Orbital Interaction Theory of Organic Chemistry

Figure 4.7. Diagrams for the interaction of two adjacent s bonds with C bonded to (a) a less electronegative group and (b) a more electronegative group.

On the other hand, bonds from C to an element more electronegative than C (the normal situation with most substituents) will have the larger coe½cient on C in the s orbital and smaller in the s orbital. Therefore, the two s bonds will experience a weaker interaction than the two s orbitals. This situation is depicted in Figure 4.7b. Carbon and hydrogen have similar electronegativities, and so CÐC and CÐH bonds are essentially nonpolarized. However, it does not follow that the intrinsic interaction between two spn hybridized orbitals (i.e., the CÐC s bond) is the same as the intrinsic interaction of an spn orbital and a 1s orbital (the CÐH bond). Relative CÐC and CÐH bond dissociation energies (see, e.g., Table 4.1) suggest that the CÐC interaction is weaker and that the CÐC bond will be higher in energy than a CÐH bond. Conversely, the s orbitals are reversed, that of the CÐC bond being lower.

through-bonds interactions on the ionization potentials of a number of nonconjugated dienes as a function of skeletal structure and substitution has been investigated [88].

The spectroscopic and chemical properties of 1,4-diazabicyclo[2.2.2]octane (DABCO) are consistent with a strong interaction of the in-phase combination of the nonbonded electron pairs of the nitrogen atoms with the symmetric combination of the CÐC s bonds, one consequence of which is that the in-phase combination is the HOMO. The two lowest IPs are 7.6 and 9.7 eV [89]. Compare these to the IPs of trimethyl amine (8.44 eV) and ammonia (10.5 eV) [90]. The relative importance of intramolecular orbital interactions through space and through bonds has been reviewed by Ho¨mann [6].

s BONDS AS ELECTRON DONORS OR ACCEPTORS

With respect to the ability of s bonds to accept or donate electrons, several circumstances may act to change the norm (which is that they are neither donors nor acceptors). Substituents adjacent to the s bond may act to raise the energy of the bonding orbital or to lower the energy of the s antibonding orbital and thereby increase the involvement of the bond in two-electron, two-orbital interactions. Whether the bond acts as a donor in an interaction with a low-lying virtual orbital or as an acceptor in an interaction with a high-lying occupied orbital, the consequences for the bond are the same, a reduction of the bond order and a consequent weakening of the bond. The extreme consequence is a rupture of the bond, as occurs in a hydride transfer or a nucleophilic substitution (SN2). When the interaction does not ``go all the way,'' the bond weakening is often apparent in the infrared spectrum as a shift to longer wavelength of the bond-stretching frequency and a lengthening of the bond itself. The fact that both consequences are usually observed has suggested an inverse relationship between bond strength as measured by the force constant and the bond length [91]. This relationship, which is widely accepted, has no direct theoretical derivation, and exceptions, particularly in the case of NÐF bonds, have been noted and attributed to ``polar'' e¨ects [92].

s BONDS AS ELECTRON ACCEPTORS

The acceptor ability may be improved in two ways, by lowering the energy of the s orbital and by polarizing the orbital toward one end. The ®rst improves the interaction between it and a potential electron donor orbital by reducing the energy di¨erence, eA ÿ eB, the second by increasing the possibility of overlap and therefore increasing the value of the intrinsic interaction matrix element, hAB.

As a s Acceptor

The general features (orbital distribution and energy) for a s bond between C and a more electronegative element or group, X, are shown in Figures 4.1a, 4.2, and 4.3, where center A is carbon and center B is X. The energy of the s orbital will be relatively low and the orbital is polarized toward carbon. Optimum interaction between the s orbital and a localized nonbonding orbital of a Lewis base will occur along the axis of the orbital and from the carbon end, as shown in Figure 4.9a. The two-orbital, two-electron interaction is accompanied by charge transfer into the s orbital and consequent reduction of

82 SIGMA BONDS AND ORBITAL INTERACTION THEORY

Figure 4.9. (a) Sigma-type acceptor interaction between the HOMO, n, of a base and the LUMO, s , of a polarized s bond. (b) Pi-type acceptor interaction between the HOMO, n, of an X:-type group and the LUMO, s , of an adjacent polar s bond.

the bond order, as well as partial s bond formation between C and the incoming base. Carried to the extreme, a substitution reaction with inversion of con®guration at C (SN2) ensues, as discussed in Chapter 9. If the center A is H rather than C, the corresponding reaction is a proton abstraction, that is, a Lowry±Bronsted acid±base reaction. If the interaction falls short of proton abstraction, the attractive interaction is called a hydrogen bond. Both aspects are discussed further in Chapter 10.

Interhalogen bonds are accompanied by very low LUMOs (sXX; see Figure 4.5) and thus can function as good s electron acceptors. The donor±acceptor complexes between ammonia and F2, Cl2, and ClF have been investigated theoretically [93] and found to have linear structures, as expected on the basis of the above discussion.

As a p Acceptor

The s orbital associated with a s bond between C and a more electronegative element or group, X, is polarized toward carbon. Optimum interaction between the s orbital and an adjacent localized nonbonding orbital of an X:-type group will occur if the s orbital and the p (or spn) nonbonded orbital of the neighboring group are coplanar, as shown in Figure 4.9b. The two-orbital, two-electron interaction is accompanied by charge transfer into the s orbital and consequent reduction of the bond order, as well as partial p bond formation between C and the adjacent group. Carried to the extreme, an elimination reaction (E1cb) ensues, as discussed in Chapter 10. The tendency of the neighboring group to assist the departure of the leaving group is called anchimeric assistance or the neighboring group e¨ect. If the interaction falls short of elimination, the attractive interaction is called negative hyperconjugation [67]. The tendency to alter geometry or change conformation so as to maximize the interaction is called the anomeric e¨ect [94].

s BONDS AS ELECTRON DONORS

The donor ability of a s bond may be improved in two ways, by raising the energy of the s orbital and by polarizing the orbital toward one end. The ®rst improves the interaction between it and a potential electron acceptor orbital by reducing the energy di¨erence eA ÿ eB, the second by increasing the possibility of overlap and therefore increasing the value of the intrinsic interaction matrix element, hAB. Speci®cally, a bond between C and an element (e.g., a metal, Li, Na, Mg) or group (e.g., ÐBRÿ3 , ÐSiR3) less electronegative than C will have the required features. Referring to Figure 4.1a, the role of C will be played by group B. Since H is also somewhat less electronegative than C, CÐH bonds are also potential electron donors when the electron demand is high. So are bonds to H from metals or metal-centered groups (e.g., NaH, LiAlH4, NaBH4).

As a s Donor

The general features (orbital distribution and energy) for a s bond between C and a less electronegative element or group, M, are shown in Figure 4.1a, where center A is M and center B is C. The energy of the s orbital will be relatively high and the orbital is polarized toward carbon. Optimum interaction between the s orbital and a localized empty orbital of a Lewis acid will occur between the C and M, closer to the carbon end, as shown in Figure 4.10a, or from the backside if steric hindrance by M is severe. The two-orbital, two-electron interaction is accompanied by charge transfer from the s orbital and consequent reduction of the s bond order, as well as partial s bond forma-

Figure 4.10. (a) Sigma-type donor interaction between the s bond and the LUMO, s , of a polarized s bond (shown as a p orbital). (b) Pi-type donor interaction between the s bond and the LUMO (shown as a p orbital), which may be the p orbital of an adjacent Z-type substituent, or s of a polarized s bond.

84 SIGMA BONDS AND ORBITAL INTERACTION THEORY

tion between C and the incoming acid. Carried to the extreme, a substitution reaction ensues in which the con®guration at C may be retained. If the center B is H rather than C, the corresponding reaction is a hydride transfer (abstraction), as in the Cannizzaro or Meerwein±Pondorf±Verley reactions. If the interaction falls short of abstraction, a hydride bridge may be formed. Both aspects are discussed further in Chapter 10.

As a p Donor

A s bond between C and a less electronegative element or group, M, is polarized toward carbon. Optimum interaction between the s orbital and an adjacent localized empty orbital of an electron p acceptor group like carbonyl will occur if the s orbital and the empty p orbital of the neighboring group are coplanar, as shown in Figure 4.10b. The two-orbital, two-electron interaction is accompanied by charge transfer from the s orbital and consequent reduction of the bond order, as well as partial p bond formation between C and the adjacent group. The competitive p donation involving CÐH and CÐC s bonds in cyclohexanones has been the subject of much discussion in the recent literature [95]. The carbonyl group distorts from planarity so as to achieve better alignment of the carbon 2p component of its p orbital with the s bond, a secondary consequence of which may be substantial preference for attack by nucleophiles at the face opposite to the s bond involved. Where the adjacent group is a carbocationic center, distortion of the donor s bond toward the acceptor site or migration of the bond (i.e., the group, M, attached to the other end) may occur. In the latter case, the reaction is a 1,2 hydride shift (M ˆ H) or a Wagner±Meerwein rearrangement (M ˆ alkyl). The weakening of the bond may also result in elimination of M‡. If the interaction falls short of elimination or migration, the attractive interaction is called hyperconjugation. The tendency to alter the geometry or change the conformation so as to maximize the attractive interaction is well documented [96]. In an extreme case, the group M may adopt a position midway between the C and the adjacent group, forming a two-electron, threecenter bond as in nonclassical structures of carbocationsÐethyl [97] (M ˆ H), norbornyl [98] (M ˆ alkyl). The bonding in (car)boranes is another example [99].

If the LUMO is the sp hybrid orbital at the C end of a polarized s bond, such as to a halide, geometric distortion also occurs, particularly a lengthening of the receiving s bond. Carried to the extreme, an elimination reaction occurs (E1cb, as discussed in Chapter 10). Migration of M to the adjacent group does not occur.

BONDING IN CYCLOPROPANE

The above discussion applies to ``normal'' s bonds in saturated compounds, as occur in molecules where the internuclear angles can reasonably approach the tetrahedral interorbital angle expected of sp3 hybridization. Many molecules exist which encompass small rings, the prototypical molecule being cyclopropane, where the internuclear angle of 60 is far from ``ideal.'' For the purpose of understanding the properties of cyclopropanes using orbital interaction diagrams, we adopt the Walsh picture [100, 101], shown in Figure 4.11. Each carbon atom is considered to be sp2 hybridized (Figure 4.11a). Two of the sp2 hybrid orbitals are used for the external s bonds, as expected for the wider bond angle (HCH angle ˆ 114 in cyclopropane). The set of three sp2 hybrid orbitals, one from each center, are directed toward the center of the ring and interact strongly to form the unique bonding combination, W1, and the pair of antibonding MOs,

Figure 4.11. Bonding in cyclopropane: (a) 2p and sp2 hybrid orbitals; (b) Walsh MOs. One of the degenerate HOMOs, W2, and the LUMO, W4, will interact in a p fashion with a substituent on the ring.

W5 and W6. The set of three (unhybridized) 2p orbitals are oriented tangentially to the ring and interact weakly to form the degenerate pair of bonding MOs, W2 and W3, which constitute the HOMOs, and the unique antibonding MO, W4, which becomes the LUMO. We do not o¨er any explanation for why the orbital patterns originate as shown in Figure 4.11. We shall see in the next chapter that any two-dimensional cyclic array of orbitals that can overlap completely in phase (a HuÈckel array) will have the same orbital pattern as displayed for the sp2 set (W1, W5, and W6), namely a unique lowest energy orbital and pairs of degenerate orbitals at higher energies. We state without proof that a cyclic array, such as the ring of 2p orbitals, which cannot have all positive overlaps (a Mùbius array) will have a degenerate pair of orbitals at the lowest energy and the remaining orbitals also in degenerate pairs unless there is an odd number, as in the present case. Orbitals W2, W3, and W4, are closer together simply because the 2p orbitals overlap poorly in the orientation imposed by the three-membered ring geometry.

In the absence of substituents, the orientation of the nodal surfaces of the pairs of degenerate MOs is arbitrary, but the orientation will be as shown in Figure 4.11b for a substituent at the lower vertex. Notice that one of the HOMOs, W2, and the LUMO, W4, will interact with a substituent in this position in a p fashion. Because of the poor overlap of the tangentially oriented 2p orbitals, the HOMO energy will be quite high, and the LUMO energy will be low. The cyclopropyl ring will therefore be expected to act both as a good p donor and a good p acceptor.

‡

D

D

‡

Figure 5.1. (a) SHMO results for ethylene. (b) The interaction diagram for ethylene: note that DeL ˆ DeU because overlap is assumed to be zero in SHMO theory.

Thus, all of the diagonal elements are a ÿ e. The o¨-diagonal elements are b if the two atoms involved are bonded and zero if they are not. It is usual to divide each row of the determinant by b. This corresponds to a change of energy units and leaves either 1's or 0's in the o¨-diagonal positions which encode the connectivity of the molecule. The diagonal elements become …a ÿ e†=b, which is usually represented by x. While the determinant was expanded in Chapter 3 to yield the secular equation, it is more convenient in general to diagonalize the determinant using a computer. An interactive computer program, SHMO, has been written to accompany this book [102].

The SHMO calculation on ethylene yields the results shown in Figure 5.1a. The p and p orbitals are precisely one b unit above and below a. The SHMO results are presented in Figure 5.1b in the form of an interaction diagram. In this case, DeL and DeU are assigned the same value, namely 1jbj, in the spirit of SHMO theory, but we know that the e¨ect of proper inclusion of overlap would yield DeU > DeL.

The SHMO results for the series of ``linear'' p systems allyl, butadiene, and pentadienyl are shown in Figure 5.2. The molecular species are portrayed with realistic angles (120 ) and, in the case of the last two, in a speci®c conformation. Simple HuÈckel MO theory does not incorporate any speci®c geometric information since all non-nearest- neighbor interactions are set equal to zero. As a result, the SHMO results (MO energies and coe½cients) are independent of whether the conformation of butadiene is s-trans, as shown in Figure 5.2, or s-cis, as may be required for the Diels±Alder reaction. Likewise the results for the pentadienyl system shown in the ``U'' conformation in Figure 5.2 are identical to the results for the ``W'' or ``sickle'' conformations. The MOs are displayed as linear combinations of 2p atomic orbitals seen from the top on each center, with changes of phase designated by shading. The relative contribution of each atomic 2p orbital to the p MO is given by the magnitude of the coe½cient of the eigenvector from the solution of the SHMO equations. In the display, the size of the 2p orbital is proportional