Heavy Atom Secondary Kinetic Isotope Effect on H-Tunneling - The

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Heavy Atom Secondary Kinetic Isotope Effect on H-Tunneling André Kristopher Eckhardt, Dennis Gerbig, and Peter R. Schreiner J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b12118 • Publication Date (Web): 10 Jan 2018 Downloaded from http://pubs.acs.org on January 12, 2018

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The Journal of Physical Chemistry

Heavy Atom Secondary Kinetic Isotope Effect on H-Tunneling André K. Eckhardt, Dennis Gerbig, and Peter R. Schreiner* Institute of Organic Chemistry, Justus-Liebig University, Heinrich-Buff-Ring 17, 35392 Giessen (Germany); [email protected]

ABSTRACT: Although frequently employed, heavy atom kinetic isotope effects (KIE) have not been reported for quantum mechanical tunneling reactions. Here we examine the secondary KIE through

13

C-substitution of the carbene atom in methylhydroxycarbene (H3C–C̈–OH) in its

[1,2]H-tunneling shift reaction to acetaldehyde (H3C–CHO). Our study employs matrix-isolation IR spectroscopy in various inert gases and quantum chemical computations. Depending on the choice of the matrix host gas the KIE varies within a range of 1.0 in xenon and 1.4 in neon. A KIE of 1.1 was computed using the WKB, CVT/SCT, and instanton approaches for the gas phase at the B3LYP/cc-pVTZ level of theory. Computations with explicit consideration of the noble gas environment indicate that the surrounding atoms influence the tunneling reaction barrier height and width. The tunneling half-lives computed with the WKB approach are in a good agreement with the experimental results in the different noble gases.

INTRODUCTION Hund predicted in 1927 that the wavelike properties of matter make it possible for light particles, e.g., electrons or hydrogen atoms, to pass through potential energy barriers that are 1 ACS Paragon Plus Environment

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energetically too high to be surmounted.1 Wigner called this phenomenon “tunneling” for the first time in 1932.2 Today, it is known that quantum mechanical tunneling (QMT) can influence the selectivity of chemical reactions.3-4 We showed in 2011 that methylhydroxycarbene (1), generated by high-vacuum flash pyrolysis (HVFP) of pyruvic acid (2) and trapped together with other pyrolysis products in solid argon at 8 K, rearranges to acetaldehyde (3) through H-tunneling.5 Based on chemical intuition and substantiated by high-level ab initio coupled cluster computations this finding was surprising: Adhering to the principle of thermodynamic vs. kinetic control, a reaction of 1, if any, to the kinetic product vinyl alcohol (4) was expected under cryogenic conditions. The formation of a product other than the kinetic one through a higher but narrower potential energy barrier was termed tunneling control.5-6 Since then, several other examples of tunneling controlled reactions have been investigated experimentally and theoretically.

Reactions of other hydroxycarbenes, such

as

cyclopropyl-7 (5) or

tert.-butylhydroxycarbene8 (8) are also governed by tunneling control: The formation of cyclopropyl- (6) and pivaldehyde (9) by H-tunneling is preferred over the expected ring expansion to cyclobut-1-en-1-ol (7) and C–H insertion to 2,2-dimethylcyclopropan-1-ol (10), respectively. Kozuch and Borden showed theoretically that H-tunneling through the higher but narrower barrier in noradamantyl methyl carbene (11) to vinyl noradamantane (12) is preferred over the ring expansion to methyladamantene (13) at cryogenic temperatures.9 Karmakar and Datta predicted in a computational study of 2,2a,5,7b-tetrahydro-1H-cyclobuta[e]indene derivatives (R = H or CH3; 14) that the [1,5]H-shift (15) is preferred over the 6π-cycloreversion (16) below 170 K (Scheme 1).10 Recently, we showed that H-tunneling can occur in a conformer-specific fashion.11 In the case of trifluoromethylhydroxycarbene (17), the high energy syn-conformer was generated photochemically from the anti-conformer, marking the first experimental observation of the 2 ACS Paragon Plus Environment

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syn-rotamer of a hydroxycarbene. For other small organic molecules, e.g., carboxylic acids isolated in solid inert gas matrices at cryogenic temperatures, rotamerizations by H-tunneling are well known.12-17 In the case of 17, however, only the anti-conformer showed H-tunneling to trifluoroacetaldehyde while the syn-conformer remained unchanged. Surprisingly, equilibration of syn- and anti-17 by H-tunneling does not occur, that is, the well-established Curtin-Hammett1819

principle is not applicable.11 As tunneling is a mass-dependent phenomenon, deuteration of carboxylic acids significantly

slows the rotamer equilibration. For hydroxycarbenes, tunneling is even prevented completely by deuteration of the hydroxy group. Amongst other factors, the very large observed H/D kinetic isotope effects (KIE) are an indication for a tunneling process. The isotopic composition of a compound may not only influence its reactivity but also determine its selectivity in chemical transformations.

In a theoretical study, Kozuch et al. showed that 1-methoxycyclo-

propylmethylcarbene undergoes rapid H-migration to 1-methoxy-1-vinyl-cyclopropane, whereas D-substituted

1-methoxycyclopropyl-d3-methylcarbene

undergoes

ring

expansion

to

1-d3-methylcyclobutene. The authors termed this change in reaction outcome isotope-controlled selectivity (ICS).20

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H [1,2]H-shift

H

OH

H H

Tunneling control

H

4

H

H

[1,2]H-shift

OH

Kinetic control

H

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H

O H

1 OH

OH

Kinetic control

H

7

Tunneling control

H OH

Kinetic control

10

[1,2]H-shift 9

H

•

CH3 Ring expansion

CH3

Kinetic control 13

[1,2]H-shift

• 6π-Cycloreversion R

•

H

Tunneling control

11

H

O

Tunneling control

8

•

O H 6

•

C–H Insertion

OH

16

[1,2]H-shift

5

•

•

H

•

Ring expansion

•

3

H 12

•

[1,5]H-shift

H

Tunneling control

Kinetic control R

H

R

14

15

Scheme 1: Examples of tunneling controlled reactions. While examples of heavy atom tunneling are rare,4,

21-24

we describe herein the effect of

13

C-substitution of the carbene atom in 1 on H-tunneling (Scheme 2). In general, changes in

zero-point vibrational energy (ZPVE) due to heavy atom substitution influence the height and width of reaction barriers and thereby rates of (thermal) chemical reactions.25 The ratio of the reaction rate of the lighter isotopologue divided by the rate of the heavier determines the KIE. When atoms other than hydrogen are substituted for heavier isotopes, the effect is usually termed a heavy atom isotope effect. For classic chemical reactions, there is a pronounced difference in magnitude between primary and secondary isotope effects. When a bond between isotopes forms or breaks in the rate-determining step of a typical over-the-barrier reaction, the KIE is primary in nature. Otherwise, the KIE is defined as secondary; a KIE can be normal (KIE > 1) or inverse (KIE < 1). For QMT at low temperatures, the tunneling rate in good approximation equals the rate of the reaction and is thus drastically affected by isotopic substitution. Here, a primary KIE 4 ACS Paragon Plus Environment

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is defined as the KIE arising from the substitution of the transferred atom by a heavier isotope. In the case of the hydroxycarbene family very large primary KIEs were observed due to deuterium substitution: Tunneling of O-d-1 was not observed experimentally and the computed tunneling half-life amounts to thousands of years. Secondary KIEs are thus defined as KIEs arising from substitution of atoms other than the transferred one by a heavier isotope.26 Following these definitions, a KIE due to

13

C-substitution of the carbene atom in 1 is best described as a heavy

atom secondary kinetic isotope effect. To the best of our knowledge, these kinds of quantum tunneling KIEs have hitherto not been discussed in the literature, prompting us to re-examine the tunneling behavior of 1 and 1-13C-1 in solid noble gas and dinitrogen matrices under cryogenic conditions. H O 13C

H3C

13C

H O

1. HVFP, 900 °C 2. Ar, 3 K

O 2

– 13CO2

H 13 H C H C O H

tunneling control

1

H 13C

H C H

O

3 H H

13C

C H

O

H

4

Scheme 2: Preparation of 1-13C-methylhydroxycarbene 1 by high-vacuum flash pyrolysis of 1,213

C-pyruvic acid 2 and subsequent H-tunneling to 1-13C-acetaldehyde 3.

METHODS Experimental Section For all matrix isolation studies a Sumitomo cryostat system consisting of a F-70 compressor unit and a RDK 408D2 closed-cycle refrigerator was used. The vacuum shroud surrounding the coldhead was outfitted with polished KBr windows, whereas the coldhead was equipped with a 5 ACS Paragon Plus Environment


CsI window for IR-measurements.

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Spectra were recorded with a Bruker Vertex 70 FT-IR

spectrometer with a spectral range of 4000–350 cm–1 and a resolution of 0.7 cm–1, a SiC globar MIR light source, a KBr beamsplitter, and a DLaTGS detector. For a single measurement, a total of 25 scans was accumulated. All measurements were performed at 3 K. The temperature of the cold window was measured with a Si-diode connected to a Lakeshore 336 temperature controller. For the combination of high-vacuum flash pyrolysis with matrix isolation, we employed a small, home-built, water-cooled oven, which was directly connected to the vacuum shroud of the cryostat. The pyrolysis zone consisted of an empty quartz tube with an inner diameter of 8 mm, which was resistively heated over a length of 50 mm by a coaxial wire. The temperature was monitored with a NiCr–Ni thermocouple. The host gas flow was regulated by a Pfeiffer EVN 116 gas dosing valve with separate shut-off. For all experiments we used Ar of 99.999% purity. Pyruvic acid (received from Sigma Aldrich and further purified through distillation and degassed by repeated freeze-pump-thaw cycles) was evaporated at –20 °C from a storage bulb into the hot quartz pyrolysis tube (900 °C). At a distance of approximately 70 mm, all pyrolysis products were co-condensed with a large excess of Ar on the surface of the matrix window at 12 K. A high-pressure mercury lamp (HBO 200, Osram) with a monochromator (Bausch & Lomb) was used for irradiation. For wavelengths ≥405 nm, Schott 375 nm cutoff filter was added to the beam path. Analogous experiments were also performed with 1,2-13C-pyruvic acid (99 atom %

13

C

received from Sigma Aldrich and used without further purification). Tunneling kinetics of matrix isolated isotopologues of 1 were evaluated by recording infrared spectra in regular intervals for a period of 15 min. To avoid IR photochemistry, induced by the light source of the FTIR spectrometer, the optical path was blocked between the measurements.


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During the measurements, the matrix apparatus was not moved in order to prevent errors arising from different thicknesses of the deposited matrices. Computational Details All coupled cluster computations were carried out with the CFOUR 1.027 program package. In general, the all electron coupled cluster level of theory including single, double, and pertubatively included triple excitations [CCSD(T)]28-31 utilizing the Dunning correlation consistent split valence basis set cc-pCVQZ32 was employed for geometry optimizations and frequency calculations. All computations employing the computationally less demanding B3LYP33-35 DFT functional were performed with the Gaussian0936 program package, revision D.01.

For

computations with an explicit solvent model Grimme’s dispersion correction37, Ahlrich’s triple zeta def2tzvpp38-39 basis set and the universal force field40 as implemented in Gaussian09 were employed. Intrinsic reaction paths were mapped using the Hessian based predictor-corrector integrator41-42 and projected frequencies were computed along the path.

WKB tunneling

computations were carried out with Wolfram Mathematica 10.3,43 CVT/SCT and CVT/ZCT computations with POLYRATE 201044-46 using Gaussrate 2009 as interface between Gaussian09 and POLYRATE.

Instanton47 computations were performed with DL-FIND included in

chemshell.48-49

RESULTS AND DISCUSSION Methylhydroxycarbene and its 1-13C isotopologue were generated by HVFP at 900 °C of 2 and 1,2-13C-2, respectively. All pyrolysis products were trapped in different matrix materials (Ne, Ar, Kr, Xe, and N2). The observed signals and assignments for 1 are summarized in Tables S1 and S2. The IR spectra are in full accord with previous studies.5 For minimization of the experimental error, the tunneling half-lives τ of 1 and 1-13C-1 were determined by evaluation of 7 ACS Paragon Plus Environment


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the strongest signal, the same matrix-site of the 12/13C–O stretching mode of 1 and 1-13C-1 (Figure 1), only. For 1 and 8 different matrix sites previously showed slightly different tunneling halflives.5, 8 An exponential first order kinetic fit was applied for the determination of tunneling rates and KIEs. The results are summarized in Table 1. Detailed IR spectra and kinetic evaluations are depicted in the SI (Figures S1–S50 and Tables S3–S12). Table 1: Experimental tunneling half-lives τ (in h) of 1-12/13C-1 in different matrix materials and resulting KIE.

12

τ (1- C-1) τ (1-13C-1) KIE

Ne (3 K) 1.41±0.04 2.00±0.03 1.42±0.06

Figure 1: Signal decrease of the

Ar (3 K) 1.28±0.01 1.51±0.01 1.17±0.02

12/13

Kr (3 K) 2.93±0.06 3.75±0.07 1.28±0.05

Xe (3 K) 4.61±0.12 4.55±0.18 0.99±0.07

N2 (8 K) 24.73±0.27 24.86±0.40 1.01±0.03

C–O stretching vibration of the isotopologues of 1-12/13C-1

due to H-tunneling to 1-12/13C-2 over a time range of approximately 18 h. 8 ACS Paragon Plus Environment

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The absolute tunneling half-lives of 1 depend on the matrix material. The shortest half-life was determined for the tunneling reaction in argon with approximately 1.3 h, in excellent agreement with the reported value.5 The half-life increases in the order of neon, krypton, xenon, and N2 from several hours up to approximately one day (Table 1). Such a behavior is known from conformational tunneling of carboxylic acids, e.g., formic or acetic acid.12-13 The rotamerization of formic acid is fastest in solid neon, followed by argon, krypton, and xenon in that order. However, for their O-deuterated isotopologues, the order is reversed. Other hydroxycarbenes do not show such an extreme dependence of the tunneling half-life on the matrix material. For 1-13C-1, larger half-lives were observed in neon, argon, and krypton. However, for xenon and N2, the half-lives remain almost unchanged. Note that kinetics in krypton and xenon were more difficult to follow due to increased scattering of the matrix leading to larger error bars. As for the primary H/D tunneling KIEs in formic acid12, 50 the calculated relative secondary KIEs also vary with the matrix material. The largest KIE was found in neon with 1.4, followed by argon and krypton with approximately 1.2. In xenon and N2, the KIEs effectively equal unity. The origin of this matrix effect on tunneling KIE is currently unclear.14 In comparison to classic secondary KIEs, the effect is rather large. Several aspects concerning the influence of the matrix material on tunneling rates have been discussed. Pettersson et al.50 suggested for the H-tunneling process in formic acid that the barrier height changes due to solvation and increases in more polarizable media. Furthermore, it has been suggested that tunneling may involve different accepting states with different couplings to the initial state.50 The order of the phonon process that is responsible for energy dissipation may also be different because there is a change between the energy gaps between initial and accepting levels due to solvation. Domanskaya et al.12 expanded these concepts and computed with a 9 ACS Paragon Plus Environment


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polarizable continuum model (PCM) the solvation energies for cis and trans formic acid in different noble gases that agree well with the experimental results. For H-tunneling in acetic acid Maçôas et al.13 suggested that the methyl torsion and lower energy vibrational modes of the methyl group might also be involved in the tunneling mechanism in addition to the phonon modes. Therefore, we performed tunneling computations with an explicit solvent model to gain information about the experimentally observed matrix-sites and the influence of matrix reorganization energies on the computed tunneling half-lives in different noble gases (vide infra). Dinitrogen matrices stabilize carbenes and other trapped intermediates due to non-covalent interactions.51-52 In the case of hydroxycarbenes, this is reflected in the large observed tunneling half-lives in comparison to those in noble gases. Another reactive intermediate that was trapped after pyrolysis of 2 was 4. In noble gases, only energetically preferred syn-4 could be isolated (c.f. Figure S61).53 The energy difference between syn- and the anti-4 is approximately 1 kcal mol–1 at the AE-CCSD(T)/cc-pCVQZ level of theory. Both conformers are connected by a transition state that lies only 3 kcal mol–1 above syn-4. However, in N2 matrices, anti-4 was also observed after pyrolysis and slowly converts to syn-4 by H-tunneling. The conformers can readily be interconverted photochemically by NIR irradiation (for IR difference spectra, signal assignments and tunneling computations see Figures S54–56 and Tables S17–S23).

We

attempted to generate the anti-4 in noble gas matrices, but tunneling back to syn-4 apparently is very rapid. The computed tunneling half-life for the gas phase with a simple semiclassical Wentzel-Kramers-Brillouin54-56 (WKB) approach at the B3LYP/cc-pVTZ level of theory yields approximately 1 ms. In N2 matrices, the tunneling half-life is extended to several hours. The large observed KIE in neon, argon, and krypton nicely demonstrates the mass dependence of QMT and the participation of every atom in the tunneling process.57 We computed the potential energy surface (PES) around 1 at AE-CCSD(T)/cc-pCVQZ with ZPVE corrections 10 ACS Paragon Plus Environment

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(Figures 2 and S61). The barrier height does not change significantly due to isotope exchange. The tunneling half-lives for both isotopologues of 1 and KIE were computed using the WKB approach at B3LYP/cc-pVTZ level of theory. The computed barrier height at B3LYP/cc-pVTZ is in good agreement with the high-level coupled cluster results and the WKB model has proven to be sufficiently accurate for H-tunneling reactions.5, 57-58 For WKB computations the minimum energy path of the tunneling reaction was computed for the gas phase and the ZPVE obtained from projected frequencies added to each point along the path. The computed half-lives are 6.5 h for 1 and 7.2 h for 1-13C-1. These results are larger than the experimental results in xenon (for WKB tunneling computations see Table S13), but in satisfactory agreement with experiments. From these values, a normal KIE of 1.11 results, which is lower than the experimental results in neon, argon, and krypton. All atomic motions during the tunneling process are depicted in Figure 2. For the WKB approach in a mass-weighted coordinate system, atomic motions and masses are contained within the distance of the turning points on the potential energy barrier along the intrinsic reaction coordinate (i.e., the barrier width; depicted as colored circles in Figure 2). The transferred hydrogen atom shows the largest traversed arc (1.235 Å). The central carbene carbon atom moves 0.110 Å, but contributes strongly due to its larger mass. It is for the contribution of carbon to the overall barrier width that a normal KIE of 1.11 is obtained. The computed KIE is confirmed by extensive canonical variational transition state theory (CVT) computations in combination with one-dimensional zero-curvature tunneling (CVT/ZCT) and multidimensional small curvature tunneling (CVT/SCT) corrections at the same level of theory (B3LYP/cc-pVTZ) at 20 K (Table S15). The computed tunneling half-lives for both isotopologues of 1 using the CVT/SCT approach (1: 28.6 h; 1-13C-1: 31.6 h) are larger than for WKB computations.

The best absolute tunneling half-lives were observed with the 11 ACS Paragon Plus Environment


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multidimensional instanton method with around three hours.57 In instanton theory, Feynman path integrals are used to describe all possible tunneling paths.

The instanton-derived KIE is

computed to 1.12 in a good agreement with the other theoretical methods (Table S16).

Figure 2: Potential energy surface around methylhydroxycarbene 1 (for 1-13C-1 in brackets; color code: carbon: grey, oxygen: red, hydrogen: white) at the AE-CCSD(T)/cc-pCVQZ level of theory and one-dimensional tunneling paths a and b to the thermodynamic product acetaldehyde 3 (right) or the kinetic product vinyl alcohol 4 (left). The top two structures show the atomic motions along the reaction coordinate that differ from the Euclidean straight-line distances (depicted as blue dotted lines, distances shown in Figure S62). The reaction profiles were computed at the B3LYP/cc-pVTZ level of theory.


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With an implicit PCM solvent model for argon, krypton, and xenon the computed barrier height increases slightly due to the more polarizable environment (Table S13 and S17). Hence, larger absolute tunneling half-lives (Ar: 1: 12.51 h; 1-13C-1: 14.70 h; Kr: 1: 13.91 h; 1-13C-1: 16.36 h; Xe: 1: 16.97 h; 1-13C-1: 19.97 h) than for the gas phase result with the WKB approach at B3LYP/cc-pVTZ (Table S17). The relative calculated KIEs are constant for all used noble gases and somewhat larger (1.18) than the computed value for the gas phase (1.11).

To obtain

information about the experimentally observed matrix-sites (Figure 1) and possible matrix reorganization, we also performed computations with an explicit solvent model. Similar to the work of Trakhtenberg et al.59-61 we employed computations with a static model environment: Two noble gas atoms in the face centered cubic crystal structure of the corresponding noble gas were replaced by the carbene structure that was surrounded by 18 noble gas atoms. The noble gas atoms were frozen in position and the structure of the carbene was optimized. By changing the position of the carbene in this static 18 atoms noble gas cluster we found two different minima (Figure 3) differing by 1–2 kcal mol–1 in energy for neon, argon, and krypton, but there is no energy difference in xenon. Note that the HCCO dihedral angle changes due to a torsion of the methyl group, making the carbene no longer Cs symmetric (Table S19). These two minima potentially explain the experimental observation of two distinct matrix sites (#1 and #2) for the C–O stretching vibration (Figure 1).



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Figure 3: Different orientations of methylhydroxycarbene in a static 18 argon atom cluster (color code: carbon: grey, oxygen: red, hydrogen: white, argon: grey). Note that in the right picture the HCCO dihedral angle changed to 21.6° due to torsion of the methyl group. Left: Matrix-site #1; Right: Matrix-site #2. The reaction barrier for the [1,2]H-shift of 1 to 3 in the static noble gas clusters is lower than in the gas phase computations at the B3LYP-D3BJ/def2tzvpp level of theory (Table S18 – S22) and increases slightly from neon to xenon. For both computed matrix-sites in the same noble gas the computed barrier heights for the isomerization of 1 to 3 also differ in energy. Hence different tunneling half-lives with the WKB-model were computed (Table S18 – S22). In general, the computed half-lives for neon (1: 1.14 and 0.30 h; 1-13C-1: 1.33 and 0.34 h), argon (1: 3.21 and 4.03 h; 1-13C-1: 3.73 and 4.63 h) and krypton (1: 5.04 and 11.65 h; 1-13C-1: 5.87 and 13.48 h) are smaller than the computed value for the gas phase (1: 7.70 h; 1-13C-1: 8.99 h) and fit well to the observed experimental results (Table 1). However, for xenon the computed half-lives (1: 11.74 and 65.28 h; 1-13C-1: 13.87 and 76.86 h) are larger than the two gas phase values. The half-lives for the two matrix-sites also differ by a factor of six. For all other noble gases this differences is smaller. The relative KIEs are almost constant in the range of 1.14 – 1.18 for all noble gases (Ne: #1: 1.16 and #2: 1.14; Ar: #1: 1.16 and #2: 1.15; Kr: #1: 1.14 and #2: 1.16; Xe: #1: 1.18 and #2: 1.18). The results are summarized in Table 2.

Table 2: Computed WKB-tunneling half-lives τ (in h) of 1-12/13C-1 in different matrix materials with a static explicit noble gas atom model and resulting KIE at B3LYP-D3BJ/def2tzvpp level of theory; the “#” defines the matrix-sites. Ne #1

Ar #2

#1

Kr #2

#1

Xe #2

#1

#2 14

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τ (1-12C-1) τ (1-13C-1) KIE We expanded the

1.14 0.30 3.21 1.33 0.34 3.73 1.16 1.14 1.16 static model by surrounding

4.03 4.63 1.15 the noble

5.04 11.65 11.74 65.28 5.87 13.48 13.87 78.86 1.14 1.16 1.18 1.18 gas cluster with 345 more noble gas

atoms so that the whole system approximately describes the dilution in a typical matrix environment. We performed an ONIOM model computation as implemented in Gaussian09 with two shells. The inner shell was chosen the same as in the static model and treated at the B3LYP-D3BJ/def2tzvpp level of theory while for the outer shell the standard universal force field (UFF) was used. The advantage of this QM:MM approach is that the system is allowed to relax. Again we observed two matrix sites, yet with almost equal energy (Table S25). The reaction barriers for the [1,2]H-shift of 1 to 3 in different noble gas clusters are now similar to the gas phase computations. However, the computed WKB half-lives change slightly compared to the static model, but are still in good agreement with the experimental results (Table S26 – S29). The shortest half-life for the tunneling reaction was computed in argon (1: 6.78 and 8.80 h; 1-13C1: 7.87 and 10.28 h) followed by krypton (1: 6.90 and 8.02 h; 1-13C-1: 11.21 and 13.11 h), xenon (1: 6.04 and 4.52 h; 1-13C-1: 19.92 and 14.90 h) and neon (1: 10.57 and 10.85 h; 1-13C-1: 12.34 and 12.65 h). The computed tunneling half-lives for the two matrix-sites in neon and argon are almost equal but differ by a factor of approximately three and two in xenon and krypton, respectively. The relative KIE does not change for the computations in neon (#1: 1.17 and #2: 1.14), argon (#1: 1.16 and #2: 1.17) and krypton (#1: 1.16 and #2: 1.17). However, in xenon an inverse KIE (0.75) is computed for both matrix sites. The trend for a smaller KIE in xenon was also observed experimentally in an almost neutral determined KIE. The results are summarized in Table 3.



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Table 3: Computed WKB-tunneling half-lives τ (in h) of 1-12/13C-1 in different matrix materials with an explicit two layer ONIOM noble gas atom model and resulting KIE at B3LYP-D3BJ/def2tzvpp level of theory; the “#” defines the matrix-sites. Ne 12

τ (1- C-1) τ (1-13C-1) KIE

#1 10.57 12.34 1.17

Ar #2 10.85 12.65 1.14

#1 6.78 7.87 1.16

Kr #2 8.80 10.28 1.17

#1 6.90 8.02 1.16

Xe #2 11.21 13.11 1.17

#1 6.04 4.52 0.75

#2 19.92 14.90 0.75

We compared the computed harmonic frequencies of both matrix-sites of the static and the ONIOM noble gas cluster model with the experimental values (Table S30). The relative shifts of the ONIOM model frequencies of the two matrix-sites fit well to the experimental relative shifts. In summary, our computations with explicit noble gas atoms indicate that in general reaction barrier heights and widths are influenced by the surrounding media. For tunneling reactions that are very sensitive to the barrier width and height, this small influence is represented in different tunneling half-lives for different matrix materials. Our simple modeling computations confirm the experimental trends and results but need to be improved.

CONCLUSION AND OUTLOOK We present the first investigation of a secondary heavy atom kinetic isotope effect on Htunneling

by

determining

the

tunneling

kinetics

for

the

[1,2]H-shift

of

1-13C-methylhydroxycarbene to 1-13C-acetaldehyde in different inert gases. Depending on the choice of the matrix host gas the KIE varied within a range of approx. 1.0 in xenon and 1.4 in neon. The origin of the influence of the matrix material on KIE is not entirely clear. The KIE was computed as 1.11 and 1.12 for the gas phase using the one-dimensional WKB, multidimensional CVT/SCT, and instanton approaches. With an explicit static and ONIOM 16 ACS Paragon Plus Environment

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noble gas solvent model the WKB computed tunneling half-live changes agree well with the experimental ones.

As found experimentally, two matrix-sites could be identified in the

computations as well. The computed relative KIEs are almost constant for all noble gases. A quantitative explanation of the experimentally observed tunneling rates and KIEs in different inert gases still offers a formidable challenge. ASSOCIATED CONTENT A description of the experimental procedures, detailed matrix isolation spectra, tables with assigned vibrational frequencies, a description of the employed kinetic analysis, a description of the employed theoretical methods and the geometries, electronic and zero-point vibrational energies and the complete citation for ref 27 and 36 are provided in the Supporting Information.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT We thank Jan Meisner and Johannes Kästner (University of Stuttgart) for helpful discussions concerning the instanton tunneling computations and Henrik Quanz (Justus-Liebig University) for technical support. This work was supported by the Fonds der Chemischen Industrie (Fellowship to A.K.E.). 17 ACS Paragon Plus Environment


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REFERENCES

1.

Hund, F., Zur Deutung der Molekelspektren. III. Zeitschrift für Physik A Hadrons and

Nuclei 1927, 43, 805-826. 2.

Wigner, E., Über das Überschreiten von Potentialschwellen bei Chemischen Reaktionen.

Z. Phys. Chem. 1932, 19, 203-216. 3.

Ley, D.; Gerbig, D.; Schreiner, P. R., Tunnelling Control of Chemical Reactions - the

Organic Chemist's Perspective. Org. Biomol. Chem. 2012, 10, 3781-3790. 4.

Borden, W. T., Reactions That Involve Tunneling by Carbon and the Role That

Calculations Have Played in Their Study. WIREs Comput. Mol. Sci. 2016, 6, 20-46. 5.

Schreiner, P. R.; Reisenauer, H. P.; Ley, D.; Gerbig, D.; Wu, C. H.; Allen, W. D.,

Methylhydroxycarbene: Tunneling Control of a Chemical Reaction. Science 2011, 332, 13001303. 6.

Schreiner, P. R., Tunneling Control of Chemical Reactions: The Third Reactivity

Paradigm. J. Am. Chem. Soc. 2017, 139, 15276-15283. 7.

Ley, D.; Gerbig, D.; Wagner, J. P.; Reisenauer, H. P.; Schreiner, P. R.,

Cyclopropylhydroxycarbene. J. Am. Chem. Soc. 2011, 133, 13614-13621. 18 ACS Paragon Plus Environment

Page 19 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


8.

Ley, D.; Gerbig, D.; Schreiner, P. R., Tunneling Control of Chemical Reactions: C-H

Insertion versus H-Tunneling in tert-Butylhydroxycarbene. Chem. Sci. 2013, 4, 677-684. 9.

Kozuch, S.; Zhang, X.; Hrovat, D. A.; Borden, W. T., Calculations on Tunneling in the

Reactions of Noradamantyl Carbenes. J. Am. Chem. Soc. 2013, 135, 17274-17277. 10. Karmakar, S.; Datta, A., Tunneling Control: Competition Between 6π-Electrocyclization and [1,5]H-Sigmatropic Shift Reactions in Tetrahydro-1H-cyclobuta[e]indene Derivatives. J. Org. Chem. 2017, 82, 1558-1566. 11. Mardyukov, A.; Quanz, H.; Schreiner, P. R., Conformer-Specific Hydrogen Atom Tunnelling in Trifluoromethylhydroxycarbene. Nat Chem 2017, 9, 71-76. 12. Domanskaya, A.; Marushkevich, K.; Khriachtchev, L.; Räsänen, M., Spectroscopic Study of cis-to-trans Tunneling Reaction of HCOOD in Rare Gas Matrices. J. Chem. Phys. 2009, 130, 154509. 13. Maçôas, E. M. S.; Khriachtchev, L.; Pettersson, M.; Fausto, R.; Räsänen, M., Rotational Isomerism of Acetic Acid Isolated in Rare-Gas Matrices: Effect of Medium and Isotopic Substitution on IR-Induced Isomerization Quantum Yield and cis→trans Tunneling Rate. J. Chem. Phys. 2004, 121, 1331-1338. 14. Wagner, J. P.; Reisenauer, H. P.; Hirvonen, V.; Wu, C.-H.; Tyberg, J. L.; Allen, W. D.; Schreiner, P. R., Tunnelling in Carbonic Acid. Chem. Commun. 2016, 52, 7858-7861. 15. Schreiner, P. R.; Wagner, J. P.; Reisenauer, H. P.; Gerbig, D.; Ley, D.; Sarka, J.; Császár, A. G.; Vaughn, A.; Allen, W. D., Domino Tunneling. J. Am. Chem. Soc. 2015, 137, 7828-7834.



Page 20 of 26

16. Gerbig, D.; Schreiner, P. R., Hydrogen-Tunneling in Biologically Relevant Small Molecules: the Rotamerizations of alpha-Ketocarboxylic Acids. J. Phys. Chem. B 2015, 119, 693-703. 17. 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. 18. Seeman, J. I., Effect of Conformational Change on Reactivity in Organic Chemistry. Evaluations, Applications, and Extensions of Curtin-Hammett Winstein-Holness Kinetics. Chem. Rev. 1983, 83, 83-134. 19. Oki, M., Reactivity of Conformational Isomers. Acc. Chem. Res. 1984, 17, 154-159. 20. Nandi, A.; Gerbig, D.; Schreiner, P. R.; Borden, W. T.; Kozuch, S., Isotope-Controlled Selectivity by Quantum Tunneling: Hydrogen Migration versus Ring Expansion in Cyclopropylmethylcarbenes. J. Am. Chem. Soc. 2017, 139, 9097-9099. 21. Schleif, T.; Mieres-Perez, J.; Henkel, S.; Ertelt, M.; Borden, W. T.; Sander, W., The Cope Rearrangement of 1,5-Dimethylsemibullvalene-2(4)-d1: Experimental Evidence for Heavy-Atom Tunneling. Angew. Chem. Int. Ed. 2017, 56, 10746-10749. 22. Wu, Z.; Feng, R.; Li, H.; Xu, J.; Deng, G.; Abe, M.; Begue, D.; Liu, K.; Zeng, X., Fast Heavy-Atom Tunneling in Trifluoroacetyl Nitrene. Angew. Chem. Int. Ed. 2017, 56, 1567215676. 23. Zuev, P. S.; Sheridan, R. S.; Albu, T. V.; Truhlar, D. G.; Hrovat, D. A.; Borden, W. T., Carbon Tunneling From a Single Quantum State. Science 2003, 299, 867-870. 20 ACS Paragon Plus Environment

Page 21 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


24. Zhang, X.; Datta, A.; Hrovat, D. A.; Borden, W. T., Calculations Predict a Large Inverse H/D Kinetic Isotope Effect on the Rate of Tunneling in the Ring Opening of Cyclopropylcarbinyl Radical. J. Am. Chem. Soc. 2009, 131, 16002-16003. 25. Scheiner, S., Calculation of Isotope Effects From First Principles. Biochim. Biophys. Acta 2000, 1458, 28-42. 26. Meisner, J.; Kästner, J., Atom Tunneling in Chemistry. Angew. Chem. Int. Ed. 2016, 55, 5400-5413. 27. Stanton, J.; Gauss, J.; Harding, M.; Szalay, P.; Auer, A.; Bartlett, R.; Benedikt, U.; Berger, C.; Bernholdt, D.; Bomble, Y., et al. CFOUR, Coupled-Cluster techniques for Computational Chemistry, a quantum chemical program package. For the current version, see http://www.cfour.de. 28. Čížek, J., On the Correlation Problem in Atomic and Molecular Systems. Calculation of Wavefunction Components in Ursell-Type Expansion Using Quantum-Field Theoretical Methods. J. Chem. Phys. 1966, 45, 4256-4266. 29. Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M., A Fifth-Order Perturbation Comparison of Electron Correlation Theories. Chem. Phys. Lett. 1989, 157, 479483. 30. Bartlett, R. J.; Watts, J. D.; Kucharski, S. A.; Noga, J., Non-Iterative Fifth-Order Triple and Quadruple Excitation Energy Corrections in Correlated Methods. Chem. Phys. Lett. 1990, 165, 513-522.



Page 22 of 26

31. Stanton, J. F., Why CCSD(T) Works: a Different Perspective. Chem. Phys. Lett. 1997, 281, 130-134. 32. Dunning, J., Thom H., Gaussian Basis Sets for use in Correlated Molecular Calculations. I. The Atoms Boron Through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007-1023. 33. Becke, A. D., Density-Functional Exchange-Energy: Approximation With Correct Asymptotic Behavior. Phys. Rev. A 1988, 38, 3098-3100. 34. Becke, A. D., Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648-5652. 35. Lee, C.; Yang, W.; Parr, R. G., Development of the Colle-Salvetti Correlation-Energy Formula Into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785-789. 36. Frisch, M. J., Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, Revision D.01; Gaussian, Inc.: Wallingford, CT, 2009. 37. Grimme, S.; Ehrlich, S.; Goerigk, L., Effect of the Damping Function in Dispersion Corrected Density Functional Theory. J. Comput. Chem. 2011, 32, 1456-1465. 38. Weigend, F.; Ahlrichs, R., Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H to Rn: Design and Assessment of Accuracy. Phys. Chem. Chem. Phys. 2005, 7, 3297-3305. 39. Weigend, F., Accurate Coulomb-Fitting Basis Sets for H to Rn. Phys. Chem. Chem. Phys. 2006, 8, 1057-1065.


Page 23 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


40. Rappe, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A.; Skiff, W. M., UFF, a Full Periodic Table Force Field for Molecular Mechanics and Molecular Dynamics Simulations. J. Am. Chem. Soc. 1992, 114, 10024-10035. 41. Hratchian, H. P.; Schlegel, H. B., Following Reaction Pathways Using a Damped Classical Trajectory Algorithm. J. Phys. Chem. A 2002, 106, 165-169. 42. Hratchian, H. P.; Schlegel, H. B., Accurate Reaction Paths Using a Hessian Based Predictor-Corrector Integrator. J. Chem. Phys. 2004, 120, 9918-9924. 43. Mathematica, version 10.3; software for technical computation; Wolfram Research: Champaign, IL, 2015. 44. Zheng, J.; Zhang, S.; Lynch, B. J.; Corchado, J. C.; Chuang, Y.-Y.; Fast, P. L.; Hu, W.-P.; Liu, Y.-P.; Lynch, G. C.; Nguyen, K. A.et al. POLYRATE 2010-A; 2010. 45. Kuppermann, A.; Truhlar, D. G., Exact Tunneling Calculations. J. Am. Chem. Soc. 1971, 93, 1840-1851. 46. Skodje, R. T.; Truhlar, D. G.; Garrett, B. C., A General Small-Curvature Approximation for Transition-State-Theory Transmission Coefficients. J. Phys. Chem. 1981, 85, 3019-3023. 47. Rommel, J. B.; Goumans, T. P. M.; Kästner, J., Locating Instantons in Many Degrees of Freedom. J. Chem. Theory Comput. 2011, 7, 690-698. 48. Kästner, J.; Carr, J. M.; Keal, T. W.; Thiel, W.; Wander, A.; Sherwood, P., DL-FIND: An Open-Source Geometry Optimizer for Atomistic Simulations. J. Phys. Chem. A 2009, 113, 11856-11865.



Page 24 of 26

49. Skell, P. S.; Wescott, L. D.; Golstein, J. P.; Engel, R. R., Reactions of Carbon Vapor. I. Reactions of Triatomic Carbon with Olefins. J. Am. Chem. Soc. 1965, 87, 2829-2835. 50. Pettersson, M.; Maçôas, E. M. S.; Khriachtchev, L.; Lundell, J.; Fausto, R.; Räsänen, M., Cis→trans Conversion of Formic Acid by Dissipative Tunneling in Solid Rare Gases: Influence of Environment on the Tunneling Rate. J. Chem. Phys. 2002, 117, 9095-9098. 51. Marushkevich, K.; Räsänen, M.; Khriachtchev, L., Interaction of Formic Acid with Nitrogen: Stabilization of the Higher-Energy Conformer. J. Phys. Chem. A 2010, 114, 1058410589. 52. Moore, C. B.; Pimentel, G. C., Matrix Reaction of Methylene with Nitrogen to Form Diazomethane. J. Chem. Phys. 1964, 41, 3504-3509. 53. Rodler, M.; Blom, C.; Bauder, A., Infrared Spectrum and General Valence Force Field of syn-Vinyl Alcohol. J. Am. Chem. Soc. 1984, 106, 4029-4035. 54. Wentzel, G., Eine Verallgemeinerung der Quantenbedingungen für die Zwecke der Wellenmechanik. Z. Physik 1926, 38, 518-529. 55. Kramers, H. A., Wellenmechanik und Halbzahlige Quantisierung. Z. Physik 1926, 39, 828-840. 56. Brillouin, L., La Mécanique Ondulatoire de Schrödinger; une Méthode Générale de Résolution par Approximations Successives. CR Acad. Sci 1926, 183, 24-26. 57. Kästner, J., Path Length Determines the Tunneling Decay of Substituted Carbenes. Chem. Eur. J. 2013, 19, 8207-8212.


Page 25 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


58. Schreiner, P. R.; Reisenauer, H. P.; Pickard IV, F. C.; Simmonett, A. C.; Allen, W. D.; Matyus, E.; Csaszar, A. G., Capture of hydroxymethylene and its fast disappearance through tunnelling. Nature 2008, 453, 906-909. 59. 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. 60. 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. 61. Trakhtenberg, L. I.; Fokeyev, A. A.; Mebel, A. M., H/D Kinetic Isotope Effect in HCOOH cis–trans Conversion of Formic Acid in Noble Gas Matrices. Chem. Phys. Lett. 2013, 574, 47-50.



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Heavy Atom Secondary Kinetic Isotope Effect on H-Tunneling - The

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