Orbitals HOMO-LUMO interactions

We may redraw 6 as 7a and 7b, in terms of frontier MOs. Here we emphasize the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) interactions that operate in the transition state 7a depicts the LUMO(carbene)/HOMO(alkene) or p-n interaction 7b shows the HOMO (carbene)/LUMO(alkene) or a-71 interaction. These formulations are especially... 

We have established earlier in the chapter that there will be favourable Frontier Orbital HOMO-LUMO interactions when two molecules approach for a cycloaddition reaction if there are 4n + 2 electrons involved in a fully suprafacial reaction, or 4n electrons if there is an antarafacial component. For delocalization of electrons in the transition state, the fully suprafacial cycloaddition reaction will result in a continuous cyclic overlap of atomic orbitals in the transition state without a phase change, for which 4n + 2 electrons will give aromatic stabilization. For a cycloaddition with one antarafacial component, the cyclic overlap of orbitals will give a Mobius system for which 4n electrons will provide stabilization. Thus the two approaches, Frontier Orbitals and the Aromatic Transition State will always be in agreement favourable... 

The concepts of frontier orbital HOMO LUMO interactions, the idea of an aromatic transition state, and the alternative concept of conservation of orbital symmetry (not developed in this chapter) all lead to the same result for pericyclic reactions which involve a cyclic overlap of orbitals in the transition slate, thermal reactions are allowed for reactions involving 4n + 2 electrons in Hiickel systems (no change in phase between overlapped orbitals in the cyclic transition state) or for 4/j electrons in Mobius systems (phase between overlapped orbitals in the cyclic transition state changes once on going round the ring). For photochemical systems, these rules are reversed. 

Fig. 6 Molecular orbital (HOMO-LUMO) interaction of two molecules (a) and of a molecule with semiconductor surface states (b-d). Different results are obtained after interaction with shallow acceptor states (occupied surface states close to the VB) (b), deep acceptor states (occupied states close to midgap) (c), and shallow donor states (close to the CB) (d). In general, the donor HOMO level is slightly stabilized by the interaction, whereas the acceptor LUMO level is slightly destabilized.

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 ... 

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. 

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.

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... 

The endo selectivity in many Diels-Alder reactions has been attributed to attractive secondary orbital interactions. In addition to the primary stabilizing HOMO-LUMO interactions, additional stabilizing interactions between the remaining parts of the diene and the dienophile are possible in the endo transition state (Figure 3). This secondary orbital interaction was originally proposed for substituents having jr orbitals, e.g. CN and CHO, but was later extended to substituents with tt(CH2) type of orbitals, as encountered in cyclopropene57. 

Cycloaddition reactions using tropone or another cyclic triene as the 6ji partner have been abundantly described in the literature. It has been found that virtually all metal-free [6 + 4] cycloadditions of cyclic trienes afford predominantly exo adducts. This has been rationalized by consideration of the HOMO-LUMO interactions between the diene and triene partners. An unfavorable repulsive secondary orbital interaction between the remaining lobes of the diene HOMO and those of the triene LUMO develops during an endo approach. The exo transition state is devoid of this interaction (Figure 9). 

These results have been interpreted in terms of HOMO-LUMO interactions. As a result of the orbital perturbation, the interaction of the HOMO of the cyclohexene double bond with the LUMO of the developing cation may become effective. At the first stage of this interaction, an overlap of the LUMO of the cyclobutyl cation with the p lobe of the double bond located close to the cation center is probably important. However, when the reaction progresses, the interaction with the p lobe on the remote carbon atom has been assumed to increase significantly. 

An important question concerns the kind of relationships that exist between the dissociation energy, Dq, and various other molecular properties. What are the main factors responsible for the chemical bonding How does Dq depend upon the charge on the heavy atom Does the HOMO-LUMO interaction of the fragments determine the magnitude of Dq And what is the role of d orbitals on higher elements ... 

The 1,3-dipolar cycloaddition of organic azides with nitriles could give rise to two regioisomers. Since organic azides are Type II 1,3-dipoles on the Sustmann classification (approximately equal HOMO-LUMO gaps between the interacting frontier orbital pairs) the reactions could be dipole HOMO or LUMO controled and the regioselectivity should be determined by the orbital coefficients for the dominant HOMO-LUMO interaction. Such systems show U-shaped kinetic curves in their... 

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. 

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