Article Cite This: J. Org. Chem. 2018, 83, 4024−4033
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How the Arrangement of Alkyl Substituents Affects the Stability of Delocalized Carbocations Paul R. Rablen* and Nathalie A. Perry-Freer Department of Chemistry and Biochemistry, Swarthmore College, 500 College Ave., Swarthmore, Pennsylvania 19081, United States S Supporting Information *
ABSTRACT: G-4 calculations are used to explore which carbon atoms of methylated butadienes, methylated cyclopentadienes, and methylated benzenes are most readily protonated to yield delocalized allyl and pentadienyl cations. While it is not surprising that alkylation of the positions bearing formal positive charge stabilizes these cations, several other effects are less obvious. First, alkylation of positions in the delocalized cation that do not bear formal charge is beneficial, to an extent about a quarter to a third as great as at charged positions. Second, alkylation of the position receiving the proton disfavors protonation. Finally, at least in the acyclic systems, the more symmetrical substitution pattern that is 2° at both ends is moderately preferred to the less symmetrical pattern that is 3° at one end and 1° at the other. Taking all three of these factors into account, as well as substitution at the formally charged centers, models the stability of all 94 delocalized cations quite well.
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INTRODUCTION Carbocations constitute an important class of reactive intermediates and have been studied extensively via electronic structure calculations as well as experimental methods.1 Alkyl groups are well-known to stabilize carbocations in general, but how does this influence play out when the positive charge is delocalized over more than one center, as in allyl and other conjugated systems? This question often arises in the context of addition reactions of conjugated dienes and polyenes. There is no doubt that alkyl groups stabilize such carbocations,2,3 as does charge delocalization,1,2,4−7 but does the arrangement of the alkyl groups matter? For instance, compared to the parent allyl cation that is primary at both ends, is it better to add two methyl groups both to the same terminal position or one to each terminus? Also, is there a saturation effect, such that as more and more alkyl groups are added to the framework, they have progressively less influence? Mayr, Förner, and Schleyer addressed these questions for allyl cation and its various methylated derivatives in 1979, using gas-phase STO-3G calculations as well as experimental data.2 Some of these allyl systems have also subsequently been studied individually or in small groups at higher levels of theory.1,3−8 In the gas-phase, Mayr and co-workers found that successive methylation of the terminal positions of an allyl cation yielded progressively decreasing stabilization: 17, 15, 13, and 11 kcal/mol.2 They also observed significant stabilization from methylation of the middle position (5 kcal/mol), and a steric cost of 3−5 kcal/mol for placing methyl groups in the endo positions. In general, they found that even HF/STO-3G calculations reproduced the available gas-phase experimental data rather well. Here, we extend the study in four ways: We include cyclic as well as acyclic structures, which eliminates some of the complications and ambiguities that arise from conformational flexibility; © 2018 American Chemical Society
we include (cyclic) pentadienyl as well as allyl cations; we use a higher level of electronic structure theory than was possible in 1979; and we include a simulated solvent, to more closely correspond to the solution environment that is most often of interest to an organic chemist. Accordingly, the structures and energies of a series of cyclic and acyclic allyl and pentadienyl carbocations have been computed using G-4 theory, with a polarizable continuum model to simulate the presence of a methanol solvent. The goal is to discern usefully generalizable patterns that emerge from consideration of many examples together.
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RESULTS Molecules Studied. We have chosen here to consider the following cases: (1) All carbocations obtained by replacing zero or more of the hydrogen atoms of the parent allyl carbocation with a methyl group (structures 1−12, Figure 1). (2) All allyl carbocations obtained by protonation, at all possible sites, of all the dienes obtained by replacing zero or more of the hydrogen atoms of 1,3-butadiene with a methyl group (Figure 2). (3) All carbocations obtained by protonation, at all possible sites, of all the structures obtained by replacing zero or more of the hydrogen atoms of benzene with a methyl group (Table 1). (4) All carbocations obtained by protonation, at all possible sites, of all the structures obtained by replacing zero or more of the hydrogen atoms on carbons 1, 2, 3, and 4 of 1,3-cyclopentadiene with a methyl group (Table 2). Received: February 12, 2018 Published: March 8, 2018 4024
DOI: 10.1021/acs.joc.8b00415 J. Org. Chem. 2018, 83, 4024−4033
Article
The Journal of Organic Chemistry
to be free of interfering effects, but of course that is never really the case, and so the results depend to some degree on the choice of reference. Methyl-Transfer Energy. Since organic chemists often take alkanes as an implicit, “unbiased” reference system, the hydride affinities of carbocations represent a reasonable measure of stability. That is, carbocation stability can be estimated as the energy released by adding hydride ion to the site of positive charge, forming a new alkane C−H bond. Equivalently, one can use hydride-transfer energies, corresponding to the energy of removing a hydride ion from a reference alkane, to make a reference carbocation, while simultaneously adding the hydride to the carbocation in question, to make a neutral hydrocarbon. Such hydride-transfer energies,9 as well as hydride affinities,3 have been used previously as measures of carbocation stability. We use a closely related measure, the methyl-transfer energy (Scheme 3), with the thought that a C−C bond is a more unbiased (thoroughly nonpolar) reference than a C−H bond.10 In this reaction, a methyl group is removed from propane, to yield ethyl cation (the reference), and transferred to a site of formal charge on the cation for which a stability measure is desired.11 Scheme 4 depicts the reaction that we use to define methyl-transfer energies more generally. Figure 1 lists the so-defined methyl-transfer energies for the structures 1−12, while Figure 2 provides them for the protonation products of all possible methylation patterns of 1,3-butadiene. (Figure S2 in the Supporting Information shows the same cations and energies and also the nondelocalized homoallyl 3° cations that can in some cases be obtained through protonation of the dienes.) An ambiguity arises in many cases, because more than one site of positive charge exists. For instance, the unsymmetrical cation 4 in Scheme 3 has two possible methyl-transfer reactions, although the symmetrical cation 6 has only one. Therefore, Figures 1 and 2 each list two methyl-transfer energies for each unsymmetrical allyl cation, corresponding to the two different methyl-transfer reactions, as shown for the general case in Scheme 4.12 Reassuringly, the energies are generally similar.13 Proton-Transfer Energy. The protonation energies of conjugated dienes can also be considered in a more general fashion. Scheme 5 shows a reaction that defines the proton-transfer from a given allyl cation to ethylene, yielding ethyl cation and a diene.10 The energy of this reaction indicates how readily the carbocation is formed via protonation of the diene, with everything scaled relative to the ethyl cation. The more endothermic the reaction (the more positive the energy), the more stable the allyl cation. These proton-transfer energies provide a measure of carbocation stability relevant for processes in which the cation is generated by protonation of a diene (or simple alkene). Figures 1 and 2 list these proton-transfer energies in green and in parentheses. When a cation has two different possible precursors, energies corresponding to both are provided. It is worth making a point here to avoid confusion. Although one measure is a methyl-transfer energy (Scheme 4), and the other is a proton-transfer energy (Scheme 5), these measures differ by more than just whether a methyl or a hydrogen is transferred. The reference process in the former case (Scheme 4) is substitution and involves transferring a methyl anion. It is perhaps especially relevant for cations formed by departure of a leaving group. The reference process in the latter case (Scheme 5) is electrophilic addition and involves transferring a proton, that is, a cation. Presumably it is more relevant for cations formed by protonation.
Figure 1. Methylated allyl cations. Methyl-transfer energies (relative to ethyl cation, defined in Scheme 4) are shown in red; different values correspond to different reference alkenes, when such differences are possible. Proton-transfer energies (relative to ethyl cation, defined in Scheme 5) are shown in green in parentheses, and again different values correspond to different reference alkenes. All are solvated standard enthalpies at 0 K in kcal/mol.
Measures of Carbocation Stability. Several ways to define carbocation stability come to mind in the present context.3 First, one might evaluate strictly isomeric structures, the energies of which can be compared directly. The first line of Scheme 1 shows such a comparison for the cations obtained by adding two methyl groups either both to one terminus, or else one to each terminus, of the parent allyl cation. The symmetrical 2°/2° structure is calculated to be 2.2 kcal/mol more stable than the unsymmetrical 3°/1° structure. That agrees fairly well with the 3.6 kcal/mol energy difference calculated by Mayr and co-workers in the gas phase at STO-3G.2,8 Experimentally derived hydride affinities yield a similar gas-phase energy difference of 2.6 kcal/mol.3 Here and throughout this work, the calculated energies we report are what one might call methanol-solvated G-4 standard enthalpies at absolute zero. The ΔH° (0 K) term is equivalent to an electronic energy corrected for zero-point vibrational energy. However, the calculation, including geometry optimization, includes a solvation free energy correction. As explained in the Computational Methods section, this combination of enthalpy and free energy is not entirely rigorous, but is quite practical for the present purposes. However, no single ordinary reaction could generate both of these structures. Therefore, one might wish instead to compare carbocations that can at least in principle be obtained via protonation of a common diene or triene precursor. This set of circumstances applies to the addition reactions of conjugated systems, where one wants to know which of two or more sites most readily undergoes protonation. The resulting structures are of necessity still isomeric, and so their energies can again be compared directly. Scheme 2 provides an example of such a comparison. Table S6 in the Supporting Information provides a complete listing of such comparisons. One also might wish to compare carbocations that are not isomeric and that necessitates a different approach.3 When the structures are not isomeric, no single strategy is clearly “correct”. Whether explicit or implicit, a comparison to a reference system is always required. One generally imagines the reference system 4025
DOI: 10.1021/acs.joc.8b00415 J. Org. Chem. 2018, 83, 4024−4033
Article
The Journal of Organic Chemistry
Figure 2. Allyl carbocations obtained by protonating methylated 1,3-butadienes. Methyl-transfer energies (relative to ethyl cation, defined in Scheme 4) are shown in red; different values correspond to different reference alkenes. Proton-transfer energies (relative to ethyl cation, defined in Scheme 5) are shown in green in parentheses, and again different values correspond to different reference alkenes. All are solvated standard enthalpies at 0 K in kcal/mol.
Benchmark Comparisons. Figure 3 provides both proton and methyl-transfer energies for some common benchmark systems, for comparison. Pentadienyl and Cyclic Systems. To gain further insight, it is desirable to extend the analysis to pentadienyl cations. However, the conformational flexibility of allyl cations, and of their alkene and diene precursors, already complicates the task of discerning how alkyl substitution affects their stability. These complexities only grow worse with pentadienyl cations and trienes, which have more rotatable bonds. These conformational difficulties can be avoided by considering cyclic structures, which by their nature have little or no conformational freedom. With this motivation in mind, protonation energies were computed for methylated 1,3-cyclopentadienes and benzenes. The energy to transfer a proton from the cation in question to ethylene, making an ethyl cation, was used as a measure of relative cation stability, as depicted in Schemes 6 and 7 (and analogous to Scheme 5). Tables 1 and 2 list the energies for the delocalized cations that can be obtained by
protonation of methylated benzenes (Table 1) and methylated cyclopentadienes (Table 2). Nondelocalized Carbocations. For completeness, Figure 4 depicts the stable carbocations that can be obtained via the protonation reactions represented in Figure 2, but that are not delocalized. The carbocations of this nature that would in principle be 1° or 2° are all unstable and spontaneously rearrange. Several of the 3° carbocations also rearrange without barrier and so are not shown. Others, however, do have at least a small barrier to rearrangement and are thus local minima, and they are listed in Figure 4. These cations are generally a few kcal/mol lower in energy than one might expect by comparison to the case of t-butyl cation. That is presumably because they are homoallyl, and the remaining π bond can still stabilize the positive charge to some degree. The minimum energy conformations have C(+)−C−C(vinyl) bond angles
