Methylhydroxycarbene: Tunneling Control of a Chemical Reaction

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Science  10 Jun 2011:
Vol. 332, Issue 6035, pp. 1300-1303
DOI: 10.1126/science.1203761


Chemical reactivity is conventionally understood in broad terms of kinetic versus thermodynamic control, wherein the decisive factor is the lowest activation barrier among the various reaction paths or the lowest free energy of the final products, respectively. We demonstrate that quantum-mechanical tunneling can supersede traditional kinetic control and direct a reaction exclusively to a product whose reaction path has a higher barrier. Specifically, we prepared methylhydroxycarbene (H3C–C–OH) via vacuum pyrolysis of pyruvic acid at about 1200 kelvin (K), followed by argon matrix trapping at 11 K. The previously elusive carbene, characterized by ultraviolet and infrared spectroscopy as well as exacting quantum-mechanical computations, undergoes a facile [1,2]hydrogen shift to acetaldehyde via tunneling under a barrier of 28.0 kilocalories per mole (kcal mol–1), with a half-life of around 1 hour. The analogous isomerization to vinyl alcohol has a substantially lower barrier of 22.6 kcal mol–1 but is precluded at low temperature by the greater width of the potential energy profile for tunneling.

The conceptual foundations of chemical kinetics were laid by the development of transition state theory (TST) (1, 2), a powerful model that describes a chemical reaction as the passage of a system through an activated complex and over the top of a barrier on a molecular potential energy surface (3). This passage entails the evolution of the atomic positions from reactants to products along the most favorable path, whose critical point of highest energy is the transition state, a saddle point on the overall potential energy landscape.

The practical application of such theories of physical chemistry to competing organic reactions led to the principle of kinetic versus thermodynamic control of chemical transformations, first proposed graphically by Woodward and Baer (4) and then explicitly by Ingold and co-workers (5). The advent of multistep organic syntheses of complex molecules helped establish this principle as an effective means of predicting chemical selectivity.

As originally constructed and usually employed, kinetic control refers to a reaction system regulated by the relative energies of competing transition states, the process with the lower activation barrier being preferred. More general but less intuitive definitions of kinetic control that do not invoke TST have been proposed (6). In reactions under thermodynamic control, the products form in proportions determined by the equilibrium constants for their interconversion, the species with the lower free energy being favored; there must be sufficient thermal activation in the system to surmount the barriers for those interconversions necessary for equilibration.

The rate of a reaction can be substantially affected by quantum-mechanical tunneling (7), a classically forbidden process whereby the system yields products by passing under an energy barrier rather than over the top. Even in Eyring’s earliest formulation of TST, the possibility of tunneling was recognized (1). Tunneling becomes especially important at low temperatures and for reactions involving light atoms. Typical theoretical treatments of chemical kinetics are based on classical TST, with tunneling included as a secondary correction factor for reaction rates (8). Here we present a combination of experiments and theoretical analyses on methylhydroxycarbene (1), pyruvic acid (2), acetaldehyde (3), and vinyl alcohol (4) (Fig. 1) to demonstrate that tunneling can dominate a reaction mechanism sufficiently to redirect the outcome away from traditional kinetic control.

Fig. 1

Preparation of methylhydroxycarbene (1) by high-vacuum flash pyrolysis of pyruvic acid (2) and subsequent deposition in a cryogenic Ar matrix. Isomerization of 1 occurs by H transfer from the OH rather than the CH bond to yield acetaldehyde (3) preferentially to vinyl alcohol (4).

Recently, we observed (911) that hydroxymethylene (5, H–C–OH), the simplest hydroxycarbene, exhibits remarkably fast intramolecular H tunneling (with a half-life t1/2 ≈ 2 hours) under a large barrier of nearly 30 kcal mol–1. This unexpected isomerization mechanism, yielding formaldehyde, helps explain why 5, an implicated intermediate in coal liquefaction (Fischer-Tropsch chemistry) (12) as well as the prebiotic formation of carbohydrates (13), had not been isolated previously. Similarly, phenylhydroxycarbene (6, Ph–C–OH) undergoes facile H tunneling to benzaldehyde under a comparable barrier (14). Neither 5 nor 6 possesses an H atom bound to an α carbon, and thus no potentially competitive [1,2]H-shift rearrangement is possible. One of the simplest structures with more than one possible channel for [1,2]H tunneling is methylhydroxycarbene (or hydroxyethylidene, 1, Fig. 1), in which H transfer could occur from either the O–H or C–H bond. Carbene 1 is a common ligand in transition metal complexes and has also been posited as the activated form of acetaldehyde in the pyruvate cycle (15), as bound within the so-called Breslow intermediate (16).

Although 1 has not yet been characterized in isolated form, its presence has been inferred in mass spectrometric studies (17, 18). Other studies of the gas-phase pyrolysis and photolysis of pyruvic acid (2) (1922), as well as the reactions of arc-generated C atoms with carbonyl compounds (23), have suggested the existence of 1 as an intermediate that rearranges to acetaldehyde (3) much more rapidly than to vinyl alcohol (4, ethenol) (19, 2123). The preference for the formation of 3 is enigmatic and at variance with traditional kinetic control, because the computed H-shift barrier from 1 to 4 is lower than that from 1 to 3 (24). The intermediacy of 4 en route to 3 through a [1,3]H shift was excluded on the basis of deuterium labeling experiments (19, 21, 23). An unrecognized factor in these previous observations is the H-tunneling mechanism discovered here for the isomerization of 1 that overrides the expected kinetic preference for 4 and changes the course of the reaction to yield product 3 exclusively.

Building on the successful matrix isolation of hydroxycarbenes 5 and 6 as well as dihydroxycarbene (7) (9, 14, 25), we report here the synthesis, spectroscopic identification, and reactivity of 1. Our approach (Fig. 1) uses the thermal extrusion of CO2 from 2 under high-vacuum flash pyrolysis conditions and the subsequent trapping of the products in an Ar matrix at 11 K, as described previously (9). Several trials were performed in order to determine the optimal pyrolysis temperature (900°C). Under these conditions the decarboxylation reaction was not complete. Unreacted 2 was present in the Ar matrix in its two most stable conformers, having symmetry designations (E,E) and (E,Z) with respect to the central bonds of the (O=C–C=O, O=C–O–H) chains. The less stable (E,Z) form was strongly enhanced relative to the deposition without pyrolysis (19, 26). The (E,Z) rotamer slowly converts to the more stable (E,E) form through H tunneling at 11 K with a t1/2 ≈ 10 hours, as observed for other carboxylic acids (27, 28). The main pyrolysis products in the matrix were CO2, acetaldehyde (3), and very small amounts of vinyl alcohol (4) (29). The yield of matrix-isolated 1 as compared to that of 3 was estimated to be 2 to 5% through comparison of their experimental and computed infrared (IR) band intensities. Irradiation of the pyrolysis products with light at a wavelength (λ) of 435 nm led to fast and complete disappearance of the IR bands of 1 and to the concomitant enhancement of signals for 3 and 4. By measuring the spectral differences of irradiated and non-irradiated matrices, it was possible to elaborate the vibrational and electronic properties of 1, despite its low concentration in the complex reaction mixture. The OD isotopologue of methylhydroxycarbene (d-1) was prepared from CH3COCO2D (d-2) and characterized analogously.

The experimental IR spectra of the s-trans-isomers 1t and d-1t were assigned by comparison with computed anharmonic fundamental (ν) vibrational frequencies, as shown in Fig. 2 and table S7. Previous studies (9, 30) of the HCOH parent molecule 5 have documented the importance of vibrational anharmonicity in hydroxycarbenes. The theoretical vibrational spectra of 1t and d-1t were obtained by applying second-order vibrational perturbation theory to a complete quartic force field evaluated with a definitive electronic structure method, namely all-electron (AE) coupled-cluster theory including single, double, and perturbative triple excitations [CCSD(T)] conjoined with a correlation-consistent triple-ζ atomic-orbital basis set (cc-pCVTZ). The theoretical vibrational frequencies are first-principles quantum-mechanical results devoid of empirical adjustments. For 9 of the 11 assigned bands of 1t and d-1t, the mean deviation between theory and experiment is only 8.2 cm–1. The remaining two bands correspond to the (O–H, O–D) stretch of (1t, d-1t), for which the measured values are downshifted by (52, 36) cm–1 as compared to theory. These shifts are close to those previously observed for hydroxymethylene (9) and may be attributed primarily to matrix effects on the H stretching frequencies.

Fig. 2

(Lower trace) IR difference spectrum of trans-methylhydroxycarbene (1t, Cs point group) in an Ar matrix at 11 K; absorption differences were taken after irradiation at λ = 435 nm for 2 min (see fig. S1 for the raw spectra). The downward peaks arise from the photorearrangement to acetaldehyde (3) and s-cis-vinyl alcohol (4c). Taking difference spectra is a well-established approach to identifying a species by selective photolysis at wavelengths close to the target’s maximum absorption. (Upper trace) Computed AE-CCSD(T)/cc-pCVQZ anharmonic fundamental (ν) vibrational frequencies with corresponding AE-CCSD(T)/cc-pCVTZ intensities.

The ultraviolet (UV) difference spectrum of 1t (Fig. 4B) exhibits a broad weak band with maximum absorption near 393 nm (3.2 eV) that extends to around 460 nm (2.7 eV). Our computations show that this S0(1A′) → S1(1A″) band arises from a highest occupied molecular orbital (a′) → lowest unoccupied molecular orbital (a″) electronic transition involving excitation from the carbene lone pair into the empty p orbital of the divalent C atom. Multireference coupled-cluster computations (Mk-MRCC) with a large basis set (aug-cc-pVTZ) cement the assignment of the UV spectrum of 1t and fully characterize the associated electronic states [supporting online material (SOM), sections 4, 5, and 8]. Upon excitation from the ground state (S0, figs. S3 and S7) to the open-shell singlet excited electronic state (S1), 1t distorts to an equilibrium structure with a widened C–C–O angle of 124.5° and a nonplanar C–C–O–H framework having a dihedral angle of 112.4°. Our best [Mk-MRCCSD(T)/aug-cc-pVTZ] computed vertical and adiabatic electronic excitation energies are Tv = 3.38 eV and T0 = 2.70 eV, respectively, in excellent agreement with the experimental absorption spectrum.

To elucidate the chemistry of methylhydroxycarbene, we computed all relevant equilibrium structures and transition states on the potential energy surface (PES) surrounding 1t with state-of-the-art theory, specifically the AE-CCSD(T) method with a quadruple-ζ cc-pCVQZ basis set. Exhaustive quantum-mechanical focal-point analyses (FPAs) were then used to converge the salient energetic features to around 0.1 kcal mol–1, as demonstrated previously (9). Structural depictions, optimized geometries, FPA energetic tables, and complete PES schematics are provided in the SOM. The essential [1,2]H-shift energy profiles for 1 appear in Fig. 3. Our definitive computations confirm the general accuracy (±1 kcal mol–1) of earlier G2 and CBS-Q computations (18, 24) on the PES surrounding 1t.

Fig. 3

PES profiles for [1,2]H-shift isomerizations of trans-methylhydroxycarbene (1t); relative energies ΔH0 (in kcal mol–1) were computed from the convergent focal-point analyses detailed in the SOM. The bond lengths (Å) and angles (°) given for 1t are ground-state optimum geometrical parameters given by AE-CCSD(T)/cc-pCVQZ theory (C, light gray larger atoms; O, dark gray large atom; H, light gray small atoms). The s-cis isomer 1c (not shown) lies 3.1 kcal mol–1 above 1t. The curves are drawn quantitatively with the intrinsic reaction coordinate in mass-weighted Cartesian space as the abscissa in order to reflect the proper barrier heights and widths for the two competing reactions. Simple visual inspection thus indicates a higher H-tunneling probability for the more narrow energy profile of path a. The intrinsic reaction coordinate of path b yields s-trans-vinyl alcohol (4t) as shown; the cis form of 4 (4c, not shown) lies slightly lower on the energy diagram at –40.9 kcal mol–1.

Some disparities exist among experimentally derived enthalpy changes ΔH(43) between gaseous vinyl alcohol and acetaldehyde. However, calorimetric experiments on 3 (31) and ionization measurements on 4 (32) can be conjoined to obtain ΔH298(43) = 10.2 ± 0.4 kcal mol–1, in excellent agreement with the 10.3 kcal mol–1 we compute for the corresponding 298 K enthalpy difference between 3 and the cis form of 4 (4c). The [1,3]H-shift barrier from 4c to 3 is prohibitively high (+66.3 kcal mol–1) for direct interconversion in our experiments. Our precisely determined energy of 1t relative to 3 (+50.7 kcal mol–1) brings into question the value (+57 ± 4 kcal mol–1) derived from collision-induced flowing afterglow measurements employing protonated butadione (18). Our computations pinpoint the singlet-triplet splitting of 1t as ∆EST = –30.6 kcal mol–1, broadly validating the experimentally inferred value of ∆EST = –28 kcal mol–1 (18). The large ∆EST gap emphasizes the singlet ground-state nature of 1, as for other hydroxycarbenes (9, 14, 25). A considerable singlet-triplet separation is maintained along the entire reaction paths for 1t3 and 1t4t (SOM, section 8), indicating that intersystem crossing is not a factor in these transformations. The key conclusion from Fig. 3 is that 1t is blocked from 3 and 4 by large potential energy barriers of 28.0 and 22.6 kcal mol–1, respectively, which are much too high to be overcome by the energy available under matrix isolation conditions (11 K).

Notwithstanding the kinetic barriers surrounding 1t, we observed rapid disappearance of this molecule after cryogenic trapping. The IR and UV bands of 1t gradually diminished on standing at 11 K in the dark, whereas those of 3 grew. We investigated the reaction kinetics by acquiring IR spectra every 30 min while carefully shielding the matrix from all external light sources. The decay of the two most intense peaks at 3554 (OH stretch) and 1257 cm–1 (CO stretch, Fig. 4) followed first-order kinetics with a t1/2 = 66 (± 5) min in Ar (SOM, section 3). In stark contrast, the bands of the deuterium isotopologue d-1t did not change under identical conditions for extended periods of time (at least 16 hours, fig. S5). The t1/2 values measured for 1t in Kr and Xe at 11 K were 196 (±4) min and 251 (±2) min, respectively. Such an increase in the H-tunneling half lives from Ar to Xe matrices has also been observed for conformational isomerizations of carboxylic acids (33).

Fig. 4

(A) Part of the time-dependent IR spectrum showing the disappearance of 1t over 4 hours at 11 K; full spectra are shown in fig. S2. (B) Experimental UV difference spectrum of 1t at 11 K, based on absorption changes after 19 hours in the dark (see fig. S3 for raw spectra).

Our kinetic experiments indicate that 1t isolated in its ground electronic and vibrational state exhibits facile [1,2]H tunneling and that two conspicuous phenomena occur simultaneously: efficient penetration of a formidable 28.0 kcal mol–1 barrier to yield 3, and complete obstruction of the formation of 4 despite a much lower 22.6 kcal mol–1 barrier. We have established the theoretical basis of these phenomena by computing pure tunneling rates for both 1t3 and 1t4t (SOM, sections 4 and 10). The AE-CCSD(T)/cc-pCVTZ method was used to precisely map out the associated intrinsic reaction paths descending from transition states TS1t-3 and TS1t-4t (Fig. 3) and to determine zero-point vibrational energies (ZPVEs) along these steepest-descent routes. Final potential energy curves for the isomerization paths were then constructed from high-quality AE-CCSD(T)/cc-pCVQZ energy points appended with the ZPVEs. Within a reaction-path Hamiltonian model, Wentzel-Kramers-Brillouin tunneling probabilities (κ) were evaluated from barrier penetration integrals (θ) computed numerically from our highly accurate electronic structure results. This first-principles approach to quantifying H-tunneling rates has proved very effective for other hydroxycarbenes (9, 14).

The reaction modes of 1t that lead to TS1t-3 and TS1t-4t have harmonic vibrational frequencies (ω0) of 1346 and 736 cm–1, respectively; and 0 K energies (ε) for barrier collisions may be ascribed as ω0/2 in each case. Tunneling rates were computed as the product of the transmission coefficient [κ(ε)] and the classical rate (ω0) at which the reactant hits the barrier. This theoretical analysis yields a tunneling t1/2 of 71 min for 1t3, in close agreement with the observed rate of decay. Moreover, the computed t1/2 for 1t4t is 190 days, nicely explaining why vinyl alcohol is not the preferred product of methylhydroxycarbene isomerization, despite the lower barrier for formation of 4t. Our computational procedure also yields a tunneling t1/2 for d-1t of 4000 years, consistent with the observed shutdown of the methylhydroxycarbene decay mechanism upon deuterium substitution.

The penetration integral θ(ε) and hence the tunneling probability κ(ε)e2θ(ε) depend principally on three factors (7, 34): the width of the barrier w(ε), the square root of the difference between the overall barrier height (V*) and ε, and the square root of the effective mass. Analytic mathematical expressions relating θ to these three factors are given in the SOM for several common barrier models. As shown in Fig. 3, the reduced width of the 1t3 barrier amply overcomes the reduced height of the 1t4t barrier, resulting in respective κ values of 4 × 10−18 and 2 × 10−21. In brief, barrier width trumps barrier height (34) because θ scales linearly with the former but only as the square root of the latter.

The relative widths of the barriers for 1t3 and 1t4t can be traced directly to geometric requirements for these chemical transformations (fig. S6). Variations in the potential energy curves for both reactions persist over the entire range of arc lengths in Fig. 3, and the total arc length for the multidimensional 1t4t reaction path is 19% greater than in the 1t3 case. Accordingly, the respective θ values exhibit almost the same proportion. The increased arc length for 1t4t has two main causes. First, the migrating H must travel 2.42 Å to its final position in the 1t4t reaction but only 2.11 Å in the 1t3 case. Second, a concomitant conformational change is required for 1t4t in order to bring all atoms into the same plane in the product; in particular, a second methyl H in 1t must shift from 53° out of the C–C–O plane to a coplanar position in 4t.

Methylhydroxycarbene demonstrates the need to consider tunneling control in addition to classical kinetic or thermodynamic control in order to analyze, predict, and understand the full diversity of chemical reactivity. Tunneling control may be considered a type of nonclassical kinetic control in which the decisive factor is not the lowest activation barrier. Chemical reactions governed by tunneling mechanisms can be a general phenomenon, especially if H transfer is involved, and such processes need not be restricted to cryogenic temperatures. Much more research is necessary to reveal the possibilities of tunneling control in fields ranging from biochemistry to materials science.

Supporting Online Material

Materials and Methods

SOM Text

Figs. S1 to S9

Tables S1 to S10

References (35–77)

References and Notes

  1. Acknowledgments: The work in Giessen was supported by European Research Area Chemistry (administered by the Deutsche Forschungsgemeinschaft), the Fonds der Chemischen Industrie (fellowship to D.L.), and the Hessische Graduiertenförderung (fellowship to D.G.). P.R.S. thanks A. G. Császár for discussions. The research in Athens was funded by the U.S. Department of Energy, Office of Basic Energy Sciences, Combustion Program (grant no. DE-FG02-97ER14748); resources were used from the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under contract no. DE-AC02-05CH11231.
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