Assessment of density functional methods for the study of olefin metathesis catalysed by ruthenium alkylidene complexes

Chemical Physics Letters 493 (2010) 273–278

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Assessment of density functional methods for the study of olefin metathesis catalysed by ruthenium alkylidene complexes Paweł S´liwa, Jarosław Handzlik * Faculty of Chemical Engineering and Technology, Cracow University of Technology, ul. Warszawska 24, PL 31-155 Kraków, Poland

a r t i c l e

i n f o

Article history: Received 9 March 2010 In final form 20 May 2010 Available online 24 May 2010

a b s t r a c t Performance of 31 DFT methods in thermochemistry of olefin metathesis involving the model catalyst (PH3)2(Cl)2Ru@CH2 is studied using the CCSD(T) reference energies. The best methods are M06, xB97X-D and PBE0, followed by MPW1B95, LC-xPBE, M05-2X and B1B95. Among 20 functionals tested in reproduction of experimental PCy3 dissociation energy for the Grubbs catalyst (H2IMes)(PCy3)(Cl)2Ru@CHPh, the M06-class and M05-2X methods are most accurate. xB97X-D overestimates the dissociation energy, whereas MPW1B95, LC-xPBE, PBE0 and B1B95 underestimate it, similarly to other methods, which give larger errors. LC-xPBE, B1B95, MPW1B95 and PBE0 provide the best geometries. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction Calculations of chemical reactivity require a choice of an adequate theoretical method. The most popular approach today – density functional theory – offers now a large number of exchange-correlation functionals [1–31]. DFT methods can be classified according to the number and kind of the ingredients in the functional. The local spin density approximation (LSDA) functionals depend only on the electron density. The generalized gradient approximation (GGA) functionals depend on the electron density and its gradient, whereas meta-GGA functionals also depend on the kinetic energy density. Hybrid GGA and hybrid meta-GGA functionals include additionally a portion of Hartree-Fock exchange. In the field of catalysis, the selection of the DFT method applied can significantly affect the results, especially for systems containing transition metals [32–37]. Olefin metathesis is a catalytic reaction of a great importance. Ruthenium alkylidene complexes of a general formula L(PR3)(X)2 Ru@CHR0 , known as Grubbs catalysts, are extremely useful in organic and polymer chemistry because of their high functional group tolerance [38,39]. The so-called dissociative mechanism of olefin metathesis employing the Grubbs-type catalyst includes two key steps: phosphine dissociation leading to a 14-electron Ru complex, followed by olefin coordination and rearrangement to a ruthenacyclobutane intermediate [38,39]. Further splitting of the ruthenacyclobutane complex to a new ruthenium alkylidene and an olefin product enables continuation of the catalytic cycle (Fig. 1). There are experimental [38] and theoretical [33] evidences * Corresponding author. Fax: +48 12 6282037. E-mail address: [email protected] (J. Handzlik). 0009-2614/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2010.05.066

confirming this mechanism and excluding the competitive associative mechanism that assumes olefin coordination to the catalyst to form an 18-electron intermediate. As breaking and formation of transition metal bonds and organic bonds are involved in olefin metathesis mechanism, accurate theoretical description of the process requires methods which perform well for both main-group elements and transition metals. Many computational works on ruthenium-catalysed olefin metathesis have been reported so far [33–37,40–44]. The most popular density functionals employed in this field are BP86 [33,34,36, 40,41], PBE0 [34,42,43] and B3LYP [33–35,37,40,43]. Other methods, like MPW1K [43], PW91 [34,44], TPSSh [33,34], B97-D [33] or M05 [43] were used rather occasionally. Recently, new M06 and M06-L DFT methods have been successfully applied for investigations of the Grubbs catalysts for olefin metathesis [34–37]. The former was developed as a general-purpose hybrid functional recommended for main-group and transition metals thermochemistry, kinetics and the study of noncovalent interactions [27]. The latter is a computationally less demanding local functional also designed for general use, but especially recommended for applications to organometallics [10,27,34]. It was reported that attractive noncovalent interactions, well described by the M06-class functionals, are essential for proper description of phosphine and olefin binding to the ruthenium catalyst [34,35]. Other authors also indicated a significant influence of the choice of the functional on the calculated energy profiles for olefin metathesis catalysed by ruthenium alkylidene complexes [33,36,37]. In this work, the performance of various DFT methods in thermochemistry of olefin metathesis catalysed by the Grubbs-type catalysts has been investigated. In the first part of the study, the model ruthenium complex (PH3)2(Cl)2Ru@CH2 has been applied.

P. S´liwa, J. Handzlik / Chemical Physics Letters 493 (2010) 273–278

274

L X

R'

Ru PR3

X

-PR3

L X

1 R' + R CH=CH2

Ru

+PR3

- R1 CH=CH2

X

L X X Ru R

1

L X X Ru R

L X

R

Ru PR3

X

L

1

-PR3

X

R

1

+ R'CH=CH2

Ru X

+PR3

R'

R'

1

L X X Ru

R

1

- R'CH=CH2

R'

Fig. 1. Mechanism of olefin metathesis catalysed by the Grubbs-type catalyst.

The calculated DFT energies of PH3 ligand dissociation and formation of ruthenacyclobutane complex from (PH3)(Cl)2Ru@CH2 and ethene are compared with the reference CCSD(T) energies. In the second part of the work, PCy3 dissociation energies have been calculated with selected DFT methods, using the structure of the Grubbs second-generation catalyst (H2IMes)(PCy3)(Cl)2Ru@CHPh [39]. In this case, the experimental dissociation energies for solution [38] and gas phase [36] are taken as the reference data. Additionally, theoretical and experimental [39] bond lengths for the ruthenium complex are compared as well.

been tested (Table 1) [1–31]. Two of them, LC-xPBE [21] and xB97X-D [22] are the long-range corrected (LC) hybrids, which employ 100% exact exchange for long-range electron-electron interactions. The latter also includes empirical dispersion corrections, like the B97-D functional [9]. In the first series of the tests, geometries of the model ruthenium complexes have been optimised with the quadruple-f valence def2-QZVPP basis set (abbreviated as QZVPP) [45] using all density functionals studied. The 28 innermost electrons of Ru are replaced by the Stuttgart effective core potential [46]. In the second series of the tests, geometry optimisation using all density functionals in combination with the split-valence def2-SVP basis set (abbreviated as SVP) [45] has been performed, followed by single point calculations using the triple-f valence def2-TZVPP basis set (abbreviated as TZVPP) [45]. Such a methodology is practical for calculations of real systems. Finally, in the third series of the tests, a set of single point calculations with the TZVPP basis set and B3LYP/QZVPP geometries have been done. These geometries have been also used for the reference CCSD(T)/QZVPP calculations. In the case of the real catalyst structures, 20 DFT methods have been selected to carry out full geometry optimisation using the SVP basis set, followed by single point calculations with the TZVPP basis set. Zero-point vibrational energies (ZPE) and thermal

2. Computational methods Thirty-one density functionals belonging to four classes of DFT methods: GGA, meta-GGA, hybrid GGA and hybrid meta-GGA have Table 1 DFT methods tested in this work. Method

Type

References

BLYP BP86 G96LYP HCTH/407 OLYP PBE PW91 B97-D M06-L mPWKCIS TPSS TPSSKCIS B3LYP B3PW91 B97-2 B98 MPWLYP1M O3LYP PBE0 LC-xPBE xB97X-D B1B95 BMK M05 M05-2X M06 M06-2X MPW1B95 MPW1KCIS TPSS1KCIS TPSSh

GGA GGA GGA GGA GGA GGA GGA GGA-D meta-GGA meta-GGA meta-GGA meta-GGA hybrid GGA hybrid GGA hybrid GGA hybrid GGA hybrid GGA hybrid GGA hybrid GGA LC hybrid GGA LC hybrid GGA-D hybrid meta-GGA hybrid meta-GGA hybrid meta-GGA hybrid meta-GGA hybrid meta-GGA hybrid meta-GGA hybrid meta-GGA hybrid meta-GGA hybrid meta-GGA hybrid meta-GGA

[1,2] [1,3] [2,4] [5] [2,6] [7] [8] [9] [10] [11,12] [13] [12,13] [14,15] [14] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25,26] [26] [27] [27] [28] [29] [30] [31]

Fig. 2. Structures of the catalyst model (PH3)2(Cl)2Ru@CH2 (1), the active catalyst form (PH3)(Cl)2Ru@CH2 (2) and ruthenacyclobutane (PH3)(Cl)2Ru(CH2CH2CH2) (3). The geometries are optimised at the B3LYP/QZVPP level.

P. S´liwa, J. Handzlik / Chemical Physics Letters 493 (2010) 273–278

corrections have been evaluated in the rigid-rotor and harmonicoscillator approximations. Single point calculations using the PCM model [47] have been performed to evaluate the solvent effects (toluene, e = 2.3741). For the PCy3 dissociation energy calculated with some selected density functionals, the basis set superposition error (BSSE) has been estimated using the counterpoise method [48]. The calculations have been done using the GAUSSIAN 03 [49] and GAUSSIAN 09 [50] sets of programs.

Table 2 Reaction energies (DE, kJ mol1) and mean unsigned errors in reaction energies (MUE, kJ mol1) for the model compounds in gas phase. Methoda

BLYP BP86 G96LYP HCTH/407 OLYP PBE PW91 B97-D M06-L mPWKCIS TPSS TPSSKCIS B3LYP B3PW91 B97-2 B98 MPWLYP1M O3LYP PBE0 LC-xPBE xB97X-D B1B95 BMK M05 M05-2X M06 M06-2X MPW1B95 MPW1KCIS TPSS1KCIS TPSSh CCSD(T)c

3. Results and discussion 3.1. Model compounds To enable coupled cluster calculations providing accurate reference energies, small model compounds have been used in the first part of the work (Fig. 2). Ruthenium complex (PH3)2(Cl)2Ru@CH2 (1) corresponds to the Grubbs first-generation catalyst (PR3)2(X)2 Ru@CHR’ [38,39]. After PH3 dissociation, the active species 2 is formed:

ðPH3 Þ2 ðClÞ2 Ru@CH2 ! ðPH3 ÞðClÞ2 Ru@CH2 þ PH3

ð1Þ

Reaction of 2 with ethene results in the ruthenacyclobutane 3 formation:

ðPH3 ÞðClÞ2 Ru@CH2 þ C2 H4 ! ðPH3 ÞðClÞ2 RuðCH2 CH2 CH2 Þ

ð2Þ

The next step in ethene metathesis, cycloreversion, can be regarded as the reverse reaction (2). In our tests we have not considered the intermediate in which ethene is coordinated to ruthenium. For all DFT methods studied, both the geometries and energies of the compounds have been determined with using the large QZVPP basis set that is close to the basis set limit. The ruthenium complexes 1 and 2 have C2v and Cs symmetry, respectively (Fig. 2). The ruthenacyclobutane 3 having a flat ring (Cs symmetry) is a local minimum if optimised with the B3LYP and some other functionals, whereas one imaginary frequency appears when the rest of the DFT methods are used. In these cases, another ruthenacyclobutane structure, mostly possessing a puckered ring, has been optimised without symmetry constraints to obtain an energy minimum. For each DFT method, the energy differences between both structures are negligible (see Supplementary data) and the ruthenacyclobutane with the flat ring has been always taken for energy comparisons, in accordance with the reference CCSD(T) calculations. To check the basis set effect, we have performed the second series of the tests, carrying out the geometry optimisation with the relatively small SVP basis set and calculating the single point energies using the TZVPP basis set. Another reason for the examination of these methodology is the fact that it is applicable for practical calculations involving large molecules of the real catalysts. The bond lengths obtained with the SVP basis set are slightly longer than those calculated with the QZVPP one. For example, considering PBE0 geometries of ruthenium alkylidene 1, the differences are 0.002, 0.016 and 0.021 Å for the Ru@C, Ru–P and Ru–Cl bonds, respectively. Similarly, in the case of ruthenacyclobutane 3, the Ru–C bond distances are increased by 0.002 and 0.003 Å. The differences in corresponding reaction energies from the first and second series of the calculations are insignificant, below 2 and 3 kJ mol1 for the reaction (1) and (2), respectively. Finally, we have also done a third series of tests, calculating single point energies with the TZVPP basis set for the B3LYP/QZVPP geometries. The energies of the reactions (1) and (2) differ by less than 3 and 4 kJ mol1, respectively, as compared to the corresponding values from the first test series. Our reference CCSD(T)/QZVPP//B3LYP/QZVPP energies for reaction (1) (112 kJ mol1) and (2) (60 kJ mol1) can be compared

275

a

DE b

MUE

Reaction (1)

Reaction (2)

65 84 56 54 44 92 95 78 87 77 91 86 76 85 78 87 74 54 97 105 100 90 96 75 95 102 79 97 81 88 93 112

15 24 22 10 19 38 38 17 43 15 32 22 12 36 27 35 1 2 59 77 60 54 99 52 69 59 56 65 29 34 41 60

61 32 69 64 73 21 19 39 21 40 25 32 42 25 34 25 49 60 8 12 6 14 27 22 13 6 19 10 31 25 19

The geometries and energies have been obtained with using the QZVPP basis

set. b c

T = 0 K; zero-point energy is not included. CCSD(T)/QZVPP//B3LYP/QZVPP calculations.

with the reported results of QCISD(T) calculations (107 and 68 kJ mol1, respectively), which were performed for the same model compounds with using a basis set of triple-f quality [33]. The calculated reaction energies and the mean unsigned errors (MUE), referred do the CCSD(T) values, are presented in Table 2 (the reaction enthalpies and Gibbs free energies are given in Supplementary data). One can see that all the density functionals underestimate the phosphine dissociation energy. This is generally consistent with other reported computational studies on the Grubbs catalysts [33,40] but we have shown that a great number of the DFT methods exhibit this tendency. Interestingly, the binding energy calculated with the M06-L functional is clearly too low, although this method reproduces much more precisely the experimental dissociation energy of large PCy3 ligand [36]. M06 is more accurate than M06-L for reaction (1), but LC-xPBE gives the best result (Table 2). xB97X-D, PBE0, MPW1B95, BMK, PW91, M05-2X and some others are also among the functionals showing reasonable accuracy. It can be noticed that M05 gives much bigger error for the Ru–P binding energy than M05-2X. In the case of the reaction (2), most of the DFT methods predict a less exothermic effect than indicated by the CCSD(T) calculations (Table 2). The results obtained with the BLYP, G96LYP, HCTH and OLYP GGA functionals show even a clearly endothermic formation of ruthenacyclobutane 3. MPWLYP1M and O3LYP hybrids also give large errors. On the other hand, xB97X-D, PBE0 and M06 provide practically the same reaction energy as the reference value. M062X, MPW1B95, B1B95, M05 and M05-2X are only slightly less accurate.

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According to the MUE values (Table 2), the best methods are M06, xB97X-D and PBE0, followed by MPW1B95, LC-xPBE, M05-2X and B1B95. They all belong to the hybrid functionals. It can be noticed that the PBE0 method was often used for theoretical description of ruthenium-catalysed olefin metathesis [34,42,43]. The new M06 functional also attracted attention [35,37], similarly to the local M06-L one [34–37] that shows lower but still reasonable accuracy in this test. The nonempirical local PW91, PBE and TPSS functionals give errors of the similar range as well. Interestingly, these three methods performed very well in calculations of reaction energies for molybdenum compounds [32]. On the other hand, popular B3LYP [33–35,37, 40,43] and BP86 [33,34,36,40,41] methods give more significant errors, but not such large as in the case of OLYP, G96LYP, HCTH, BLYP, O3LYP and MPWLYP1M. On the average, the GGA functionals perform worse than other considered here classes of DFT methods, whereas the most accurate are long-range corrected and hybrid meta-GGA functionals.

Fig. 3. Structures of the (H2IMes)(PCy3)(Cl)2Ru@CHPh catalyst (4) and two conformers of the active intermediate (H2IMes)(Cl)2Ru@CHPh (5, 6). The geometries are optimised at the PBE0/SVP level.

3.2. Structures of the real catalyst species As the results obtained for the model compounds may not be fully transferable to the real systems, mainly because of the important role of the interactions between the large ligands in the catalyst [34,35], we have included the structure of the Grubbs secondgeneration catalyst (H2IMes)(PCy3)(Cl)2Ru@CHPh (4) (Fig. 3) in our studies. Concerning the active 14-electron intermediate formed after PCy3 dissociation:

ðH2 IMesÞðPCy3 ÞðClÞ2 Ru@CHPh ! ðH2 IMesÞðClÞ2 Ru@CHPh þ PCy3 ð3Þ two rotational isomers have been considered (Fig. 3, structures 5 and 6). The orientation of the benzylidene ligand in 5 is energetically favoured [40], as compared to the conformer 6. The geometry of the latter is more or less conserved from the initial structure 4, in which the benzylidene moiety is approximately parallel to the mesityl group, because of steric effects. Consequently, according to the all DFT methods applied, the rotamer 5 has lower energy than 6. For instance, the PBE0, LC-xPBE and M06 functionals predict the energy differences of 37, 42 and 21 kJ mol1, respectively. In Table 3, the calculated energies, enthalpies and Gibbs free energies of PCy3 dissociation leading to the conformer 5 are listed. The observed differences between the DFT methods are more significant than in the case of the model compounds. The M06-L dissociation energy (160 kJ mol1) is consistent with that reported by Zhao and Truhlar (168 kJ mol1) [34]. Dissociation energies in toluene solution, calculated with using the PCM model, are lower than the corresponding values for gas phase by 7–12 kJ mol1. Taking into account the Gibbs free energy values, thermodynamic preference either for the dissociated species or for the initial catalyst 4 is predicted, depending on the density functional applied. The calculated Ru–P bond dissociation enthalpies in toluene solution (DHs) can be compared with experimental activation enthalpy of dissociative PCy3 exchange (113 ± 8.4 kJ mol1) for (H2IMes)(PCy3)(Cl)2Ru@CHPh complex [38], assuming that the reverse association reaction is barrierless [34,40]. One can see from Table 3 that the MPW1B95, M05-2X, LC-xPBE, M06-2X, M06-L, B1B95, M06 and PBE0 methods provide the most accurate values. Including the BSSE correction can slightly change this order. Other density functionals, excluding xB97X-D, significantly underestimate the phosphine binding. This tendency was indicated for some DFT methods [33,40]. It can be especially noticed that the popular BP86 and B3LYP functionals give very large errors. As the decrease of the dissociation energy in solution estimated with the continuum solvation models is probably too small [35], the gas phase PCy3 binding energy (154.4 ± 9.6 kJ mol1) for the cationized second-generation Grubbs catalyst [36] can be a more adequate reference. In this case, the results obtained with the M06-class functionals and M05-2X are very close to the experiment (DE0, Table 3). This confirms the role of noncovalent interactions in description of the binding of the bulky ligand to the metal center. M06 appears the most accurate method if the BSSE correction is taken into account. The M05 functional performs much worse than M05-2X, in accordance with the results for the model Ru compounds (Table 2). The xB97X-D method, including empirical dispersion corrections, overestimates the Ru–P bond dissociation energy, whereas MPW1B95, LC-xPBE, PBE0 and B1B95 underestimate it, similarly to other methods, which give larger errors, however. Carbene bond distances for 4, calculated using various DFT methods with the SVP basis set, do not differ dramatically each other (Table 4). The B98 and B3PW91 results are closest to the experimental value [39], whereas the largest discrepancy is seen in the case of the M06-2X, M05-2X and LC-xPBE functionals. On

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277

Table 3 Energies, enthalpies and Gibbs free energies for PCy3 dissociation (reaction (3)) in gas phase (DE, DE0, DH, DG, kJ mol1) and toluene solution (DEs, DHs, DGs, kJ mol1). The values in parenthesis are BSSE-corrected.

a b c d e f

Methoda

DEb

DEsb

DE0c

D Hd

D Hs d

DG d

DG s d

BP86 PBE PW91 M06-L TPSS B3LYP B3PW91 B97-2 B98 PBE0 LC-xPBE xB97X-D B1B95 M05 M05-2X M06 M06-2X MPW1B95 TPSS1KCIS TPSSh exp.

52 77 82 160 (151) 66 51 56 48 76 94 (88) 108 196 96 81 155 (149) 166 (155) 158 (152) 119 69 73

44 68 73 153 (144) 57 40 45 38 65 83 (77) 96 184 87 70 143 (137) 157 (146) 147 (141) 110 58 63

43 67 73 152 (143) 58 40 46 38 65 85 (79) 98 186 84 71 146 (139) 158 (147) 149 (143) 106 61 65 154e

43 68 74 153 (144) 58 40 46 38 66 85 (79) 99 186 86 71 147 (140) 159 (148) 150 (144) 109 60 65

34 59 65 146 (137) 48 30 36 28 55 74 (68) 87 174 77 60 135 (128) 150 (139) 139 (133) 100 49 54 113f

35 9 5 74 (65) 18 38 29 39 14 14 (9) 24 110 3 5 68 (61) 84 (74) 68 (62) 23 9 11

43 18 14 67 (58) 28 48 39 49 25 3 (2) 12 98 6 16 56 (49) 75 (65) 57 (51) 13 20 22

The SVP and TZVPP basis sets have been used for the geometry optimisation and further single point calculations, respectively. T = 0 K; zero-point energy is not included. T = 0 K; zero-point energy is included. T = 298.15 K. The experimental collision-induced dissociation threshold energy for gas phase [36]. The experimental activation enthalpy of dissociative PCy3 exchange in toluene [38].

Table 4 Calculated Ru@C1 bond lengths (Å) and mean unsigned errors (MUE, Å) in selected bond distances (Ru@C1, Ru–C2, Ru–Cl1, Ru–Cl2, Ru–P) for the Grubbs catalyst 4 (Fig. 3).

a b

Methoda

Ru@C1

MUE

BP86 PBE PW91 M06-L TPSS B3LYP B3PW91 B97-2 B98 PBE0 LC-xPBE xB97X-D B1B95 M05 M05-2X M06 M06-2X MPW1B95 TPSS1KCIS TPSSh exp.b

1.848 1.845 1.845 1.840 1.853 1.842 1.831 1.826 1.838 1.826 1.805 1.818 1.823 1.815 1.802 1.825 1.797 1.820 1.842 1.844 1.835

0.033 0.030 0.029 0.038 0.030 0.039 0.022 0.027 0.030 0.017 0.011 0.022 0.014 0.045 0.028 0.030 0.038 0.014 0.026 0.023

The SVP basis set has been used. Ref. [39].

The best methods are M06, xB97X-D and PBE0, followed by MPW1B95, LC-xPBE, M05-2X and B1B95. Among 20 functionals further examined in reproduction of experimental PCy3 dissociation energy for the Grubbs second-generation catalyst (H2IMes)(PCy3)(Cl)2Ru@CHPh, the M06-class functionals and the M05-2X method turned out most accurate. xB97XD overestimates the dissociation energy, whereas MPW1B95, LCxPBE, PBE0 and B1B95 underestimate it, but they still show better performance than other methods. On the other hand, LC-xPBE, B1B95, MPW1B95 and PBE0 provide the best geometries. Generally, the M06 method performs best in thermochemistry of the reactions tested in this work. Acknowledgment Computing resources from Academic Computer Centre CYFRONET AGH (grants MNiSW/SGI3700/PK/096/2008, MNiSW/IBM_ BC_HS21/PK/096/2008 and MNiSW/SGI4700/PK/044/2007) are gratefully acknowledged. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cplett.2010.05.066. References

the other hand, the latter describes very well other bonds involving Ru, giving the lowest MUE in Ru–C, Ru–Cl and Ru–P distances. B1B95, MPW1B95 and PBE0 also belong to the methods that are most accurate, on the average, in predicting the bond lengths. 4. Conclusions Accuracy of 31 DFT methods in thermochemistry of olefin metathesis involving the model (PH3)2(Cl)2Ru@CH2 catalyst has been studied using the CCSD(T) energies as the reference data.

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