Rauk Orbital Interaction Theory of Organic Chemistry

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Figure 10.2. Orbital interaction diagrams for symmetrical two-center hydrogen bonding.

…sOH† interaction. Water trimer has been studied experimentally [227] and shown theoretically [228] to adopt a cyclic array of hydrogen bonds with an average bond strength of about 20 kJ/mol. The complex [H3O‡ Fÿ], is responsible for the anomalously low acidity of HF …pKa ˆ 3:2† in aqueous solution. The HOMO is essentially nonbonding. If the HOMO is high in energy, that is, A: and B: are not very electronegative and/or interact strongly with each other, then simple orbital interaction theory would predict that it makes little di¨erence to the thermodynamic stability whether that MO is occupied or not. Such bonding is observed in electron-de®cient systems and is discussed below. If B is substantially less electronegative than A:, proton transfer will occur and the H bond will be as depicted on the right-hand side of Figure 10.1.

Symmetrical and Bifurcated Hydrogen Bonds

The vast majority of hydrogen-bonded systems are unsymmetrical, even when the hydrogen bond is between like atoms. The reason for this is readily understood from Figure 10.2, where the pattern of orbitals shown in the middle of Figure 10.1 is derived from the interaction of the 1s orbital of a hydrogen atom (situated at the midpoint) with the inand out-of-phase group MOs of two equal Lewis bases. It is clear that the hydrogen atom cannot interact with the HOMO of the base pair, only with the lower symmetric MO. If the hydrogen shifted away from the nodal plane, interaction with HOMO (as well as the lower MO) is possible. These considerations apply even when the two bases are not exactly equivalent. However, optimum symmetrical hydrogen bonding occurs when the two bases A and B are balanced in electronegativity, have maximum electronegativity, are far enough apart not to interact strongly with each other, and one is negatively charged. The strongest H-bonded complex is probably FHFÿ, with a binding energy of about 210 kJ/mol. Symmetrical H bonds of the type [ÐOHOÐ]ÿ have

140 BONDS TO HYDROGEN

also been found between two oxygen atoms, for example in monoanions of dicarboxylic acids in nonpolar solvents [229].

It is very di½cult to locate hydrogen atoms in large molecules by crystallographic methods. Nevertheless, proximity observations of heavy atoms strongly suggest the existence of bifurcated hydrogen bonds of the type shown below:

These are taken as to be expected in biological systems and are part of empirical potentials for protein and DNA structure. For example, bifurcated hydrogen bonding is assumed in the interstrand region of DNA [230], at the nucleation sites for protein b- sheets [231], and at other sites in proteins [232]. An examination of neutron di¨raction data on 18 monosaccharide structures for hydrogen-bonding con®gurations revealed that ``an appreciable fraction (15%) are of the bifurcated type'' [233]. The symmetrical threecenter case may be examined by consideration of the orbital interaction diagram in Figure 10.3a, where the three heavy atoms are considered to be equivalent and sym-

…a†

…b†

Figure 10.3. Orbital interaction diagrams for (a) symmetrical three-center hydrogen bonding and (b) bifurcated hydrogen bonding.

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141

metrically disposed at the corners of an equilateral triangle, with the hydrogen atom at the center. Such an arrangement is obviously favorable energetically, but by reasoning analogous to that put forth for symmetrical two-center bonding (Figure 10.2), it is unlikely to be the most favorable arrangement. At the midpoint of the triangle, the hydrogen 1s orbital cannot interact with either of the two HOMOs. On this basis, symmetrical three-center hydrogen bonding should be an extremely unlikely occurence.

Proton Abstraction Reactions

Many reaction steps in organic chemistry require the abstraction of a proton by a Lewis base. Interaction diagrams for the elementary stages for the reaction B: ‡ HÐA ! BÐH ‡ A: are shown in Figure 10.1. The reaction parallels the SN2 reaction; it is a nucleophilic substitution at H. We will restrict our attention to reactions which involve an abstraction of a proton from C. As stated above, the s orbital of a CÐH bond is unlikely to be the LUMO of HÐA. However, if the s orbital of a CÐH bond is not too high in energy, the probability of reaction may still be relatively high due to the exposed nature of the hydrogen, the polarization toward H, and the lack of nodes. The ®rst factor makes close approach possible; the other two factors allow large orbital overlap from a wide range of angles of approach.

The energy of the sCH may be lowered by two distinct mechanisms. A change in the hybridization of the C spn orbital toward smaller n, that is, more s character, is accompanied by a lowering of the energy (or increase of electronegativity) of the hybrid orbital. The orbital interaction analysis, shown in Figure 10.4, predicts two consequences, a lowering of the s orbital and increased polarization of the s orbital toward H. Both

Figure 10.4. Trends in orbital interaction parameters in the series alkyl CÐH, alkenyl CÐH, and alkynyl CÐH.

142 BONDS TO HYDROGEN

…a†

…b†

Figure 10.5. Activation of a CÐH bond by a neighboring substituent: (a) Z substituent; (b) ``C'' substituent.

factors combine to increase the interaction of a base with the s orbital and increase the reactivity toward a given base. The e¨ect on the rate of proton abstraction is not predicted to be large since the s orbitals are close in energy and polarization changes are small. The e¨ects are larger on acid equilibrium values since these are governed by the stability of the conjugate bases where the orbital di¨erences are greater; the pKa values for HÐCH2CH3, HÐCHÐCH2, and HÐCÐCH are 48, 44, and 24, respectively, corresponding to an overall change of about 150 kJ/mol in DG at 25 C.

The second mechanism for lowering the energy of the s CH orbital is via admixture into lower energy unoccupied MOs, especially the LUMO. This occurs whenever a Z or ``C'' substituent is attached to the carbon atom which bears the CÐH bond, as shown in Figure 10.5 The generic p orbital of the Z substituent (Figure 10.5a) or ``C'' substituent (Figure 10.5b) would be the orbital of a p system at the point of attachment of the carbon bearing the H in question. The LUMO of the Z or ``C'' substituent is lowered somewhat by in-phase interaction with the sCH orbital. Because the resulting LUMO has some admixture of the sCH orbital, there is an increased probability that the nucleophile will overlap with the hydrogen 1s orbital, resulting in rupture of the CÐH bond and yielding a p-delocalized carbanion. Of course, the dominant component of the new LUMO is the LUMO of the substituent, and attack of the nucleophile is most likely at that site in the absence of additional considerations such as steric e¨ects, or strong Coulomb interactions. The pKa values of several Z-substituted carbon acids are HÐCH(C(O)CH3)2 9; HÐCH2NO2, 10; HÐCH2C(O)CH3, 20; HÐCH2C(O)OCH3, 24; HÐCH2SO2CH3, 31 (DMSO); and HÐCH2CN, 31 (DMSO). Allylic and benzylic (i.e., ``C'' substituted) carbon acids are considerably weaker (C6H5CH2 ÐH, 41; CH2 Ð CHÐCH2 ÐH, 43) unless more than one ``C'' substituent is present [(C6H5)2CHÐH, 33] or the resulting carbanion may be ``aromatic'' (cyclopentadiene 16).

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…a†

…b†

Figure 10.6. Activation of a CÐH bond by a neighboring (a) CÐX bond and (b) carbocationic center.

Two special cases need to be considered: activation by alkyl halide and by a formal cationic center. The interaction diagrams are shown in Figures 10.6a,b, respectively. These are involved in elimination reactions of alkyl halides, E2 and E1, respectively.

E2 Elimination Reaction

The LUMO of a molecule with an alkyl halide bond ¯anked by a CÐH bond is shown in Figure 10.6a. The LUMO is composed primarily of the sCX with some sCH mixed in in phase. The amount of interaction, and therefore the energy of the LUMO, depends on the orientation of the CÐH and CÐX bonds. Interaction is strongest when the two bonds are coplanar and slightly better if they are anti-coplanar. Interaction of the LUMO with the HOMO of a Lewis base (nucleophile) will direct the base to the points where the best overlap occurs, namely to the backside of the C end of the CÐX bond, as already discussed, resulting in a nucleophilic substitution by the SN2 mechanism. However, there is a possibility of attack at the H end of the CÐH bond, and this mode may be the most probable if the Lewis base is not a ``good nucleophile'' or if attack at C is sterically hindered. Attack by a Lewis base (i.e., addition of electrons) at the H end of the LUMO is accompanied by a reduction of the s bond order of the CÐH and CÐX bonds and an increase of p bond order between the two carbon atoms. Thus, the overall course of the reaction is a concerted formation, by anti elimination, of a CÐC p bond and a BÐH s bond and rupture of the CÐH and CÐX s bonds. If the CÐH and CÐX cannot adopt a coplanar con®guration, the LUMO is not lowered in energy, the CÐC p bond cannot be formed, and there is no mechanism for breaking the CÐX

144 BONDS TO HYDROGEN

bond if base attack is at the CÐH bond. Operation of the E2 mechanism therefore has a very strong stereoelectronic requirement that the CÐH and CÐX bonds be able to achieve a (nearly) coplanar arrangement. In terms of the intrinsic stabilization, there is not much di¨erence between the syn coplanar and anti coplanar arrangements. The observation that the E2 reaction proceeds predominantly by anti elimination is easily explained on steric grounds. The anti arrangement of two bonds at adjacent tetracoordinated centers corresponds to a minimum in the potential function for rotation about the single bond, whereas the syn (or eclipsed) arrangements corresponds to a maximum. In cyclic systems, where adjacent CÐH and CÐX bonds are forced into syn coplanar arrangements by ring constraints, the E2 elimination still proceeds, albeit at a reduced e½ciency probably due to steric shielding of the CÐH bond by the adjacent halogen.

The gas-phase E2 reaction of CH3CH2Cl with Fÿ and PH2ÿ (proton a½nities 1554 and 1552 kJ/mol) has been investigated by high-level ab initio computations [234]. With Fÿ as the nucleophile, a small di¨erence of 4 kJ/mol was found, favoring the SN2 pathway over the E2 (anti) pathway. However, the E2 (anti) pathway was preferred over the E2 (syn) route by 53 kJ/mol. Fluoride was predicted to be considerably more reactive than PH2ÿ, for which relative transition state energies of 0.0, 49, and 84 kJ/mol were found for the SN2, E2 (anti), and E2 (syn) transition states, respectively.

E1cB Mechanism Reaction

The E1cB mechanism has the same features as the E2 mechanism except that proton abstraction by the base proceeds essentially to completion prior to departure of the leaving group. A variant of this mechanism may intervene whenever the leaving group is a poor leaving group or an exceptionally stable carbanion may be formed (i.e., due to the presence of Z substituents in addition to the polar s bond and/or a hybridization e¨ect). The factors which lead to stabilization of carbanions have been discussed in Chapter 7.

E1 Elimination Reaction

The rate-determining step of the E1 elimination reaction is precisely the same as previously discussed for the SN1 reaction. The interaction diagram for the CÐH bond and an adjacent carbocationic center is shown in Figure 10.6b. Because the s and s CÐH bond orbitals are equally spaced relative to the energy of the p orbital at the cationic site, the LUMO energy is approximately the same as the energy of the unperturbed cationic p orbital. Reactivity with Lewis bases remains very high but is reduced somewhat by delocalization of the orbital (smaller coe½cient on the p orbital). Notice that the presence of the adjacent CÐH bond results in stabilization of the carbocation by a lowering of the energy of the sCH orbital. Concomitant delocalization of the CÐH bonding electrons is accompanied by weakening of the CÐH bond and partial bond formation between the H and the C at the cationic site. Hydride transfer may result if this is energetically favorable. The most probable course of the reaction with a Lewis base is formation of a s bond at the cationic site. However, there is a possibility of attack at the H end of the CÐH bond, and this mode may be enhanced if the base is a ``good'' Lowry± Bronsted base (forms a strong bond to H). Both addition of the nucleophile to C and proton abstraction are reversible. The equilibrium may often be channeled toward proton abstraction by removal of the more volatile ole®n by distillation.

REACTION WITH ELECTROPHILES: HYDRIDE ABSTRACTION AND HYDRIDE BRIDGING

145

REACTION WITH ELECTROPHILES: HYDRIDE ABSTRACTION AND HYDRIDE BRIDGING

The CÐH bond is normally not very basic and will not interact with Lewis acids as a rule. However, in the presence of very powerful Lewis acids, such as carbocations, or if substituted by powerful p electron donors (X: or ``C'' substituents), hydride abstraction from a carbon atom may be accomplished, corresponding to an oxidation of the C atom.

Activation by p Donors (X: and ``C'' Substituents)

Abstraction of a hydride from carbon is almost invariably an endothermic process. The rate of the reaction depends on the stability of the transition structure which closely resembles the product carbocation and is expected to be stabilized by the same factors, among them, substitution by X: and ``C'' substituents. Nevertheless, initial interactions set the trajectory for the hydride abstraction reaction. The interaction of a CÐH bond with a ``C'' substituent is shown in Figure 10.7b. The feature relevant to the present discussion is that the HOMO which involves some admixture of the CÐH bond has been raised in energy. Therefore, attack by electrophiles, while most likely at the p bond of the ``C'' substituent, is also possible at the CÐH bond. The interaction of an X: substituent with a CH bond is shown in Figure 10.7a. In general a single X: or ``C'' substituent is not su½cient to activate the CÐH bond toward hydride abstraction.

Hydride Abstraction

The interaction of a CÐH bond with a strong Lewis acid (low-energy LUMO) is shown in Figure 10.8a. The p orbital of a carbocation as the LUMO is shown by way of example. Examples of hydride abstraction reactions are shown in Scheme 10.1.

…a†

…b†

Figure 10.7. Activation of a CÐH bond toward electrophilic attack by a neighboring substituent: (a) X: substituent; (b) ``C'' substituent (only the adjacent p orbital is shown).

146 BONDS TO HYDROGEN

…a†

…b†

Figure 10.8. Interaction of a CÐH bond with a strong Lewis acid: (a) initial interaction; (b) bonding MOs of a hydride bridge.

The ®rst reaction provides a route for the reduction of alkyl halides since the carbocation (isopropyl, in R1) may be prepared from action of AlCl3 on the corresponding alkyl halide. Reactions of the type R1 are also important in the process, catalytic cracking, in the manufacture of gasoline. They have also been studied in mass spectrometric experiments [235]. Reaction R2 is one route to the preparation of carbocations under stable ion conditions. Reaction R3 is employed in the laboratory synthesis of the tropylium cation. Reaction R4, the (crossed) Cannizzaro reaction, is unusual in that it takes place under strongly basic conditions. The oxy dianion is an intermediate in the reaction of concentrated hydroxide with the aldehyde, R1CHO. None of R1, R2, or R3 may have hydrogen atoms a to the carbonyl groups. Formaldehyde (R1 ˆ H) is readily

Scheme 10.1

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147

oxidized and is useful in the reduction of other ketones or aldehydes. Reaction R5, a 1,2 migration of hydride, may be regarded as a special case of this class of reaction, although we will see it again in connection with the Wagner±Meerwein rearrangement as a thermally allowed [1, 2] sigmatropic rearrangement in connection with our discussion of pericyclic reactions (Chapter 12).

Hydride Bridges

Hydride bridge bonding is common in boron compounds, the simplest example of which is B2H6, and in transition metal complexes. We restrict our discussion here to instances where hydride bridging occurs between carbon atoms. The MOs of a hydride bridged carbocation are shown in Figure 10.8b. These are entirely analogous to the MOs previously shown for two-electron three-center bonding (middle of Figure 10.7), except that the nonbonding orbital is higher in energy and unoccupied. One of the isomers of protonated ethane, C2H7‡ 1, has precisely the bonding shown in Figure 10.5b:

The CÐHÐC bond is not linear, the angle being about 170 according to high-level MO calculations. Several bridged cycloalkyl carbocations of the type 2 have been prepared [236]. Complexes between a number of alkyl cations and alkanes have been detected in mass spectrometric experiments [235]. The ``nonclassical'' structure of the ethyl cation, 3, may be cited as another example of hydride bridging (for a discussion, see ref. 55).

REACTION WITH FREE RADICALS: HYDROGEN ATOM ABSTRACTION AND ONEOR THREE-ELECTRON BONDING

The CÐH bond is normally not very polar. As a result, the sCH and sCH orbitals are widely separated and more or less symmetrically disposed relative to a. A sluggish reaction is expected with carbon free radicals, but a rapid reaction may be anticipated with both electrophilic and nucleophilic free radicals. Examples of both kinds of reactions are ubiquitous in organic chemistry. An ab initio investigation of the former, involving oxygen-centered free radicals, has been carried out [237]. The reactivity spectrum may be modi®ed by substitution on the carbon bearing the hydrogen atom. As we have seen in Chapter 7, all three kinds of substituents stabilize the carbon-centered free-radical intermediate.

HYDROGEN-BRIDGED RADICALS

In most cases the bond to hydrogen is from an element more electronegative than it is, including carbon, and therefore the s orbital, which may be the LUMO, is polarized toward H. Since one-electron bonding is more favorable than three-electron bonding in general, the complex formed between HÐX and a free-radical center will involve a hydrogen bridge. If the interaction carries to extreme, a hydrogen atom abstraction

148 BONDS TO HYDROGEN

Figure 10.9. Orbitals for a hydrogen atom abstraction reaction. The middle is the orbital diagram for the transition state for H transfer.

occurs. The observation of negative activation energies in a number of reactions between carbon-centered free radicals and HX (X ˆ Br, I) [238, 239] has been interpreted as evidence of intermediate complex formation. The existence of the complex between methyl radical and HCl or HBr as a hydrogen-bridged species has been established by high-level ab initio calculations [68]. In the complex, the CÐH bond is considerably elongated compared to the HÐX bond.

HYDROGEN ATOM TRANSFER

Figure 10.9 shows the orbital interactions for typical hydrogen atom transfer reaction. It is in fact the same diagram that described proton and hydride transfers (Figures 10.1 and 10.8, respectively). However, unlike the cationic and anionic cases, the author is not aware of any symmetrical hydrogen atom-bridged structures. The best candidate would be [FÐHÐF].. The middle of Figure 10.9 would then represent the bonding of the TS to H atom transfer between equal fragments.

Sigma bonds are involved so generic s orbitals are shown for A and B in Figure 10.9. According to the principles described in Chapters 3 and 7, both the SOMO±HOMO and SOMO±LUMO interactions are attractive and a complex is expected. The SOMO± HOMO interaction becomes less important as the reagents approach each other (i.e., decreases as overlap increases) compared to the SOMO±LUMO interaction. The energy of the TS for H transfer will depend on the absolute importance of the two attractive interactions. The three-orbital interaction results in stabilization of the lowest orbital, and the middle singly occupied orbital moves slightly up or down depending on whether SOMO±HOMO or SOMO±LUMO is dominant. Because of its importance in oxidative damage by free radicals in biological systems, the activation parameters for many hydride transfer reactions have been determined experimentally or by high-level calculations, and a number of ``rules'' [240, 241] evolved to predict the magnitudes of the barriers,