base-catalyzed enolizations: a

Research Article Received: 7 July 2012,

Revised: 14 August 2012,

Accepted: 16 August 2012,

Published online in Wiley Online Library: 19 September 2012

(wileyonlinelibrary.com) DOI: 10.1002/poc.3031

Proton shuffling in acid/base-catalyzed enolizations: a computational study Rafik Karamana* and Fredric M. Mengerb Enolization of acetaldehyde catalyzed by the combined action of a general base (ammonia) and a general acid (formic acid) was examined by density functional theory at the B3LYP/6-311 + G(3df,2p) level while manipulating distance relationships among the reactants. Computations were carried out in the gas phase, in the presence of four water molecules, and with a dielectric constant of 78.4. Enolization involves an early transition state where general-base catalysis is more developed than general-acid catalysis. Although formic acid does not promote enolization by itself, it does facilitate a-proton transfer from acetaldehyde to the general base by several orders of magnitude. Formic acid accomplishes this feat via a hydrogen bond at a van der Waals distance to the carbonyl oxygen as opposed to forming a low-barrier hydrogen bond. A low-barrier hydrogen bond would indeed be capable of accelerating the enolization were it not for the energy cost of generating it. Formic acid may also facilitate enolization by internal solvation of the ammonium ion that is partially formed in the transition state via carbon-to-nitrogen proton transfer. General-base catalysis by trimethylamine, which is out of position to coordinate with the formic acid carboxyl, actually has lower activation energy than that of ammonia catalysis, possibly owing to basicity/shielding effects. Computations also demonstrate that the proton removed by the ammonia nitrogen remains on the nitrogen throughout rather than being transferred via low-energy rotation processes and secondary proton transfers to an oxygen atom of formic acid or the enol itself. Finally, stepwise and concerted mechanisms for enolizations have been proposed in the literature, with experimental evidence being provided for both. The concerted/non-concerted disagreement seems to stem from the continuum of organic mechanisms that Nature bestows onto organic chemistry. Thus, acid/base catalysis varies from stepwise at one extreme to synchronous at the other extreme with an infinite number of concerted mechanisms in between. Since the degree of concertedness undoubtedly depends upon the particular acid, base, substrate, and solvent, disparate enolization models are to be expected. Copyright © 2012 John Wiley & Sons, Ltd. Supporting information may be found in the online version of this paper. Keywords: acid/base catalysis; computations; concertedness; distance dependence; enolization; proton transfer

INTRODUCTION

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Many important enzyme-catalyzed reactions involve rapid proton removal from weak carbon acids. Such proton abstractions are accomplished with the aid of a general-base catalyst at the active site, e.g. histidine (mandelate racemase),[1]aspartate (Δ5-3-ketosteroid isomerase),[2] and glutamate (triose phosphate isomerase).[3] Since the pKas of protons alpha to carbonyls are typically 18–20, and since the pKas of enzymes’ general bases are typically 106 rate enhancement.

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Figure 1. Distance parameters for the reactant (R), transition state (TS), and product (P) in Å units for Eqn. 2 carried out in the absence of water. Red = oxygen; blue = nitrogen; and orange = carbon

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Figure 2. Distance parameters for the reactant (R), transition state (TS), and product (P) and four water molecules in Å units for Eqn. 2

Bond distances, defined in Fig. 1 and given in Table 2, show a curious trend. Thus, although the weakly acidic C2/H1 bond in acetaldehyde is stretched a substantial 0.30 Å in the TS, the C3/O4 bond, initially a carbonyl, is lengthened only slightly in the TS. More specifically, the C3/O4 bond increases its length from 1.22 Å in R to a mere 1.25 Å in the TS as the acetaldehyde makes its way toward an enol with its 1.36 Å C3/O4single bond. In contrast, the C2/C3 bond in the TS (1.42 Å) lies intermediate between a single bond (1.49 Å) and a double bond (1.33 Å). The implication is that C2/C3 double-bond formation progresses well ahead of conversion of the C3/O4double bond into a single bond. (One is reminded here of the principle of “nonperfect synchronization”).[46] Proton delivery from the formic acid H5 to the acetaldehyde O4 oxygen is likewise undeveloped in the TS. Although the O6/H5 formic acid bond remains largely intact in the TS, it lengthens from 1.03 Å to 1.79 Å as the TS progress to product P. In other words, proton delivery to the acetaldehyde carbonyl oxygen from the formic acid seems to require prior partial removal of the a-proton. Stated in another way, generalbase catalysis outpaces general-acid catalysis in the pathway to the transition state. Figure 1 also shows that a 10-membered ring is formed as formic acid within the TS simultaneously engages in two hydrogen bonds. Internal solvation of the ammonium ion, as it abstracts an a-proton from the acetaldehyde, presents a possible rate advantage to the reaction in a non-polar medium. In other words, a contribution by the formic acid to the overall catalysis might involve, in addition to proton donation, chelation of the ammonium that is transiently formed in the transition state. Internal solvation of the incipient ammonium brings up a point that has become almost a cliché in the enzyme-relevant

Copyright © 2012 John Wiley & Sons, Ltd.

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ACID/BASE-CATALYZED ENOLIZATIONS Table 1. Activation enthalpies in kcal/mol for Eqn. 2 in the gas phase without and with the presence of four water molecules (column 1) and the same systems in a dielectric constant of 78.4

System

Enthalpic activation energy gas phase (kcal/mol)

Enthalpic activation energy in water (kcal/mol)

20.0 12.1

14.4 10.4

Acetaldehyde + NH3 + Formicacid Acetaldehyde + NH3 + Formicacid + 4H2O

Table 2. Distances of covalent bonds in the reactants (R), transition state (TS), and products (P) of Eqn. 2 in Å units. Reaction is in the gas phase without water and with four water molecules. See Fig. 1 for the numbering of atoms Acetaldehyde

R TS P R x 4H2O TS x 4H2O P x 4H2O

catalysis. Basicities of the two general bases (with trimethylamine having a much greater proton affinity than ammonia), in addition to charge-shielding effects, might account for the difference. Thus, at the present time, it is difficult to specify the exact contribution of hydrogen bonding between an ammonium proton and the formic acid carbonyl to the overall catalysis.

Formic Acid

C2/H1

C2/C3

C3/O4

O6/H5

C7/O6

1.09 1.39 3.03 1.09 1.46 5.05

1.49 1.42 1.33 1.49 1.40 1.33

1.22 1.25 1.36 1.26 1.27 1.37

1.00 1.03 1.79 1.00 1.05 1.82

1.32 1.31 1.31 1.32 1.30 1.23

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We now return to a question raised earlier. What is the fate of the a-proton (H1) after departing from the acetaldehyde methyl group? Initially, of course, the proton is abstracted by the nitrogen of the general base. If the resulting ammonium species is able to rotate somewhere along the pathway, then this proton could end up hydrogen bonding with formic acid’s O8. Ultimately, the proton could be transferred to the formic acid in the product (and possibly even on the enolic –OH if the formic acid also has rotational freedom along the pathway). To test this possibility, the computations were repeated with deuterium tagging so that proton movement could be traced. We found that: (i) H1 is removed by N from C2 after which it remains on the N in the product; (ii) a proton, originally on the nitrogen, is transferred onto formic acid’s carbonyl oxygen, O8, which becomes the –OH portion of the formic acid in the product; and (iii) H5, the acidic proton originally on O6 of the formic acid, is found in the product, bonded to O4 of the enol. In summary, Fig. 1 accurately portrays the pathway without, inadvertently, overlooking conceivable low-energy rotations. In order to investigate the distance dependence of the general-base/general-acid catalysis, a major concern of this study, we computed the enthalpic energy as the N•••H1 distance was decreased from 2.6 Å down to 1.4 Å in 0.1 Å increments. Concurrently, the C = O4•••H5 distance was held at one particular constant value (i.e. 2.0 Å, 1.8 Å, 1.5 Å, 1.3 Å, or 1.1 Å) as each N•••H1 distance scan was carried out. In this manner, the interconnection between the general-base/general-acid modes of catalysis could be established. The data are summarized in Fig. 3. Table 3 gives the numbers for one particular C = O4•••H5 distance (1.3 Å)



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computational arena. Enzymes operate in water, whereas computations in Fig. 1 lack the presence of solvent. The fact of the matter is that most active sites are cavities in a protein surface where the environment is almost certainly not bulk-water-like. In many cases, a non-polar solvent (or non-polar solvent/water mixture) might be a more suitable model for the enzyme environment than pure water. Unfortunately, substantial ignorance pervades the subject. As seen in Table 1, we have addressed the problem by (a) including an arbitrarily selected four water molecules in the elimination reaction and (b) increasing the dielectric constant to that of bulk water (78.4). Geometries and distances of the reactants including four waters, and the resulting transition state and products, given in Fig. 2 and Table 2, are now discussed. The transition state has a longer C2H1partial bond when water is present (1.46 Å) than when water is absent (1.39 Å). Clearly, water favors greater proton removal from the aldehyde. Moreover, the transition state has a more developed proton delivery from formic acid to the acetaldehyde carbonyl oxygen when water is present (H5/O4 = 1.44 Å) than when water is absent (H5/O4 = 1.53 Å). Hydrogen bonding of a water molecule to the O6 of formic acid’s –OH may enhance the latter’s acidity. In any event, the differences in partial bond lengths correspond to the much lower enthalpic activation energy in the hydrated state (Table 1). Let it be emphasized again that with or without water, we are dealing here with chemical models and, interesting though the comparisons may be, relevance to the enzyme themselves is indirect. As mentioned above, concurrent proton donation/acceptance by formic acid in the cyclic TS of Fig. 1 might play a role in the catalysis. To test this speculation, we repeated the computation using trimethylamine instead of ammonia. Concerted proton transfer from the general base to a formic acid oxygen, as in Fig. 1, is now no longer possible. The resulting transition state, given below, has partial bond lengths comparable to those of the TS in Fig. 1. Yet the activation energy for trimethylamine catalysis is actually 4 kcal/mol lower than that for ammonia

R. KARAMAN AND F. M. MENGER

Figure 3. The enthalpy (kcal/mol) profile as the ammonia nitrogen approaches acetaldehyde’s a-proton in 0.1 Å increments while retaining the O4/H5 distance at 2.0 Å, .8 Å, 1.6 Å, 1.5 Å, 1.4 Å, 1.3 Å and 1.1 Å (series 1–7, respectively). Linear N/H/C and O/H/O trajectories are maintained throughout

Table 3. Relative enthalpy vs. N/H1 distance between the ammonia nitrogen and acetaldehyde’s a-proton while fixing the O4/H5 distance between the acetaldehyde carbonyl oxygen and formic acid acidic proton at 1.3 Å N/H Distance (Å) 2.6 2.5 2.4 2.3 2.2 2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.4

ΔH (kcal/mol) 0 0 0 0.11 0.38 0.91 1.78 3.1 5.1 5.2 8.1 8.9 11.0

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as the N•••H1 distance was decreased in stepwise fashion. To our knowledge, this distance-oriented approach, having not been previously attempted, distinguishes this work from previous studies. For a discussion of the stereoelectronic requirements for hydrogen-bond-catalyzed enolizations, see Ref. 47. According to Figure 3, between N•••H1 distances of 2.6 – 2.2 Å, the energy changes are invariant at all preset C = O4•••H5 distances. Energies begin to rise slowly as the N. . .H1 distance is compressed from 2.2 to 1.9 Å, but this effect is independent of the C = O4•••H5 distance. However, below an N•••H1 distance of 1.9 Å, the coordination of the acetaldehyde carbonyl with the formic acid increasingly manifests itself. For example, at N•••H1 = 1.4 Å and


C = O4•••H5 = 2.0 Å, the enthalpy =15.7 kcal/mol. In contrast, at N•••H1 = 1.4 Å but C = O4•••H5 = 1.1 Å, the enthalpy = 6.21 kcal/mol. A distance-dependent coordination of the carbonyl with the general acid obviously facilitates removal of the a-proton by the general base. Although the effect is hardly surprising, the data place it on a quantitative footing. One must not conclude from the preceding comments that the reaction pathway passes through the very shortest C = O4•••H5 distance where the N•••H1 approach energy is at its minimum. This point is best appreciated from the optimized structure, labeled TS1 below, where the N•••H1 and C = O4•••H5 distances have been fixed at 1.40 Å and a very short 1.1 Å, respectively. This structure has an energy that is 6.2 kcal/mol above the “zero” starting point where the N•••H1 and C = O4•••H5 distances are 2.6 Å and 1.1 Å, respectively. More importantly, the structure lies 4 kcal/mol above the actual transition state (Fig. 1). Clearly, the energy cost of “jamming” the formic acid proton into the acetaldehyde carbonyl more than eliminates the resulting benefit to the ammonia-promoted a-proton removal. A compromise is inevitably struck so that the proton/ carbonyl distance in the TS is set at 1.53 Å. Yet another property of general-acid-catalyzed enolization is worthy of note. In the absence of a general base (ammonia in our case), formic acid by itself was shown not to induce enolization by a cyclic mechanism (where its H5 is donated to the carbonyl, and its O8 accepts H1). Thus, compressing the C = O4•••H5 distance from 2.0 Å to 1.1 Å slightly increases (by 0.014 Å) the C2/C3 bond length. A bond-length decrease would have been expected if enolization and C2/C3 double-bond formation were occurring. At a C = O4•••H5 distance of 1.1 Å, the O6•••H5•••O4 distance is roughly 2.2 Å which is far less than the sum of the van der Waals radii (ca. 2.5 Å). This means that the short C = O4•••H5 distance of 1.1 Å creates a “low-barrier hydrogen bond”, sometimes referred to as an LBHB, of the type postulated by Gerlt and Gassman[7] and whose participation in enzymes has its proponents[48] and detractors.[49] In our case, as just seen, a strong LBHB does not promote enolization because its energy cost for formation overrides its catalytic benefit. Thus, the TS in the general-base/general-acidcatalyzed enolization in Fig. 1 has an O6•••H5•••O4 distance of 2.5 Å which corresponds closely to the sum of the van der Waals radii. Perrin has argued recently that short, low-barrier hydrogen bonds are not particularly strong or stable. Moreover, the role of such hydrogen bonds in enzyme-catalyzed reactions was ascribed mainly to the “relief of strain.”[50] This viewpoint is consistent with our results showing that compression of a hydrogen bond beyond van der Waals contact provides no net gain in reactivity. In our case, the compression was imposed by a computer at an energy cost to the system. Enzymes would have to expend binding energy to similarly shorten a hydrogen bond, and it is by no means clear that the subsequent rate advantage, if any, would “pay the energy bill.” The data in Figures 1 and 2 and Table 1 are relevant to the ideas set forth in the spatiotemporal hypothesis.[51] This hypothesis states that enzymatic rates are fast in large measure because reactive entities are held at “contact distances”, i.e. distances approximating van der Waals radii and certainly less than 3 Å (the diameter of water). It can be seen from our computations that if an enzyme holds a reactive species at van der Walls distances approaching those in the TS, then a large portion of the activation energy barrier will have been surmounted. From where will the energy needed to establish such active site orientations derive? Clearly, binding energy must be sacrificed for the benefit of the


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ACID/BASE-CATALYZED ENOLIZATIONS kinetics. This point has been extensively discussed in a construct that treats an enzyme’s reactive and binding sites as separate entities.[51] Non-covalent interactions enforce productive geometries at the active site. As is evident from Eqn. 1 where a reaction proceeds at enzyme-like rates despite the creation of 39 kcal/mol strain energy, covalent bonding can do the same thing. As mentioned in the introduction, there is considerable disagreement in the literature over whether acid/base catalysis of enolizations is concerted (alternatively described as synchronous, push-pull, and ternary) or non-concerted (where acid catalysis precedes base catalysis or vice verse). Where do we stand on the issue? The mechanisms in Figs. 1 and 2 are clearly concerted. When the formic acid was omitted from the reaction (leading to exclusive ammonia catalysis), the activation energy was elevated by 7.2 kcal/mol, corresponding to a general-acid catalysis worth >105 in rate. It is important to recognize, however, that this acceleration arises in part from a mere van der Waals contact between the acidic formic acid proton and the acetaldehyde carbonyl. Actual proton transfer from the general acid to the carbonyl is poorly developed in the transition state. Stated in another way, the general-acid/base reaction is concerted but not strictly synchronous. As with many organic reactions, there exists a continuum of mechanisms.[52] Thus, acid/base catalysis varies from stepwise to synchronous at the two extremes, with an infinite number of concerted mechanisms in between. The degree of concertedness undoubtedly depends upon the particular substrate, general acid, general base, and solvent. Whether one regards a particular concerted process as single-step or two-step is often a matter of philosophy.

CONCLUSION In summary, enolization of acetaldehyde catalyzed by the combined action of a general base (ammonia) and a general acid (formic acid) was examined by DFT while manipulating distance relationships among the reactants. Enolization involves an early transition state where general-base catalysis is more developed than general-acid catalysis. Although formic acid does not promote enolization by itself, it does facilitate a-proton transfer from acetaldehyde to the general base by several orders of magnitude. Formic acid accomplishes this feat via a hydrogen bond at a van der Waals distance to the carbonyl oxygen as opposed to forming a low-barrier hydrogen bond. A low-barrier hydrogen bond would indeed be capable of accelerating the enolization were it not for the energy cost of generating it. No proton tunneling was detected. Formic acid may also facilitate enolization by internal solvation of the ammonium ion that is partially formed in the transition state via carbon-to-nitrogen proton transfer. General-base catalysis by trimethylamine, which is out of position to coordinate with the formic acid carbonyl, actually has lower activation energy than that of ammonia catalysis, possibly owing to basicity/shielding effects. Computations also demonstrate that the proton removed by the ammonia nitrogen remains on the nitrogen throughout rather than being transferred via low-energy rotation processes and secondary proton transfers to an oxygen atom of formic acid or to the enol itself.[53]

SUPPORTING INFORMATION

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Acknowledgements RK thanks the Karaman Co. and the German-Palestinian-Israeli agency for supporting the computational facilities. FM thanks the National Institutes of Health for past funding.

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Supporting Information Available: Cartesian coordinates for the global minimum (R and R x 4H2O) transition state (TS and

TS x 4H2O) and product (P and P x 4H2O) structures for the reactions of ammonia and trimethylamine with acetaldehyde in the presence of formic acid. This material is available free of charge via the internet at http://pubs.acs.org.

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