Communication pubs.acs.org/JACS
Isotope-Controlled Selectivity by Quantum Tunneling: Hydrogen Migration versus Ring Expansion in Cyclopropylmethylcarbenes Ashim Nandi,† Dennis Gerbig,‡ Peter R. Schreiner,‡ Weston Thatcher Borden,§ and Sebastian Kozuch*,† †
Department of Chemistry, Ben-Gurion University of the Negev, Beer-Sheva 841051, Israel Justus-Liebig University, Heinrich-Buff-Ring 17, 35392 Giessen, Germany § Center for Advanced Scientific Computing and Modeling (CASCAM), Department of Chemistry, University of North Texas, Denton, Texas 76203, United States ‡
S Supporting Information *
Scheme 1. Singlet Cyclopropylmethylcarbene in its Most Stable Conformation (1R) and the Three Potential Reactions: Ring Expansion (RE) to 1-Methylcyclobutene (2R), [1,2]H-Shift (HS) to Form Vinylcyclopropane (3R), and Another, but Highly Unfavorable [1,2]H-Shift to Ethylidenecyclopropane (4R) in Graya
ABSTRACT: Using the tunneling-controlled reactivity of cyclopropylmethylcarbene, we demonstrate the viability of isotope-controlled selectivity (ICS), a novel control element of chemical reactivity where a molecular system with two conceivable products of tunneling exclusively produces one or the other, depending only on isotopic composition. Our multidimensional small-curvature tunneling (SCT) computations indicate that, under cryogenic conditions, 1-methoxycyclopropylmethylcarbene shows rapid H-migration to 1-methoxy-1-vinylcyclopropane, whereas deuterium-substituted 1-methoxycyclopropyl-d3methylcarbene undergoes ring expansion to 1-d3-methylcyclobutene. This predicted change in reactivity constitutes the first example of a kinetic isotope effect that discriminates between the formation of two products.
a
H
ydrogen tunneling has been a well-known phenomenon for the past 80 years.1 However, reactions involving heavy (i.e., non-hydrogen) atom quantum mechanical tunneling (QMT) were, until recently, uncommon. Starting with the seminal work of Carpenter et al. on π-bond shifting of cyclobutadiene,2 recent times have seen a multitude of reactions in which heavy atom tunneling has been predicted and/or experimentally observed.3 Among these, heavy atom QMT has most frequently been computed and/or observed in ring expansion (RE) reactions of carbenes.4−9 Carbenes, due to their high intrinsic reactivity, tend to react with low activation energies and, most critical for heavy-atom tunneling, with short tunneling distances.2−4,7,10 In the case of cyclopropylmethylcarbene (1H, Scheme 1), there are three potentially competing tunneling reactions: RE to 1-methylcyclobut-1-ene (2H) through the shift of a methylene group (marked with a blue dot in Scheme 1), a [1,2]H-shift (HS) to vinylcyclopropane (3H), and a different [1,2]H-shift to ethylidenecyclopropane (4H). The latter reaction, however, is associated with a prohibitively high (20.5 kcal mol−1) and wide barrier, so that tunneling will not occur (vide inf ra). At high temperatures, where all of these reactions occur by over-the-barrier thermal mechanisms, RE is favored because it is associated with the lowest barrier. On the other hand, due to © 2017 American Chemical Society
Computed barriers at B3LYP/6-31G(d,p) given for R = H.
the light mass of hydrogen and the short distance for hydrogen migration, HS by tunneling has been shown to be preferred at low temperatures despite its higher activation barrier.6,8,9,11 This type of change in selectivity on going from high to low temperatures due to tunneling has been termed tunneling control,12 to distinguish it from the traditional kinetic and thermodynamic control schemes.3,8,9,11,13 Since the two competing reactions depicted in Scheme 1 can conceivably both occur via tunneling at very low temperatures, where there is insufficient energy to overcome the thermal barriers, we ask: Can the preferred product of tunneling be switched f rom HS to RE by isotopic substitution? HS should be much more sensitive to deuterium substitution in the methyl group than RE. Considering this, can we find a substituted trideuteriomethylcyclopropylcarbene (1R-d3) that forms the corresponding 1-trideuteriomethylcyclobut-1-ene (2R-d3) by RE at all temperatures? This is in contrast to the undeuterated parent carbene, which is expected to favor the formation of 3R by HS under cryogenic conditions. In order to address this question, we computed the relative rates of the two competing reactions. The reaction rates were computed using the multidimensional, small-curvature tunnelReceived: May 4, 2017 Published: June 21, 2017 9097
DOI: 10.1021/jacs.7b04593 J. Am. Chem. Soc. 2017, 139, 9097−9099
Communication
Journal of the American Chemical Society ing (SCT) method,14 implemented in the program Polyrate.15 All geometries and energies were computed at the B3LYP/631G(d,p) level with Gaussian09,16 using Gaussrate17 as the interface between the two software packages. This DFT methodology has been previously proven to be sufficiently accurate for carbene reactions.6 However, considering the possible sensitivity of the computed tunneling rates to the method used, we created a benchmark set of HS and RE rate constants, taken from previous experimental results.4,5,9,18 The B3LYP/6-31G(d,p) combination was selected because it provided the best agreement with experimental rate constants, while being computationally inexpensive. The Supporting Information (SI) contains the complete benchmarking analysis based on two H-shift and two ring expansion reactions in cryogenic matrices,4,5,9,18 as well as CCSD(T) computations confirming that the reactions occur on the singlet potential energy surface. Table 1 shows the calculated rate constants (k) at cryogenic temperatures (10 K) for HS and RE for unsubstituted 1H and
order to obtain ICS, the rate of ring expansion must be massively accelerated. To probe the effect of π-electron donating groups at the C-1 position of the cyclopropane ring on the reactivity of the system, we selected substituents at C-1 (R in Scheme 1) that should be able to transfer electron density to one of the cyclopropyl Walsh MOs (see SI for a MO and NBO explanation), thereby aiding in the interaction of the cyclopropyl moiety with the carbene center. Consequently, the RE barrier should be lowered while that of the HS should be little affected. Indeed, fluorine at C-1 in 1F drastically lowers the barrier of RE from 7.5 to 3.1 kcal mol−1, without affecting the HS barrier (12.1 kcal mol−1 for 1H, 12.0 for 1F). However, even though the computed rate constants for REH and RED are higher by more than 5 orders of magnitude in 1F compared to unsubstituted 1H, this increase is not enough to make kRED (6.5 × 10−5 s−1) greater than kDS (2.7 × 10−4 s−1) for the deuterium shift. Thus, although with the substitution of fluorine at C-1 the rate of ring expansion is calculated to grow to within a factor of 4, our calculations do not indicate that 1F would exhibit ICS behavior. However, the higher RE rate constant calculated for 1F indicates that a π-electron-donating group at C-1 of 1R does produce the desired type of change in reactivity. Unfortunately, substitution at C-1 of an NH2 or OH group (1NH2 and 1OH) yields much larger RE than HS rate constants (cf. SI). Therefore, neither molecule will show either ICS or tunneling control. Dimethylamino-substituted 1NMe2 does not show ICS due to the steric hindrance that impedes conjugation of the N lone pair with the ring, raising the RE barrier compared to 1NH2 (see SI). Upon investigating the effects of the methoxy group at C-1 of 1OMe (Figure 1), we found that the computed tunneling rate
Table 1. Calculated Rate Constants and Enthalpies of Activation at 10 K in s−1 and in kcal mol−1 for HS and RE Reactions of Undeuterated and Deuterated Methyl Carbenesa
a
Except for the parent 1H and 1F, all of the other molecules in the table are predicted to exhibit ICS. Figure 1. Computed Arrhenius plots for the [1,2]H/D-shifts (HS and DS, respectively), and the corresponding ring expansions (REH and RED, respectively) of 1-methoxycyclopropylmethylcarbene (1OMe). At temperatures below 40 K both isotope controlled selectivity and tunneling control dominate the reactivity of 1OMe.
methyl-deuterated 1H-d3, as well as for several ring-substituted derivatives. The [1,2]H-shift to 4H can safely be excluded, because its calculated SCT tunneling rate is on the order of 10−44 s−1. Tables of rate constants for all the studied tunneling controlled reactions in different conformations at various temperatures can be found in the SI. In order for a clear prediction of isotope-controlled selectivity (ICS) to be obtained, kREH and kRED (i.e., the rate constants for ring expansion with undeuterated and deuterated reactants, respectively) must be smaller than the rate constant for hydrogen-shifting (kHS), but greater than the one for deuterium-shifting (kDS). The first line of Table 1 shows that parent 1 cannot possibly show ICS, since kREH = 3.7 × 10−10 s−1 and kRED 2.8 × 10−10 s−1 are both several orders of magnitude smaller than kHS = 16 s−1 and kDS = 5.3 × 10−4 s−1. Clearly, in
constant for RE lies between those for HS and DS. As shown in Table 1, kHS is calculated to be about 1500 times larger than kREH, but kRED is predicted to be larger than kDS by more than an order of magnitude. Consequently, 1OMe should preferentially react via hydrogen migration, but 1OMe-d3 should undergo ring expansion faster than a [1,2]D-shift. To the best of our knowledge, this is the f irst prediction of ICS in a tunneling reaction. We tested the effects of additional substituents at other positions, considering that they may further lower the activation energy of RE. Herein we only show the respective 9098
DOI: 10.1021/jacs.7b04593 J. Am. Chem. Soc. 2017, 139, 9097−9099
Communication
Journal of the American Chemical Society
(6) Kozuch, S.; Zhang, X.; Hrovat, D. A.; Borden, W. T. J. Am. Chem. Soc. 2013, 135, 17274−17277. (7) Kozuch, S. Phys. Chem. Chem. Phys. 2014, 16, 7718−7727. (8) Gerbig, D.; Ley, D.; Schreiner, P. R. Org. Lett. 2011, 13, 3526− 3529. (9) Ley, D.; Gerbig, D.; Wagner, J. P.; Reisenauer, H. P.; Schreiner, P. R. J. Am. Chem. Soc. 2011, 133, 13614−13621. (10) Kästner, J. WIREs Comput. Mol. Sci. 2014, 4, 158−168. (11) Ley, D.; Gerbig, D.; Schreiner, P. R. Org. Biomol. Chem. 2012, 10, 3781. (12) Schreiner, P. R.; Reisenauer, H. P.; Ley, D.; Gerbig, D.; Wu, C.H.; Allen, W. D. Science 2011, 332, 1300−1303. (13) Karmakar, S.; Datta, A. J. Org. Chem. 2017, 82, 1558−1566. (14) Fernandez-Ramos, A.; Ellingson, B. A.; Garrett, B. C.; Truhlar, D. G. In Reviews in Computational Chemistry; Lipkowitz, K. B., Cundari, T. R., Eds.; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2007; Vol. 3, pp 125−232. (15) POLYRATE 2016−2A: Computer Program for the Calculation of Chemical Reaction Rates for Polyatomics; Truhlar, D. G. et al.; University of Minnesota, MN (see full reference in SI). (16) Gaussian 09, Rev. D01; Frisch, M. J. et al.; Gaussian, Inc.: Wallingford, CT, 2009 (see full reference in SI). (17) GAUSSRATE 2016: Zheng, J.; Zhang, S.; Corchado, J. C.; Meana-Pañeda; Chuang, Y.-Y.; Coitiño, E. L.; Ellingson, B. A.; Truhlar, D. G.; Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, MN 55455. (18) Schreiner, P. R.; Reisenauer, H. P.; Pickard, F. C., IV; Simmonett, A. C.; Allen, W. D.; Mátyus, E.; Császár, A. G. Nature 2008, 453, 906−909. (19) This can be achieved by matrix isolation of a diazirine precursor at cryogenic conditions, followed by carbene generation by flash photolysis and characterization of products by IR spectroscopy. See for instance refs 4 and 5.
rate constants, leaving the full analysis to the SI. Four more systems were found to produce ICS: 1FMeβ, 1FMeMe, 1FFα, and 1FFFs (Table 1). The latter, with three fluorine atoms, is particularly promising since the rate of ring expansion lies right between that of HS and DS and, therefore, close to the maximum selectivity attainable for methylcarbenes. To summarize, using quantum chemical computations that include small curvature tunneling, we predict the existence of a novel effect that we term isotope-controlled selectivity (ICS). In such a reaction, where several possible products can arise from QMT, the chemo- and regioselectivity depends on whether hydrogen or deuterium atoms are involved in the tunneling process. We show that ICS can be maximized via substituent fine-tuning, as exemplified by the cyclopropylmethylcarbene derivatives in Table 1. The major effect of the substituents is to alter the RE barrier. Promising candidates in which to experimentally observe ICS are predicted to be 1OMe, 1FMeβ, 1FMeMe, and 1FFFs. As shown in Figure 1, ICS can be turned on and off by a change in temperature, thus adding another viable control element to these chemical reactions. Since the calculated reaction times are short (t1/2 of only 4 min at cryogenic temperatures for the slowest possible reaction of 1OMe, RED), it should be relatively easy to test our predictions experimentally. In fact, we are currently in the process of exploring these selectivity predictions, e.g., by matrix isolation spectroscopy.19
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.7b04593. Benchmark analysis, description of systems with more than one substituent, explanation of substituent effects, XYZ geometries, complete kinetic tables as a function of temperature, example of POLYRATE output, and full refs 15 and 16 (PDF)
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AUTHOR INFORMATION
Corresponding Author
*
[email protected] ORCID
Weston Thatcher Borden: 0000-0003-4782-3381 Sebastian Kozuch: 0000-0003-3070-8141 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This research was supported by the Israel Science Foundation (grant 631/15), the Lise Meitner−Minerva Center for Computational Quantum Chemistry, and a start-up grant from the Ben−Gurion University of the Negev.
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REFERENCES
(1) Bell, R. P. The Tunnel Effect in Chemistry; Chapman and Hall: London; New York, 1980. (2) Carpenter, B. K. J. Am. Chem. Soc. 1983, 105, 1700−1701. (3) Borden, W. T. WIREs Comput. Mol. Sci. 2015, 20−46. (4) Zuev, P. S.; Sheridan, R. S.; Albu, T. V.; Truhlar, D. G.; Hrovat, D. A.; Borden, W. T. Science 2003, 299, 867−870. (5) Moss, R. A.; Sauers, R. R.; Sheridan, R. S.; Tian, J.; Zuev, P. S. J. Am. Chem. Soc. 2004, 126, 10196−10197. 9099
DOI: 10.1021/jacs.7b04593 J. Am. Chem. Soc. 2017, 139, 9097−9099
