Computational Prediction of Excited-State Carbon Tunneling in the

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Computational Prediction of Excited-State Carbon Tunneling in the Two Steps of Triplet Zimmerman Di-#-Methane Rearrangement Xin Li, Tao Liao, and Lung Wa Chung J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.7b07539 • Publication Date (Web): 16 Oct 2017 Downloaded from http://pubs.acs.org on October 17, 2017

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Journal of the American Chemical Society

Computational Prediction of Excited-State Carbon Tunneling in the Two Steps of Triplet Zimmerman Di-π 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 Supporting Information Placeholder 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, DLPNOCCSD(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 12C/13C kinetic isotope effects (KIEs) were affected significantly by carbon tunneling and temperature. Our predictions of electronically excitedstate carbon tunneling and two consecutive carbon tunneling are unprecedented. Heavy-atom tunneling in some photoinduced reactions with reactive intermediates and narrow barriers can be potentially observed at relatively low temperature in experiments.

The 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 (∆R: ~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-atom (e.g., carbon) tunneling participated in some organic transformations such as automerization of cyclobutadiene, ring-expansion of methylcyclobutylfluorocarbene, ring-opening of cyclopropylcarbinyl radical, Bergman cyclization of an enediyne and allyla-

tion.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 GarciaGaribay.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., tunnelingcontrolled reactivity reported by Schreiner) in some studies.3-8,10 Scheme 1. The triplet di-π π-methane rearrangement of dibenzobarrelene (DBB)/barrelene/benzobarrelene to form dibenzosemibullvalene/semibullvalene/benzosemibullvalene products via intersystem crossing (ISC). For the rearrangement of DBB, the key distances of C9-C9a and C12-C9a computed by the M06-2X method are shown (in Å, taken from ref. 2a).

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 excited-state carbon tunneling as well as two consecutive carbon tunneling. The stationary points for the rearrangement of DBB, benzobarrelene and barrelene were first located at the UM06-2X/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

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high-level DLPNO-CCSD(T)/cc-pVTZ and DLPNOCCSD(T)/aug-cc-pVTZ methods using ORCA14d (Figure 1). The rate constants without quantum-mechanical 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 DLPNO-CCSD(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 ∆E = -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, as shown in Figure 1.

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ingly, 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 at 300 K, 2.72 at 200 K and 7203 at 100 K, and for the second step by a factor of 1.35 at 300 K, 2.04 at 200 K and 27.9 at 100 K (Table 1).15 Owing to the 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.

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

kCVT+SCT

100 K 200 K 300 K

4.68 × 10-9 1.75 × 102 6.74 × 105

3.37 × 10-5 4.78 × 102 1.01 × 106

100 K 200 K 300 K

-5

1.19 × 10 9.57 × 103 1.01 × 107

100 K 200 K 300 K

3.79 × 10-8 5.46 × 102 1.52 × 106

KIECVT

KIECVT+SCT

DBB

Figure 1. The PESs calculated by UM06-2X/6-31G(d), DLPNOCCSD(T)/cc-pVTZ (in parentheses), and DLPNO-CCSD(T)/augcc-pVTZ (in square brackets) for the triplet DPM rearrangement of DBB (A, black solid line), barrelene (B, red dashed line), and benzobarrelene (C, green dashed line). 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. Interest-

1.153 1.079 1.058

2.536 1.165 1.088

Barrelene 2.52 3.60 × 104 1.68 × 107

1.213 1.101 1.074

3.210 1.246 1.113

1.227 1.108 1.070

3.456 1.226 1.112

Benzobarrelene


1.41 × 10-3 1.68 × 103 2.38 × 106

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Also, excited-state carbon tunneling has a pronounced effect on the computed 12C/13C KIE for the first- and rate-determining-step in the rearrangement of DBB. For the case of substitution of 13C for 12C at C8a, C9a and C12 of DBB (Scheme 1 and Figure 3a), the computed 12C/13C KIEs with carbon tunneling are strongly dependent upon temperature. As shown in Table 1, the computed 12 13 C/ C KIE at 100/200 K is 1.153/1.079 (without tunneling) and 2.536/1.165 (with tunneling), while 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 (replacement of deuterium for hydrogen at C11 and C12, Figure S7).

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, significant and similar effects of the carbon tunneling on the reaction rates and 12C/13C KIE were also observed for benzobarrelene (Figures 2-3, and Table 1), suggesting larger tunneling for barrelene/benzobarrelene than DBB. Table 2. Computed intramolecular 13C KIEsa for the first and irreversible rearrangement step of DBB, barrelene, and benzobarrelene without and with tunneling at 100, 200 and 300 K. Temp

KIECVT

100 K 200 K 300 K

1.061 1.033 1.025

100 K 200 K 300 K

1.064 1.034 1.026

KIECVT+SCT

∆KIESCTb

%KIESCTc

0.634 0.048 0.017

91% 59% 40%

DBB 1.695 1.081 1.042 Barrelene 1.297 1.085 1.044

0.233 0.051 0.018

78% 60% 41%

0.269 0.054 0.021

82% 62% 49%

Benzobarrelene 100 K 200 K 300 K

1.060 1.033 1.022

1.329 1.087 1.043

a. Defined by the rate constant ratios of 13C for C11 and C12. b. KIECVT+SCT - KIESCT. c. ∆KIESCT/(KIECVT+SCT - 1) × 100%.

Figure 3. Arrhenius plots of the 12C/13C KIE for the ratedetermining step of the rearrangement of (a) DBB (the first step) and (b) barrelene and benzobarrelene (the second step) by the CVT, SCT and M06-2X methods. 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 non-linear 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 at 300 K, 3.61 at 200 K and 2792 at 100 K, and for the second step by 1.66 at 300 K, 3.76 at 200 K and 2.12 × 105 at 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 12C/13C KIE

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 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 increase in the KIE by carbon tunneling contributes to ~40-49 % at 300 K, ~59-62 % at 200 K, and ~78-91 % at 100 K of the total isotope effect. These results 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 S4S5).3-4 Namely, Singleton and coworkers 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 S5) in Claisen rearrangement,10a Shi epoxidation18a and decarboxylation reactions,18b as well as novel dynamical effect.17d,18c-18f In summary, our calculations predict that electronically excitedstate 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 (104276/35-67 %) 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



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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 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).

ASSOCIATED CONTENT Supporting Information Computational details, complete citation of ref. 14a-c, Table S1S5, Figures S1-S13, example of POLYRATE input file, rate constants at different temperatures, Cartesian coordinates and energies of all optimized structures. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author [email protected]

Author Contributions

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‡These authors contributed equally

Notes The authors declare no competing financial interests.

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

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Computational Prediction of Excited-State Carbon Tunneling in the

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