Ethylene, HOMO/LUMO

After this, Martinez and Ben-Nun applied the method to the photoexcitation of ethylene [88,247]. The lowest energy excitation is the HOMO-LUMO n n transition. These states are labeled A and Close in energy to... 

HOMO-LUMO energy difference in ethylene is greater than that of cis trans 1 3 cyclooctadiene... 

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. 

Thermal dimerization of ethylene to cyclobutane is forbidden by orbital symmetry (Sect 3.5 in Chapter Elements of a Chemical Orbital Theory by Inagaki in this volume). The activation barrier is high E =44 kcal mof ) [9]. Cyclobutane cannot be prepared on a preparative scale by the dimerization of ethylenes despite a favorable reaction enthalpy (AH = -19 kcal mol" ). Thermal reactions between alkenes usually proceed via diradical intermediates [10-12]. The process of the diradical formation is the most favored by the HOMO-LUMO interaction (Scheme 25b in chapter Elements of a Chemical Orbital Theory ). The intervention of the diradical intermediates impfies loss of stereochemical integrity. This is a characteric feature of the thermal reactions between alkenes in the delocalization band of the mechanistic spectrum. 

Now let us take the case of a reaction between ethylene and an allyl anion. In both cases the HOMO-LUMO interaction leads to bonding at both terminals. 

We first consider the relative electronic transition energies in cis and trans 1,2-disubstituted ethylenes. From Fig. 28 we can clearly see that the pi HOMO-LUMO energy gap is larger for the case of the cis isomer relative to the trans isomer. Hence, the mr transition is expected to occur at shorter wavelengths in cis 1,2-disubsti-tuted ethylenes. 

Diradicals represent the most clear-cut application of the SF approach because in these systems the non-d namical correlation derives from a single HOMO-LUMO pair (e.g., n and n in twisted ethylene). In this section we present results for methylene and trimethylenemethane (TMM). 

An additional point of interest concerns the behaviour of homo and lumo orbitals of reactants in allowed reactions. Fukui (1970, 1975) has pointed out that the frontier-orbital gap actually narrows as the reaction proceeds. This has been confirmed computationally for the cycloaddition of ethylene and butadiene (Townshend et al., 1976), and contrasts with what one might expect based on a static homo-lumo interaction. Such an interaction causes the energy gap between resultant orbitals to widen, as indicated in Fig. 29. 

Figure 11.4 HOMO-LUMO interactions in the approach of an ethylene to a butadiene.

LUMO) is antisymmetric with respect to this plane. For the diene component, the HOMO is antisymmetric and the LUMO is symmetric. Based on these symmetries, it is seen that the HOMO-LUMO interaction between butadiene and ethylene is symmetry allowed and thus can proceed productively to product. 

It is also pertinent that there are two HOMO-LUMO interactions possible between butadiene and ethylene, one in which die HOMO is diat of die diene, which acts as die electron donor, and one in which the HOMO is that of the olefin, which would be die electron donor. A normal Diels-Alder reaction is one in which die diene is electron rich and acts as the electron donor and the... 

The energy of electromagnetic radiation is inversely proportional to its wavelength. Since excitation of an electron for the tt — rr transition of ethylene occurs at a shorter wavelength (Amax = 170 nm) than that of cis, trans- 1,3-cyclooctadiene (Amax= 230 nm), the HOMO-LUMO energy difference in ethylene is greater. 

The HOMO (LUMO) of 12 having a different symmetry than the LUMO (HOMO) of ethylene, Reaction (4.1) is forbidden. In this particular case, the FO method is simpler than the PMO approach. 

The reaction mixture contains two dienophiles ethylene and butadiene. The HOMO-LUMO gap is 2.236/1 when butadiene is the dienophile and 3.236/1 for ethylene. Thus, rule 2 states that the dimerization of butadiene will occur preferentially and the major product will be vinylcyclohexene.24... 

The orbital in ethylene that receives these electrons is the lowest-energy orbital available, the Lowest Unoccupied Molecular Orbital (LUMO). In ethylene, the LUMO is the tt antibonding orbital. If the electrons in the HOMO of butadiene can flow smoothly into the LUMO of ethylene, a concerted reaction can take place. 

Comparison of HOMO-LUMO energy differences. In buta- 1,3-diene, the 77 — 77 transition absorbs at a wavelength of 217 nm (540 kJ/mol) compared with 171 nm (686 kJ/mol) for ethylene. This longer wavelength (lower-energy) absorption results from a smaller energy difference between the HOMO and LUMO in butadiene than in ethylene. 

The HOMO-LUMO based reactivity theories are at the heart of mechanistic pictures in organic chemistry /110/ and the simplest prototypical representative with well established pictures of HOMO and LUMO is the ethylene molecule for which Hiickel theory calculations are routine in characterizing its frontier orbitals. While qualitative correlations abound /18,19/, a rigorous quantitative investigation of this simple prototypical polyatomic molecule is specially significant /45,46/ and results from our own calculations are discussed below. 

The situation is different with the other HOMO-LUMO interaction. These orbitals are antisymmetric with respect to the symmetry element, and the two ends of the new linkage are separated by a nodal plane. Therefore, two separate chemical bonds will form, each connecting an ethylene carbon atom with a terminal butadiene carbon atom. From this consideration, it follows that the first symmetric interaction is the dominant one. Also, the symmetric pair (HOMO of ethylene and LUMO of butadiene) are closer in energy and thus give a stronger interaction. 

Exercise 1.3. Consider a coordination compound formed from BH3 and C2H4. From the HOMO-LUMO properties of each species predict the geometric structure of the Lewis acid-base adduct. Now predict the structure of a compound formed by replacing one CO ligand of Fe(CO)5 with C2H4. Note the parallelism between the main group and transition metal examples. The second compound is a stable and isolatable compound, whereas the first is a transient intermediate in the hydro-boration of ethylene to ethyl borane and has only been characterized as a transient intermediate in a fast-flow system by modulated mass spectrometry. 

The structural and bonding features of this complex comply with the trigonal in-plane conformational preference observed in d (olefin)ML2 complexes. In molecular orbital terms, the dominant bonding interaction is between the bi HOMO of the ML2 fragment and the ethylene tt LUMO ... 

Figure 3 The development of a polyene band structure from the molecular orbitals (MOs) of ethylene. From left to right, the molecular orbitals progressively develop into a band structure as the length of the conjugated chain is increased. For shorter polyene chains, A represents the HOMO-LUMO gap. Forthe infinite polyene chain, vb and cb denote the valence band and the conduction band, respectively, and E is the band gap...

Interestingly, the energy of the HOMO of bicyclobutane was found to be higher than that of ethylene The first electronic transition in bicyclobutane, namely the n-n (HOMO-LUMO) transition, is lower in energy than in ethylene" The position of the onset of the first band in its photoelectron spectrum suggests an adiabatic ionization energy of 8.70... 

Figure 29.20. Symmetry-allowed thermal [4 + 2] cycloaddition 1,3-butadiene and ethylene. Overlap of (a) HOMO of 1,3-butadiene and LUMO of ethylene, and (b) HOMO of ethylene and LUMO of 1,3-butadiene.

Concerted four electron cycloaddition reactions are not thermally allowed. All this really means is that the transition state for an allowed process is much lower than that of a nonallowed process. HOMO-LUMO theory can explain why the concerted 2 + 2 cycloaddition of two ethylenes is not favored. Bonding overlap between a HOMO and a LUMO lowers the transition state energy of the allowed process, making it favorable. With the concerted 2 + 2 cycloaddition of two ethylenes, no such transition state stabilization is achieved, as shown in Figure 12.17. Any bonding overlap is exactly cancelled out by an equivalent antibonding overlap, yielding no net stabilization. 

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