HOMO-LUMO interaction symmetry

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. 

Thus far, in the alkaloid series discussed, the nitrogen atom has always been part of the core of the alkaloid strucmre, rather than acting in a dipolarophilic manner in the cycloaddition of the carbonyl ylide. Recently, Padwa et al. (117) addressed this deficiency by conducting model studies to synthesize the core of ribasine, an alkaloid containing the indanobenzazepine skeleton with a bridging ether moiety (Scheme 4.57). Padwa found that indeed it was possible to use a C = N 7i-bond as the dipolarophile. In the first generation, a substimted benzylidene imine (219) was added after formation of the putative carbonyl ylide from diazoketone 218. The result was formation of both the endo and exo adduct with the endo adduct favored in an 8 1 ratio. This indicates that the endo transition state was shghtly favored as dictated by symmetry controlled HOMO—LUMO interactions. 

Such cycloadditions involve the addition of a 2tt- electron system (alkene) to a 4ir- electron system (ylide) and have been predicted to occur in a concerted manner according to the Woodward-Hoffmann rules. The two most important factors involved in the cycloaddition reactions are (i) the energy and symmetry of the reacting orbitals and (ii) the thermodynamic stability of the cycloadduct. The reactivity of 1,3-dipolar systems has been successfully accounted for in terms of HOMO-LUMO interactions using frontier MO theory (71TL2717). This approach has been extended to explain the 1,3 reactivities of the nonclassical A,B-diheteropentalenes <77HC(30)317). 

Figure 10.12 In a four-center approach of H2 and F2, symmetry prevents HOMO-LUMO interaction. Only HOMO-HOMO and LUMO-LUMO interactions can occur, and these do not lower the energy.

Figure 10.14 Frontside attack of a nucleophile, symbolized by N, on a C—X bond. Symmetry prevents HOMO-LUMO interaction the only interaction is between filled levels. The reaction will not take this path.

If we try instead a mechanism in which a hydrogen atom attacks the Fa molecule at an end (Figure 10.13), the symmetry permits HOMO-LUMO interaction, and the perturbed orbital at the center in Figure 10.13 shows that the electron from hydrogen is being transferred to the fluorine.9... 

Figure 10.16 The electrophilic bimolecular substitution can occur from the front, because symmetry permits HOMO-LUMO interaction and stabilization.

Having established that the mirror plane is a proper symmetry element even if the chains are distorted, we look at HOMO-LUMO interactions. If we restrict our attention to chains with even numbers of electrons and focus on the HOMO and the LUMO, we can see that there are only two kinds of chains those in which the HOMO is symmetric and the LUMO antisymmetric, and those in which the HOMO is antisymmetric and the LUMO symmetric. Goldstein and Hoffmann have named these types respectively Mode 2 and Mode 0.14 Table 10.1 shows a few examples. Note that anions and cations are covered as well as neutral molecules. 

Figure 11.5 The approach of two butadiene molecules. The symmetries do not permit HOMO-LUMO interaction the interaction between filled levels, permitted by the symmetry, gives no stabilization.

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... 

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. 

The essential features of the Diels-Alder reaction are a four-electron n system and a two-electron it system which interact by a HOMO-LUMO interaction. The Diels-Alder reaction uses a conjugated diene as the four-electron n system and a it bond between two elements as the two-electron component. However, other four-electron it systems could potentially interact widi olefins in a similar fashion to give cycloaddition products. For example, an allyl anion is a four-electron it system whose orbital diagram is shown below. The symmetry of the allyl anion nonbonding HOMO matches that of the olefin LUMO (as does the olefin HOMO and the allyl anion LUMO) thus effective overlap is possible and cycloaddition is allowed. The HOMO-LUMO energy gap determines the rate of reaction, which happens to be relatively slow in this case. 

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. 

Although these surface scans are approximate, and probably suffer somewhat from the requirement of D3h symmetry, they do reveal that this remarkably exothermic, and thermally allowed, reaction has an unusually high activation barrier. Acetylene is neither a good donor nor a good acceptor, and the approach of three acetylenes, even in a geometry which produces both in-plane and out-of-plane aromatic sextets, results in no strong HOMO-LUMO interactions. Repulsive interactions due to the overlap of filled orbitals of the three molecules occur, but the filled and vacant orbitals of the acetylenes are too far apart in energy for any appreciable stabi-... 

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. 

Isomerization of allylboranes proceeds not by a dehydroboration-rehydroboration mechanism that would involve the intermediacy of allenes, but by an allylic rearrangement or 1,3-metallotropy that is a symmetry-allowed concerted process. The probable HOMO-LUMO interactions suggested for the 1,3-metallotropy are shown in formulas XXI and XXH. 

Consideration of the HOMO-LUMO interactions also indicates that the [2Tr+2Tr] addition is allowed photochemically. The HOMO in this case is the excited alkene tt orbital. The LUMO is the tt of the ground state alkene, and a bonding interaction is present between both pairs of carbons where new bonds must be formed. Similarly, the concept of aromatic transition states shows that the reaction has an antiaromatic 4tt combination of basis set orbitals, which predicts an allowed photochemical reaction. Thus, orbital symmetry considerations indicate that photochemical [2tt- -2tt] cycloaddition of alkenes is feasible. 

The Diels—Alder reaction may also be analyzed by a similar consideration of the molecular orbitals of butadiene and ethene. In this case, there are two possible HOMO—LUMO interactions. Since the phases of the 1,4-lobes of the HOMO of butadiene match with those in the LUMO of ethene, the [7r" s + TT s] cycloaddition is thermally allowed. We reach a similar conclusion by considering the symmetry of LUMO of butadiene and the HOMO of ethene (Figure 4.10). However, on energetic grounds the latter interaction will make a smaller contribution than the former. 

Since 1,3-DPCA reactions involve Trr-electrons from the 1,3-dipole and 2TT-electrons from the dipolarophiles, it may be considered as symmetry-allowed [tt" s + TT s] cycloaddition resembling Diels—Alder reaction. There is HOMO—LUMO interaction in which either reactant can be the electrophilic or nucleophilic component (Figure 5.12). 

---