Computational Prediction of Excited-State Carbon Tunneling in the

Oct 16, 2017 - We have applied state-of-the-art quantum mechanical methods, including M06-2X, DLPNO-CCSD(T) and variational transition-state theory wi...
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Cite This: J. Am. Chem. Soc. 2017, 139, 16438-16441

Computational Prediction of Excited-State Carbon Tunneling in the Two Steps of Triplet Zimmerman Di-π-Methane Rearrangement Xin Li,‡ Tao Liao,‡ and Lung Wa Chung* Department of Chemistry, South University of Science and Technology of China, Shenzhen 518055, China S Supporting Information *

Scheme 1. Triplet Di-π-Methane Rearrangement of DBB/ Barrelene/Benzobarrelene To Form Dibenzosemibullvalene/ Semibullvalene/Benzosemibullvalene Products via Intersystem Crossing (ISC)a

ABSTRACT: The photoinduced Zimmerman di-π-methane (DPM) rearrangement of polycyclic molecules to form synthetically useful cyclopropane derivatives was found experimentally to proceed in a triplet excited state. We have applied state-of-the-art quantum mechanical methods, including M06-2X, DLPNO-CCSD(T) and variational transition-state theory with multidimensional tunneling corrections, to an investigation of the reaction rates of the two steps in the triplet DPM rearrangement of dibenzobarrelene, benzobarrelene and barrelene. This study predicts a high probability of carbon tunneling in regions around the two consecutive transition states at 200−300 K, and an enhancement in the rates by 104− 276/35−67% with carbon tunneling at 200/300 K. The Arrhenius plots of the rate constants were found to be curved at low temperatures. Moreover, the computed 12 C/13C kinetic isotope effects were affected significantly by carbon tunneling and temperature. Our predictions of electronically excited-state carbon tunneling and two consecutive carbon tunneling are unprecedented. Heavyatom tunneling in some photoinduced reactions with reactive intermediates and narrow barriers can be potentially observed at relatively low temperature in experiments.

a

For DBB, the key distances of C9−C9a and C12−C9a computed by the M06-2X method are shown (in Å, taken from ref 2a).

atom (e.g., carbon) tunneling participated in some organic transformations such as automerization of cyclobutadiene, ringexpansion of methylcyclobutylfluorocarbene, ring-opening of cyclopropylcarbinyl radical, Bergman cyclization of an enediyne and allylation.3−5 In contrast, light hydrogen tunneling has been widely observed in many organic and enzymatic reactions.6−9 Moreover, several examples of hydrogen tunneling in an excited singlet or triplet state have been reported.7,9 Specifically, hydrogen tunneling in triplet o-methylanthrones was studied by Houk and Garcia-Garibay.7a Truhlar reported hydrogen tunneling in the photodissociation of phenol in the first singlet state,7d and tunneling in excited-state proton transfer in green fluorescent protein has been observed experimentally.9 Computational chemistry has played an important role in elucidation and even prediction of tunneling, as well as providing new insights and concepts (e.g., tunneling-controlled reactivity reported by Schreiner) in some studies.3−8,10 In this Communication, we report a state-of-the-art computational investigation using M06-2X,11a DLPNO-CCSD(T),11b and variational transition-state theory (VTST) including multidimensional tunneling methods12 on the reaction rate of the triplet DPM rearrangement. Our calculations predict that excited-state carbon tunneling plays a vital role in the reaction rates and the 12C/13C kinetic isotope effects (KIEs) of the triplet DPM rearrangement of DBB, benzobarrelene and barrelene.1,2,13 To the best of our knowledge, this is the first example of excitedstate carbon tunneling and two consecutive carbon tunneling. The stationary points for the rearrangement of DBB, benzobarrelene and barrelene were first located at the UM06-

T

he di-π-methane (DPM) rearrangement is an important photochemical and synthetic transformation, pioneered by Zimmerman, to form cyclopropane derivatives, which has attracted the wide attention from chemists.1 The DPM rearrangement of polycyclic molecules (e.g., dibenzobarrelene (DBB)) were found experimentally to occur in a triplet state (T1, Scheme 1).1d Recently, the reaction mechanism and the reaction dynamics (static and dynamic calculations) of the triplet DPM rearrangement of DBB have been deciphered by Houk and coworkers2 who suggested that the one-step and two-step pathways, involving two diradical intermediates in T1, are competitive. Encouraged by the computed small change of the reacting carbon distances in the intermediates (ΔR ∼ 0.8−0.9 Å) in Houk’s seminal study,2a we envisioned that carbon tunneling through narrow reaction barriers could contribute to this important photochemical reaction (Scheme 1). Owing to the larger mass of the carbon or oxygen atoms, examples of heavy-atom tunneling in chemical reactions through narrow barriers are scarce.3−6 Recently, Borden, Carpenter, Doubleday, Schreiner, Singleton, Truhlar and others have demonstrated computationally and even predicted that heavy© 2017 American Chemical Society

Received: July 19, 2017 Published: October 16, 2017 16438

DOI: 10.1021/jacs.7b07539 J. Am. Chem. Soc. 2017, 139, 16438−16441

Communication

Journal of the American Chemical Society 2X/6-31G(d) level of theory. Tunneling calculations were then performed using POLYRATE with the GAUSSRATE interface to G09,14 by the UM06-2X method. The energetics of the reactions computed by the UM06-2X method are quite similar to those computed by high-level DLPNO-CCSD(T)/cc-pVTZ and DLPNO-CCSD(T)/aug-cc-pVTZ methods using ORCA14d (Figure 1). The rate constants without quantum-mechanical

Figure 1. Computed PESs for the triplet DPM rearrangement of DBB (A, black solid line), barrelene (B, red dashed line) and benzobarrelene (C, green dashed line).

Figure 2. Arrhenius plots of the rate constants for the rate-determining step of the triplet DPM rearrangement of (a) DBB and (b) barrelene and benzobarrelene by the CVT, SCT and M06-2X methods.

tunneling (kCVT) were evaluated by canonical variational transition state theory (CVT).12a The reaction rates with the effect of multidimensional tunneling (kCVT+SCT) were computed by including a small curvature tunneling (SCT) approximation.12 Our calculated potential energy surfaces (PESs) for the DPM rearrangement of DBB, benzobarrelene and barrelene in T1 are displayed in Figure 1. The PES for DBB calculated by the UM062X method is the same as the previous computational work by Houk,2a and is quite similar to that computed by the DLPNOCCSD(T) methods. These computational results suggest that the first step for DBB via TS1A is the rate-determining step and requires an energy-barrier of about 10.8 kcal/mol calculated by the UM06-2X method or 9.1−9.3 kcal/mol by the DLPNOCCSD(T) methods. The corresponding diradical product 2A (BR-I)2a was computed to be less stable than 1A (DBB*)2a by approximately 0.9 kcal/mol by the UM06-2X method and 1.6− 1.7 kcal/mol by the DLPNO-CCSD(T) methods. Comparatively, the energy barrier of the second step for DBB (∼2.2−2.8 kcal/mol) is much lower than that of the first step due to the formation of the stable diradical product 3A (BR-II,2a ΔE = −13.3 ∼ −14.8 kcal/mol). For the rearrangement of barrelene, the energy barrier of the first step via TS1B is about 5.7 and 3.9−4.1 kcal/mol by the UM06-2X and DLPNO-CCSD(T) methods, respectively. Compared to barrelene, the higher barrier and lower reaction energy for DBB can be attributed to a loss of aromaticity from the reacting phenyl moiety. The second step for barrelene via TS2B becomes the rate-determining step, with an energy barrier of 8.9 and 5.3−5.6 kcal/mol by the UM06-2X and DLPNO-CCSD(T) methods, respectively. Comparatively, the most favorable pathway for the rearrangement of benzobarrelene has a similar PES as barrelene. The barriers of the first and second steps for benzobarrelene via TS1C and TS2C are slightly higher than those for barrelene. However, the diradical products 3C and 3A are similar in energy. Overall, the rearrangements of DBB, benzobarrelene and barrelene have different energetic features. The reaction rates and possibility of carbon tunneling in the triplet DPM rearrangement of DBB, benzobarrelene and barrelene were examined by VTST. As shown in Figures 2a

and S3a, for the first and second steps of DBB, the Arrhenius plots show that the reaction rates with and without tunneling effect at high temperatures (160−400 K) are linear and temperature-dependent. Interestingly, the rates become temperature-independent upon inclusion of tunneling at low temperatures (below 160 K). Carbon tunneling was also computed to increase the reaction rate for the first step by a factor of 1.49/ 2.72/7203 at 300/200/100 K, and for the second step by a factor of 1.35/2.04/27.9 at 300/200/100 K (Table 1).15 Owing to the Table 1. Computed Rate Constant (k, s−1) and 12C/13C KIE for the Rate-Determining Rearrangement Step of DBB, Barrelene and Benzobarrelene without and with Tunneling at 100, 200, and 300 K Temp

kCVT

DBB 100 K 4.68 × 10−9 200 K 1.75 × 102 300 K 6.74 × 105 Barrelene 100 K 1.19 × 10−5 200 K 9.57 × 103 300 K 1.01 × 107 Benzobarrelene 100 K 3.79 × 10−8 200 K 5.46 × 102 300 K 1.52 × 106

kCVT+SCT

KIECVT

KIECVT+SCT

3.37 × 10−5 4.78 × 102 1.01 × 106

1.153 1.079 1.058

2.536 1.165 1.088

2.52 3.60 × 104 1.68 × 107

1.213 1.101 1.074

3.210 1.246 1.113

1.41 × 10−3 1.68 × 103 2.38 × 106

1.227 1.108 1.070

3.456 1.226 1.112

higher barrier, the first step has a smaller rate constant, but has a higher carbon tunneling contribution to the rate constant than the second step. These results indicate that excited-state carbon tunneling through narrow barriers (Figure S5) plays a key role in the rates of the two consecutive8c rearrangement steps. Also, excited-state carbon tunneling has a pronounced effect on the computed 12C/13C KIE for the first- and ratedetermining-step in the rearrangement of DBB. For the case of substitution of 13C for 12C at C8a, C9a and C12 of DBB (Scheme 16439

DOI: 10.1021/jacs.7b07539 J. Am. Chem. Soc. 2017, 139, 16438−16441

Communication

Journal of the American Chemical Society 1 and Figure 3a), the computed 12C/13C KIEs with carbon tunneling are strongly dependent upon temperature. As shown in

significant and similar effects of the carbon tunneling on the reaction rates and 12C/13C KIE were also observed for benzobarrelene (Figures 2 and 3, and Table 1), suggesting larger tunneling for barrelene/benzobarrelene than DBB. Furthermore, intramolecular 13C KIE at natural abundance can be conveniently measured accurately in experiment.17 Our intramolecular KIE calculations for the first and irreversible step of DBB, barrelene and benzobarrelene also predict that more 13C should be observed at C11 in the product than at C12 (Scheme 1 and Table 2), as 12C at C12 preferentially undergoes the bond Table 2. Computed Intramolecular 13C KIEsa for the First Rearrangement Step of DBB, Barrelene, and Benzobarrelene without and with Tunneling at 100, 200, and 300 K Temp

KIECVT

DBB 100 K 1.061 200 K 1.033 300 K 1.025 Barrelene 100 K 1.064 200 K 1.034 300 K 1.026 Benzobarrelene 100 K 1.060 200 K 1.033 300 K 1.022

Figure 3. Arrhenius plots of the 12C/13C KIE for the rate-determining step of the rearrangement of (a) DBB and (b) barrelene and benzobarrelene by the CVT, SCT and M06-2X methods. a b

Table 1, the computed 12C/13C KIE at 100/200 K is 1.153/1.079 (without tunneling) and 2.536/1.165 (with tunneling), whereas at 300 K, the KIE reduces to 1.058 (without tunneling) and 1.088 (with tunneling). These results again support carbon tunneling even at 300 K through vibrationally activated tunneling16 around the transition state regions (Figure S6). For a single substitution of 13C for 12C (Table S2), the calculated 12C/13C KIE for the first step reveals important tunneling effect at the reacting C9a and C12, but not at C9. Hydrogen tunneling is insignificant in the computed H/D KIE (Figure S7). Excited-state carbon tunneling has also been found to participate in the rearrangement of barrelene. As shown in Figures 2b and S8, the Arrhenius plots of the computed rate constant with the inclusion of tunneling are clearly nonlinear at low temperatures (below 160 K). The reaction rate of the first step is larger than that of the second step due to the lower energy barrier of the first step (Figures 1, 2b and S3b). Similarly, carbon tunneling can be predicted to enhance the reaction rate for the first step by 1.67/3.61/2792 at 300/200/100 K, and for the second step by 1.66/3.76/2.12 × 105 at 300/200/100 K (Table 1). A larger contribution of carbon tunneling to the rate constants at 300 K was also observed for barrelene, by a factor of 1.66−1.67, compared to DBB (1.35−1.49). Moreover, the computed 12C/13C KIE for the rearrangement of barrelene is significantly influenced by carbon tunneling and is temperature-dependent (Figures 3b and S9a). Upon replacement of 12C by 13C at C8a, C9a, C9 and C12, the computed 12 C/13C KIE for the second- and rate-determining-step at 100/ 200 K is 1.213/1.101 without tunneling and 3.210/1.246 with tunneling, but the KIE at 300 K decreases to 1.074 without tunneling and 1.113 with tunneling (Table 1). Interestingly, with incorporation of deuterium at C9, C9a, C11 and C12, the H/D KIE was computed to be modestly affected by hydrogen tunneling and temperature (Figure S10). Similar to barrelene,

KIECVT+SCT

ΔKIESCTb

%KIESCTc

1.695 1.081 1.042

0.634 0.048 0.017

91% 59% 40%

1.297 1.085 1.044

0.233 0.051 0.018

78% 60% 41%

1.329 1.087 1.043

0.269 0.054 0.021

82% 62% 49%

Defined by the rate constant ratios of 13C for C11 and C12. KIECVT+SCT − KIESCT. cΔKIESCT/(KIECVT+SCT − 1) × 100%.

formation (relative to 13C). The computed enhancement in KIE by carbon tunneling increases from ∼0.02/∼0.05 at 300/200 K to ∼0.23−0.63 at 100 K. Notably, such an increase in the KIE by carbon tunneling contributes to ∼40−49/∼59−62/∼78−91% at 300/200/100 K of the total isotope effect, that reveal a key role of carbon tunneling in the intramolecular KIEs. Overall, our computational results predict that the enhancement of the reaction rates and 12C/13C KIE by excited-state carbon tunneling are not negligible around 200−300 K. Our computed increased rates and 12C/13C KIEs (∼1.08−1.25) by carbon tunneling at 200 K are qualitatively similar to the recent studies (Tables S4 and S5).3,4 Namely, Singleton and co-workers carried out 12C/13C KIE experiments and calculations to uncover heavy-atom tunneling in ring opening of cyclopropylcarbinyl radical (1.138) and allylation (1.047−1.052) reactions at ∼173− 195 K.3d,4b Moreover, Singleton, Houk and others reported comparable 12C/13C KIE values (Table S4) in Claisen rearrangement,10a Shi epoxidation18a and decarboxylation reactions,18b as well as novel dynamical effect.17d,18c−f In summary, our calculations predict that electronically excited-state carbon tunneling plays a key role in the two consecutive steps of the DPM rearrangement of DBB, barrelene and benzobarrelene in T1. The computed enhancement in rate constants (104−276/35−67%) and 12C/13C KIEs (0.086− 0.145/0.030−0.042) due to carbon tunneling are not negligible even at 200/300 K. Practically, it could be possible to experimentally measure the reaction rate (∼103 s−1) and KIEs (∼1.1−1.2) as well as observe more 13C at C11 than at C12 in the product for benzobarrelene ∼200 K (Scheme 1). The intramolecular 13C KIE could be readily tested by experiments via 13C NMR at natural abundance.17 To the best of our knowledge, this is the first example of excited-state carbon tunneling. Reports of 16440

DOI: 10.1021/jacs.7b07539 J. Am. Chem. Soc. 2017, 139, 16438−16441

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Journal of the American Chemical Society

VCH: Weinheim, Germany, 2007; Vols. 1−4. (d) Meisner, J.; Kästner, J. Angew. Chem., Int. Ed. 2016, 55, 5400. (e) Schreiner, P. R. J. Am. Chem. Soc. 2017, DOI: 10.1021/jacs.7b06035. (7) (a) Campos, L. M.; Warrier, M. V.; Peterfy, K.; Houk, K. N.; Garcia-Garibay, M. A. J. Am. Chem. Soc. 2005, 127, 10178. (b) Shelton, G. R.; Hrovat, D. A.; Borden, W. T. J. Am. Chem. Soc. 2007, 129, 164. (c) Zhang, X.; Datta, A.; Hrovat, D. A.; Borden, W. T. J. Am. Chem. Soc. 2009, 131, 16002. (d) Xu, X.; Zheng, J.; Yang, K. R.; Truhlar, D. G. J. Am. Chem. Soc. 2014, 136, 16378. (e) Gerbig, D.; Schreiner, P. R. Angew. Chem., Int. Ed. 2017, 56, 9445. (f) Dybala-Defratyka, A.; Paneth, P.; Banerjee, R.; Truhlar, D. G. Proc. Natl. Acad. Sci. U. S. A. 2007, 104, 10774. (g) Cha, Y.; Murray, C. J.; Klinman, J. P. Science 1989, 243, 1325. (h) Sandala, G. M.; Smith, D. M.; Coote, M. L.; Golding, B. T.; Radom, L. J. Am. Chem. Soc. 2006, 128, 3433 and ref 16. (8) (a) 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. (b) Schreiner, P. R.; Reisenauer, H. P.; Ley, D.; Gerbig, D.; Wu, C.-H.; Allen, W. D. Science 2011, 332, 1300. (c) Schreiner, P. R.; Wagner, J. P.; Reisenauer, H. P.; Gerbig, D.; Ley, D.; Sarka, J.; Császár, A. G.; Vaughn, A.; Allen, W. D. J. Am. Chem. Soc. 2015, 137, 7828. (d) Mardyukov, A.; Quanz, H.; Schreiner, P. R. Nat. Chem. 2016, 9, 71. (e) Nandi, A.; Gerbig, D.; Schreiner, P. R.; Borden, W. T.; Kozuch, S. J. Am. Chem. Soc. 2017, 139, 9097 and ref 6e. (9) (a) Chattoraj, M.; King, B. A.; Bublitz, G. U.; Boxer, S. G. Proc. Natl. Acad. Sci. U. S. A. 1996, 93, 8362. (b) Fang, C.; Frontiera, R. R.; Tran, R.; Mathies, R. A. Nature 2009, 462, 200. (10) (a) Meyer, M. P.; DelMonte, A. J.; Singleton, D. A. J. Am. Chem. Soc. 1999, 121, 10865. (b) Nowlan, D. T.; Gregg, T. M.; Davies, H. M. L.; Singleton, D. A. J. Am. Chem. Soc. 2003, 125, 15902. (11) (a) Zhao, Y.; Truhlar, D. G. Theor. Chem. Acc. 2008, 120, 215. (b) Riplinger, C.; Sandhoefer, B.; Hansen, A.; Neese, F. J. Chem. Phys. 2013, 139, 134101. (12) (a) Truhlar, D. G.; Garrett, B. C. Annu. Rev. Phys. Chem. 1984, 35, 159. (b) Liu, Y.-P.; Lu, D.-H.; Gonzalez-Lafont, A.; Truhlar, D. G.; Garrett, B. C. J. Am. Chem. Soc. 1993, 115, 7806. (13) (a) Frutos, L. M.; Sancho, U.; Castaño, O. Org. Lett. 2004, 6, 1229. (b) Zimmerman, H. E.; Kutateladze, A. G.; Maekawa, Y.; Mangette, J. E. J. Am. Chem. Soc. 1994, 116, 9795. (14) (a) Zheng, J.; et al. POLYRATE 2010-A; University of Minnesota: Minneapolis, MN, 2010. (b) Zheng, J.; Zhang, S.; Corchado, J. C.; Chuang, Y.-Y.; et al. GAUSSRATE 2009-A; University of Minnesota: Minneapolis, MN, 2009. (c) Frisch, M. J.; et al. Gaussian 09 D.01; Gaussian, Inc.: Wallingford, CT, 2009. (d) Neese, F. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2012, 2, 73. (e) See computational details in SI. (15) The slightly larger carbon tunneling effects were supported by the CVT, SCT, and DLPNO-CCSD(T)//M06-2X methods (Table S3). (16) (a) Dewar, M. J. S.; Merz, K. M., Jr.; Stewart, J. J. P. J. Chem. Soc., Chem. Commun. 1985, 166. (b) Dormans, G. J. M.; Buck, H. M. J. Am. Chem. Soc. 1986, 108, 3253. (c) Liu, Y.-P.; Lynch, G. C.; Truong, T. N.; Lu, D.; Truhlar, D. G.; Garrett, B. C. J. Am. Chem. Soc. 1993, 115, 2408. (d) Johnson, B. A.; Hu, Y.; Houk, K. N.; Garcia-Garibay, M. A. J. Am. Chem. Soc. 2001, 123, 6941. (17) (a) Singleton, D. A.; Schulmeier, B. E. J. Am. Chem. Soc. 1999, 121, 9313. (b) Singleton, D. A.; Szymanski, M. J. J. Am. Chem. Soc. 1999, 121, 9455. (c) Ussing, B. R.; Hang, C.; Singleton, D. A. J. Am. Chem. Soc. 2006, 128, 7594. (d) Kelly, K. K.; Hirschi, J. S.; Singleton, D. A. J. Am. Chem. Soc. 2009, 131, 8382 and ref 4b. (18) (a) Singleton, D. A.; Wang, Z. J. Am. Chem. Soc. 2005, 127, 6679. (b) Zipse, H.; Apaydin, G.; Houk, K. N. J. Am. Chem. Soc. 1995, 117, 8608. (c) Bekele, T.; Christian, C. F.; Lipton, M. A.; Singleton, D. A. J. Am. Chem. Soc. 2005, 127, 9216. (d) Ussing, B. R.; Hang, C.; Singleton, D. A. J. Am. Chem. Soc. 2006, 128, 7594. (e) Thomas, J. B.; Waas, J. R.; Harmata, M.; Singleton, D. A. J. Am. Chem. Soc. 2008, 130, 14544. (f) Gonzalez-James, O. M.; Kwan, E. E.; Singleton, D. A. J. Am. Chem. Soc. 2012, 134, 1914.

heavy-atom tunneling in chemical reactions in an electronically ground state are limited, but this study suggests some photoinduced reactions with reactive intermediates and narrow barriers can be a promising field to experimentally measure reactivity and KIE of the rare heavy-atom tunneling at relatively low temperature (∼200 K).

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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.7b07539. Computational details (PDF)

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AUTHOR INFORMATION

Corresponding Author

*[email protected] ORCID

Lung Wa Chung: 0000-0001-9460-7812 Author Contributions ‡

These authors contributed equally

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This paper is dedicated to Professor Yun-Dong Wu on the occasion of his 60th birthday. We sincerely thank Professor Weston T. Borden for an insightful suggestion on intramolecular KIE. We gratefully acknowledge the financial support from the NSFC (21373203 and 21672096), the Shenzhen Peacock Program (KQTD20150717103157174) and SUSTech.

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REFERENCES

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DOI: 10.1021/jacs.7b07539 J. Am. Chem. Soc. 2017, 139, 16438−16441