Molecular orbital for ethylene

FIGURE 5.15 Molecular orbitals for ethylene. Promotion of an electron from the ground state to the excited state is known as a n - n transition and is usually accompanied by an absorption of radiation in the ultraviolet region of the spectrum. 

In molecular orbitals, as in atomic orbitals, nodes are regions of zero electron density that divide an orbital into lobes with amplitudes of opposite sign. When a node coincides with a nuclear position, there are no lobes depicted on that atom. In the following diagram, we see that the bonding v molecular orbital for ethylene has no nodes perpendicular to the bond axis, whereas the antibonding tt orbital has one node perpendicular to the bond axis. 

Figure 11.1 showed the molecular orbitals for ethylene, and these are labeled 7 and 8 in Figure 11.2. In this figure, the magnitude of each orbital is shown, called the orbital coefficient. The + and - signs correlate with the + (dark) or - (light) symmetry of the orbital, which is somewhat arbitrary, but useful for examining the directionality of two reactive orbitals. When two jt systems differ in their substitution pattern, there will be differences in the magnitude of orbital densities (larger or smaller orbitals). Predictions concerning reactivity must, therefore, indicate the magnitude of electron density in each orbital.

Highest occupied molecular orbital for formaldehyde (tapI and ethylene... 

In Chapter 1 we considered only interactions among atomic orbitals. It would be useful, however, to be able also to deal with interactions between molecular orbitals. For example, suppose that we have two molecules of ethylene, which are approaching each other as shown in 1, so that the n orbitals of the two molecules come in closer and closer contact. We might ask whether the following reaction will occur ... 

Let us now apply this method to a specific example. Consider the ethylene molecule with D2h symmetry. As can be seen from the character table of the L 2h point group (Table 6.4.2), this group has eight symmetry species. Hence the molecular orbitals of ethylene must have the symmetry of one of these eight representations. In fact, the ground electronic configuration for ethylene is... 

So the eight pairs of electrons of this molecule occupy delocalized molecular orbitals lag to 1 3U, while the first vacant orbital is l g- Note that the names of these orbitals are simply the symmetry species of theZ)2h point group. In other words, molecular orbitals are labeled by the irreducible representations of the point group to which the molecule belongs. So for ethylene there are three filled orbitals with Ag symmetry the one with the lowest energy is called lag, the next one is 2ag, etc. Similarly, there are two orbitals with Z iu symmetry and they are called lb u and 2bi . All the molecular orbitals listed above, except the first two, are illustrated pictorially in Fig. 6.4.2. By checking the >2h character table with reference to the chosen coordinate system shown in Fig. 6.4.2, it can be readily confirmed that these orbitals do have the labeled symmetry. In passing, it is noted that the two filled molecular orbitals of ethylene not displayed in Fig. 6.4.2, lag and l iu, are simply the sum and difference, respectively, of the two carbon Is orbitals. 

If the wavefunctions for the two p orbitals are added, we form a bonding orbital (n) if the wavefunctions are subtracted, we form an antibonding orbital (it ). Molecular tt orbitals are commonly represented by the atomic orbitals that combine to form them. In the accompanying diagram, the orbitals on the left are the atomic orbitals. These are used to form the molecular orbitals of ethylene, which appear on the right. The atomic orbitals that are combined to form the molecular orbitals are called the basis set. 

Figure 12.5 The interaction of two ethylenes to give the molecular orbitals for 1,3-butadiene.

Fig. 10. Correlation diagram for molecular orbitals for two ethylenes and cyclobutane...

The energies for the molecular orbitals for these two extremes are shown in Fig. 2.4 with the allyl cation and the separate oxyanion on the left and butadiene on the right. The energies of the n and n orbitals of ethylene are placed for reference as dashed lines l ft above and below, respectively. The true orbital energy for the orbitals of acrolein must be in between those of the corresponding orbitals of the allyl cation and... 

Unlike the pi bonding molecular orbitals in ethylene, those in benzene form delocalized molecular orbitals, which are not confined between two adjacent bonding atoms, but actually extend over three or more atoms. Therefore, electrons residing in any of these orbitals are free to move around the benzene ring. For this reason, the structure of benzene is sometimes represented as... 

Similar considerations for a non-zero overlap integral between the occupied ttu molecular orbital of ethylene and the unfilled Ss atomic orbital... 

The left side of Figure 18.9 builds up the molecular orbitals for Zeise s salt, cthylcne-PtClT The ethylene tt level is stabilized by the 2a acceptor orbital. One member of the group of nonboiiding metal functions, namely the 1)2 level, has the... 

Figure 9.4 Canonical and localized molecular valence orbitals for ethylene...

The construction of the molecular orbitals of ethylene is similar to the process used for carbon monoxide, but the total number of atomic orbitals is greater, twelve instead of eight, because of the additional atomic orbitals from hydrogen. We must... 

Thus we have the same type of energy-level scheme for the t molecular orbitals of ethylene as we had for the c molecular orbitals of the hydrogen molecule. The diagram for C2H4 is shown in Fig. 8-4. 

Because molecular orbitals must recognize the symmetry of a molecule, a symmetry operation must either preserve the value of the wavefunction or simply change the sign of the wavefunction. The wavefunction therefore provides a basis for a representation of the molecule s point group. Inspection of the HOMO and LUMO molecular orbitals of ethylene (Fig. 4.6) shows that the HOMO transforms as the irreducible representation and z in the D2h point group (Table 4.2), whereas the LUMO transforms as Bj,g and yz. 

If butadiene and an appropriately substituted ethylene approach and begin to overlap as in Equation 5.2, there is a favorable phase relationship using the HOMO of the diene and the LUMO of ethylene (the frontier molecular orbitals) for a face-to-face joining. This is, of course, the familiar Diels-Alder reaction, and it is thermally allowed. With respect to both components of the reaction, the reaction occurs from the same face, termed suprafacial addition. Because there are four % electrons in butadiene and two % electrons in ethylene, the Diels-Alder reaction is named as a [ 4 -i- 2 ] reaction. The stereochemical consequences of this approach are further illustrated in Section 8.6. 

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