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Role of Heavy Atom Tunneling in Myers−Saito Cyclization of Cyclic Enyne-Cumulene Systems Sharmistha Karmakar and Ayan Datta* Department of Spectroscopy, Indian Association for the Cultivation of Science, 2A and 2B Raja S. C. Mullick Road, Jadavpur − 700032, Kolkata, West Bengal, India S Supporting Information *

ABSTRACT: Direct dynamics calculation using canonical variational transtition state theory (CVT) inclusive of small curvature tunneling (SCT) reveals heavy atom tunneling in Myers− Saito cyclization of 10- and 9-membered cyclic enyne−cumulene systems like 1,6didehydro[10]annulene and derivative of neocarzinostatin, respectively. The pure density functional theory functional, BLYP at a 6-31+G (d,p) basis set reproduce the observed reaction energies and barriers within 1.0 kcal/mol. The calculated rate constants of cyclization inclusive of heavy atom tunneling (kCVT+SCT = 3.26 × 10−4 s−1 at 222 K; t1/2 = 35 min) are in excellent agreement with experiments (t1/2 ∼ 21−31 min). Both primary and secondary kinetic isotope effect (KIE) become enhanced significantly upon inclusion of quantum mechanical tunneling. An Arrhenius plot of KIE shows measurable curvature at the experimental temperature of 222 K. The translation vector for the cyclization reactions in the transition-states (TS) show significant motion of primary and secondary carbon atoms explaining the origin of large KIE.

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INTRODUCTION Quantum mechanical tunneling (QMT) is being realized as a key factor in many chemical1−7 and biological8−10 transformations. Many H atoms mediated reactions are expected to involve QMT effects;11−15 examples of reactions governing by heavy atom tunneling are comparatively rare. The automerisation of cyclobutadiene is known to involve carbon atom tunneling.16−18 Other important reactions where carbon atom tunneling has been documented are ring closure of cyclopentane-1,3-diyl and cyclobutane-1,3-diyl,19−21 rearrangement of cyclopropylcarbenes,22 ring opening of the cyclopropylcarbinyl radical,23,24 rearrangement of semibullvalene,25 Bergman cyclization of a 10-membered-ring enediyne,26 and ring expansion of noradamantyl carbenes and their analogs.27 A salient feature of the mentioned list of reactions is a rather low reaction barrier accompanied by a small displacement of carbon atoms from reactant to product. Recently, Doubleday and co-workers have predicted strong signatures of heavy atom tunneling in the Bergman cyclization of a cyclic 10-membered ene−diyne moiety, (3Z)-cyclodec-3en-1,5-diyne.26 Many anticancer antibiotics such as esperamicin,28 calicheamicin,29,30 dynemicin31 and other related compounds possess a common structural motif, namely, an ene−diyne fragment within a ring that converts to an aromatic diradical via Bergman cyclization.32 These benzenoid type diradicals are known to abstract hydrogen atoms from sugar phosphate backbone of DNA leading to DNA strand cleavage.33,34 Another similar class of antitumor antibiotics neocarzinostatin (NCS)35 contains a diene-diyne moiety as an active chromophore.36 NCS chromophore is known to rearrange by thiol activation to a 9-membered cyclic (Z)enyne−cumulene 5a (Scheme 1) that then follows the © XXXX American Chemical Society

Scheme 1. Myers−Saito Cyclization for 1a and 3a

cyclization pathway.37 The 9- and 10-membered cyclic enyne−cumulene38−41 systems, derivative of NCS(3a) and 1,6-didehydro[10]annulene (1a) respectively, follow the similar reactivity pattern like enyne−allene42 and undergo Myers− Saito (MS) cyclization to generate highly reactive biradical accounting for its cytotoxics behavior.43−46 An understanding of the role of heavy atom tunneling in Myers−Saito cyclization for 1a and 3a would therefore shed light on NCS-based antitumor agents. Received: December 21, 2015 Revised: January 15, 2016

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DOI: 10.1021/acs.jpcb.5b12465 J. Phys. Chem. B XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry B

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COMPUTATIONAL DETAILS It is computationally challenging to study MS reaction because a closed shell reactant transforms to a trans-biradical product along the reaction coordinate. Biradical systems with small S-T gap can lead to significant configurational mixing. Hence, multireference techniques with dynamic correlation, such as CASPT2 (CASSCF method with inclusion of second order perturbation) and multireference configuration interaction (MRCI) methods should be ideal to handle them.47 However, these methods are known to suffer from systematic errors with respect to the active space dimension.48 Other ab initio method involving coupled cluster methods, such as CCSD(T)49 are computationally intractable for direct dynamics calculations. Though the hybrid density functional theory (DFT) functionals are known to overestimate the barrier height,50,51 the pure DFT functional BLYP gives excellent agreement with experiment.52 Schreiner and co-workers have studied Myers−Saito and Schmittel cyclization for a series of parent enyen−allene sytems and described BLYP level of theory as a reasonable choice for these purpose.42 We also calibrated various functionals including empirically corrected dispersion methods and BLYP indeed appears to be most suitable to describe the experimental energy barriers (see Table 1) for the MS reactions.

RESULT AND DISCUSSION 1. Suitability of BLYP Functional. To get accurate tunneling correction and rate constants it is necessary to describe the molecular potential energy surface properly. Hence, it is important to verify the performance of pure BLYP DFT functional with other dispersion corrected functional. To check the performance of pure DFT functional BLYP in describing the molecular potential energy surface, we have performed additional single point calculation on BLYP geometries at B97D3 and BLYPD3 level using 6-31+G(d,p) basis set. Table 1 lists the barrier height at different levels for the reaction 1a → 2a and 3a → 4a. The BLYP functional results show close agreement with experimental results; hence, all further calculations, namely, the tunneling calculations, were performed at BLYP/6-31+G(d,p) level. 2. Myers−Saito versus Schmittel Cyclization. Scheme 1 represents the MS cyclization for 10- and 9-membered enyne− cumulene ring systems; 1a and 3a.They undergo C3−C8 cyclization generating trans (σ−σ) biradical that eventually abstracts hydrogen atom from sugar phosphate backbone of DNA. Another alternative mode of cyclization, namely, Schmittel cyclization,65 was computationally proposed by Engels et al. for some model enyne−cumulene systems where five-membered ring cyclization occurs between C3−C7 centers leading to syn biradical product.66 Although Schmittel cyclization is very well-known for enyne−allene system, there is no experimental evidence for this C3−C7 cyclization in case of enyne−cumulene systems. Any attempt to locate the corresponding TS at BLYP level of theory reverts back to the initial reactant. Hence, we proceed with MS cyclization as the only mode of action for these NCS-based chromophores. Table 2 represents the reaction energy and activation energy at 298 K for 1a and 3a. For both the cases, the reactions are

Table 1. Enthalpy of Activation and Free Energy of Activation (at 298.15 K) in kcal/mol Calculated with Different Functional Using 6-31+G(d,p) Basis Set for 1a and 3aa density functional BLYP B97D3//BLYP BLYPD3//BLYP

1a 3a 1a 3a 1a 3a

→ → → → → →

2a 4a 2a 4a 2a 4a

ΔH‡

ΔG‡ (expt)

16.1 16.8 14.2 15.9 17.0 17.5

17.3(16.3 ± 0.1) 17.9(18.0 ± 0.1) 15.3 16.9 18.1 18.6

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Table 2. Enthalpy of Activation, Free Energy of Activation, and the Associated Reaction Energies (at 298.15 K) in kcal/ mol Calculated at BLYP/6-31+G (d,p) Level for 1a and 3aa

a

Corresponding experimental values are also mentioned in parentheses.

1a → 2a 3a → 4a

Therefore, pure DFT functional BLYP53−55 along with 631+G(d,p)56 basis set was employed for the estimation of reaction energies, barrier height, and direct dynamics calculations for MS reaction of the studied systems. The classical rate constants were computed using canonical variational transition state theory (CVT).57 All the calculations were performed for the singlet energy surface. Quantum effects on the reaction dynamics were incorporated, using the small curvature tunneling (SCT) approximation.58,59 All electronic structure calculations were performed with Gaussian09.60 Direct dynamics calculations were carried out with GAUSSRATE61 as the interface between Gaussian 09 and POLYRATE.62 Intrinsic reaction coordinate (IRC) calculations were performed to verify that the transition states are connected to the corresponding reactant and product. Harmonic approximation was used to determine vibrational levels of the reactant state for quantized reactant state tunneling (QRST) calculations.63 The reorientation of the dividing surface (RODS) algorithm has been applied to get accurate VaG (vibrational ground-state adiabatic potential energy) surfaces.64

ΔH

ΔG

ΔH‡

ΔG‡ (expt)

9.1 8.0

10.9 9.3

16.1 16.8

17.3(16.3 ± 0.1) 17.9(18.0 ± 0.1)

a

Corresponding experimental values are also mentioned in parentheses. The experimental temperatures for 1a and 3a are 222 and 235 K, respectively.

found to be endergonic by 9−10 kcal/mol. The free energy of activation for the compounds 1a and 3a matches well with experiment (within ∼1 kcal/mol).41 For endergonic reaction, a particle can tunnel only if it has vibrational adiabatic ground-state energy equal or greater than product valley. Hence, tunneling correction at low temperature for endergonic reaction can be erroneous. Hence, we have calculated the rate with and without tunneling at the exergonic direction, that is, 2a → 1a, then scaled them by a factor of exp(−ΔVad/kBT)67 where ΔVad represents the difference in ground-state vibrational adiabatic energy between product and reactant side, kB is the Boltzmann constant, and T symbolizes temperature. 3. Role of QMT in MS Cyclization for 9- and 10Membered Enyne−Cumulene Systems. Table 3 lists the kCVT, kCVT+SCT rate constants, and tunneling transmission coefficient (κSCT) for 1a and 3a at different temperatures (T = 150, 200, and 298 K). The rate of cyclization for 3a with and B

DOI: 10.1021/acs.jpcb.5b12465 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B Table 3. CVT, CVT+SCT Rate Constants, and Tunneling Transmission Coefficient (κSCT) Calculated at BLYP/631+G (d,p) Level for 1a and 3a at 150, 200, and 298 Ka T(K) 1a→2a

3a→4a

a

150 200 298 150 200 298

CVT 2.34 3.59 1.97 2.39 2.57 1.69

× 10−12 × 10−6 × 10−13 × 10−7

CVT+SCT 4.17 4.93 2.52 4.43 3.72 1.95

× 10−12 × 10−6 × 10−13 × 10−7

κSCT 1.8 1.4 1.2 1.9 1.4 1.2

The rate constants, k, are reported in s−1.

without inclusion of tunneling is lower than 1a because of large activation energy. At low temperature (∼100 K), the contribution from heavy atom tunneling is significant, resulting a 5−10 times rate enhancement in both the cases, which gradually decreases with an increase in temperature. Despite the higher barrier, κSCT for 3a is greater than 1a at low temperature and they eventually become similar for T ≥ 200 K. A comparison of barrier height and width for 1a → 2a and 3a → 4a is worthwhile. The free energy of activation for 3a lies 0.6 kcal/mol above than that of 1a. The average change in C3−C8 distance on traversing from reactant to TS is 1.26 Å for 1a and 1.14 Å for 3a. Hence the barrier width for 3a → 4a is narrower by ∼0.12 Å. The variation of tunneling probability (T) with the barrier height (V0), width (w) and the mass of moving particle (m) can be approximately written as T ∼ e−w V0m .1 Hence, an alteration of barrier width affects the tunneling probability more in comparison to a similar change in barrier height. As a result, the contribution from QMT is more in 3a for which the barrier is larger yet narrower. With the increase in temperature, a larger contribution of thermal activation makes the κSCT factors similar for both of the systems. Inclusion of tunneling enhances the classical rate by a factor 1.32 for 1a, giving kCVT+SCT = 3.26 × 10−4 s−1 at 222 K. At reaction temperature, the activation energy (Ea) and the preexponential factor (A) are Ea= 17.1 kcal/mol and log A = 13.3 s−1 at CVT level, and Ea = 16.8 kcal/mol and log A= 13.0 s−1 at CVT+SCT level. QMT increases the rate of cyclization by lowering the effective barrier height. The representative tunneling energy (RTE) lies ∼0.14 kcal/mol below the maxima of the VaG surface at 222 K. This is indicative of QMT from thermally activated states rather than the lowest vibrational level (v = 0).68 The half live (t1/2) of transformation was calculated to be 45 and 35 min at CVT and CVT+SCT level, respectively, at 222 K. The experimental t1/2 lies in the range 21−31 min.41 Hence, the t1/2 calculated at CVT+SCT level shows a better agreement with the experimental result, which is also evident from the Arrhenius plot of 1a. Figure 1 shows the CVT+SCT Arrhenius plots for the transformation 1a→ 2a in the temperature range 150−300 K along with the experimentally measured rate. A similar rate enhancement was also predicted for 3a resulting in kCVT = 2.56 × 10−5 s−1 and kCVT+SCT = 3.36 × 10−5 s−1 at 235 K. The calculated t1/2 for this reaction was 7.5 and 5.7 h at CVT and CVT+SCT level, respectively, while the experimental t1/2 value was found to be ∼2 h at 235 K.38−40 It is important to mention that even though the CVT+SCT t1/2 is in relatively better agreement with the experimental rate constant, the difference in their absolute magnitude probably arises due to structural modification in our computational model compared to the experimental structure (Scheme 1).

Figure 1. Arrhenius plot of the CVT+SCT rate constants for 1a from 150 to 300 K.

4. Kinetic Isotope Effect (KIE) Study on 1a. Substitution of 12C by its heavier analog 13C is expected to reduce tunneling. Therefore, a ratio of rates involving 12C and 13C, that is, k12C/ k13C (KIE) should magnify the tunneling effects of 12C with respect to 13C. For light atom mediated reactions like hydrogen atom migration, the tunneling probability is majorly governed by the movement of the light atom along the reaction coordinate. However, for reactions where the movement of the heavy atom takes part, the tunneling probability depends strongly on the motion of different parts of the reacting system participating in the transition state imaginary mode. Hence a detailed KIE study has been carried out where both the carbon atom C-2 and C-3 has been substituted by 13C. Replacement of 12 C-3, 12C-2, and 12C-2 + 12C-3 by 13C leads to primary (1°), secondary (2°), and both (1° + 2°) KIE, respectively. Table 4 lists the KIE values for 1a → 2a transformation at different temperatures. Table 4. 1°, 2°, and 1° + 2° KIE for 1a at Three Different Temperatures; T = 200, 220, and 298 K 1a→2a primary (1°)

secondary (2°)

both (1° + 2°)

T (K)

CVT

CVT+SCT

CVT

CVT+SCT

CVT

CVT+SCT

200 220 298

1.027 1.024 1.017

1.109 1.099 1.085

1.006 1.005 1.003

1.035 1.033 1.025

1.034 1.030 1.020

1.148 1.135 1.109

As can be seen from Table 4, the computed KIE at CVT +SCT level are larger than CVT KIE. Though both CVT and CVT+ SCT KIE decreases with increase in temperature, the variation in CVT KIE is small while the CVT+SCT KIE value shows appreciable decrease with temperature. For 1a → 2a, the PKIE at CVT level is 1.024, which enhances significantly upon inclusion of tunneling to 1.099 at 222 K. The difference in activation energy, Ea (1a′ → 2a′) − Ea (1a → 2a), is 24.3 cal/ mol at CVT level and 41.3 cal/mol at CVT+SCT level, respectively, at 222 K. The κSCT factor is 1.22 for 13C (1a′ → 2a′) and 1.32 for 12C (1a → 2a) at the same temperature. Hence, thermally activated tunneling by the lighter isotope is C

DOI: 10.1021/acs.jpcb.5b12465 J. Phys. Chem. B XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry B

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facilitated by not only mass effect but also by a decrease in activation energy, resulting higher KIE value at CVT+SCT level. The 2° KIE is nominal at CVT level that increases modestly with inclusion of tunneling. At 222 K, the 2° KIE for 1a is 1.005 at CVT level and 1.033 at CVT+SCT level. Although the primary carbon atom (C-3) moves by the maximum extent during the bond formation, the secondary carbon atom (C-2) also involves significant displacement along the reaction coordinate. It leads to non-negligible SKIE at CVT+SCT level.69 This is verified by animating the translational vectors of TS structure for 1a → 2a, which shows contribution from C2 as well (see Supporting Information). Substitution of both primary and secondary carbon atom by 13C gives the CVT +SCT (1° + 2°) KIE = 1.134, which is approximately 9% greater than its classical value, T = 222 K. An Arrhenius plot of ln KIE versus 1/T for 1a (Figure 2) shows appreciable curvature in the CVT+SCT curve that can clearly be seen for T = 160−200 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/acs.jpcb.5b12465. Optimized geometries, energies, thermal corrections, and harmonic frequencies for 1a−4a and the transition structure connecting them, CVT and CVT+SCT rate constants from 100 to 300 K, image of imaginary mode translational vector of TS connecting 1a and 2a, plot of VaG and VMEP surfaces for 1a and 3a and the complete lists of authors for refs 60 and 62. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS S.K. thanks CSIR India for SRF. A.D. thanks DST, INSA, and BRNS for partial funding. We thank Professor A. Fernandez Ramos for discussion on calculation of CVT+SCT rates for endothermic reactions.

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REFERENCES

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Figure 2. Arrhenius plots of CVT and CVT+SCT KIE for 1a from 100 to 300 K.

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SUMMARY In summary, calculations inclusive of small curvature tunneling reveal the role of QMT in the Myers−Saito cyclization for cyclic enyne−cumulene systems. Compared to 1a the effect of QMT is pronounced for 3a at low temperature for which the reaction passes through a narrower yet larger barrier. For both 1a and 3a, the calculated t1/2 at CVT+SCT level shows better agreement with experiments. Incorporation of tunneling enhances the KIE significantly and is shown to magnify the importance of QMT. QMT also leads to a significant curvature in Arrhenius plot of 12C/13C KIE at temperatures much higher than the cryogenic limit. Clearly, examples of heavy atom tunneling need not always be to confined to cryogenic temperatures and for small molecules. The present case shows that tunneling indeed can be relevant as well as observable at ambient conditions for important chemical transformations beyond just academic interests. D

DOI: 10.1021/acs.jpcb.5b12465 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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NOTE ADDED AFTER ASAP PUBLICATION This paper was published ASAP on January 28, 2016. The abstract was updated. The revised paper was reposted on January 29, 2016. F

DOI: 10.1021/acs.jpcb.5b12465 J. Phys. Chem. B XXXX, XXX, XXX−XXX