Ethylene point group

Some molecular orbitals of ethylene (point group Z>2h)- All are completely filled except l 2g in the ground state. The x axis points into the paper. 

The point group is the same as 2 - Ethylene (Figure 4.1a) and naphthalene (Figure 4.3c) belong to the >2 point group in which, because of the equivalence of the three mutually perpendicular C2 axes, no subscripts are used for the planes of symmetry. 

The vibrations of acetylene provide an example of the so-called mutual exclusion mle. The mle states that, for a molecule with a centre of inversion, the fundamentals which are active in the Raman spectmm (g vibrations) are inactive in the infrared spectmm whereas those active in the infrared spectmm u vibrations) are inactive in the Raman spectmm that is, the two spectra are mutually exclusive. Flowever, there are some vibrations which are forbidden in both spectra, such as the torsional vibration of ethylene shown in Figure 6.23 in the >2 point group (Table A.32 in Appendix A) is the species of neither a translation nor a component of the polarizability. 

The addition of salts to the aqueous phase of concentrated emulsions can have profound effects on their stabilities. Water-in-oil HIPEs are generally stabilised by salt addition [10,12,13,21,80,90,112] however, the nature of the salt used was found to be important [13]. Salts which decrease the cloud point of the corresponding nonionic surfactant aqueous solutions, i.e. which have a salting-out effect, were more active. The interactions of the surfactant molecules at the oil/water interface were increased due to dehydration of the hydrophilic ethylene oxide groups on addition of salt. This was verified experimentally [113] by an ESR method, which demonstrated that the surfactant molecules at the oil/water interface become more ordered if the salt concentration is increased. 

The MOs and electronic states of carbene have been discussed in Chapter 7. The orbital and state correlation diagrams for addition of CH2 to ethylene is shown in Figure 14.9. The Walsh bonding picture for the MOs of cyclopropane requires that the and a MOs of the ethylene also be included in the diagram. The a2 and least-motion pathway preserves a vertical plane of symmetry (as well as the other elements of the C2v point group), and the... 

The treatment of the UPS of the tr-allyl complex (CsHs)2Nb(C3Hs) is similar to that of the ethylene complexes. One significant difference between the ethylene and tr-allyl complexes, however, is that the symmetry is reduced to C2 in the latter. The correlations between the appropriate orbital symmetries in the C2v and Cs point groups are indicated in Table XIV. 

Cycloaddition reactions, 162-165, 197-198 component analysis, 168 Diels-Alder, 162, 198 ethylene + ethylene, 198 orbital correlation diagram, 198 stereochemistry, 162-163 Cycloalkanols, synthesis, 277 Cyclobutadiene barrier, 91 ground state, 91 point group of, 5 self-reactivity, 97 SHMO, 151 structure, 309-310 Cyclobutane... 

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. 

Fig. 3.1. The linear Hiickel-Hubbard spectrum of ethylene. The letters constitute a point group classification of states.

Figure 7-10. The -it MO of one ethylene molecule alone does not belong to any irreducible representation of the point group of the system of two ethylene molecules.

The rules for the state correlation diagrams are the same as for the orbital correlation diagrams only states that possess the same symmetry can be connected. In order to determine the symmetries of the states, first the symmetries of the MOs must be determined. These are given for the face-to-face dimerization of ethylene in Table 7-1. The D2h character table (Table 7-2) shows that the two crucial symmetry elements are the symmetry planes a(xy) and v"(yz). The MOs are all symmetric with respect to the third plane, vide supra). The corresponding three symmetry operations will unambiguously determine the symmetry of the MOs. Another possibility is to take the simplest subgroup of D2t, which already contains the two crucial symmetry operations, that is, the C2v point group (cf.,... 

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