopropane, we feel imcomfortable about drawing molecular pictures with bonds that... 

Overlap of sp hybrid orbitals in the bent bond description of ethene. 

The most exciting application of bond order indices concerns the description of chemical reactions involving the simultaneous change of several bonds. An example is the unimolecular decomposition of ethanol, which can happen at high temperature or IR multiphoton excitation of the molecule. Out of the possible dissociation channels, the lowest barrier characterizes the concerted water loss of the molecule, yielding ethene and H20 [30]. 

Several quantitative descriptions of [4 + 2] cycloadditions have been reported applying equation 15 or derived equations. HOMO and LUMO energies can be calculated from ionization potentials or electron affinities. Orbital coefficients have been calculated for simple ethenes and dienes using various quantum mechanical methods, e.g. INDO, CNDO/2, AMI and STO-3G. These different methods may, however, lead to substantially different results54-56. 

The SC descriptions of the electronic mechanisms of the three six-electron pericyclic gas-phase reactions discussed in this paper (namely, the Diels-Alder reaction between butadiene and ethene [11], the 1,3-dipolar cycloaddition offulminic acid to ethyne [12], and the disrotatory electrocyclic ring-opening of cyclohexadiene) take the theory much beyond the HMO and RHF levels employed in the formulation of the most popular MO-based treatments of pericyclic reactions, including the Woodward-Hoffmarm mles [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman model [4—6]. The SC wavefunction maintains near-CASSCF quality throughout the range of reaction coordinate studied for each reaction but, in contrast to its CASSCF counterpart, it is very much easier to interpret and to visualize directly. 

A comparison of various calculations revealed <1997PCA9421> that an accurate description of the ozonolysis of ethene is obtained at the CCSD(T) level with a TZ+2P basis set, while other methods, which cover less correlation effects, fail to provide a consistent description of all reaction steps. It was shown that the primary ozonides (1,2,3-trioxolanes) are not collisionally stabilized under atmosphere conditions <1997PCA9421>. 

The description of the bonding of ethene to transition metals is known as the Dewar-Chatt-Duncanson model. This builds on the previous descriptions for CO and CH2 with the exception that we must now consider the frontier orbitals of the ligand to be molecular orbitals delocalized over the two (or more) donor atoms. The basic features are presented for ethene however, the bonding scheme applies in principle to the side-on coordination of any multiple bond to a transition metal. 

According to the relationship between three-membered rings and 7r-complexes, cyclopropane can be considered as a resonance hybrid of three equivalent methylene-ethene n-complexes Of course, such Ti-complexes do not exist but this is also true in the case of the two cyclohexatriene resonance structures normally used to present benzene. Spin-coupled valence bond calculations of Karadakov and coworkers reveal that there is a small but significant contribution of 3.7% to the electronic structure of 1 resulting from 7r-com-plex structures (see Section V. E). This indicates that the Ti-complex description of is not totally unreasonable and, although seldom used, helps to unravel some of the peculiarities of bonding in 1 ... 

The detailed description of all the proposed mechanisms is not the aim of this work (see Reference (i) for more details), but a few concepts are briefly discussed in the following (a) Scheme 11 may be read in two dimensions in the vertical direction, the evolution of the initial species upon addition of one ethene molecule is represented, whereas, in the horizontal direction, all the possible isomeric structures characterized by an average C fCv ratio equal to 2, 3, and 4 are reported, (b) In all the proposed reactions, the metal formally becomes Cr(IV) as it is converted into the active site. This hypothesis is supported by investigations of the interaction of molecular transition metal complexes with ethene (226,227). Furthermore, it has... 

The six SC orbitals from the rightmost column in Fig. 6 fall into two distinct groups, each of which is associated with one of the two reactants. The orbital pair 4) is responsible for the ethene carbon-carbon n bond. The remaining four orbitals are localised on the diazomethane fragment and very much reproduce the well-known SC description of isolated according to which the central... 

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