Ethylenes symmetry

Fig. 24. Stabilizing orbital interactions in cis and trans 1,2-difluoro-l,2-dihydroxy ethylene. Symmetry labels are with respect to a rotational axis (trans isomer) and mirror plane (cis isomer)...

Koppel H, Gadea FX, Klatt G, Schirmer J, Cederbaum LS (1997) Multistate vibronic coupling effects in the k-shell excitation spectrum of ethylene symmetry breaking and core-hole localization. J Chem Phys 106 4415... 

HMO theory is named after its developer, Erich Huckel (1896-1980), who published his theory in 1930 [9] partly in order to explain the unusual stability of benzene and other aromatic compounds. Given that digital computers had not yet been invented and that all Hiickel s calculations had to be done by hand, HMO theory necessarily includes many approximations. The first is that only the jr-molecular orbitals of the molecule are considered. This implies that the entire molecular structure is planar (because then a plane of symmetry separates the r-orbitals, which are antisymmetric with respect to this plane, from all others). It also means that only one atomic orbital must be considered for each atom in the r-system (the p-orbital that is antisymmetric with respect to the plane of the molecule) and none at all for atoms (such as hydrogen) that are not involved in the r-system. Huckel then used the technique known as linear combination of atomic orbitals (LCAO) to build these atomic orbitals up into molecular orbitals. This is illustrated in Figure 7-18 for ethylene. 

Figure 4-10 [he Poteiitiiil Energy Form lor Ethylene. The midpoint of the range of (>) is (T and the end points -F180 . that is. [ a. Tt], The mid point and end points are identical by molecular symmetry. 

In the case of ethylene, because of 2-fold symmetry, odd terms drop out of the series, V3, V5,... = 0. In the case of ethane, because of 3-fold symmeti-y, even temis drop out, V2, V4,... = 0. Terms higher than three, even though permitted by symmetry, are usually quite small and force fields can often be limited to three torsional terms. Like cubic and quaitic terms modifying the basic quadratic approximation for stretching and bending, terms in the Fourier expansion of Ftors (to) beyond n = 3 have limited use in special cases, for example, in problems involving octahedrally bound complexes. In most cases we are left with the simple expression... 

FIGURE 10 11 The HOMO of 1 3 butadiene and the LUMO of ethylene have the proper symmetry to allow cr bond formation to occur at both ends of the diene chain in the same tran sition state... 

Let us now examine the Diels-Alder cycloaddition from a molecular orbital perspective Chemical experience such as the observation that the substituents that increase the reac tivity of a dienophile tend to be those that attract electrons suggests that electrons flow from the diene to the dienophile during the reaction Thus the orbitals to be considered are the HOMO of the diene and the LUMO of the dienophile As shown m Figure 10 11 for the case of ethylene and 1 3 butadiene the symmetry properties of the HOMO of the diene and the LUMO of the dienophile permit bond formation between the ends of the diene system and the two carbons of the dienophile double bond because the necessary orbitals overlap m phase with each other Cycloaddition of a diene and an alkene is said to be a symmetry allowed reaction... 

HOMO of one ethylene mol ecule and the LUMO of an other do not have the proper symmetry to permit two O bonds to be formed in the same transition state for concerted cycloaddition... 

Figure 10 12 shows the interaction between the HOMO of one ethylene molecule and the LUMO of another In particular notice that two of the carbons that are to become ct bonded to each other m the product experience an antibondmg interaction during the cycloaddition process This raises the activation energy for cycloaddition and leads the reaction to be classified as a symmetry forbidden reaction Reaction were it to occur would take place slowly and by a mechanism m which the two new ct bonds are formed m separate steps rather than by way of a concerted process involving a sm gle transition state... 

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 chemistry of propylene is characterized both by the double bond and by the aHyUc hydrogen atoms. Propylene is the smallest stable unsaturated hydrocarbon molecule that exhibits low order symmetry, ie, only reflection along the main plane. This loss of symmetry, which implies the possibiUty of different types of chemical reactions, is also responsible for the existence of the propylene dipole moment of 0.35 D. Carbon atoms 1 and 2 have trigonal planar geometry identical to that of ethylene. Generally, these carbons are not free to rotate, because of the double bond. Carbon atom 3 is tetrahedral, like methane, and is free to rotate. The hydrogen atoms attached to this carbon are aUyflc. 

By applying these rules and recognizing the elements of symmetry present in the molecule, it is possible to construct MO diagrams for more complex molecules. In the succeeding paragraphs, the MO diagrams of methane and ethylene are constructed on the basis of these kinds of considerations. 

The process of constructing the MOs of ethylene is similar to that used for carbon monoxide, but the total number of AOs is greater, 12 instead of 8, because of the additional AOs from hydrogen. We must first define the symmetry of ethylene. Ethylene is known from experiment to be a planar molecule. 

The remaining AOs are the four H 1, two C 1, and four C 2p orbitals. All lie in the molecular plane. Only two combinations of the C 2s and H U orbitals meet the molecular symmetry requirements. One of these, nearest-neighbor atoms. No other combination corresponds to the symmetry of the ethylene molecule. 

Frontier orbital theory also provides the basic framework for analysis of the effect that the symmetiy of orbitals has upon reactivity. One of the basic tenets of MO theory is that the symmetries of two orbitals must match to permit a strong interaction between them. This symmetry requirement, when used in the context of frontier orbital theory, can be a very powerful tool for predicting reactivity. As an example, let us examine the approach of an allyl cation and an ethylene molecule and ask whether the following reaction is likely to occur. 

The positively charged allyl cation would be expected to be the electron acceptor in any initial interaction with ethylene. Therefore, to consider this reaction in terms of frontier orbital theory, the question we need to answer is, do the ethylene HOMO and allyl cation LUMO interact favorably as the reactants approach one another The orbitals that are involved are shown in Fig. 1.27. If we analyze a symmetrical approach, which would be necessary for the simultaneous formation of the two new bonds, we see that the symmetries of the two orbitals do not match. Any bonding interaction developing at one end would be canceled by an antibonding interaction at the other end. The conclusion that is drawn from this analysis is that this particular reaction process is not favorable. We would need to consider other modes of approach to analyze the problem more thoroughly, but this analysis indicates that simultaneous (concerted) bond formation between ethylene and an allyl cation to form a cyclopentyl cation is not possible. 

Cycloaddition involves the combination of two molecules in such a way that a new ring is formed. The principles of conservation of orbital symmetry also apply to concerted cycloaddition reactions and to the reverse, concerted fragmentation of one molecule into two or more smaller components (cycloreversion). The most important cycloaddition reaction from the point of view of synthesis is the Diels-Alder reaction. This reaction has been the object of extensive theoretical and mechanistic study, as well as synthetic application. The Diels-Alder reaction is the addition of an alkene to a diene to form a cyclohexene. It is called a [47t + 27c]-cycloaddition reaction because four tc electrons from the diene and the two n electrons from the alkene (which is called the dienophile) are directly involved in the bonding change. For most systems, the reactivity pattern, regioselectivity, and stereoselectivity are consistent with describing the reaction as a concerted process. In particular, the reaction is a stereospecific syn (suprafacial) addition with respect to both the alkene and the diene. This stereospecificity has been demonstrated with many substituted dienes and alkenes and also holds for the simplest possible example of the reaction, that of ethylene with butadiene ... 

How do orbital symmetry requirements relate to [4tc - - 2tc] and other cycloaddition reactions Let us constmct a correlation diagram for the addition of butadiene and ethylene to give cyclohexene. For concerted addition to occur, the diene must adopt an s-cis conformation. Because the electrons that are involved are the n electrons in both the diene and dienophile, it is expected that the reaction must occur via a face-to-face rather than edge-to-edge orientation. When this orientation of the reacting complex and transition state is adopted, it can be seen that a plane of symmetry perpendicular to the planes of the... 

An orbital correlation diagram can be constructed by examining the symmetry of the reactant and product orbitals with respect to this plane. The orbitals are classified by symmetry with respect to this plane in Fig. 11.9. For the reactants ethylene and butadiene, the classifications are the same as for the consideration of electrocyclic reactions on p. 610. An additional feature must be taken into account in the case of cyclohexene. The cyclohexene orbitals tr, t72. < i> and are called symmetry-adapted orbitals. We might be inclined to think of the a and a orbitals as localized between specific pairs of carbon... 

Fig. 11.9. Symmetry properties of ethylene, butadiene, and cyclohexene orbitals with respect to cycloaddition.

When the orbitals have been classified with respect to symmetry, they can be arranged according to energy and the correlation lines can be drawn as in Fig. 11.10. From the orbital correlation diagram, it can be concluded that the thermal concerted cycloadditon reaction between butadiene and ethylene is allowed. All bonding levels of the reactants correlate with product ground-state orbitals. Extension of orbital correlation analysis to cycloaddition reactions involving other numbers of n electrons leads to the conclusion that the suprafacial-suprafacial addition is allowed for systems with 4n + 2 n electrons but forbidden for systems with 4n 7t electrons. 

The complementary relationship between thermal and photochemical reactions can be illustrated by considering some of the same reaction types discussed in Chapter 11 and applying orbital symmetry considerations to the photochemical mode of reaction. The case of [2ti + 2ti] cycloaddition of two alkenes can serve as an example. This reaction was classified as a forbidden thermal reaction (Section 11.3) The correlation diagram for cycloaddition of two ethylene molecules (Fig. 13.2) shows that the ground-state molecules would lead to an excited state of cyclobutane and that the cycloaddition would therefore involve a prohibitive thermal activation energy. 

Figure 15.11 Reaction of two ethylenes to form cyclobutane under C2v symmetry...

Figure 15.16 Reaction of butadiene and ethylene to form cyclohexene under Cj symmetry...

Let us finally consider two Z-matrices for optimization to transition structures, the Diels-Alder reaction of butadiene and ethylene, and the [l,5]-hydrogen shift in Z-1,3-pentadiene. To enforce the symmetries of the TSs (Cj in both cases) it is again advantageous to use dummy atoms. 

Let us now apply these results to the ethylene molecule (Fig. 14), for which we attempt to build the bonding molecular orbitals. Clearly there are three symmetry planes. Two of these are of special interest... 

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