HOMO-LUMO interactions

The formation of new bonds in file Diels-Alder reaction requires that file n electrons in file individual diene and olefin n systems become reorganized and shared in file new bonding pattern of the cyclic product. It follows that for this bonding change to occur, file two n systems must overlap so that electrons can move into new orbitals. The most straightforward way file needed orbital overlap can occur is for one n system to function as an electron donor and file other r system to function as an electron acceptor. Therefore file bonding changes in file Diels-Alder reaction result from a donor-acceptor interaction between the diene and olefin jt systems. 

It is well known that n electrons are less tightly bound than a electrons, and consequently they can readily be donated to a variety of electrophiles (e.g., bromine, protons, mercuric ion), so it is easy to imagine a it system acting as an electron donor. In contrast, n systems, being electron rich, are not often thought of as electron acceptors (which would make them even more electron rich). 

For a 7t system to function as an electron acceptor, it must have unfilled orbitals available to accept electrons. In the case of olefins or dienes those are n antibonding molecular orbitals. Thus interaction of the HOMO of one n system with file LUMO of a second n system produces a donor-acceptor pair (HOMO donating to LUMO) enabling electrons to be transferred from one n system to another with resulting bond formation. 

One requirement for a successful HOMO-LUMO interaction is that the symmetry of the HOMO must match the symmetry of the LUMO (either both symmetric or both antisymmetric). If so, then the interaction is symmetry allowed and will lead to productive cycloaddition. If file symmetries do not match, then the HOMO-LUMO overlap is symmetry forbidden and cycloaddition will not proceed. Molecular orbitals can be classified by their phase symmetry with respect to a plane normal to the n system. The symmetry is related to the number of nodal planes which occur in each individual molecular orbital. For the olefin component, file it orbital (HOMO) is symmetric with respect to this plane and file it orbital 

It turns out that the orbitals for any diene and any olefin have the same symmetry properties so that all Diels-Alder reactions are symmetry allowed. 

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When both the 1,3-dipoIe and the dipolarophile are unsymmetrical, there are two possible orientations for addition. Both steric and electronic factors play a role in determining the regioselectivity of the addition. The most generally satisfactory interpretation of the regiochemistry of dipolar cycloadditions is based on frontier orbital concepts. As with the Diels-Alder reaction, the most favorable orientation is that which involves complementary interaction between the frontier orbitals of the 1,3-dipole and the dipolarophile. Although most dipolar cycloadditions are of the type in which the LUMO of the dipolarophile interacts with the HOMO of the 1,3-dipole, there are a significant number of systems in which the relationship is reversed. There are also some in which the two possible HOMO-LUMO interactions are of comparable magnitude. 

Consideration of the HOMO-LUMO interactions also indicates that the [2n + 2ti] additions would be allowed photochemically. The HOMO in this case is the excited alkene 71 orbital. The LUMO is the ti of the ground-state alkene, and a bonding interaction is present between the carbons where new bonds must be formed ... 

Figure 15.14 2s + 2s HOMO-LUMO interaction leading to two new cr-bonds...

The frontier orbital theory [7-9] assumes that the stabihzation by the electron delocalization could control chemical reactions. The stabilization comes from the interactions between the occupied molecular orbitals of one molecule and the unoccupied molecular orbitals of another (Sect. 1.4). The strong interaction occurs when the energy gap is small (Sect. 1.3). The HOMO and the LUMO are the closest in energy to each other. The HOMO-LUMO interaction, especially the interaction between the HOMO of electron donors and the LUMO of electron acceptors, controls the chemical reactions (Scheme 20). The HOMO and the LUMO are termed the frontier orbitals. ... 

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. 

Scheme 20 HOMO-LUMO interaction in the perepoxide quasi-intermediate for the cis-effect and the regioselectivity (percent) of the hydrogen abstractions...

Benzyne shares a feature with A in the [2+2] cycloaddition reactions. The HOMO-LUMO interaction prefers the three-centered interaction (Scheme 4) [115]. This is in agreement with the calculated reaction path [116]. 

HOMO-LUMO interactions are comparable II. Diene HOMO and dienophile LUMO interactions are dominant III. Diene LUMO and dienophile HOMO interactions are dominant... 

Fig. 6.2. HOMO-LUMO interactions rationalize regioselectivity of Diels-Alder reactions.

Fig. 6.13. HOMO-LUMO interactions in the [2 + 2] cycloadditions of an alkene and a ketene (a) frontier orbitals of the alkene and ketene (b) [2tts + 2ttJ representation of suprafacial addition to the alkene and antarafacial addition to the ketene (c) [2tts + (2tts + 2tts)] alignment of orbitals.

An HSAB analysis of singlet carbene reactivity based on B3LYP/6-31G computations has calculated the extent of charge transfer for substituted alkenes,122 and the results are summarized in Figure 10.3 The trends are as anticipated for changes in structure of both the carbene and alkene. The charge transfer interactions are consistent with HOMO-LUMO interactions between the carbene and alkene. Similarly, a correlation was found for the global electrophilicity parameter, co, and the ANmax parameters (see Topic 1.5, Part A for definition of these DFT-based parameters).123... 

HOMO-LUMO interactions in carbene alkene addition... 

Nakatani, K. Matsuno, T. Adachi, K. Hagihara, S. Saito, I. Selective intercalation of charge neutral intercalators into GG and CG steps implication of HOMO-LUMO interaction for sequence-selective drug intercalation into DNA. J. Am. Chem. Soc. 2001, 123, 5695-5702. 

Scheme 3 HOMO-LUMO interaction schemes for concerted four-centered carbometallation reactions.

Fig. 1 (a) Resonance and (b) HOMO-LUMO interaction in simple amides. 

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. 

HOMO-LUMO) interactions the LUMO being the antibonding cr x orbital [45], the HOMO a non-bonded electron pair, formally available at both 90° and about 180° to the C-X bond [46], Much similar work supports this interpretation. Contacts between halogens (X) and electrophilic centres E (all metal ions) [47] fall almost exclusively in the range 9O<0E<12O°, while, for better electron donors Nu, 0Nu generally lies between 150° and 180°. 

The detailed study of the molecular orbitals in the different species allowed a better understanding of the interactions under way. It was proved that the charge-transfer from the HOMO of the metal moiety to the n orbital of C02 is the most important interaction in the transition state and that the anti-bonding mixing of the n orbital of C02 also plays a significant role. The leading role of this HOMO-LUMO interaction also explains why the M-OCOH species is more easily formed than the M-COOH species. 

These opposite signs can be explained by considering a twofold orbital interaction between the two parts of an arenediazonium ion, namely between the jr-HOMO of the diazonio group and the cr-LUMO of the aryl residue, and between the jr-HOMO of the aryl residue and the jr-LUMO of the diazonio group. These two overlaps stabilize the C—N bond and reduce the rate of dediazoniation into a phenyl cation and a nitrogen molecule. The two opposing HOMO-LUMO interactions are shown in Figure 1. Thus... 

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