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Prediction of ring formation efficiency via diene ring closing metathesis (RCM) reactions using the M06 density functional
Chemical Physics Letters 476 (2009) 37–40
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Prediction of ring formation efficiency via diene ring closing metathesis (RCM) reactions using the M06 density functional Shanthi Pandian a, Ian H. Hillier a,*, Mark A. Vincent a, Neil A. Burton a, Ian W. Ashworth b, David J. Nelson c, Jonathan M. Percy c,*, Giuseppe Rinaudo c a
School of Chemistry, University of Manchester, Manchester, M13 9PL, UK AstraZeneca Process R&D, Silk Road Business Park, Charter Way, Macclesfield, SK10 2NA, UK c WestCHEM Department of Pure and Applied Chemistry, 295 Cathedral Street, Glasgow G1 1XL, UK b
a r t i c l e
i n f o
Article history: Received 28 April 2009 In final form 5 June 2009 Available online 9 June 2009
a b s t r a c t Using density functional theory employing the M06 functional, we predict the reaction path energetics of ring formation via diene ring closing metathesis (RCM) reactions, and thence the effective molarity (EM) for the formation of cyclohexene, which is in good accord with the experimental lower limit which we report here. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction The importance of alkene metathesis reactions has grown spectacularly since well defined and air stable catalysts 1 and 2 (Fig. 1) became commercially available [1]. The closure of highly-functionalised carbocycles and heterocycles of a wide range of sizes can be achieved under mild conditions, and many groups have executed elegant syntheses of complex natural products based on ring closing metathesis (RCM) strategies. While a number of groups have studied the fundamental mechanism of alkene metathesis, characterising the organometallic intermediates in the reaction sequence for simple prototypical reactions (and others have explored stereochemical preferences in more complex systems [2]) using electronic structure calculations, synthetic practice has far exceeded our understanding of the interplay of structure and reactivity in the reaction. The mechanism used most commonly to describe RCM of the prototypical a,x-dienes to afford the corresponding Z-cycloalkenes is shown in Fig. 2. Ruthenium methylidene (3) cross metathesis with the diene affords volatile ethene and a new metal alkylidene (A) which can begin cyclisation via a cyclic g2-complex (B), progressing to a bicyclic metallocyclobutane (C) and on to an g2-complex of the cycloalkene product (D) from which the 14-electron ruthenium methylidene is released. However, intermolecular cross metathesis reactions, which convert an acyclic diene to dimer (E0 ) and ethene may compete with intramolecular RCM and lead to the formation of dimers and higher oligomers. The relative importance of these two mechanisms can be quantified by the concept of effec-
* Corresponding authors. Fax: +44 161 275 4734. E-mail addresses: [email protected], [email protected] (I.H. Hillier). 0009-2614/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2009.06.021
tive molarity (EM) [3,4], which gives the relative amounts of the cyclic and dimer product. We here describe the first direct comparison between theory and experiment for a RCM reaction [5]. We present electronic structure calculations designed to explore the mechanism and energetics of the competing inter- and intra-molecular reactions in the case of 1,7-octadiene (n = 2 in Fig. 2), and compare the computed EM with a newly measured value reported here. 2. Computational details and results Calculations on full systems of this size are only feasible using density functional theory (DFT) methods. We thus first need to decide the most appropriate functional for this study. We have used the standard B3LYP functional to explore the intra- and intermolecular reactions (Fig. 2). The calculations employed basis B1 to obtain optimal structures, which were characterized by the computation of harmonic frequencies. Basis B1 consisted of the effective core potential (ECP) and double zeta basis (LanL2DZ) on Ru (with an added f-function of exponent 0.5780), the 6-31G* basis on heavy atoms, and 6-31G on hydrogens. Free energies were computed for structures determined at the B3LYP/B1 level, from electronic energies obtained with the B2 basis and using thermodynamic corrections determined at the B3LYP/B1 level (employing the harmonic oscillator, rigid rotor approximations and a temperature of 298 K). Basis B2 consisted of the SDD ECP [6] and corresponding basis set on Ru with the same f-function as B1, with a 6-311G** basis on all other atoms. The effect of solvation was included via the conductor-like polarisable continuum model (CPCM) with an effective dielectric of 8.9 (dichloromethane (DCM)). The resulting free energy surface is shown in Fig. 3 for the RCM reaction leading to the formation of cyclohexene. We have also calculated this energy surface using the B3LYP/B1 structures
38
S. Pandian et al. / Chemical Physics Letters 476 (2009) 37–40
Fig. 1. Alkene metathesis catalysts.
and the newly developed M06 and M06-L functionals of Truhlar and coworkers [7], which we have implemented in GAUSSIAN 03 [8]. We see that the reaction appears to be more favourable energetically for the M06 and M06-L functionals and in this case might be classified to be under thermodynamic control rather than the kinetic control implied by the B3LYP results, as all the intermediates and transition states lie below or are close to the initial state (A). It is not possible to carry out ab initio calculations including a high level of electron correlation (e.g. CCSD(T)) on systems of this size in order to assess the accuracy of the competing functionals. We have therefore taken the two structures which we have obtained for the smaller reaction involving heptadiene, alkylidene A, and metallocyclobutane C, leading to the formation of cyclopentene, and constructed truncated models 4 and 5 by removal of the two mesitylene groups and simplification of the diene (Fig. 4). The electronic energies were evaluated using basis B2 at the CCSD(T) level and with the B3LYP, M06 and M06-L functionals (Table 1). Although a larger basis than B2 would be expected to recover more correlation energy, it is clear from the data of Table 1 that the CCSD(T) calculation allows an assessment of the performance of the three functionals and clearly shows that the new M06 functionals are significantly superior to B3LYP. A similar conclusion was recently reported by Zhao and Truhlar for the much simpler reaction of phosphane dissociation from second generation Grubbs pre-catalyst [9]. Piacenza et al. [10] have also found that the B3LYP
Fig. 3. Calculated free energy surfaces for cyclohexene formation in DCM with the different functionals.
Fig. 4. Models used for CCSD(T) calculations.
functional produces large errors in their study of ruthenium catalyzed metathesis. We have computed the reaction profile for the cyclisation of octadiene at the M06/B2//B3LYP/B1 level (Fig. 5) [11,12]. We assume that the dimerisation reaction is independent of chain length
Fig. 2. Mechanism of intra- and inter-molecular metathesis reactions.
S. Pandian et al. / Chemical Physics Letters 476 (2009) 37–40
39
Table 1 Electronic energies of 5 (kcal mol1) relative to truncated methylidene 4. 5 B3LYP M06-L M06 CCSD(T)
13.6 22.1 25.3 23.7
Fig. 5. Comparative free energy surfaces with the M06 functional for cyclohexene formation versus dimerisation of 1,6-heptadiene (E-triene product) in DCM.
for heptadiene and larger hydrocarbons, and thus consider the dimerisation of heptadiene for computation of the EM value. Lowest energy pathways between A and cycloalkene products E were found by a combined approach in which the known most stable cycloalkene product conformers were tracked back to the initial g2-complexes, in conjunction with Monte Carlo conformational searching of the metallocyclobutane intermediates in Spartan’06 [13] and investigation of related g2-complexes. This was designed to achieve our goal of ensuring that any special conformers enforced by the spatial demands of the metal and bulky carbene ligand were not missed. In Fig. 5 the free energy surface for the intramolecular cyclisation of 1,7-octadiene is compared with that for the dimerisation of 1,6-heptadiene. We see that for most of the pathway the surface for the dimerisation is above that for the intramolecular reaction, due in large part to the loss of entropy in the former reaction. However, this shift is not displayed by the initial transition structure for the intermolecular reaction which has rather more vibrational entropy (by 10 eu) than subsequent structures. As far as the energies of each of the surfaces are concerned, we see from Fig. 5 that for both reactions, the conversion of ( A, A0 ) to (B, B0 ) is relatively fast, and the rate limiting step is the conversion of the metallocyclobutane (C, C0 ) to the g2-complex (D, D0 ). The rate of this step depends upon the barrier height and the concentration of (C, C0 ) which is in equilibrium with (B, B0 ). Thus, assuming a common pre-exponential factor we may evaluate the reaction rate (R) as
R ¼ ½C; C0 expðDGz =RTÞ where DGà is the barrier between (C, C0 ) and (D, D0 ), and the concentrations [C, C0 ] depend on the equilibrium constants for
BðB0 Þ CðC0 Þ which can be evaluated from the relative free energies of (B, B0 ) and (C, C0 ).
Fig. 6. Partial 500 MHz 1H NMR spectra of (a) RCM reaction mixture in CDCl3 (4.1 M in 1,7-octadiene with 2 mol% 2, after 17 h); (b) commercial cyclohexene (4.0 M) in CDCl3; (c) RCM reaction mixture in CD2Cl2 (4.0 M in 1,7-octadiene with 2 mol% 2, after 17 h), and (d) commercial cyclohexene (3.95 M in CD2Cl2). All samples contain 1,3,5-trimethoxybenzene standard.
We may thus use our calculated barrier heights, together with the free energy difference between (B, B0 ) and (C, C0 ) to evaluate the relative rates for the competing reactions, which we can compare with the measured EM value. This procedure resulted in an EM value of 82.
3. Experimental We have carried out RCM of 1,7-octadiene at 298K in CDCl3 and in CD2Cl2 containing an NMR standard in each case, at a catalyst loading of 2 mol% of 2 based on diene substrate. Reactions were stirred overnight at room temperature. Fig. 6 shows the 500 MHz 1 H NMR spectra of the RCM reaction solution without work-up, dilution or concentration [(a) in CDCl3 (c) in CD2Cl2], and commercial cyclohexene [(b) in CDCl3 (d) in CD2Cl2]. Cyclohexene was the only product at a 1,7-octadiene concentration of 4 M; at the NMR detection limit, the ratio of cyclohexene to oligomer would be 20:1 and therefore EM = 20 [diene]. This corresponds to a minimum EM of 80 M for cyclohexene formation. 4. Conclusion In conclusion, we have shown that we may use the new M06 density functional to probe the mechanism of RCM reactions. The reaction for both ring closure and for dimerisation is predicted to be facile, and to yield an estimate of the preference for cyclisation of octadiene consistent with the lower bound given by experiment. Further studies will investigate different ring sizes and substituted rings, to probe the efficiency of cyclisation more fully.
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S. Pandian et al. / Chemical Physics Letters 476 (2009) 37–40
Acknowledgements We thank the EPSRC and AstraZeneca (Industrial CASE Award to DJN) and the University of Strathclyde Principal’s Fund (fellowship to GR). SP acknowledges an Overseas Research Student (ORS) award. References [1] [2] [3] [4]
A.H. Hoveyda, A.R. Zhugralin, Nature 450 (2007) 243. S.E. Vyboishchikov, W. Thiel, Chem.-Eur. J. 11 (2005) 3921. A.J. Kirby, Adv. Phys. Org. Chem. 17 (1980) 183. C. Galli, L. Mandolini, Eur. J. Org. Chem. (2000) 3117.
[5] Straub made a detailed ESC study of an enyne metathesis of an unique ring size: see J.J. Lippstreu, B.F. Straub, J. Am. Chem. Soc. 127 (2005) 7444. [6] D. Andrae, U. Haeussermann, M. Dolg, H. Stoll, H. Preuss, Theor. Chim. Acta 77 (1990) 123. [7] Y. Zhao, D.G. Truhlar, Acc. Chem. Res. 41 (2008) 157. [8] M.J. Frisch et al., GAUSSIAN 03 Revision D.02, Gaussian, Inc., Wallingford CT, 2004. [9] Y. Zhao, D.G. Truhlar, Org. Lett. 9 (2007) 1967. [10] M. Piacenza, I. Hyla-Kryspin, S. Grimme, J. Comput. Chem. 28 (2007) 2275. [11] Goddard has recently explored cross metathesis using the M06 functionals: see D. Benitez, E. Tkatchouk, W.A. Goddard, Chem. Commun. (2008) 6194. [12] Chen has examined aspects of norbornene ROMP: see S. Torker, D. Merki, P. Chen, J. Am. Chem. Soc. 130 (2008) 4808. [13] Spartan’06, Wavefunction, Irvine, CA, 2006.
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Prediction of ring formation efficiency via diene ring closing metathesis (RCM) reactions using the M06 density functional Shanthi Pandian a, Ian H. Hillier a,*, Mark A. Vincent a, Neil A. Burton a, Ian W. Ashworth b, David J. Nelson c, Jonathan M. Percy c,*, Giuseppe Rinaudo c a
School of Chemistry, University of Manchester, Manchester, M13 9PL, UK AstraZeneca Process R&D, Silk Road Business Park, Charter Way, Macclesfield, SK10 2NA, UK c WestCHEM Department of Pure and Applied Chemistry, 295 Cathedral Street, Glasgow G1 1XL, UK b
a r t i c l e
i n f o
Article history: Received 28 April 2009 In final form 5 June 2009 Available online 9 June 2009
a b s t r a c t Using density functional theory employing the M06 functional, we predict the reaction path energetics of ring formation via diene ring closing metathesis (RCM) reactions, and thence the effective molarity (EM) for the formation of cyclohexene, which is in good accord with the experimental lower limit which we report here. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction The importance of alkene metathesis reactions has grown spectacularly since well defined and air stable catalysts 1 and 2 (Fig. 1) became commercially available [1]. The closure of highly-functionalised carbocycles and heterocycles of a wide range of sizes can be achieved under mild conditions, and many groups have executed elegant syntheses of complex natural products based on ring closing metathesis (RCM) strategies. While a number of groups have studied the fundamental mechanism of alkene metathesis, characterising the organometallic intermediates in the reaction sequence for simple prototypical reactions (and others have explored stereochemical preferences in more complex systems [2]) using electronic structure calculations, synthetic practice has far exceeded our understanding of the interplay of structure and reactivity in the reaction. The mechanism used most commonly to describe RCM of the prototypical a,x-dienes to afford the corresponding Z-cycloalkenes is shown in Fig. 2. Ruthenium methylidene (3) cross metathesis with the diene affords volatile ethene and a new metal alkylidene (A) which can begin cyclisation via a cyclic g2-complex (B), progressing to a bicyclic metallocyclobutane (C) and on to an g2-complex of the cycloalkene product (D) from which the 14-electron ruthenium methylidene is released. However, intermolecular cross metathesis reactions, which convert an acyclic diene to dimer (E0 ) and ethene may compete with intramolecular RCM and lead to the formation of dimers and higher oligomers. The relative importance of these two mechanisms can be quantified by the concept of effec-
* Corresponding authors. Fax: +44 161 275 4734. E-mail addresses: [email protected], [email protected] (I.H. Hillier). 0009-2614/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2009.06.021
tive molarity (EM) [3,4], which gives the relative amounts of the cyclic and dimer product. We here describe the first direct comparison between theory and experiment for a RCM reaction [5]. We present electronic structure calculations designed to explore the mechanism and energetics of the competing inter- and intra-molecular reactions in the case of 1,7-octadiene (n = 2 in Fig. 2), and compare the computed EM with a newly measured value reported here. 2. Computational details and results Calculations on full systems of this size are only feasible using density functional theory (DFT) methods. We thus first need to decide the most appropriate functional for this study. We have used the standard B3LYP functional to explore the intra- and intermolecular reactions (Fig. 2). The calculations employed basis B1 to obtain optimal structures, which were characterized by the computation of harmonic frequencies. Basis B1 consisted of the effective core potential (ECP) and double zeta basis (LanL2DZ) on Ru (with an added f-function of exponent 0.5780), the 6-31G* basis on heavy atoms, and 6-31G on hydrogens. Free energies were computed for structures determined at the B3LYP/B1 level, from electronic energies obtained with the B2 basis and using thermodynamic corrections determined at the B3LYP/B1 level (employing the harmonic oscillator, rigid rotor approximations and a temperature of 298 K). Basis B2 consisted of the SDD ECP [6] and corresponding basis set on Ru with the same f-function as B1, with a 6-311G** basis on all other atoms. The effect of solvation was included via the conductor-like polarisable continuum model (CPCM) with an effective dielectric of 8.9 (dichloromethane (DCM)). The resulting free energy surface is shown in Fig. 3 for the RCM reaction leading to the formation of cyclohexene. We have also calculated this energy surface using the B3LYP/B1 structures
38
S. Pandian et al. / Chemical Physics Letters 476 (2009) 37–40
Fig. 1. Alkene metathesis catalysts.
and the newly developed M06 and M06-L functionals of Truhlar and coworkers [7], which we have implemented in GAUSSIAN 03 [8]. We see that the reaction appears to be more favourable energetically for the M06 and M06-L functionals and in this case might be classified to be under thermodynamic control rather than the kinetic control implied by the B3LYP results, as all the intermediates and transition states lie below or are close to the initial state (A). It is not possible to carry out ab initio calculations including a high level of electron correlation (e.g. CCSD(T)) on systems of this size in order to assess the accuracy of the competing functionals. We have therefore taken the two structures which we have obtained for the smaller reaction involving heptadiene, alkylidene A, and metallocyclobutane C, leading to the formation of cyclopentene, and constructed truncated models 4 and 5 by removal of the two mesitylene groups and simplification of the diene (Fig. 4). The electronic energies were evaluated using basis B2 at the CCSD(T) level and with the B3LYP, M06 and M06-L functionals (Table 1). Although a larger basis than B2 would be expected to recover more correlation energy, it is clear from the data of Table 1 that the CCSD(T) calculation allows an assessment of the performance of the three functionals and clearly shows that the new M06 functionals are significantly superior to B3LYP. A similar conclusion was recently reported by Zhao and Truhlar for the much simpler reaction of phosphane dissociation from second generation Grubbs pre-catalyst [9]. Piacenza et al. [10] have also found that the B3LYP
Fig. 3. Calculated free energy surfaces for cyclohexene formation in DCM with the different functionals.
Fig. 4. Models used for CCSD(T) calculations.
functional produces large errors in their study of ruthenium catalyzed metathesis. We have computed the reaction profile for the cyclisation of octadiene at the M06/B2//B3LYP/B1 level (Fig. 5) [11,12]. We assume that the dimerisation reaction is independent of chain length
Fig. 2. Mechanism of intra- and inter-molecular metathesis reactions.
S. Pandian et al. / Chemical Physics Letters 476 (2009) 37–40
39
Table 1 Electronic energies of 5 (kcal mol1) relative to truncated methylidene 4. 5 B3LYP M06-L M06 CCSD(T)
13.6 22.1 25.3 23.7
Fig. 5. Comparative free energy surfaces with the M06 functional for cyclohexene formation versus dimerisation of 1,6-heptadiene (E-triene product) in DCM.
for heptadiene and larger hydrocarbons, and thus consider the dimerisation of heptadiene for computation of the EM value. Lowest energy pathways between A and cycloalkene products E were found by a combined approach in which the known most stable cycloalkene product conformers were tracked back to the initial g2-complexes, in conjunction with Monte Carlo conformational searching of the metallocyclobutane intermediates in Spartan’06 [13] and investigation of related g2-complexes. This was designed to achieve our goal of ensuring that any special conformers enforced by the spatial demands of the metal and bulky carbene ligand were not missed. In Fig. 5 the free energy surface for the intramolecular cyclisation of 1,7-octadiene is compared with that for the dimerisation of 1,6-heptadiene. We see that for most of the pathway the surface for the dimerisation is above that for the intramolecular reaction, due in large part to the loss of entropy in the former reaction. However, this shift is not displayed by the initial transition structure for the intermolecular reaction which has rather more vibrational entropy (by 10 eu) than subsequent structures. As far as the energies of each of the surfaces are concerned, we see from Fig. 5 that for both reactions, the conversion of ( A, A0 ) to (B, B0 ) is relatively fast, and the rate limiting step is the conversion of the metallocyclobutane (C, C0 ) to the g2-complex (D, D0 ). The rate of this step depends upon the barrier height and the concentration of (C, C0 ) which is in equilibrium with (B, B0 ). Thus, assuming a common pre-exponential factor we may evaluate the reaction rate (R) as
R ¼ ½C; C0 expðDGz =RTÞ where DGà is the barrier between (C, C0 ) and (D, D0 ), and the concentrations [C, C0 ] depend on the equilibrium constants for
BðB0 Þ CðC0 Þ which can be evaluated from the relative free energies of (B, B0 ) and (C, C0 ).
Fig. 6. Partial 500 MHz 1H NMR spectra of (a) RCM reaction mixture in CDCl3 (4.1 M in 1,7-octadiene with 2 mol% 2, after 17 h); (b) commercial cyclohexene (4.0 M) in CDCl3; (c) RCM reaction mixture in CD2Cl2 (4.0 M in 1,7-octadiene with 2 mol% 2, after 17 h), and (d) commercial cyclohexene (3.95 M in CD2Cl2). All samples contain 1,3,5-trimethoxybenzene standard.
We may thus use our calculated barrier heights, together with the free energy difference between (B, B0 ) and (C, C0 ) to evaluate the relative rates for the competing reactions, which we can compare with the measured EM value. This procedure resulted in an EM value of 82.
3. Experimental We have carried out RCM of 1,7-octadiene at 298K in CDCl3 and in CD2Cl2 containing an NMR standard in each case, at a catalyst loading of 2 mol% of 2 based on diene substrate. Reactions were stirred overnight at room temperature. Fig. 6 shows the 500 MHz 1 H NMR spectra of the RCM reaction solution without work-up, dilution or concentration [(a) in CDCl3 (c) in CD2Cl2], and commercial cyclohexene [(b) in CDCl3 (d) in CD2Cl2]. Cyclohexene was the only product at a 1,7-octadiene concentration of 4 M; at the NMR detection limit, the ratio of cyclohexene to oligomer would be 20:1 and therefore EM = 20 [diene]. This corresponds to a minimum EM of 80 M for cyclohexene formation. 4. Conclusion In conclusion, we have shown that we may use the new M06 density functional to probe the mechanism of RCM reactions. The reaction for both ring closure and for dimerisation is predicted to be facile, and to yield an estimate of the preference for cyclisation of octadiene consistent with the lower bound given by experiment. Further studies will investigate different ring sizes and substituted rings, to probe the efficiency of cyclisation more fully.
40
S. Pandian et al. / Chemical Physics Letters 476 (2009) 37–40
Acknowledgements We thank the EPSRC and AstraZeneca (Industrial CASE Award to DJN) and the University of Strathclyde Principal’s Fund (fellowship to GR). SP acknowledges an Overseas Research Student (ORS) award. References [1] [2] [3] [4]
A.H. Hoveyda, A.R. Zhugralin, Nature 450 (2007) 243. S.E. Vyboishchikov, W. Thiel, Chem.-Eur. J. 11 (2005) 3921. A.J. Kirby, Adv. Phys. Org. Chem. 17 (1980) 183. C. Galli, L. Mandolini, Eur. J. Org. Chem. (2000) 3117.
[5] Straub made a detailed ESC study of an enyne metathesis of an unique ring size: see J.J. Lippstreu, B.F. Straub, J. Am. Chem. Soc. 127 (2005) 7444. [6] D. Andrae, U. Haeussermann, M. Dolg, H. Stoll, H. Preuss, Theor. Chim. Acta 77 (1990) 123. [7] Y. Zhao, D.G. Truhlar, Acc. Chem. Res. 41 (2008) 157. [8] M.J. Frisch et al., GAUSSIAN 03 Revision D.02, Gaussian, Inc., Wallingford CT, 2004. [9] Y. Zhao, D.G. Truhlar, Org. Lett. 9 (2007) 1967. [10] M. Piacenza, I. Hyla-Kryspin, S. Grimme, J. Comput. Chem. 28 (2007) 2275. [11] Goddard has recently explored cross metathesis using the M06 functionals: see D. Benitez, E. Tkatchouk, W.A. Goddard, Chem. Commun. (2008) 6194. [12] Chen has examined aspects of norbornene ROMP: see S. Torker, D. Merki, P. Chen, J. Am. Chem. Soc. 130 (2008) 4808. [13] Spartan’06, Wavefunction, Irvine, CA, 2006.