Reactive Intermediate Chemistry

Figure 22.4. Schematic depiction of the electronic structures of the lowest singlet states of phenylcarbene (1a) and phenylnitrene (1b).

places both nonbonding electrons in the hybridized s orbital. As depicted in the second resonance structure for 1a in Figure 22.4, the empty 2p–p AO on the carbenic carbon can accept p electrons from the benzene ring in 1a.

In contrast to the case in 1a, in 1b both of the nonbonding orbitals on nitrogen are pure 2p AOs. Electronic structure calculations30 revealed that in the lowest singlet state of 1b, the 2p–s AO on nitrogen, which lies in the plane of the benzene ring, is occupied by one nonbonding electron. The other nonbonding electron formally occupies a 2p–p orbital on nitrogen, but this electron is largely delocalized into the benzene ring, The equilibrium geometry calculated for this state indicates that its electronic structure can be depicted schematically as in Figure 22.4, with the s and p nonbonding electrons occupying very different regions of space.

Confining these two electrons of opposite spin to different regions of space minimizes the Coulombic repulsion between these electrons.30b Consequently, the singlet– triplet energy gap in 1b is computed to be only about one-half the size of those measured in N H31 and in methylnitrene.32 Experimental evidence that the electronic structure calculations are correct came from the excellent agreement between two independent measurements of the singlet–triplet energy splitting in 1b33 and the values predicted by the calculations.30

The difference between the reactivities of 1a and 1b toward ring expansion is nicely explained by the difference between the electronic structures of their lowest singlet states.29 With incluson of dynamic electron correlation, calculations of the PESs connecting 1a to 3a34 and 1b to 3b35 found that in both reactions electrocyclic ring opening of 2 to 3 has a low barrier, so that the rate-determining step is ring closure of 1 to 2. In agreement with experiment, the barrier-to-ring closure, com-

puted by (8/8)CASPT2 calculations, was found to be considerably lower for

1b ! 2b than for 1a ! 2a.35

The greater reactivity of 1b than 1a is easily rationalized by the depictions of the lowest singlet states in Figure 22.4. Just bending the nitrogen out of the plane of the benzene ring in 1b is sufficient to allow bonding between the s nonbonding electron on nitrogen and the p nonbonding electron of opposite spin in the benzene ring. On the other hand, cyclization of 1a not only requires bending the carbenic carbon out of the plane of the benzene ring but also an increased contribution from the ionic resonance structure in the lowest singlet state.

984 THE PARTNERSHIP BETWEEN ELECTRONIC STRUCTURE CALCULATIONS

Without the calculations that showed that there is a fundamental difference between the lowest singlet states of 1a and 1b,30 and that this difference is responsible for the difference between their reactivities,35 it is not clear how the correct explanation for the much faster ring expansion of 1b than of 1a would ever have been found.

From the understanding, provided by the calculations, of the mechanism by which 1b cyclizes, what can be predicted about how the rate of this reaction might be affected by substituents on the benzene ring? The substituent effects would, in fact, be expected to be small, except for possible steric effects due to substituents in the ortho positions. If both ortho positions are substituted, one would expect to see a decrease in rate, relative to unsubstituted 1b. On the other hand, if only one ortho position is substituted, cyclization should be about as fast as in unsubstituted 1b; but cyclization should preferentially occur at the unsubstituted ortho carbon. Additional (8/8)CASPT2/6-31G* calculations by Bill Karney in our group36 and subsequent experiments by the Platz group37 confirmed these qualitative predictions about the effects of ortho substituents.

Although electronic effects of substituents on the rate of cyclization of 1b should be small, it does seem possible that radical-stabilizing substituents on the benzene ring might have at least a modest effect on the rate of cyclization. If the unpaired p electron in 1b tends to localize at a ring carbon to which a radical-stabilizing substituent is attached, this effect should tend to favor cyclization at an ortho carbon that bears such a substituent. In contrast, if a radical-stabilizing substituent were attached to the para carbon, the rate of cyclization should be retarded. Confirmation of these qualitative expectations for radical-stabilizing cyano substituents came from a combined computational–experimental study by our group and Platz’s.38

Unlike the case with phenylcarbene (1a) and phenylnitrene (1b), ring expansion of phenylphosphinidene (1c) to 1-phospha-1,2,4,6-cycloheptatetraene (3c) has not been observed; and 1c lives long enough to undergo intermolecular reactions.39 Explaining why chemical reactions do not occur can be as important as explaining why they do take place; and recent (8/8)CASPT2/6-31G* calculations offer a very simple explanation of why the reaction 1c ! 3c has never been observed40—the calculations predict that this reaction is quite endothermic. The difference between the thermodynamics of this reaction and the ring expansions of 1a and 1b is that the bonds which would be formed to phosphorus in the ring expansion of 1c are much weaker than the corresponding bonds formed to carbon and to nitrogen in the ring expansions of, respectively, 1a and 1b.

Interestingly, the calculations find the difference in the bond strengths to the heteroatoms in 3b and 3c to be largely compensated for in 2b and 2c by the greater ability of phosphorus, compared to nitrogen, to accommodate the small bond angle at the heteratom in the cyclopropene ring. As a result, closure of 1c to 2c is predicted to be considerably less endothermic than the next step in the ring expansion, the electrocyclic ring opening of 2c to 3c. Therefore, the CASPT2 calculations offer some hope that it may be possible to trap the small amount of 2c that is predicted to be in equilibrium with 1c, using a reagent that reacts with 2c but not with 1c.

Figure 22.5. The MP2/6-31G* bond lengths and net Mulliken charges (in italics) at C H groups, computed for cubyl cation 4. Resonance structures A and B are consistent with the calculated bond lengths and charges; whereas, structure C is not.

4.2. Why Is Cubyl Cation Formed So Easily?

Another example of the power of a partnership between calculations and experiments is provided by cubyl cation (4 in Fig. 22.5). As pointed out by Eaton, ‘‘Everything about the cubyl cation seems unfavorable: (1) the geometry about the positively charged carbon is very far from flat; (2) the exocyclic orbitals in cubane are . . . . rich [in 2s character, making the bonds to potential leaving groups unusually strong], and hyperconjugative stabilization would require high-energy, cubene-type structures.’’41 Nevertheless, Eaton et al.42 and Moriarity et al.43 both found that this cation can be formed by solvolysis under surprisingly mild conditions.

For many polycyclic carbocations there is a good correlation between the changes in strain energies on carbocation formation, predicted by molecular

mechanics calculations, and the solvolysis rates. However, at 70 cubyl cation is formed 1015 times faster than expected from this correlation.41,44 What is respon-

sible for this huge rate acceleration?

4.2.1. Calculations and Additional Experiments on Cubyl Cations. In order to answer the question, posed by the experiments of Eaton and Moriarity, we undertook electronic structure calculations on 4. Calculations at the HF level did not predict the special stability, found experimentally for 4, but MP2 calculations did.45 It was known that inclusion of dynamic electron correlation is necessary for the proper description of ‘‘nonclassical’’ cations, in which delocalization of electrons in s bonds provides stabilization.46 Therefore, the contrast between the HF and MP2 results suggested that 4 was stabilized by such delocalization. But what was the nature of this delocalization?

The optimized geometry of 4, obtained at the MP2/6-31G* level and shown in Figure 22.5, offered more clues about the type of delocalization that is not responsible for the stabilization of 4 than about the type of delocalization that is. If delocalization of the strained bonds between the carbons, a and b to the cationic center, were involved and occurred in the manner depicted in resonance structure C, the bonds between the ipso and a carbons should have considerable double-bond

986 THE PARTNERSHIP BETWEEN ELECTRONIC STRUCTURE CALCULATIONS

character. One would then expect these bonds to be much shorter than they are in the MP2/6-31G* optimized structure of 4 in Figure 22.5. One would also expect to see lengthening of the bonds between the a and b carbons. These latter bonds are longer than those in the MP2/6-31G* optimized geometry for cubane, but only by

˚

0.011 A.

The Mulliken charges at the C H groups, which are shown in Figure 22.5, are also inconsistent with an appreciable contribution from resonance structures like C. Such structures place positive charges on the b C H groups, but these carbons are computed to be the least positively charged in 4. The most positively charged carbons are predicted to be those a to the cationic carbon and, surprisingly, the carbon g to it. The population analyses suggest that resonance structures such as A and B in Figure 22.2 best describe the delocalized bonding in 4.

Bonding between the b carbons and the ipso carbon, as depicted in structures A and B, is suggested by the positive bond orders that are computed between the rele-

˚

vant orbitals on these carbons. The distance between these carbons (2.034 A) in the MP2/6-31G* optimized geometry, although longer than in cyclobutyl cations where there is only one b carbon,47 is about the same as some of the distances, found by

calculations, in the transition structures for many pericyclic reactions (e.g., the chair Cope rearrangement)19,48 Thus the distance between the b carbons and the ipso car-

bon in the optimized geometry of 4 is short enough to allow significant bonding to occur between these carbons.

The most intriguing result of the electronic structure calculations is the prediction of substantial positive charge on the g carbon in 4. Indeed, it was known from experiments, which had already been completed at the time that our calculations were performed, that halogens and other inductively withdrawing substituents at the g carbon depress the rate of formation of 4.42,43 However, a methyl substituent, although rate accelerating when attached to an a carbon, at the g carbon had also been found to be slightly rate retarding. Since methyl substituents usually stabilize carbocations, Moriarity argued that development of positive charge at the g carbon of 4 seemed highly unlikely.43

We pointed out45 that the lowest unoccupied (LU)MO of 4 must have the same cylindrical symmetry (a1 in the C3v point group) at the g carbon that it has at the ipso carbon. Since methyl groups stabilize carbocations principally through hyperconjugative donation of electrons from p-like combinations of C H bonds, and since the C H orbitals of a methyl group at the g carbon with p symmetry (e in C3v) are orthogonal to the LUMO, a methyl substituent at the g carbon of 4 should provide much less stabilization than a methyl at an a carbon.

Our calculations did predict that a g methyl group should provide a small amount of stabilization for 4 in the gas phase.18 However, subsequent calculations that included solvation effects did find, in agreement with experiment, that a g methyl group on 4 should slightly depress the rate of carbocation formation.49

After the publication of our article on 4,45 Eaton showed that a methoxyl substituent is also rate retarding when attached to the g carbon.44 Since a methoxyl group is a strongly p-electron-donating but s-electron-withdrawing substituent, this finding makes perfect sense in terms of the symmetry of the LUMO of 4.

Figure 22.6. 1,4-Dehydrocubane (5), showing the nonbonding orbital that is essentially doubly occupied in the lowest singlet. Both A and B are two of the six, equivalent resonance structures that contribute to the low energy of this state, relative to the triplet.

Because silyl and stannyl groups are good s-electron donors, their attachment at the g carbon of 4 should be stabilizing and thus accelerate the rate of formation of 4. In agreement with this conjecture, our calculations predicted that stabilization of 4 by a g substituent should increase in the order Me < SiR3, < SnR3.18 Eaton’s experiments confirmed these predictions.44

4.2.2.Why Is Singlet 1,4-Dehydrocubane Predicted to Lie Far Below the Triplet in Energy? Our calculations on 4 led to the solution of two more

puzzles, one posed by the results of calculations and the other by the results of experiments. (2/2)CASSCF and MR–CI calculations by Michl and co-workers50 and (2/2)CASSCF calculations by Hrovat51 had previously found that the singlet state of 1,4-dehydrocubane (5) lies 10–13 kcal/mol below the lowest triplet. Not only are the singly occupied AOs at C1 and C4 in 5 too far apart to interact significantly through space; but, as indicated in Figure 22.6, the calculations also found that the nonbonding MO with the largest occupation number is comprised of the out-of-phase combination of these two AOs. Clearly, the interaction between these AOs in 5 must be through the bonds of the cube, not through space.

The results of our calculations on cubyl carbocation 4, which showed that stabilization of 4 comes from interactions between the ipso carbon and the b carbons (as represented by resonance structures A and B in Fig. 22.5), suggested that stabilization of diradical 5 comes from the same types of interactions. These too can be represented by resonance structures, two of which are shown in Figure 22.6. Delocalization of electrons from all six of the bonds between the a and b carbons in 5 requires that the in-phase combination of nonbonding AOs be left empty, and that is why the pair of nonbonding electrons preferentially occupies the out-of- phase combination of nonbonding AOs at C1 and C4.

4.2.3.Why Are the Cubyl Hydrogens of Methylcubane More Reactive than the Methyl Hydrogens Toward Abstraction by tert-Butoxyl Radicals? The experimental puzzle, which our calculations on 4 helped to solve, was posed by Della’s finding that tert-butoxyl radicals preferentially abstract hydrogens from the carbons of the cube in methylcubane (6), rather than from the methyl

988 THE PARTNERSHIP BETWEEN ELECTRONIC STRUCTURE CALCULATIONS

group.52 Although the cubyl hydrogens are attached to tertiary carbons, both the large amount of 2s character in these C H bonds and the inability of the radical center in cubyl radical to planarize, make the C H bonds in cubane unusually strong. As Della noted, the C H bonds of the cube are, in fact, stronger than the methyl C H bonds in 6. Therefore, why are the C H bonds of the cube in 6 more reactive than the weaker C H bonds of the methyl group toward tert-butoxyl radicals?

Polar effects in the TSs for hydrogen atom abstraction reactions by radicals—the development of opposite charges at the hydrogen-donor and hydrogen-acceptor atoms, are known to have an accelerating effect on these reactions.53 The Borden group reasoned that the stability of the cubyl cation would favor the separation of charge that is depicted in the bottom resonance structure in Figure 22.7, thus accelerating the rate of abstraction of cubyl hydrogens by tert-butoxyl radical. In order to test this explanation, we performed unrestricted13 (U)HF and UMP2/6-31G* calculations on this reaction; but, for the sake of computational convenience, we replaced tert-butoxyl radical with methoxyl radical.

The results of the UMP2 calculations, which included dynamic electron correlation, confirmed our hypothesis.54 The UMP2 calculations found, in agreement with the results of Della’s experiments,52 that abstraction of a cubyl hydrogen has a lower energy barrier than abstraction of a methyl hydrogen in the reaction of 6 with an alkoxyl radical. Moreover, when population analyses were performed on the TSs for both reactions, the TS for abstraction of a cubyl hydrogen was found to be much more polar and to have much more positive charge on the hydrocarbon moiety than the TS for abstraction of a methyl hydrogen.

H 3C

H

OR

H3C

RO

H

6 H 3C

+

H – OR

Figure 22.7. Schematic depiction of the TS for hydrogen atom abstraction from methylcubane (6) by an alkoxyl radical. The polarity of the TS, depicted in the bottom resonance structure, was confirmed by the results of population analyses.54

4.3. Can Hyperconjugation in a 1,3-Diradical Control the Stereochemistry of Cyclopropane Ring Opening and Make a Singlet the Electronic Ground State of the Diradical?

We began our calculations of the PES for the ring opening of cyclopropane in an attempt to resolve an apparent conflict between the results of experiments by Berson and co-workers55 and by Baldwin and co-workers.56 However, graduate students in our research group were among the experimentalists whose research ultimately benefited the most from the predictions made by our calculations.

4.3.1. Calculations and Experiments on the Stereomutation of Cyclopropane. In 1965, Hoffmann published a seminal paper on trimethylene, another name for propane-1,3-diyl (8).57 He used extended hu¨ckel (EH) calculations and an orbital interaction diagram to show that hyperconjugative electron donation from the central methylene group destabilizes the symmetric combination of 2p–p AOs on the terminal carbons in the ‘‘(0,0)’’ conformation of this diradical. Hoffmann’s calculations predicted that the resulting occupancy of the antisymmetric combination of 2p–p AOs in 8 should favor conrotatory opening of cyclopropane (7), as depicted in Figure 22.8.

Numerous experiments with alkyl-substituted cyclopropanes failed to detect any sign of the preference predicted by Hoffmann’s EH calculations.58 In retrospect, this failure was due to shortcomings in both the calculations and in the design of the experiments. The EH calculations used a single configuration to represent the wave function for 8; whereas, as noted in Section 3.2.3.6, the wave function for such a singlet diradical should include a second configuration, in which the symmetric combination of 2p–p AOs is doubly occupied.13 Therefore, the experimental preference for conrotatory opening of 7 is expected to be much weaker than was predicted by Hoffmann’s EH calculations.

Figure 22.8. Conrotatory ring opening of cyclopropane (7) to what Hoffmann called the ‘‘(0,0)’’ conformation of propane-1,3-diyl (8).57 The in-phase combination of 2p–p AOs in the LUMO is destabilized by an antibonding interaction with the ‘‘p’’ combination of C H bonding orbitals at C2. A lower energy MO, which is not shown, is stabilized by hyperconjugative electron donation; that is, the bonding version of this interaction. The out- of-phase combination of 2p–p AOs in the HOMO has a node at C2; hence, it does not mix with the C H orbitals at this carbon.

990 THE PARTNERSHIP BETWEEN ELECTRONIC STRUCTURE CALCULATIONS

Alkyl substituents are not just stereochemical markers. At C1 and C3 of 8 they can hyperconjugatively donate electrons to both the symmetric and antisymmetric combinations of 2p–p AOs at these carbons. As a result, hyperconjugative destabilization of both these combinations of 2p–p AOs by electron donation from alkyl substituents at C1 and C3 should reduce the preference for the configuration in which the antisymmetric combination of 2p–p AOs is doubly occupied. In fact, our (2/2)CASSCF calculations on 8a and on its 1,3-dimethyl derivative indicated that the methyl substituents should wipe out almost completely the weak preference for conrotation over monorotation that we computed for the stereomutation of unsubstituted 7.59

In 1975, Berson and co-workers55 disclosed the results of elegant experiments on the stereomutation of 7b, using deuterium atoms, instead of alkyl groups, as the stereochemical markers. From measurements of the relative rates of enantiomerization and trans ! cis isomerization of optically active 7b, Berson and co-workers55 found that there was, indeed, a preference for double over single methylene rotations.

However, quantitative evaluation of the size of this preference depended on knowing the size of the secondary deuterium isotope effect on which C C bond in 7b cleaves. With the seemingly reasonable assumption of a secondary isotope effect of 1.10 on bond cleavage, the experimental data led to the conclusion that double methylene rotation was favored over single methylene rotation by a factor of 50 in the stereomutation of 7b. Although the error limits on the measurements were large enough to allow the actual ratio to be much smaller, Berson wrote, ‘‘There is no doubt that the double rotation mechanism predominates by a considerable factor.’’55

Sixteen years later Baldwin and co-workers56 published the results of even more elegant experiments in which the stereomutation of optically active 7-1-13C-1,2,3- d3 was studied. Because a deuterium atom is attached to each of the carbons in this compound, it was unnecessary for Baldwin to assume the size of a secondary deuterium isotope effect on which bond cleaves, in interpreting his kinetic data, The results of his experiments led him to conclude, ‘‘the double rotation mechanism does not predominate by a substantial factor.’’56

In discussing the contrast between his findings on the stereomutation of 7-1-13C- 1,2,3-d3 and Berson’s results on the stereomutation of 7-1,2-d2, Baldwin attributed the difference between them to Berson’s having made ‘‘some reasonable but nevertheless erroneous assumptions about kinetic isotope effects. . . .’’56 In order to test this conjecture, Steve Getty (in our group) calculated the size of the secondary kinetic isotope effects that electronic structure theory predicts for Berson’s experiments.60

Getty performed (2/2)CASSCF/6-31G* geometry optimizations and single-point calculations, in which dynamic correlation was added by allowing SD excitations from the (2/2)CASSCF wave functions. He then used the vibrational frequencies from the (2/2)CASSCF calculations in the Biegeleisen equation to compute the isotope effects for all of the possible reaction pathways—conrotation, disrotation, and monorotation—in the ring opening of 7 to 8.

The calculations found that the secondary isotope effect predicted for Berson’s experiments was 1.13, close to the value of 1.10 assumed by Berson. This

computational result led us to write, ‘‘On the basis of these computational findings, we conclude that there is no way to reconcile the experimental results [obtained] by Berson and by Baldwin.’’60 Subsequent isotope effect calculations by Baldwin et al.61 led to the same conclusion.

What did Getty’s calculations and those of Baldwin and co-workers on the PES for ring opening of 7a predict about whether a strong preference for double rotation should be expected in the experiments of Berson and Baldwin? At the temperatures at which these experiments were performed, both sets of calculations did predict conrotatory ring opening to be faster than either disrotatory and monorotatory ring opening, but by factors of only 2 4. However, whether these computational results mean that double methylene rotation is actually predicted to be preferred to single methylene rotation in the automerization of 7a depends on what is assumed about the behavior of diradical 8a, formed by crossing the TSs for conrotatory and disrotatory ring opening of 7a.

Suppose that, as Getty calculated,60 conrotation is favored over disrotation by a factor of 3 in the ring opening of 7a to 8a. Then, if all branching ratios are assumed to be predictable from transition state theory (TST), without explicit inclusion of any possible dynamical effects, conrotation must be favored over disrotation by exactly the same factor of 3 in the closure of 8a to 7a. Thus, a TST model predicts that three-quarters of the molecules of 8a, whether formed by conrotatory or disrotatory ring opening, will undergo conrotatory ring closure to 7a. Since 7a is three times more likely to undergo conrotatory than disrotatory ring opening to 8a, a TST model then predicts the ratios of molecules undergoing con/con, dis/dis, con/dis, and dis/con ring opening and ring closure should be, respectively: 3 3/4 : 1 1/4 : 3 1/4 : 1 3/4, or 2.25 : 0.25 : 0.75 : 0.75.

Both our lab and Baldwin et al. noted that, for 7b, con/dis and dis/con ring opening and closure both produce the same net stereochemical outcome as monorotation. In addition, in the experiments of Berson and Baldwin, con/con and dis/dis opening and closure are operationally indistinguishable, and both contribute to the net amount of double methylene rotation observed. Thus, if conrotation is preferred to disrotation by a factor of 3, a TST model predicts that, of the molecules of 7b which undergo stereomutation by passage through the (0,0) geometry, the

group, which is operationally indistinguishable from cleavage of the bond between C1 and C2 in 7b and passage over a monorotatory TS. Consequently, if a TST model were correct in predicting the partitioning of the (0,0) diradical, ring opening of 7b by coupled rotations of the C1 and C2 methylene groups would be expected to make a substantial contribution to the formation of product, found to have undergone net rotation of just one methylene group in Berson’s experiments.61

On the other hand, it is conceivable that, if 7a undergoes disrotatory ring opening to 8a, energy remains in the disrotatory mode of methylene rotations for the short time that 8a takes to cross the TS for disrotatory closure to 7a. In this dynamical model, disrotatory ring opening to 8a, rather than resulting in preferential