Ethylene orbitals

Figure 1.14 The structure of ethylene. Orbital overlap of two sp hybridized carbons forms a carbon-carbon double bond. One part of the double bond results from a (head-on) overlap of sp2 orbitals (green), and the other part results from (sideways) overlap of unhybridized p orbitals (red/blue). The ir bond has regions of electron density on either side of a line drawn between nuclei.

In Ag-SAPO-ll/C2H4 zeolite the EPR at 77 K shows the spectra of Ag° atoms and C2H5 radicals. After annealing at 230 K those species disappeared and then an anisotropic EPR sextet was recorded. Based on DFT calculation the structure of complex was proposed in which two C2H4 ligands adopted eclipsed confirmation on either side of the Ag atom. As a result the overwhelming spin density is localised on ethylene orbitals. 

The reason for this becomes apparent when one compares the shapes of the localized it orbitals with that of the ethylene 7r orbital. All of the former have a positive lobe which extends over at least three atoms. In contrast, the ethylene orbital is strictly limited to two atoms, i.e., the ethylene 7r orbital is considerably more localized than even the maximally localized orbitals occurring in the aromatic systems. This, then, is the origin of the theoretical resonance energy the additional stabilization that is found in aromatic conjugated systems arises from the fact that even the maximally localized it orbitals are still more delocalized than the ethylene orbital. The localized description permits us therefore to be more precise and suggests that resonance stabilization in aromatic molecules be ascribed to a "local delocalization of each localized orbital. One infers that it electrons are more delocalized than a electrons because only half as many orbitals cover the same available space. It is also noteworthy that localized it orbitals situated on joint atoms (n 2, it23, ir l4, n22 ) contribute more stabilization than those located on non-joint atoms, i.e. the joint provides more paths for local delocalization. 

It is a straightforward task to carry the procedure one step further. In order to find the butadiene orbitals, it is easiest to allow two ethylene units to come together end to end. Figure 10.20 illustrates the results. The important interactions are between orbitals of the same energy we simply treat the ethylene orbitals as the basis, and combine the bonding pair in the two possible ways and the antibonding pair in the two possible ways. 

Figure 2. Initially, in a thermal reaction, there are two electrons in each of the ethylene -orbitals, and it is apparent that if the reaction follows the symmetrical reaction path, the initial state correlates with a highly excited state of the product. Configuration interaction between the two Aig states leads to an avoided crossing, but there is still a considerable activation energy (Figure 3a). The thermal reaction is...

At this stage we turn to the use of the two-particle density matrix. We shall find it convenient to introduce bonding and antibonding ethylenic orbitals... 

We now imagine the two-particle matrix to be expanded in terms of 9 -, (p j and other atomic or ethylenic orbitals and we measure the coefficient with which the term 9 ,-,(l) (2)9P (l ), (2 ) occurs. We choose this term because, for a pure ethylenic double bond, the coefficient of this term is unity. By seeking the coefficient of this term in the full molecular two-particle matrix, we are measuring some kind of double-bond character for the bond. For a closed-shell molecule it is not difficult to show that this coefficient is... 

To make contact with the various many-electron approaches to the relaxation energy, we define the set of occupied ( i and unoccupied ( i ethylenic orbitals as... 

Since the index a runs over all n occupied ethylenic orbitals i> while the index r runs over all n unoccupied orbitals y >, we have... 

The total symmetry of each state is determined by the symmetries of the populated molecular orbitals in that state. We need not concern ourselves with molecular orbitals that are not populated with electrons. In the analysis of the [2+2] cycloaddition, there were two mirror planes defined as mirror planes. To do this, one creates a multiplication product of the symmetries of the electrons with respect to each symmetry operation. Let s start with the ground state of the mixture of ethylene orbitals. With respect to four electrons in orbitals that are S, so the state symmetry is S X S X S X S. With respect to <72/ two electrons are in an orbital that is S, and two electrons are in an orbital that is A. Therefore the product is S X S X A X A. 

Once again these perturbations of coefficients and energies of the ethylene orbitals can be anticipated using resonance. Eq. 15.8 shows the expectations for substitution of an electron wi thd rawing group on an ethylene. The 3-carbon is electrophilic. Therefore, the LUMO should he polarized to the unsubstituted carbon as seen in orbital (n). The reverse polarization is predicted for the HOMO, and this is seen in orbital (m). 

The symmetries of the butadiene molecular orbitals can be easily derived from the symmetries of the starting ethylene orbitals (Rg. 12.16). 

The change in energy when one electron in an isolated carbon p orbital spreads to occupy an ethylene % orbital is called p. The jr-bonding energy. 

---