Hydrogen-Tunneling in Biologically Relevant Small Molecules: The

Article pubs.acs.org/JPCB

Hydrogen-Tunneling in Biologically Relevant Small Molecules: The Rotamerizations of α‑Ketocarboxylic Acids Dennis Gerbig and Peter R. Schreiner* Institute of Organic Chemistry, Justus-Liebig-University, Heinrich-Buff-Ring 58, 35392 Giessen, Germany S Supporting Information *

ABSTRACT: Quantum mechanical tunneling governs the C−O bond rotamerization of simple alkyl and aryl carboxylic acid conformers at cryogenic temperatures. In this study, we report tunneling investigations on a series of electronically different α-ketocarboxylic acids including glyoxylic, pyruvic, cyclopropylglyoxylic, and phenylglyoxylic acid in solid Ar and Ne as host materials at temperatures ranging from 3 to 20 K. The higher-lying rotamers generated through photoirradiation with wavelengths of λ = 313 nm or λ > 850 nm convert to their low-energy conformers through hydrogen-tunneling, as evident from the time evolution of their infrared spectra, and the complete suppression of this process by deuteration. The conversion rates sensitively depend on the choice of matrix material and the tunneling half-lives range from a few hours to several days and are higher in Ne than in Ar for glyoxylic, pyruvic, and cyclopropylglyoxylic acid. The advent of tunneling in α-ketocarboxylic acids dominates their conformational preferences and conceivably also the reactivity of biologically and pharmacologically relevant acid congeners.

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INTRODUCTION The conformational landscape of carboxylic acids is predominantly characterized by the relative orientation of the hydroxyl hydrogen, which can either point toward or away from the carbonyl oxygen. These relative orientations are commonly referred to as (Z) and (E), respectively, with the (Z)orientation being the energetically favorable.1 The (E)conformer is sometimes accessible by either thermal annealing, or, given the presence of a suitable chromophore, by irradiation with UV light. Recently, also the wavelength-selective nearinfrared (NIR) overtone excitation of the OH-stretching vibrational mode using a tunable NIR laser source has seen more widespread use for this purpose.2−17 Many studies of excited carboxylic acid conformers have been carried out employing matrix-isolation, an experimental technique in which transient or reactive species are isolated at great dilution in an excess of an inert host material (commonly noble gases, but also nitrogen or para-hydrogen) at cryogenic temperatures.2−12,14,15,17−26 Given the conditions under which matrix isolation takes place, once isolated, reactive species should not undergo further change due to the lack of sufficient activation energy. Yet, several matrix studies on carboxylic acids have uncovered a profoundly different result: after substance deposition and excitation by irradiation, the (E)-conformer commonly reverts to the (Z)-conformer in an observable dark process. In the absence of sufficient thermal activation, this dark process could only be attributed to a quantum mechanical tunneling (QMT) mechanism.3−10,12−17,20,22−33 The interconversion of carboxylic acid conformers requires rotation around the C−O bond and, thus, movement of the hydroxyl hydrogen. Under matrix conditions, the (Z)-conformer therefore must be regenerated by hydrogen atom tunneling. The quantum mechanical nature of the phenomenon is further underlined © 2014 American Chemical Society

by a significant influence of isotopic substitution on the rate of conversion, which is by orders of magnitude slower, but not halted entirely, in the corresponding O-d-carboxylic acids.7−10,13,14,33,34 Numerous examples of QMT in carboxylic acids have been found in recent years (Scheme 1), the most prominent being the interconversions of conformers of formic (1a),4,6,10,12−16,21,22,24,26,28,30,32 acetic (1b),5,7,8,10,15,21,28 propionic (1c),9,21,28,29 S(−)-2-chloropropionic (1d),25 as well as propiolic acid (1e)31 and the aromatic meta-chlorobenzoic acid (2) along with variously para-substituted benzoic acid derivatives (3a−f).20,23 Remarkably, spectral proof for the existence of the monomeric (E)-isomer of 3 and several of its para-substituted derivatives was provided only in 2010.23 Closely related to carboxylic acids are α-ketocarboxylic acids (also referred to as α-oxoacids) that also display multiple conformers. Owing to the extra carbonyl group, α-ketocarboxylic acids possess an additional conformational degree of freedom: the orientation of the two carbonyl groups may either be syn or anti, with the latter usually being energetically favorable.35−37 Thus, for conformational considerations, only the anti-conformers usually have to be taken into account. In stark contrast to carboxylic acids, though, the anti-(E)conformer is more stable than the anti-(Z)-conformer, owing to an intramolecular hydrogen bond of the hydroxyl hydrogen with the carbonyl oxygen of the α-keto group. Hence, it is also feasible to describe both conformers based on the topology of the (hypothetical) rings that ensue through intramolecular Special Issue: William L. Jorgensen Festschrift Received: April 14, 2014 Revised: May 27, 2014 Published: June 6, 2014 693

dx.doi.org/10.1021/jp503633m | J. Phys. Chem. B 2015, 119, 693−703

The Journal of Physical Chemistry B

Article

conformers. Hence, we chose to conduct matrix-isolation studies of 4a, 4b, cyclopropylglyoxylic acid (4c), and phenylglyoxylic acid (4d), using solid Ar and Ne as the host materials as well as taking into account the possible effect of temperature and isotopic substitution (i.e., O-deuteration) on the tunneling mechanism (Scheme 3). Our experiments are

Scheme 1. Tunneling in Various Carboxylic Acids

Scheme 3. Matrix-Isolation Studies on α-Ketocarboxylic Acids

accompanied by computations based on the semiclassical Wentzel−Kramers−Brillouin (WKB) formalism for the estimation of tunneling rate constants to complement our experimental results.

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EXPERIMENTAL SECTION Matrix-Isolation Experiments. For most matrix isolation studies with Ar as the host gas, a Leybold cryostat system composed of a RW 2 compressor unit and a RGD 210 closedcycle refrigerator was used. The vacuum shroud surrounding the coldhead was outfitted with polished KBr windows, whereas the coldhead was equipped with a CsI window. The temperature of the cold window was measured at the base of the window holder with a Si-diode and could be adjusted during the experiment using a Leybold LTC60 temperature controller. The Ar flow was regulated by a MKS 1179B mass flow system operated by a MKS PR4000B control unit. In a typical experiment, 50 to 100 mbar of Ar from a 2000 mL storage bulb were condensed on the cold window. For deposition, the temperature of the cold window was varied between 8 and 11 K; a series of IR measurements were performed at 8 K and successively at 20 K on the same deposited matrix. For most measurements of O-deuterated acids, an APD HC2 cryostat system featuring a closed-cycle refrigerating unit with a custom-built vacuum shroud outfitted with KBr windows was used. The Ar flow was regulated by a calibrated needle valve and typically amounted to 50 to 100 mbar of Ar from a 2000 mL storage bulb. The temperature of the CsI cold window was observed using a combination of a Si-diode and an Air Products and Chemicals APD-T1 temperature monitor. During matrix deposition and measurement, the temperature was held constant at 15 K but could manually be increased up to 20 K by resistive heating. Using Ne as host material often has the advantage of providing a more homogeneous microscopic environment for the incorporated molecules due to its smaller atomic size compared to Ar, resulting in less locally different “sites” and thus reducing the splitting of infrared signals. Matrix isolation studies using Ne as the host gas were conducted on a Sumitomo cryostat system consisting of an F-70 compressor unit and a RDK 408D2 closed-cycle refrigerator. Similar to the setups described above, the combination of KBr windows on the vacuum shroud and a CsI cold window was employed. The temperature of the cold window was measured with a Si-diode connected to a Lakeshore 336 temperature controller. The Ne flow was regulated by an MKS 1179B mass flow system operated by a MKS PR4000B control unit. Typically, 100 to

hydrogen bonding interactions. Scheme 2 shows the conformational preference for glyoxylic acid (4a), the simplest αketocarboxylic acid, along with the aforementioned naming scheme. Scheme 2. Conformational Preference of Glyoxylic Acid (4a)

The next higher member of this family is pyruvic acid (4b), which plays a pivotal role in mammalian metabolism due to its involvement as pyruvate in the citric acid cycle. The α-ketoacid motif is also found in α-ketoglutaric acid, which is crucial for oxidative metabolic processes in conjunction with oxygenases as well as for the generation of the neurotransmitter γaminobutyric acid (GABA). Most importantly, α-ketocarboxylic acids are essential for the in vivo generation of α-amino acids via transaminases.38 In a recent pioneering study, three of the simplest α-amino acids, alanine, glycine, and cysteine, have been shown to exhibit tunneling in the interconversion of their rotamers.39,40 The reports on hydrogen tunneling in carboxylic and α-amino acids as well as the observation of a dark process for phenylglyoxylic acid, which served as a precursor for the generation of phenylhydroxycarbene in a previous study,41 motivated us to elaborate whether a similar tunneling mechanism might be effecting the interconversion of conformers in α-ketocarboxylic acids, some of which have important biological functions. Furthermore, we consider it viable to determine the factors that might impact the rate of a possible tunneling mechanism. To that end, we chose several electronically and sterically distinct, yet simple α-ketocarboxylic acids for matrix-isolation studies in different noble gases to probe the interconversion of the respective (4,4)- and (4,5)694



Article

Table 1. Observed Fundamental Infrared Signals of Glyoxylic Acid (4a) in Ar at 8 K and Computed Fundamentals at the MP2/ aug-cc-pVDZ and B3PW91/aug-cc-pVTZ levels; Experimental (νobs) and Computed Anharmonic Frequencies (νtheor in cm−1) with Computed Intensities (Itheor in km mol−1) anti-(E)-4a (Cs)

MP2/aug-ccpVDZ

B3PW91/aug-ccpVTZ

anti-(Z)-4a (Cs)

νobs

Iobs

νtheor

Itheor

νtheor

Itheor

sym.

3474.1 2906.1 1798.4 1745.1 1340.8

s w s s s

3448.2 2905.9 1760.5 1669.9 1336.4

101.4 34.9 165.7 47.9 265.2

3469.9 2849.3 1816.9 1786.5 1331.2

91.9 42.2 216.3 91.1 278.6

a′ a′ a′ a′ a′

1325.7 1155.6 993.3

s m m

1313.3 1150.8 984.9

29.8 10.9 3.5

1318.9 1156.0 1003.0

26.6 12.6 3.6

a′ a′ a″

871.1

s

866.2

55.1

867.7

44.5

a′

662.5

m

661.9

11.7

672.9

12.7

a′

638.1

s

646.7

48.7

653.0

12.7

a″

563.6

s

555.7

35.9

564.0

31.6

a″

499.5

m

494.0

5.7

492.4

5.8

a′

approximate description νOH νCH νCO (COO) νCO (HCO) νCC νC−O δHCO δCOH γHCCO

MP2/aug-ccpVDZ

B3PW91/aug-ccpVTZ

νobs

Iobs

νtheor

Itheor

νtheor

Itheor

sym.

3555.5 2876.9 1773.3 1748.5 1383.0

s w m s w

3536.0 2880.6 1738.0 1682.1 1371.6

82.8 50.9 173.5 105.0 48.1

3573.5 2817.9 1812.7 1786.9 1369.3

68.4 60.6 22.5 301.6 49.6

a′ a′ a′ a′ a′

1118.1 995.1 857.4

m w m

1145.7 987.5 853.0

96.7 2.7 48.3

1146.3 1006.2 850.0

129.8 3.0 34.5

a′ a″ a′

641.4

m

640.0

78.1

644.2

87.0

a′

635.0

w,b

637.0

96.8

640.8

90.2

a″

512.8

w

509.3

22.9

498.6

30.0

a″

νCC νC−O δOCC δOCO γOCOH

approximate description νOH νCH νCO (COO) νCO (HCO) νCC νC−O δCOH γHCCO νCC νC−O δOCC δCC−O γOCOH γCCOH γHCC−O

γOCCO γHCCO δCCO

the matrix material may generally change in the course of longterm experiments, minor shifts in the baseline were corrected manually before the kinetic analysis. Whenever possible, multiple signals of the different high-energy-conformers were evaluated and the results averaged to yield a final rate constant of tunneling (see the Supporting Information for additional details). Chemicals. Glyoxylic (as its monohydrate), pyruvic, and phenylglyoxylic acid were purchased from Sigma-Aldrich and used without further purification. Cyclopropylglyoxylic acid was prepared by potassium permanganate oxidation of cyclopropylmethyl ketone, as described previously.43 Glyoxylic acid monohydrate was dried in vacuo in the presence of phosphorus pentoxide as a drying agent. After removal of the bulk of water, repeated sublimation in high vacuum afforded a reasonably dry sample. O-deuteration of all acids was achieved by repeated dissolution in excess deuterium oxide and subsequent freezedrying of the samples in vacuo. Apart from O-d-phenylglyoxylic acid, which is readily dried, all other deuterated acids required prolonged exposure to vacuum (usually several days at approximately −15 °C). The degree of deuteration was estimated >90% in each case. Trace signals of nondeuterated material in matrix IR spectra are most likely due to partial deuterium−hydrogen exchange on the metallic surface of the vacuum shroud of the matrix apparatus. As host gases, we used Ar of 99.99999% and Ne of 99.9999% purity without further desiccation prior to use in matrix-isolation experiments. All liquid acid samples were degassed by repeated freeze−pump− thaw cycles before deposition.

200 mbar of Ne from a 2000 mL storage bulb were condensed on the cold window, the temperature of which was kept constant at 3 K for deposition and measurements. For UV irradiation, an Osram HBO 200 high-pressure Hg-lamp in combination with a Bausch & Lomb monochromator was used. Irradiation in the NIR region (λ > 850 nm) was carried out using a high-pressure Hg-lamp in conjunction with a Schott RG850 cutoff filter. Infrared Spectra. All IR spectra were recorded on a Bruker Vertex 70 FT-IR spectrometer with a spectral range of 8000− 350 cm−1 and a resolution of 0.5 cm−1 (3 mm aperture), a SiC globar MIR light source, a KBr beamsplitter, and a DLaTGS detector. For a single measurement, a total of 20 scans was accumulated. Kinetic measurements were conducted using an additional long-wave pass filter with a cutoff-wavelength of 4.5 μm in order to eliminate all infrared radiation >2500 cm−1 from the spectrometer’s measuring beam. This was necessary to ensure genuine results as it is known that IR radiation in the spectral range of the OH-stretching mode may increase tunneling rates due to vibrational excitation.3,4,6−10,12,14,16,30,32,33,42 Between measurements, the windows of the vacuum shroud were covered to shut out ambient light. Measurement of Tunneling Kinetics. The rate of conformer interconversion due to tunneling was determined by recording IR spectra of the irradiated matrix at regular intervals until the intensity of the signals due to the respective high-energy conformer were similar to the values before irradiation. Spectra were recorded in regular intervals over periods of up to 16 days. The time-dependent extinction values E were then subjected to a first-order kinetics analysis using a monoexponential fit of the form ΔE/E0 = A + a exp(−kt), in which E0 is the extinction value of the respective high-energy conformer in equilibrium and ΔE = E − E0. Using a biexponential model for data fitting did not yield more accurate results for any of the acids under study. As the constitution of

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COMPUTATIONAL For the optimization of stationary points and the generation of intrinsic reaction paths (IRP), which are required for WKB tunneling computations, we utilized density functional theory (DFT) as well as the MP2 method.44 The IRP of conformer interconversion was established by intrinsic reaction coordinate 695



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structure syn-(Z)-4a is only about 1.1 kcal mol−1 higher in energy than anti-(Z)-4a, prompting the question whether syn(Z)-4a could in principle be observable in the matrix upon irradiation of anti-(E)-4a. However, the computed barrier for the torsional motion along the central carbon−carbon bond in glyoxylic acid is as low as 2.0 kcal mol−1, suggesting that conversion of syn-(Z)-4a to anti-(Z)-4a would either occur very fast by tunneling or by the uptake of even the smallest amount of thermal energy. Hence, signals in the matrix IR spectra of glyoxylic acid can be assumed to arise from anti-(E)-4a and anti-(Z)-4a alone (cf. Table 1). This is in accordance with the assignment of the observed carbonyl stretching vibrations for anti-(E)-4a and anti-(Z)-4a conformers in our study (1748.5 and 1745.1 cm−1) and the most recent of Olbert-Majkut et al. (1748.0 and 1744.5 cm−1).72 Pyruvic Acid (4b). As in the case of 4a, conformer syn-(Z)4b is energetically very close to both anti-(E)-4b and anti-(Z)4b (Scheme 5). However, the torsional barrier for the

(IRC) computations,45,46 utilizing the Hessian-based predictorcorrector algorithm47−49 at the B3PW91/aug-cc-pVTZ,50−57 M06-2X/6-311++G(d,p),58−60 and MP2/aug-cc-pVTZ levels for glyoxylic and pyruvic acid and at the B3PW91/aug-ccpVTZ, M06-2X/6-311++G(d,p), and MP2/aug-cc-pVDZ levels for cyclopropylglyoxylic and phenylglyoxylic acid. All points on the IRP were corrected for zero-point vibrational energies by the evaluation of projected frequencies along the IRC.61 In order to obtain accurate energies along the IRP, all structures were augmented by coupled-cluster single point energies at the AE-CCSD(T)/cc-pCVTZ, CCSD(T)/cc-pVTZ or CCSD(T)/ cc-pVDZ levels,62−65 depending on the method previously employed for IRP generation. The highest possible level of computation was used whenever feasible. Computations at the AE-CCSD(T)/cc-pCVTZ level include a correlation treatment for all core electrons, whereas all other computations performed with the CCSD(T) or MP2 method utilized a frozen core (no deleted virtuals). All DFT and MP2 computations as well as the generation of the IRP were performed using Gaussian09.66 Coupled-cluster single point energies were evaluated using the ORCA program package.67 The Wentzel−Kramers−Brillouin (WKB) tunneling computations, which are described in more detail elsewhere,68−70 were done with Wolfram Mathematica 9.0.1.0.71

Scheme 5. Conformational Analysis of Pyruvic Acid (4b)a

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RESULTS AND DISCUSSION In the following part, a brief conformational analysis of 4a−4d to identify the conformers relevant to the tunneling process precedes the discussion of tunneling kinetics for the interconversion of α-ketocarboxylic acids as deduced from matrix IR spectra. Signals observed in matrix spectra are assigned accordingly in Tables 1−4 on the basis of MP2/augcc-pVDZ frequencies (including anharmonic corrections for 4a−c), which adequately reproduce the experimental isotopic shifts (Δν) for the OH- and OD-stretches for all observed acid conformers. For instance, the experimental/MP2-computed Δν values are 913/905, 888/884, and 885/881 cm−1 for the anti(E)-rotamers of 4a−c, respectively, lending confidence to the quality of the computed structures and vibrational frequencies. For the smaller molecules 4a and 4b, additional B3PW91/augcc-pVTZ fundamentals were computed. A comparison of their corresponding Δν values (913/899 and 888/886 cm−1) for the anti-(E)-rotamers shows equally good agreement with the computed IR absorption shifts upon isotopic substitution. The experimentally determined tunneling half-lives are then compared with the theoretically obtained values from our WKB computations. Conformational Analyses. Glyoxylic Acid (4a). The two most stable conformers of 4a feature an anti-arrangement of the carbonyl groups, namely anti-(E)- and anti-(Z)-4a (Scheme 4). Yet, among the two syn-conformers that can be envisioned,

Results in kcal mol−1 at the AE-CCSD(T)/cc-pCVTZ//MP2/aug-ccpVTZ, (CCSD(T)/cc-pVTZ//MP2/aug-cc-pVTZ), and [CCSD(T)/ cc-pVDZ//MP2/aug-cc-pVDZ] levels of theory.

a

conversion of syn-(Z)-4b to anti-(Z)-4b is computed as only 0.6 kcal mol−1, which is even less than the corresponding barrier in 4a. Hence, only signals of conformers anti-(E)-4b and anti-(Z)-4b are expected to be present in matrix IR spectra of 4b, which is in accordance with the results of a previous matrixisolation study (cf. Table 2).73 Cyclopropylglyoxylic Acid (4c). The conformational landscape of 4c is more complicated than that of 4a or 4b. Although only conformers with an anti-configuration of the carbonyl groups could be located computationally, the relative orientation of the cyclopropyl substituent still allows four different structures with this specific local arrangement. On the basis of the alignment of the C−H bond at the carbon atom shared by the cyclopropyl moiety and the carbon chain, a hypothetical four- or five-membered ring can be envisioned due to the hydrogen of said C−H bond interacting with either of the carbonyl oxygens. Hence, adhering to the naming scheme put forth in Introduction, the resulting conformers can be designated as (4,4)-, (5,4)- (4,5)-, and (5,5)-4c, in order from least-to-most energetically favorable (Scheme 6). The torsional barrier for the conversion of (4,4)-4c and (4,5)-4c to (5,4)-4c and (5,5)-4c, respectively, was computed as 4.6 and 6.0 kcal mol−1. Consequently, it should in principle be possible to isolate at least (4,5)-4c in the matrix, which is only 1.3 kcal mol−1 higher in energy than (5,5)-4c and 1.6 kcal mol−1 lower than (5,4)-4c. However, only signals of (5,5)-4c and (5,4)-4c are experimentally discernible (cf. Table 3). Phenylglyoxylic Acid (4d). Like for 4c, no structures with a syn-configuration of the carbonyl groups could be located for 4d. Therefore, the only conformers expected to be observable in matrix IR spectra of 4d are anti-(E)- and anti-(Z)-4d (cf. Table 4), which are separated by 3.1 kcal mol−1 (Scheme 7).

Scheme 4. Conformational Analysis of Glyoxylic Acid (4a)a

Results in kcal mol−1 at the AE-CCSD(T)/cc-pCVTZ//MP2/aug-ccpVTZ, (CCSD(T)/cc-pVTZ//MP2/aug-cc-pVTZ), and [CCSD(T)/ cc-pVDZ//MP2/aug-cc-pVDZ] levels of theory.

a

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Table 2. Observed Fundamental Infrared Signals of Pyruvic Acid (4b) in Ar at 8 K and Computed Fundamentals at the MP2/ aug-cc-pVDZ and B3PW91/aug-cc-pVTZ levels; Experimental (νobs) and Computed Anharmonic Frequencies (νtheor in cm−1) with Computed Intensities (Itheor in km mol−1) anti-(E)-4b (Cs)

MP2/aug-ccpVDZ

anti-(Z)-4b (Cs)

B3PW91/augcc-pVTZ

νobs

Iobs

νtheor

Itheor

νtheor

Itheor

νobs

3432.3 1799.7 1730.5 1384.7

m s m m

3407.3 1758.0 1683.0 1379.1

110.2 135.4 54.2 52.9

3407.8 1826.4 1766.2 1418.4

112.9 250.6 98.6 25.2

a′ a′ a′ a′

1354.9

s

1340.9

227.1

1334.3

280.5

a′

1214.6

s

1210.5

123.6

1202.9

110.7

a′

1137.0

m

1119.8

44.8

1135.4

33.0

a′

968.6

m

962.7

14.6

963.6

15.1

a′

762.3

w

750.3

11.4

752.6

7.4

a′

664.5

s

664.2

98.6

684.2

109.6

a″

approximate description νOH νCO (COO) νCO (CCO) γHCHH νCC δCOH γHCHH νCC δCOH νCC δCOH δHCC δCCC νC−O δHCC

MP2/augcc-pVDZ

B3PW91/augcc-pVTZ approximate description

νobs

Iobs

νtheor

Itheor

νtheor

Itheor

sym.

3557.2 1764.0 1751.1 1357.2

w m m w

3533.9 1726.8 1695.9 1338.9

78.1 177.8 41.4 48.6

3580.6 1791.2 1782.6 1341.5

63.6 228.4 18.0 58.9

a′ a′ a′ a′

1119.1

m

1103.6

235.2

1115.2

223.2

a′

962.0

m

955.2

27.2

953.5

34.3

a′

δHCC

592.3

m

600.6

79.6

594.3

50.8

a″

γHCCC γOCOH

588.3

m

581.1

72.8

586.7

72.3

a′

δCCO δOCO

νOH νCO (COO) νCO (CCO) γHCHH νCC δCOH δHCC νC−O

νCC δOCO γHCCC γOCOH

periods of irradiation. As has recently been demonstrated, the abundance of matrix-isolated anti-(Z)-4a can be increased by the use of an OPO setup tuned to the first harmonic of the OH-stretching mode of anti-(E)-4a.72 The conversion from anti-(Z)-4a to anti-(E)-4a is indeed only recognizable after a prolonged runtime of the experiment, which is very likely the reason why tunneling in 4a has remained unobserved in a previous matrix-isolation study (no spectral changes were observed within 17 h after initial irradiation).72 Half-lives of t1/2 = (69 ± 3) h at 8 K and t1/2 = (54 ± 1) h at 20 K in Ar were determined experimentally, corresponding to tunneling rates of approximately k = (2.8 ± 0.1) × 10−6 s−1 and k = (3.6 ± 0.1) × 10−6 s−1, respectively. Among 4a−4d, α-ketocarboxylic acid 4a is the only one for which the tunneling mechanism does not seem to be entirely temperature-independent, indicating a possible coupling to the lattice phonon modes of the solid matrix (i.e., phonon-assisted tunneling).9,28,75 Much to our dismay, we were unable to record a spectrum of 4a in Ne. Neither the variation of the rate of substance deposition nor the amount of co-condensed host material afforded matrix-isolated 4a. O-Deuteration of 4a impeded the tunneling process in the conversion from anti-(Z)-O-d-4a to anti-(E)-O-d-4a so that no change of the corresponding signals was observed even after several days. A temperature increase of the Ar matrix to 20 K also did not lead to spectral changes. Hence, in contrast to O-d1a,13 tunneling is shut down completely in O-d-4a. Pyruvic Acid (4b). For matrix-isolation in Ar, 4b (or O-d-4b) was evaporated from a storage vessel, which was held at a constant temperature of −45 °C by means of a cold bath during the experiment. Repeating this procedure with Ne as the host material failed to produce isolated 4b. Hence, a gas mixture with a 1:1000 volume ratio of 4b:Ne was prepared. The mixture

Scheme 6. Conformational Analysis of Cyclopropylglyoxylic Acid (4c)a

Results in kcal mol−1 at the CCSD(T)/cc-pVTZ//MP2/aug-ccpVDZ and (CCSD(T)/cc-pVDZ//MP2/aug-cc-pVDZ) levels of theory. a

Meanwhile, the barrier for conversion of anti-(E)- to anti-(Z)4d is about 10.0 kcal mol−1 at the CCSD(T)/cc-pVDZ//MP2/ aug-cc-pVDZ level and thus only slightly lower than the corresponding barriers in 4a−4c. Experimental Tunneling Kinetics. Glyoxylic Acid (4a). Dry 4a (or O-d-4a) was sublimed in high vacuum at 80 °C with the storage vessel attached to the matrix apparatus. Deposition of the matrix was then conducted with the sample at room temperature. For excitation of 4a (O-d-4a), the matrix was irradiated with broadband NIR light > 850 nm for several hours. Indeed, signals due to anti-(Z)-4a were found to slowly decrease over time after irradiation had ceased, while signals of anti-(E)-4a concomitantly increased in intensity (Figure 1). Due to the relatively low intensity of our NIR light source, signals of anti-(Z)-4a remained quite weak even after prolonged 697



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Table 3. Observed Fundamental Infrared Signals of Cyclopropylglyoxylic Acid (4c) in Ar at 8 K and Computed Fundamentals at the MP2/aug-cc-pVDZ Level; Experimental (νobs) and Computed Anharmonic Frequencies (νtheor in cm−1) with Computed Intensities (Itheor in km mol−1) anti-(E)-4c (Cs)

anti-(Z)-4c (Cs)

MP2/aug-cc-pVDZ

νobs

Iobs

νtheor

Itheor

sym.

3420.6 1795.8 1704.9 1457.8

m, b s s w

3386.9 1752.0 1659.8 1439.0

115.0 130.0 66.7 5.7

a′ a′ a′ a′

1314.8

s

1319.8

348.7

a′

1184.8

w

1177.4

31.0

a′

1063.4

s

1058.4

42.1

a′

1026.2 760.9

s w

1009.7 751.4

64.3 8.4

a′ a′

681.2 477.8

55.8 21.8

a″ a″

676.2 485.6

s m, b

approximate description

νobs

νOH νCO (COO) νCO (CCO) δHCH νCC (ring) νCC (chain) δCOH δCCH (ring) νCC νC−O γHCCH νCC νC−O γHCCH νCC νC−O γOCOH γOCCO

Iobs

MP2/aug-cc-pVDZ νtheor

Itheor

sym.

3554.0 1759.7 1727.6 1449.9

m m m w

3534.0 1721.2 1666.6 1434.2

80.7 192.0 35.5 5.8

a′ a′ a′ a′

1421.9

w

1397.6

14.0

a′

1093.4

w

1084.7

20.4

a′

1051.7

s

1042.8

155.3

a′

1016.3 652.5

s m

1003.9 640.1

87.4 74.0

a′ a′

625.1

114.0

a″

622.4

m, b

approximate description νOH νCO (COO) νCO (CCO) δHCH νCC (ring) δHCH νCC νC−O δHCC νCC γHCCH νCC νC−O γHCCH δCCO (ring) δOCO γOCOH

Table 4. Observed Fundamental Infrared Signals of Phenylglyoxylic Acid (4d) in Ar at 8 K and Computed Harmonic Vibrational Frequencies at the MP2/aug-cc-pVDZ Level; Experimental (νobs) and Computed Anharmonic Frequencies (νtheor in cm−1) with Computed Intensities (Itheor in km mol−1) anti-(E)-4d (Cs)

anti-(Z)-4d

MP2/aug-cc-pVDZ

MP2/aug-cc-pVDZ

νobs

Iobs

νtheor

Itheor

sym.

approximate description

3390.5 1790.2 1672.9 1602.6 1576.7

s, b s s m m

3576.8 1786.2 1660.3 1634.9 1607.2

131.5 156.7 126.1 17.5 16.1

a′ a′ a′ a′ a′

νOH νCO (COO) νCO (PhCO) νCC νCC

3547.3 1764.7 1698.5 1453.4 1372.6

s s s s w

3716.2 1768.2 1689.3 1447.7 1394.3

96.4 209.9 156.5 14.4 33.1

1383.9

s

1396.8

268.3

a′

1236.0

m

1275.0

68.2

1254.9

s

1293.2

390.3

a′

1152.8

s

1162.4

261.9

1183.3

s

1173.0

51.5

a′

961.4

s

971.9

100.3

969.5

s

976.5

74.4

a′

825.9

m

817.5

9.7

746.7

s

757.0

124.6

a″

724.4

m

720.7

30.7

683.8 660.3

s s

653.3 645.1

18.3 17.2

a′ a″

νCC νC−O νCC δCOH νCC νC−O δCOH δCC−C νCC νC−O γHCCC γOCOH δCC−C γPh

686.1 637.1

m s

698.3 632.2

92.6 72.9

515.2

m

518.7

31.3

a″

581.8

m

615.4

40.1

435.9

m

438.4

17.2

a′

γPh γCCCO δOCC

νobs

Iobs

νtheor

Itheor

sym. a

approximate description νOH νCO (COO) νCO (PhCO) νCC νCC νC−O νC−C δCOH δHCC νC−O δCC−C νCC νC−O γCC−C−C

γHCCH δCC−C γHCCH γPh δOCO δCC−C γOCOH

In the dark, anti-(Z)-4b converted back to anti-(E)-4b with measured half-lives of t1/2 = (12.7 ± 0.7) h at 8 K and t1/2 = (11.8 ± 0.9) h at 20 K in Ar, corresponding to tunneling rates of approximately k = (1.5 ± 0.1) × 10−5 s−1 and k = (1.6 ± 0.1) × 10−5 s−1, respectively. Given the experimental error margin,

was then deposited on the cold window at 3 K. Broadband NIR irradiation did not lead to sufficiently strong signals of anti-(Z)4b. Using an Hg-lamp set to 313 nm without the addition of a heat filter lead to an increased concentration of anti-(Z)-4b in the matrix after several minutes of irradiation (Figure 2). 698



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the host material. Although Ne is the least polarizable of the noble gases and should engage least in van der Waals interactions with guest molecules, it probably has a stabilizing effect on anti-(Z)-4b, thus slowing the conversion to anti-(E)4b. Despite reports of similarly significant effects of the host material on tunneling rates of matrix-isolated acids,3,8,13,28 a concluding explanation for this phenomenon is yet to be found. It is possible that the tighter packing of the Ne matrix imposes a considerable volume constraint on 4b, thus slowing the tunneling process by increasing the extent of matrix reorganization necessary to accommodate the structural change of isolated 4b.24 This phenomenon does show that tunneling rates can be strongly affected through environmental changes, an observation that may prove important in the context of tunneling control of chemical reactions,43,76,77 a concept that was introduced as the third paradigm next to well-known kinetic and thermodynamic control of chemical reactivity. Unlike for O-d-2a,8 O-deuteration renders matrix-isolated anti(Z)-O-d-4b inert toward conversion to anti-(E)-O-d-4b, even at an elevated temperature of 20 K. Cyclopropylglyoxylic Acid (4c). In matrix-isolation experiments, 4c (or O-d-4c) was evaporated from a storage vessel constantly held at −30 °C during substance deposition. Irradiation was conducted with 313 nm light. Afterward, additional signals besides those due to (5,5)-4c were observed and assigned to conformer (5,4)-4c (Figure 4). No evidence for the existence of conformer (4,5)-4c was found in either Ar or Ne matrices.

Scheme 7. Conformational analysis of phenylglyoxylic acid (4d)a

a Results in kcal mol−1 at the CCSD(T)/cc-pVDZ//MP2/aug-ccpVDZ level of theory.

Figure 1. Matrix IR spectrum (carbonyl region) of 4a in Ar after 7.5 h of broadband NIR irradiation (magenta) and after 86 h in the dark (blue); baseline after decay of anti-(Z)-4a (black). The smaller signals at 1766 and 1739 cm−1 are due to a matrix-isolated 4a···H2O complex,74 which also undergoes tunneling (hitherto unobserved but not discussed here).72

Figure 2. Matrix IR spectrum (carbonyl region) of 4b in Ar after 30 min of irradiation at 313 nm (magenta) and after 11 h in the dark (blue); baseline after decay of anti-(Z)-4b (black).

Figure 4. Matrix IR spectrum (carbonyl region) of 4c in Ar after 160 min of irradiation at 313 nm (magenta) and after 4.2 h in the dark (blue); baseline after decay of (5,4)-4c (black).

tunneling in 4b essentially is temperature-independent. In Ne, a half-life of t1/2 = (64 ± 5) h was determined, resulting in a tunneling rate of k = (3.0 ± 0.2) × 10−6 s−1 (Figure 3). As no significant change in the tunneling rate was observed upon increasing the temperature of the Ar matrix from 8 to 20 K, the pronounced decrease in the tunneling rate from anti-(Z)-4b to anti-(E)-4b in a Ne matrix must largely be due to the nature of

Structure (5,4)-4c converted back to (5,5)-4c with measured half-lives of t1/2 = (3.5 ± 0.7) h at 8 K and t1/2 = (3.4 ± 0.6) h at 20 K in Ar, corresponding to tunneling rates of approximately k = (5.5 ± 1.1) × 10−5 s−1 and k = (5.7 ± 1.0) × 10−5 s−1, respectively. As in the case of 4b, tunneling in the conversion of (5,4)-4c to (5,5)-4c is temperatureindependent. Tunneling in Ne occurs with a half-life of t1/2 = (28.2 ± 3.0) h and a rate constant of k = (6.8 ± 0.7) × 10−6 s−1, which is an order of magnitude slower than in Ar and hence shows the same strong dependence on the matrix material as tunneling in 4b (Figure 5). As for the preceding case, no immediate explanation for this considerable impediment of tunneling as compared to the experiment in Ar is evident. As expected from the results of the previously investigated deuterated α-ketocarboxylic acids, matrix-isolated O-d-(5,4)4d does not undergo conversion to O-d-(5,4)-4d through tunneling at 8 or 20 K. Phenylglyoxylic Acid (4d). Matrix spectra were obtained by evaporating 4d (or O-d-4d) from a storage vessel at room

Figure 3. Matrix IR spectrum (carbonyl region) of 4b in Ne after 50 min of irradiation at 313 nm (magenta) and after 47 h in the dark (blue); baseline after decay of anti-(Z)-4b (black). 699



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related 3. The reason for this unanticipated insensitivity of 4d toward the matrix environment is presently not clear; it is to be determined whether the same is true for host materials other than Ar and Ne. Expectedly, conversion of O-d-anti-(Z)-4d to O-d-anti-(E)-4d does not occur at temperatures of either 8 or 20 K in Ar. The experimental tunneling half-lives for 4a−4d are again summarized in Table 5. Tunneling Computations and Discussion of HalfLives. The progression of the potential energy along the IRC, which is formulated in mass-weighted coordinates and hence includes the masses and movements of all atoms in the molecule,45,46 defines the potential curve generally referred to as the IRP. Tunneling probabilities, and thus tunneling rate constants, essentially depend on the area under the IRP. Thus, the exact shape of this potential curve (the torsional potential of the OH group with respect to the C−O single bond in the case of α-ketocarboxylic acids), is the decisive factor for the evaluation of tunneling rates in the framework of a onedimensional approach such as the WKB method used herein. The shape of the potential varies with the enthalpic barrier height ΔH‡ and the barrier width, with the latter corresponding to the change in the IRC during the course of the reaction.76 As the barrier for the conversion of high- to low-energyconformers in 4a−d are computed to be very similar, the difference in tunneling rates among 4a−d must rather be due to different shapes or widths of their potential curves. While neither of the two properties changes significantly among 4a− d, the variances combined amount to noticeable differences in tunneling probabilities and, thus, tunneling rates: the increasing rate of tunneling upon going from 4a over 4b to 4c, for which the computed reaction barriers are very similar, is reflected by the decreasing barrier widths. In the case of 4d, the broader barrier is compensated by the slightly lower potential barrier. Note that, contrary to our (and perhaps common) expectations, the pronounced π-donating capability of the cyclopropyl moiety does not exert a distinctive influence on the tunneling half-life of (5,4)-4c compared to 4b or 4d, unlike its effect on hydrogen tunneling in the [1,2]H-migration in cyclopropylhydroxycarbene.43 Although our computed tunneling rates vary quite substantially among one another and do not reproduce the experimental tunneling half-lives quantitatively, the observed trend among 4a−d is essentially reflected by the theoretical results. The computed tunneling half-lives are summarized in Table 6. It is evident that, despite the use of an accurate ab initio method for single point energies, the routine of IRP generation has a profound effect on the tunneling rate: when comparing the half-lives of 4a and 4b as evaluated with CCSD(T)/cc-pVTZ single point energies, the results vary considerably by a factor of up to two. Generally, upon enlarging the basis set from double to triple-ζ quality, the computed tunneling rates increase, whereas the inclusion of corecorrelation does not significantly affect the results. However, it is not unlikely that tunneling in 4a−d would indeed occur much faster in the absence of the matrix material and hence prove the higher-level results to be actually more accurate for the gas phase. The tunneling half-lives closest to our experimental results for matrix-isolation in Ar are obtained by the CCSD(T)/cc-pVDZ method on IRPs generated at the very economical M06-2X/6-311++G(d,p) level of theory.

Figure 5. Matrix IR spectrum (carbonyl region) of 4c in Ne after 50 min of irradiation at 313 nm (magenta) and after 23 h in the dark (blue); baseline after decay of (5,4)-4c (black).

temperature. Due to the phenyl moiety acting as a chromophore, 4d (O-d-4d) responded very well to irradiation at 313 nm, which converted anti-(E)-4d into anti-(Z)-4d almost completely. Owing to the large initial intensity of the signals of anti-(Z)-4d, the tunneling rate of the reverse process could be determined more accurately than in the experiments with 4a−c (Figure 6).

Figure 6. Matrix IR spectrum (carbonyl region) of 4d in Ar after 30 min of irradiation at 313 nm (magenta) and after 2.1 h in the dark (blue); baseline after decay of anti-(Z)-4d (black).

Following irradiation, anti-(Z)-4d converted back into anti(E)-4d with experimental half-lives of t1/2 = (2.31 ± 0.11) h at 8 K and t1/2 = (2.23 ± 0.11) h at 20 K in Ar, corresponding to tunneling rates of k = (8.33 ± 0.39) × 10−5 s−1 and k = (8.65 ± 0.42) × 10−5 s−1, respectively, which is in accordance with an earlier measurement.41 Surprisingly, the experimental half-life in Ne was determined to be t1/2 = (2.3 ± 0.4) h, which is equivalent to a rate of k = (8.5 ± 1.4) × 10−5 s−1 (Figure 7) and, therefore, virtually identical to that in Ar. Despite a slightly larger uncertainty of the tunneling rate measured in Ne compared to Ar, it is evident that the tunneling process in 4d is not influenced significantly by the matrix material, much in contrast to the situation for 4a−c as well as for structurally

Figure 7. Matrix IR spectrum (carbonyl region) of 4d in Ne after 40 min of irradiation at 313 nm (magenta) and after 3.0 h in the dark (blue baseline after decay of anti-(Z)-4d (black). 700



Article

Table 5. Experimental Half-Lives (t1/2) of 4a−d in Ne at 3 K as well as in Ar in 8 and 20 K along with the Effective Barrier Widths (Δξ) and Heights (ΔH‡) Computed at the M06-2X/6-311++G(d,p) and CCSD(T)/cc-pVDZ//M06-2X/6-311++G(d,p) Levels of Theory, Respectivelya Ne, 3 K

Ar, 8 K

Ar, 20 K

t1/2 (h) n.d. (64 ± 5) (28.2 ± 0.1) (2.3 ± 0.4)

4a 4b 4c 4d a

(69 (12.7 (3.5 (2.3

± ± ± ±

3) 0.7) 0.7) 0.2)

(54 (11.8 (3.4 (2.2

± ± ± ±

Δξ [(amu)1/2 × bohr]

ΔH‡ (kcal mol−1)

3.86 3.68 3.62 3.81

11.1 11.1 10.9 10.1

1) 0.9) 0.6) 0.2)

n.d. = not determined.

Table 6. Theoretical Tunneling Half-Lives in 4a−d as Obtained by the WKB Method (Gas Phase Values) method of IRP generation M06-2X/6-311++G(d,p)

MP2/aug-cc-pVDZ

B3PW91/aug-cc-pVTZ

MP2/aug-cc-pVTZ

method for IRP single point energies CCSD(T)/ccpVDZ

CCSD(T)/ccpVTZ

CCSD(T)/ccpVDZ

CCSD(T)/ccpVTZ

75.4 15.9 7.1 9.4

6.4 1.5 0.7

303 38.3 15.9 *

25.7 3.6 1.6

CCSD(T)/ ccpVTZ

AE-CCSD(T)/ ccpCVTZ

CCSD(T)/ ccpVTZ

AE-CCSD(T)/ ccpCVTZ

8.0 1.1

16.0 2.6

14.9 2.4

theoretical half-life t1/2 in h 4a 4b 4c 4d

8.7 1.2 0.6

*

Due to an unphysically slow decay of the potential curve in the product region, no tunneling rate could be obtained for 4d at this level of theory. Using CCSD(T)/cc-pVDZ single point energies restores the correct progression of the curve.

■

CONCLUSIONS We have shown that matrix-isolated α-ketocarboxylic acids 4a− d undergo a dark process after excitation by irradiation similarly to that operative in carboxylic acids. This dark process converts high- to low-energy conformers and is shown to occur through quantum mechanical tunneling, as evident from its temperature insensitivity and the fact that deuteration completely suppresses this transformation. Furthermore, we observed that the matrix material critically influences the tunneling rate of 4a−c, but not of 4d. No evident connection between the electronic and structural properties of the studied α-ketocarboxylic acids and the observed tunneling rates can currently be made, as the 4a− d conformer interconversions follow very similar intrinsic reaction paths with only modest differences in the progression of their respective potential curves, which yet result in significantly diverse tunneling rates. This emphasizes the notion that tunneling highly sensitively depends on barrier width and height, which require rather high levels of theory for their accurate description, as well as on the matrix environment, an appropriate description of which poses a significant challenge.22,24 Here we found that an acceptable compromise to achieve qualitative agreement is offered by the economical M06-2X/6-311++G(d,p) level of theory for IRP computations in conjunction with CCSD(T)/cc-pVDZ single point energies. Further high-level computational studies are needed to define approaches to achieve quantitative agreement between experiment and theory. The observation of tunneling in α-ketocarboxylic acids bears implications also for biologically relevant transformations: the participation of tunneling in the conformational dynamics of organic acids in general and structurally related substrates may enable the interconversion of conformers even at temperatures that would not permit classical over-the-barrier pathways. In the context of E/Z isomerizations of small biologically as well as pharmacologically relevant molecules, the realization of

conformational tunneling practically makes subsets of higherlying conformations inaccessible for molecular design purposes because the corresponding lower-lying conformers inevitably will form despite appreciable barriers for conformer interconversion. Hence, the explicit consideration of quantum mechanical tunneling would greatly benefit mechanistic discussions in the fields of (pre)biotic, biological, pharmaceutical, and interstellar chemistry.

■

ASSOCIATED CONTENT

S Supporting Information *

Expanded matrix spectra of compounds 4a−4d and O-d-4a−4d (Figures S1−S11); signal assignments for O-d-4a−d (Tables S1−S4); potential energy hypersurfaces of acid conformers (Schemes S1−S4); kinetic data plots (Figures S12−S49); Cartesian coordinates for selected structures. Full ref 66. This material is available free of charge via the Internet at http:// pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

The ideas were conceived and the experiments planned by both authors. Measurements and computations were carried out by D.G. The manuscript was written by D.G. and P.R.S. Both authors have given approval to the final version of the manuscript. Funding

We gratefully acknowledge support through the Deutsche Forschungsgemeinschaft and the National Science Foundation of the USA, grant Schr 597/18-1. Notes

The authors declare no competing financial interest. 701



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Article

(17) Tsuge, M.; Marushkevich, K.; Räsänen, M.; Khriachtchev, L. Infrared Characterization of the HCOOH···CO2 Complexes in Solid Argon: Stabilization of the Higher−Energy Conformer of Formic Acid. J. Phys. Chem. A 2012, 116, 5305−5311. (18) Lundell, J.; Räsänen, M.; Latajka, Z. Matrix Isolation FTIR and Ab Initio Study of Complexes between Formic Acid and Nitrogen. Chem. Phys. 1994, 189, 245−260. (19) Lundell, J.; Räsänen, M. Photochemistry of Formic Acid in Rare Gas Matrices: Double−Doping Experiments on the 193 nm Induced Photodecomposition. J. Mol. Struct. 1997, 437, 349−358. (20) Nishino, S.; Nakata, M. Intramolecular Hydrogen Atom Tunneling in 2-Chlorobenzoic Acid Studied by Low−Temperature Matrix−Isolation Infrared Spectroscopy. J. Phys. Chem. A 2007, 111, 7041−7047. (21) Maçôas, E. M. S.; Myllyperkiö, P.; Kunttu, H.; Pettersson, M. Vibrational Relaxation of Matrix−Isolated Carboxylic Acid Dimers and Monomers. J. Phys. Chem. A 2009, 113, 7227−7234. (22) Trakhtenberg, L. I.; Fokeyev, A. A.; Zyubin, A. S.; Mebel, A. M.; Lin, S. H. Matrix Reorganization with Intramolecular Tunneling of H Atom: Formic Acid in Ar Matrix. J. Chem. Phys. 2009, 130, 144502. (23) Amiri, S.; Reisenauer, H. P.; Schreiner, P. R. Electronic Effects on Atom Tunneling: Conformational Isomerization of Monomeric Para-Substituted Benzoic Acid Derivatives. J. Am. Chem. Soc. 2010, 132, 15902−15904. (24) Trakhtenberg, L. I.; Fokeyev, A. A.; Zyubin, A. S.; Mebel, A. M.; Lin, S. H. Effect of the Medium on Intramolecular H-Atom Tunneling: Cis−Trans Conversion of Formic Acid in Solid Matrixes of Noble Gases. J. Phys. Chem. B 2010, 114, 17102−17112. (25) Bazsó, G.; Góbi, S.; Tarczay, G. Near-Infrared Radiation Induced Conformational Change and Hydrogen Atom Tunneling of 2Chloropropionic Acid in Low-Temperature Ar Matrix. J. Phys. Chem. A 2012, 116, 4823−4832. (26) Cao, Q.; Melavuori, M.; Lundell, J.; Räsänen, M.; Khriachtchev, L. Matrix−Isolation and Ab Initio Study of the Complex between Formic Acid and Xenon. J. Mol. Struct. 2012, 1025, 132−139. (27) Meyer, R.; Ha, T.-k.; Frei, H.; Günthard, H. Acetic Acid Monomer: Ab Initio Study, Barrier to Proton Tunnelling, and Infrared Assignment. Chem. Phys. 1975, 9, 393−402. (28) Maçôas, E. M. S.; Khriachtchev, L.; Pettersson, M.; Lundell, J.; Fausto, R.; Räsänen, M. Infrared-Induced Conformational Interconversion in Carboxylic Acids Isolated in Low-Temperature Rare-Gas Matrices. Vib. Spectrosc. 2004, 34, 73−82. (29) Maçôas, E. M. S.; Khriachtchev, L.; Pettersson, M.; Fausto, R.; Räsänen, M. Internal Rotation in Propionic Acid: Near-InfraredInduced Isomerization in Solid Argon. J. Phys. Chem. A 2005, 109, 3617−3625. (30) Marushkevich, K.; Khriachtchev, L.; Lundell, J.; Räsänen, M. Cis−Trans Formic Acid Dimer: Experimental Observation and Improved Stability against Proton Tunneling. J. Am. Chem. Soc. 2006, 128, 12060−12061. (31) Isoniemi, E.; Khriachtchev, L.; Makkonen, M.; Räsänen, M. UV Photolysis Products of Propiolic Acid in Noble−Gas Solids. J. Phys. Chem. A 2006, 110, 11479−11487. (32) Marushkevich, K.; Khriachtchev, L.; Lundell, J.; Domanskaya, A.; Räsänen, M. Matrix Isolation and Ab Initio Study of Trans−Trans and Trans−Cis Dimers of Formic Acid. J. Phys. Chem. A 2010, 114, 3495−3502. (33) Marushkevich, K.; Khriachtchev, L.; Räsänen, M.; Melavuori, M.; Lundell, J. Dimers of the Higher-Energy Conformer of Formic Acid: Experimental Observation. J. Phys. Chem. A 2012, 116, 2101− 2108. (34) Marushkevich, K.; Khriachtchev, L.; Lundell, J.; Domanskaya, A. V.; Räsänen, M. Vibrational Spectroscopy of Trans and Cis Deuterated Formic Acid (HCOOD): Anharmonic Calculations and Experiments in Argon and Neon Matrices. J. Mol. Spectrosc. 2010, 259, 105−110. (35) Fleury, G.; Tabacik, V. Acide Glyoxylique: Symétrie De La Molécule Libre, Spectres De Vibration Et Attribution. J. Mol. Struct. 1971, 10, 359−372.

ACKNOWLEDGMENTS The authors thank Wesley D. Allen (University of Georgia) for helpful discussions, and David Ley (now University of Miami, Florida) for his extensive contributions to the WKB software implementation.

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NOTE ADDED AFTER ASAP PUBLICATION This paper was published ASAP on June 18, 2014. The title was updated. The revised paper was reposted on June 23, 2014.

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Hydrogen-Tunneling in Biologically Relevant Small Molecules: The

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