Theoretical Studies on Myers−Saito and Schmittel Cyclization

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J. Phys. Chem. A 2010, 114, 11807–11813

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Theoretical Studies on Myers-Saito and Schmittel Cyclization Mechanisms of Hepta-1,2,4-triene-6-yne Shogo Sakai* and Misaki Nishitani Department of Chemistry, Faculty of Engineering, Gifu UniVersity, Yanagido, Gifu 501-1193, Japan ReceiVed: June 25, 2010; ReVised Manuscript ReceiVed: September 7, 2010

The mechanisms of the Myers-Saito cyclization and the Schmittel cyclization of hepta-1,2,4-triene-6-yne are studied by ab initio multireference MO methods (CASSCF and MRMP2 methods). For the Myers-Saito cyclization, two transition states with Cs and C1 symmetries are located. The transition state with C1 symmetry is only 1.5 kcal/mol lower in energy than that with Cs symmetry at the MRMP2 calculation level. The obtained activation energy at the transition state with C1 symmetry and the reaction energy are 16.6 and 16.2 kcal/mol exothermic, respectively. For the Schmittel cyclization, two transition states with Cs and C1 symmetry are also obtained. The transition state with C1 symmetry is 7.9 kcal/mol lower in energy than that with Cs symmetry. The transition state with C1 symmetry for Schmittel cyclization is 6.7 kcal/mol higher in energy than that for the Myers-Saito cyclization. The reaction mechanisms are analyzed by a CiLC-IRC method. The interactions of orbitals for the Myers-Saito and Schmittel cyclizations can be distinguished. SCHEME 1

1. Introduction The ring closure reactions of some polyunsaturated systems, such as enediynes or enyne-allenes, known as Bergman,1-4 Myers-Saito,5-9 and Schmittel10-15 cyclizations, are of particular significance for medicinal and organic materials chemistry.16-22 Such, or structurally related, moieties lead to DNA-cleaving biradicals, which have application as potent antitumor drugs.23-26 Novel types of cyclization mechanisms involving biradical systems are the Myers-Saito and Schmittel reactions, as shown in Scheme 1. The potential energy profiles of these reactions have been studied by some groups. Engels and co-workers27 studied the regioselectivity of biradical cyclization of enyneallenes by the density functional method, B3LYP, and they also calculated the potential energies of the cyclization of (Z)-1,2,4heptatriene-6-yne at the CASSCF level.28 However, they probably did not use the energy gradient procedure for geometry optimization at the CASSCF calculation level, because the energies for some stationary points differ a little from our results. Therefore, it is considered that the obtained results lack some accuracy. Most of the calculations for the geometries of the cyclization performed by other groups29-33 used density functional levels. The products of both the Myers-Saito and the Schmittel reactions are diradicals, and the transition states are also included the diradical character. Multireference molecular orbital (MO) calculation levels are very important for reactions such as the Myers-Saito and/or the Schmittel cyclization. In particular, it is important that the estimation of the electronic states between the closed-shell singlet and the singlet diradical, which are the transition states of the Myers-Saito and the Schmittel cyclization, be treated by multireference MO methods. Therefore, in this study, the potential energies of the MyersSaito and the Schmittel cyclic reactions of (Z)-1,2,4-heptatriene6-yne are obtained by multireference MO levels. The reaction mechanisms were also analyzed by a CiLC-IRC method on the basis of a multireference MO method. * To whom correspondence should be addressed. E-mail: sakai@ gifu-u.ac.jp.

2. Computational Methods The stationary point geometries were obtained by the ab initio CASSCF method34 with a 6-31G(d) basis set35,36 using the GAUSSIAN03 program package.37 For the CASSCF calculations, 10 orbitals relating to all valence π and π* orbitals of reactant 1,2,4-heptatriene-6-yne were included. The selected 10 orbitals correspond to three π and π*, σ, σ*, and two radical orbitals of the products. All configurations in active spaces were generated. Frequency calculations were performed to determine the nature of each stationary point and also used for the zeropoint energy correction. Additional calculations were performed to obtain improved energy comparison calculations using CASSCF-optimized structures, with electron correlations incorporated through the multiconfigurational second-order perturbation theories MRMP2 method38 with the 6-31G(d) and 6-311+G(d,p) basis sets.39 The intrinsic reaction coordinate (IRC)40,41 was followed from the transition state toward both reactants and products. To interpret the mechanisms of reactions, a configuration interaction (CI)/localized molecular orbital (LMO)/CASSCF calculation along the IRC pathway (CiLC-IRC) was carried out with the 6-31G(d) basis set. The details of the CiLC-IRC used

10.1021/jp105860n  2010 American Chemical Society Published on Web 10/05/2010

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Figure 1. Stationary point geometries (in Angstroms and degrees) for the Myers-Saito cyclization of hepta-1,2,4-triene-6-yne at the CASSCF(10,10)/ 6-31G(d) level.

can be obtained from previous papers.42-44 The electronic structures of bonds on the basis of CiLC calculation were presented roughly as one singlet coupling term and two polarization terms. The representation using three terms for one bond has been successful to explain the bond formation and bond extinction along a chemical reaction path on the ground state45-50 and the excited state.51

Figure 2. Potential energy diagram of the Myers-Saito cyclization of hepta-1,2,4-triene-6-yne. The units are kcal mol-1. The values in parentheses included the zero-point correction.

The calculations of the CiLC-IRC analysis and the MRMP2 calculations were performed using the GAMESS program package.52,53 3. Results and Discussion 3.1. Myers-Saito Reactions. The stationary point geometries of the six-membered ring cyclization with C2-C7 bond formation reaction of hepta-1,2,4-triene-6-yne are shown in Figure 1. The potential energy surfaces along the reaction pathways of the C2-C7 cyclic reaction are also shown in Figure 2. For the geometry of the reactant, the point of interest is the dihedral angle (24.7°) of C2-C3-C4-C5, because the angle relates closely to the transition state (TS-2) with C1 symmetry. Although the reactant structure with Cs symmetry is not a stable one, having one negative eigenvalue for the force-constant matrix, the energy difference between the reactant structures with Cs and C1 symmetries is extremely small (0.04 kcal/mol) at the CASSCF level. Two transition states for the cyclic reaction were located and have Cs and C1 symmetries. The transition

state (TS-2) with C1 symmetry is only 0.2 kcal/mol using the CASSCF method and 1.5 kcal/mol with the MRMP2 level, lower in energy than the transition state (TS-1) with Cs symmetry. Both transition states are real transition states with one negative eigenvalue for the force-constant matrix. Although the difference between the energy barriers of both transition states is extremely small, the electronic states of the transition states are different. As shown in the geometry of TS-2 (C1-C2 and C2-C3 bond distances), C1-C2-C3 denotes the allyl resonance state. The interaction orbitals of the C2-C7 bond formation at TS-1 are the side π orbitals of C2 and C7 atoms. The transition state of TS-2 relates to the Reactant and Product-1 along the IRC pathway. TS-1 relates to the reactant with Cs symmetry and the product with Cs symmetry which are not real minimal stationary points. The product (not shown here) corresponding to TS-1 has the perpendicular structure for the six cyclic ring and C1H2 plane and is about 12 kcal/mol higher in energy than Product-1 at the CASSCF level. Therefore, a

Cyclization Mechanisms of Hepta-1,2,4-triene-6-yne bifurcation occurs along the IRC pathway connecting TS-1 with Reactant and Product-1. The reaction energy from the reactant to Product-1 is exothermic by 16.2 kcal/mol at our best calculation (MRMP2/6-311+G(d,p)). This energy is in very good agreement with the experimental value5-8 of about 15 kcal/ mol. The reaction barrier is 16.6 kcal/mol according to our best calculation level, and the experimental estimation5,6 is about 22 kcal/mol. Thus, although the reaction energy at our calculation level indicates good agreement with the experimental value, the activation energy at out calculation level is about 6 kcal/mol lower than the experimental estimation. For previous calculations,27-33 density functional methods estimated the reaction energy from -2.11 to -17.01 kcal/mol and the activation energy from 17.7 to 24.71 kcal/mol. For the coupled cluster (U)CCSD level, the reaction energy was estimated from -15.1 to -16.1 kcal/mol and the activation energy was estimated from 27.0 to 28.1 kcal/mol. For inclusion of triplet excitation, (U)CCSD(T) level, the reaction energy was estimated from -11.9 to -14.11 kcal/mol and the activation energy was estimated from 21.8 to 22.3 kcal/mol. Although the coupled cluster level calculations did not show the basis set dependency, density functional methods showed large basis set dependency. For the coupled cluster level calculations, the difference in the estimation energies by inclusion and noninclusion of triplet excitation is only from 2 to 3 kcal/mol for the reaction energy but ranges from 5 to 6 kcal/mol for the activation energy. This reflects the defect of the estimation using the unrestricted method for the midrange between the singlet coupling electronic state and the diradical state. Our calculation estimated these energies at a reasonable level on the basis of multireference. In fact, the occupation numbers of two natural orbitals for Product-1 are 1.00 and 1.00, and those for TS-2 are 1.74 and 0.26. The occupation numbers of the natural orbitals indicate that Product-1 is a diradical state and TS-2 is a intermediate between a singlet closed shell state and a diradical state. Although the relative energies at the MRMP2 calculation are more than 10 kcal/mol lower than those at the CASSCF, this is normal for pericyclic reactions. Therefore, we propose a minimum activation energy of less than 20 kcal/mol. To observe the change of orbital interactions along the reaction pathway, the CiLC analysis is performed for the sixmembered cyclic reaction. The variation of the weights of configurations by the CiLC analysis along the IRC pathway is drawn in Figure 3, and some configurations are depicted in Figure 4. Configuration 1 is the reference state and does not affect bond formation and/or bond extinction. The configurations (2, 5, 7, and 8) correspond to the singlet coupling terms of bonds of 7-8 (side π-side π), 9-10 (side π-side π), 5-6 (vertical π), and 1-2 (vertical π) orbitals, respectively. The weights of the configurations (2, 5, 7, and 8) decrease from the reactant side to the product side along the IRC pathway. Configuration 9 corresponds to the singlet coupling term for the bond of 3-4 orbitals and does not decrease much from the reactant side to the product side. The variation of the weight of configuration 9 corresponds to the bond length between the C4 atom and the C5 atom. For the cyclic reaction, the important interactions are those of 1-6 orbitals (vertical π-vertical π), 1-7 orbitals (vertical π-side π), 9-6 orbitals (side π-vertical π), and 9-7 (side π-side π). For the bond formations of the C2 and C7 atoms, the weights of six configurations (13, 14, 15, 16, 17, and 18) are increasing from the reactant side to the product side through the transition state. The set of configurations (18, 13, and 14) consists of the singlet coupling term and polarization terms for the bond of

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orbitals 7 and 9 (side π), respectively. The set of configurations (17, 15, and 16) consists of the singlet coupling term and polarization terms for the bond of orbitals 1 and 6 (vertical π), respectively. Namely, for the Myers-Saito reaction, the bond is formed from the interactions of the side π-side π orbitals and the vertical π-vertical π orbitals. 3.2. Schmittel Reactions. The stationary point geometries of the five-membered ring formation (the Schmittel reaction) of hepta-1,2,4-triene-6-yne are shown in Figure 5. The potential energy profile is shown in Figure 6. We obtained two transition states for the five-membered ring cyclization; one (TS-3) has Cs symmetry, and the other (TS-4) has C1 symmetry. Both transition states have one negative eigenvalue for the forceconstant matrix, which is a real transition state for formation of a five-membered ring unit. Both transition states are a cis type for the H-C7-C6-C2 dihedral angle, and a transition state with a trans type was not located because of the direction of the active orbital of the C6 atom; in other words, the active π orbital of C6-C7 changes to two p orbitals (similar to sp2 type), which are a trans type for each other. This is very important for the substitution effect of the reaction mechanisms of a concerted and/or stepwise process for the ene reaction attendant on C2-C6 cyclization of enyne-allenes with alkane. TS-4 is about 8 kcal/mol lower in energy than TS-3 at the MRMP2 calculation level. TS-3 is the typical interaction between the side π orbitals for the skeleton structure from the comparison of the dihedral angles of H-C1-C2-C3 of TS-3 and TS-4. The transition state, TS-4, includes probably the interaction between the side π and the vertical π orbitals for both the allene and the ethynyl parts. The difference of the electronic states of both

Figure 3. Weights of configurations by CiLC calculation along the IRC pathway of the Myers-Saito cyclization of hepta-1,2,4-triene-6yne. The units are bohr amu1/2.

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Figure 4. Selected electronic configurations of the Myers-Saito cyclization of hepta-1,2,4-triene-6-yne.

transition states is similar to that of TS-1 and TS-2 for the Myers-Saito reactions. From the bond distance of C2-C6, TS-3 is a later transition state and TS-4 is an early transition state. The transition state TS-3 leads to Product-2′ (not shown here). The geometry of Product-2′ is similar to Product-2 except for the methylene radical group (C1H2) perpendicular to the fivemembered ring. Product-2′ has one negative eigenvalue corresponding to rotation of the methylene group (C1H2) for the forceconstant matrix and is about 12 kcal/mol higher in energy than Product-2 at the CASSCF level. Accordingly, a bifurcation occurs also along the IRC path connecting TS-3. The transition state TS-4 leads to Product-2 along the IRC pathway. The reaction of this step is about 10 kcal/mol endothermic and corresponds to other computational values. The activation energy barrier is 23.3 kcal/mol at the MRMP2 level and lower than other previous computational results. The difference between our values and others, such as density functional methods and coupled cluster methods, comes from the poor estimation by single-reference methods for the midrange between the diradical and coupled singlet character. This can be seen in the occupation numbers of the natural orbitals for our CASSCF calculations. The occupation numbers of two natural orbitals for Product-2 are 1.00 and 1.00 and indicate the diradical state. For TS-4, the occupation numbers corresponding to the above natural orbitals are 1.65 and 0.35 and indicate the intermediate state between a diradical and a singlet closed shell. For the comparison of the energy barriers of the Schmittel cyclization and the Myers-Saito

cyclization, the difference is about 7 kcal/mol and smaller than other estimations. For the isomerization from Product-2 to Product-3, the reaction is the inversion of the radical orbital of the C7 atom, and the inversion energy of H-C7-C6 is only 4.8 kcal/mol at the MRMP2 calculation level. Product-3 is 1.1 kcal/mol higher in energy than Product-2. The difference between Product-2 and Product-3 is the direction of the radical orbital of the C7 atom. To explain the orbital interactions between C2 and C6 atoms, reaction of the five-membered ring formation (the Schmittel reaction) was analyzed by the CiLC-IRC method. The variations of the weights of the configurations along the IRC pathway are shown in Figure 7, and some of the corresponding configurations are depicted in Figure 8. As shown in the previous reaction, the important interactions of orbitals for the cyclic reaction are those of four orbitals (two vertical π and two side π) in atoms of C2 and C6. With respect to the four orbitals of 2, 6, 7, and 10 in atoms of C2 and C6, the configurations of 15, 16, 17, and 18 relate closely to bond formation of C2-C6. The four configurations denote two sets of polarization interactions between orbitals (2 and 7) and (6 and 10). This means that bond formation of C2-C6 occurs through the orbital interactions between the vertical π and side π orbitals and not through those between the vertical π and vertical π or the side π and side π orbitals. The sets of orbital interactions for five-membered ring cyclization are different from those for the six-membered ring cyclization, as discussed in the previous section.

Cyclization Mechanisms of Hepta-1,2,4-triene-6-yne

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Figure 5. Stationary point geometries (in Angstroms and degrees) for the Schmittel cyclization of hepta-1,2,4-triene-6-yne at the CASSCF(10,10)/ 6-31G(d) level.

4. Conclusions The reaction mechanisms of six-membered cyclization (the Myers-Saito reaction) and five-membered cyclization (the Schmittel reaction) of hepta-1,2,4-triene-6-yne were studied by ab initio multireference MO methods. For the six-membered cyclization, we estimated the energy barrier of about 17 kcal/mol and reaction energy of 16 kcal/ mol exothermic at the MRMP2 level. Although our obtained reaction energy is in very good agreement with the experimental estimation of 15 kcal/mol, the obtained activation energy is lower than the experimental estimation of 22 kcal/mol. We propose a minimum activation energy of less than 20 kcal/mol. The mechanisms of the six-membered ring formation were analyzed using the CiLC method. From the variation of the

Figure 6. Potential energy diagram of the Schmittel cyclization of hepta-1,2,4-triene-6-yne. The units are kcal mol-1. The values in parentheses included the zero-point correction.

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Figure 7. Weights of configurations by CiLC calculation along the IRC pathway of the Schmittel cyclization of hepta-1,2,4-triene-6-yne. The units are bohr amu1/2.

Figure 8. Selected electronic configurations of the Schmittel cyclization of hepta-1,2,4-triene-6-yne.

Cyclization Mechanisms of Hepta-1,2,4-triene-6-yne weights of configurations along the IRC, C2-C7 bond formation occurs through the orbital interactions of the vertical π-vertical π and side π-side π. For the Schmittel reaction of the five-membered ring formation, the activation energy of 23 kcal/mol and reaction energy of 10 kcal/mol were estimated at the MRMP2 calculation level. Although the obtained reaction energy is in agreement with the previous estimation, the activation energy is lower than that in the previous calculations. The disparity in the activation energies of our calculations and the previous calculations as the density functional and the coupled cluster methods probably arises from the defect of the estimation of the electronic states by the unrestricted methods for the midrange between the singlet coupling electronic state and the diradical state. The mechanisms of the five-membered ring formation of the Schmittel reaction were also analyzed by the CiLC method. C2-C6 bond formation occurs through the orbital interactions of the vertical π-side π. The type of the orbital interactions is different from that of the Myers-Saito cyclization. Acknowledgment. This research was supported by a Grantin-Aid for Scientific Research on Priority Areas (No. 20038020) from the Ministry of Education, Science and Culture of Japan. Computer time was made available by the Computer Center of the Institute for Molecular Science. References and Notes (1) Jones, R. R.; Bergman, R. G. J. Am. Chem. Soc. 1972, 94, 660– 661. (2) Bergman, R. G. Acc. Chem. Res. 1973, 6, 25–31. (3) Darby, N.; Kim, C. U.; Salau¨n, J. A.; Shelton, K. W.; Takada, S.; Masamune, S. Chem. Commun. 1971, 1516–1517. (4) Wong, H. N. C.; Sondheimer, F. Tetrahedron Lett. 1980, 21, 217– 220. (5) Myers, A. G.; Kuo, E. Y.; Finney, N. S. J. Am. Chem. Soc. 1989, 111, 8057–8059. (6) Myers., A. G.; Dragovich, P. S.; Kuo, E. Y. J. Am. Chem. Soc. 1992, 114, 9369. (7) Nagata, R.; Yamanaka, H.; Okazaki, E.; Saito, I. Tetrahedron Lett. 1989, 30, 4995. (8) Nagata, R.; Hidenori, Y.; Murahashi, E.; Saito, I. Tetrahedron Lett. 1990, 31, 2907. (9) Myers, A. G.; Dragovich, P. S. J. Am. Chem. Soc. 1989, 111, 9130. (10) Schmittel, M.; Strittmatter, M.; Kiau, S. Tetrahedron Lett. 1995, 36, 4975. (11) Schmittel, M.; Kiau, S.; Siebert, T.; Strittmatter, M. Tetrahedron Lett. 1996, 37, 7691. (12) Schmittel, M.; Strittmatter, M.; Kiau, S. Angew. Chem. 2996, 108, 1952. (13) Schmittel, M.; Keller, M.; Kiau, S.; Strittmatter, M. Chem.sEur. J. 1997, 3, 807. (14) Gillmann, T.; Hu¨lsen, T.; Massa, W.; Wocadlo, S. Synlett 1995, 1257. (15) Garcia, J. G.; Ramos, B.; Pratt, L. M.; Rodriguez, A. Tetrahedron Lett. 1995, 36, 7391. (16) Maier, M. E. Synlett 1995, 13. (17) Nicolaou, K. C.; Dai, W. M. Angew. Chem. 1991, 103, 1453. (18) Nicolaou, K. C.; Smith, A. L.; Wendeborn, S. V.; Hwang, C. K. J. Am. Chem. Soc. 1991, 113, 3106. (19) Nicolaou, K. Chem. Ber. 1994, 33. (20) Smith, A. L.; Nicolaou, K. C. J. Med. Chem. 1996, 39, 2103.

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