First principles molecular dynamics applied to homogeneous catalysis: on ethylene insertion...

Ž .Journal of Molecular Catalysis A: Chemical 160 2000 189–197www.elsevier.comrlocatermolcata

First principles molecular dynamics applied to homogeneouscatalysis: on ethylene insertion mechanisms and metathesis

Robert J. Meier a,), Olav M. Aagaard a, Francesco Buda b

a DSM Research, P.O. Box 18, 6160 MD Geleen, Netherlandsb Chemical Laboratory of the Free UniÕersity, De Boelelaan 1083, 1081 HV Amsterdam, Netherlands

Abstract

We have summarized part of our work involving first principles molecular dynamics simulations on organometallic-basedhomogeneous catalysts. Explicit dynamics effects can be uniquely extracted from such simulations, and related to structureand reactivity. Examples given deal with metallocene-based ethylene polymerisation, ethylene insertion in a platinumhydride, and olefin metathesis. The dynamics simulations in particular reveal information on the flexibility of these

Ž .molecular systems, and elucidate mechanistic details e.g., relevance agostic interaction . For the Ru-based metathesiscatalyst an alternative simulation approach has been applied, which has enabled us to make detailed comparison between

wsimulation results and the reaction mechanism proposed by Dias et al. E.L. Dias, S.T. Nguyen, R.H. Grubbs, J. Am. Chem.Ž . xSoc. 119 1997 3887 , showing that the results of our simulations reveal and lend support to the mechanism proposed by

Grubbs. These include, in the order of appearance in the reaction scheme, the relative easiness of Cl–Ru–Cl cis–transconfigurational exchange, carbene rotation and the loss of one phosphine, formation of a metallacyclobutane intermediate,and finally completion of the metathesis reaction. The presence of a small fraction of the monophosphine complex isconfirmed by the present simulations. Starting from the observation that selective bond excitation is necessary to exhibitreactivity, the higher activity of the monophosphine system compared to bisphosphine complexes reported by Dias et al. canbe understood. q 2000 Elsevier Science B.V. All rights reserved.

Keywords: Metathesis; Ethylene insertion; Molecular modelling; Molecular dynamics

1. Introduction

Over the last decennium considerableprogress has been made in the computationalchemistry field, which now allows for the calcu-lation, at the full quantum mechanical level, ofrealistic structures of both homogeneous andheterogeneous catalysts. This new stage has been

) Corresponding author Tel.: q31-46-4761654; fax: q31-46-4761200.

Ž .E-mail address: [email protected] R.J. Meier .

accomplished through a combination of speed-up and quality improvement in computer hard-ware, software, and last but not least theoreticalmethod development. Consequently, we haveseen a considerable number of theoretical pa-pers in the scientific literature over the lastyears, a number that is still growing.

The computational chemistry field can, interms of the way of describing interatomic po-tential, be roughly divided in three clusters: theforce field approach, semi-empirical quantum

Ž .mechanics Huckel, MNDO, AM1, etc. , and ab¨

1381-1169r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.Ž .PII: S1381-1169 00 00246-6

( )R.J. Meier et al.rJournal of Molecular Catalysis A: Chemical 160 2000 189–197190

initio or first principles quantum mechanics.The latter involves brute force solution of theSchrodinger equation. The first two of these¨usually lead to reasonable geometries fororganometallic species, but there are generallyproblems related to the energetics. However,these methods may be used as pre-optimizer

Žbefore starting ab initio work although even.then considerable care is required , or applied to

deal with specific purpose, e.g. the evaluation ofbite-angles.

One of the more recent developments is theapplication of the first principles Car–Parrinello

w xmolecular dynamics method 1 in chemistry.One of the early reports on application to chem-ical reactivity was a 1994 paper on

w xmetallocene-based ethylene polymerisation 2 .This method is based on density functional the-ory, nowadays a very popular method in thestudy of many electron systems in both chem-istry and solid-state physics. The electrons aretreated fully quantum mechanically, the nucleiare treated classically in most current pro-grammes. The attractiveness of this method inthe study of chemical reactions lies in the factthat a chemical reaction inherently involvesatoms moving, and the wavefunction changesupon reaction. Therefore, a simulation techniquecomprising both nuclear dynamics and treatingthe electrons quantum mechanically seems themost appropriate tool for such an exercise. Be-cause the Car–Parrinello method is based on aplane-wave basis set rather than the traditional

Ž .localised orbital 1s 2s, 2p, . . . , etc., functionsbasis, there has been some skepticism amongchemists on the appropriateness of such a basisset for molecular calculations and its relativeaccuracy. We recently showed that very similaractivation energies are obtained for an alu-minium-based catalyst system when comparingCar–Parrinello results with traditional localised

w xorbital calculations 3 . For density functionalŽ .theory DFT , however, despite its advantages

and computational efficiency, the choice of thefunctional in terms of gradient corrections inparticular remains an issue of considerable im-

portance. Different gradient correction schemes,Žand hybrid methods like B3LYP which mix

some of the Hartree–Fock energy into the DFT.energy , may yield non-negligible differences in

relative energies, and therefore different relativestabilities, reaction enthalpies and activation en-ergies for chemical systems. Moreover, experi-ence has shown that some properties are in fact

Žexcellently calculated at the LDA level which.is the basic DFT without gradient corrections ,

whereas some other properties can only be eval-uated accurately with such corrections incorpo-rated in the calculations. Nevertheless, currentlythere is no scheme that yields correct relativeenergies. Computationally, for the most accurateenergies one still has to rely on very expensive,mostly entirely unfeasible, post-Hartree–Fockmethods such as coupled cluster and multicon-figurational methods.

Having said that, we have taken the point ofview that rather than focussing on accurate en-ergetics, which we believe is unfeasible for thereasons just mentioned, it is more appropriate totry and investigate the general mechanistic fea-tures of chemical reactions in general in order toprovide the experimental chemist with generalconcepts and ideas on reactions and reactionmechanisms. Moreover, simulations with thataim can be used to investigate already suggestedmechanistic aspects, and thus make a direct linkwith the work of the bench chemist. Althoughthe outcome of such simulations is obviouslyalso affected by the quality of the theoreticalmethod, i.e. in the present case the DFT variant,general mechanistic features can be recovered.More precise statements about the onset of phe-nomena as a function of, e.g., temperature arenot possible because of their dependence on thequality of the generated energy values.

In this contribution we first review some ofour earlier findings on homogeneous catalystsbased on first principles simulations, with em-phasis on the dynamics aspects. Next, after a

Žbrief description of the calculation details Sec-.tion 3 , we summarize our recent theoretical

Ž .work on the bisphosphine Cl PH Ru5CH2 3 2 2

( )R.J. Meier et al.rJournal of Molecular Catalysis A: Chemical 160 2000 189–197 191

complex and its monophosphine equivalentwhich were taken as model compounds for the

w xGrubbs catalyst 4 .

2. Explicit dynamics in homogeneous cataly-sis from MD simulation studies

Dynamics simulations are particularly usefulto study the flexibility, or stiffness, of molecularsystems. Full first principles calculations inher-ently take account of anharmonicity in the po-

Žtential again, precise effects will depend on thequality of the quantum mechanical method em-

.ployed, basis set size, etc. , and temperature canbe set explicitly to study systems at more realis-tic conditions than zero Kelvin as in static quan-tum mechanical calculations. Here we summa-rize some of our earlier findings.

There are several theories which could de-scribe olefin polymerisation, with those due to

w x w xCossee 5 and Brookhart and Green 6 well-known. The latter involves agostic interaction inthe insertion process. This is what was investi-

w xgated by MD simulations 2,7 . Fig. 1 displayson the left hand side the reaction profile in theform of the internal ethylene C5C bond lengthand the distance between one of the ethylenecarbon atoms and the methyl carbon bonded to

Ž . Ž .qthe metal centre in SiH Cp ZrCH C H ,2 2 3 2 4

revealing insertion of ethylene after some 150fs. The right-hand side plot of Fig. 1 displaysthe Zr–H distances for all three methyl hydro-gens as a function of time. Note that an agosticinteraction, characterised by one very shortZr–H distance, is formed prior to ethylene in-sertion. This phenomenon has been observedconsistently in series of simulations on Ti and

Ž . Ž .qFig. 1. Structure of the SiH Cp ZrCH C H complex. Left-hand side plot: Time evolution of the methylrethyl C–C distances during2 2 3 2 4

the molecular dynamics simulation. The solid curve represents the distance between the methyl carbon atom and the nearest ethylene carbonŽ . Ž .atom C13–C14 . The broken line represents the ethylene internal C–C bond length C14–C15 . Right-hand side plot: Time evolution of the

Ždistance between the Zr atom and each of the three hydrogen atoms belonging to the methyl group the original methyl group bonded to the.Zr . The time evolution of one of the hydrogen atoms depicted by the dotted curve shows the development of a-H agostic interaction. Later

Ž . Ž .on in the simulation after about 450 fs one of the other protons broken curve exhibits g-H agostic interaction.


w xZr-based metallocenes 2,7 . Another possiblynoteworthy aspect revealed from these simula-tions is the flexibility of the bis Cp system.Whereas one may anticipate that the valenceorbital system of the Cp rings may have stronginteraction with the metal’s d orbitals and there-fore the Cp rings may be tightened to the metalcentre, Fig. 2 shows significant fluctuations inthe Si–C–Cp angle.

Contrary to this bis-Cp metallocene case, theŽ . Ž .P–Pt–P angle in the H Pt PH –C H com-3 2 2 4

plex was found to show very little variationw xdespite the openness of this structure 8 . This is

illustrated in Fig. 3.These examples illustrate the potential of first

principles dynamics simulations to show ex-plicit dynamics effects and their relation to flex-ibility and stiffness of molecular species. More-over, also in a crystal structure atoms vibrate,and static structure minimisations might there-fore lead to different valence or torsional anglesas corroborated from experimental crystallo-graphic data. An example is the model structure

Ž .for the Grubbs catalyst, Cl PH Ru5CH , a2 3 2 2

system we will discuss in more detail in Section4. Experimental crystallographic studies on re-lated species give a value for the P–Ru–P bondaround 1678, whereas a static minimisation gave1808. A finite temperature simulation at Ts

Fig. 2. Time evolution of the Si–C–Cp angle in theŽ . Ž .qSiH Cp ZrCH C H system, where the coordinate taken2 2 3 2 4

for the Cp ring is the centre of gravity of the ring.

Ž . Ž .Fig. 3. Time evolution of the H Pt PH –C H complex during3 2 2 4

the molecular dynamics simulation. Shown are snapshots of themolecular structure during simulation, and a graph displaying thevariation of the P–Pt–P angle, which is very small despite thevery open structure of the species compared to the metallocenecomplex of Figs. 1 and 2.

3008C revealed an average P–Ru–P bond anglew xof 1608 9 .

3. Computational details for Ru-metathesissimulations

For a description of the soft- and hardwareemployed, and for aspects of the simulations,

w xwe refer to Refs. 2,7,9 . Vanderbilt-type pseu-dopotentials have been used, for ruthenium thevalence electrons treated explicitly included4s24p64d75s1. An energy cut-off of 25 Ry wasemployed for the plane-wave expansion. Gradi-

w xent corrections according to Perdew 10 andw xBecke 11 were included. Before starting a

molecular dynamics simulation, the molecularstructure was energy minimized using a steepestdescent routine, except for simulations starting

Ž . w xwith excess energy in the Ru–P bond s 9 .


4. Olefin metathesis with the Grubbs cata-lyst: a simulation study

Recently, olefin metathesis has attracted con-siderable attention, both for the reasons of fun-damental scientific interest as well as with re-

w xgard to potential practical applications 12 . In aw xvery interesting recent paper, Dias et al. 4

presented experimental data including a detailedŽ .study on the catalyst Cl PCy Ru5CHPh to2 3 2

investigate the mechanism of olefin metathesisusing this class of ruthenium–carbene catalysts.Their results clearly indicate that the most ac-tive species is a monophosphine complex, withthe bisphosphine complex being less active. Thehigher activity of the monophosphine was ex-plicitly demonstrated by addition of CuCl orCuCl to the bisphosphine complex, which are2

capable of binding a phosphine group capturedfrom the ruthenium complex. The pathway con-sidered most probable by Grubbs is illustrated

Ž .in the scheme below Scheme 1 . In the follow-ing part we will discuss the issue of the pres-ence and activity of the monophosphine com-plex. Further results on the bisphosphine equiv-

w xalent can be found elsewhere 9 .Our strategy in the study on the Grubbs

Ru-based metathesis catalyst, that is on theŽ .model species Cl PH Ru5CH for that cata-2 3 2 2

lyst and its monophosphine counterpartCl PH Ru5CH , has not been by probing the2 3 2

reaction path by constraining a reaction coordi-nate as normally practised in both static as wellas dynamics simulations of catalytic chemicalreactions. Our alternative approach is based onthe following considerations. Molecules un-dergo a chemical reaction when they have suffi-cient energy to overcome the activation energyfor that reactive process. In an ensemble of

Fig. 4. Maxwell–Boltzmann distribution of molecular speeds for atypical organometallic species and T s400 K.

molecules the molecular speeds show aMaxwell–Boltzmann distribution. For the molarmass of a typical homogeneous catalyst likediscussed in this paper, and a temperature ofTs400 K, this distribution looks as depicted inFig. 4. Here we see that there is a non-negligi-ble fraction, say close to 1%, that has a speed2–2.5 times the average speed, and thereforefour to six times the kinetic energy of theaverage species. Translated into the situation ofsimulating a single molecule, this implies thatsome molecules act as if they would have atemperature four to six times the given averagetemperature. Consequently, dynamics simula-tions at Ts800–1200 K could tell us some-thing about the chemistry of the molecules inthe high-end tail of the Maxwell–Boltzmannmolecular speed distribution.

We have applied this approach to the bispho-Ž .sphine complex Cl PH Ru5CH . Individual2 3 2 2

simulations were performed at Ts873, 1073and 1273 K. Results are shown in Fig. 5. Notethe strong fluctuations in the Ru–Cl distances,and the relative easy of the configurational ex-

Scheme 1.


Ž .Fig. 5. Snapshots of the Cl PH Ru5CH bisphosphine complex taken during dynamics simulations performed at Ts873, 1073 and2 3 2 2

1273 K respectively. Timings in femtoseconds as indicated with the structures. The graphs illustrate the variation of the Ru–P and Ru–CŽ .distances and the Cl–Ru–Cl bond angle 908scis, 1808s trans during the simulation. The 1073 and 1273 K plots show that at sufficiently

high temperature, or better stated for sufficiently high internal energy, the bis-phosphine is unstable and readily splits off one of itsphosphine ligands.


Ž .Fig. 5 continued .

change between cis and trans for the Cl–Ru–Clw xtriple 4 . The latter was a prerequisite for the

w xreaction scheme proposed by Dias et al. 4 toapply. The 1073 and 1273 K plots show that atsufficiently high temperature, or better statedfor sufficiently high internal energy, the bispho-sphine is unstable and readily splits off one ofits phosphine ligands. This shows that thesesimulations at least qualitatively reveal the ob-

w xservation reported by Dias et al. 4 that a fewper cent of the species is in the monophosphineform. Moreover, based on this informationwe have a qualitative explanation for the highactivity, as reported by Grubbs, of themonophosphine form compared to the bisphos-phine complex. As revealed from simulations

w xon the bisphosphine species 9 , considerablesurplus energy is required in the Ru–P bond inorder to have metathesis reactions proceed. Highenergies in a specific bond are realistic, al-though only expected in the far high-end of theMaxwell–Boltzmann distribution, and willtherefore be experienced by relatively fewmolecules only. For the bisphosphine, reactionrequires an enhancement of the energy in theP–Ru–P stretch vibrations which is signifi-cantly larger than the enhancement required for

the single Ru–P bond in the mono-phosphinecomplex. The consequence that excitation of asingle Ru–P bond in the monophosphine ismuch more likely than excitation of P–Ru–P inthe bisphosphine, qualitatively explains the highreactivity of the monophosphine compared tothe bisphosphine, although its abundance ismuch lower.

That the monophosphine is active in metathe-sis was shown from dynamics simulations pro-viding sufficient excess energy is available inthe Ru–P bond, viz. Fig. 6. Similar conclusionscould be drawn from simulations on the corre-

w xsponding bisphosphine 9 . In summary, ourdynamics simulations on both the mono- andbisphosphine complexes revealed and lend sup-port to the mechanism proposed by Dias et al.w x4 . These include, in the order of appearance inthe reaction scheme, the relative easiness ofCl–Ru–Cl cis–trans configurational exchange,carbene rotation and the loss of one phosphine,formation of a metallacyclobutane intermediate,and finally completion of the metathesis reac-tion. The presence of a small fraction of themonophosphine complex is confirmed by thepresent simulations. Starting from the observa-tion that selective bond excitation is necessary

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Fig. 6. Results from the molecular dynamics simulation on the monophosphine Cl PH Ru5CH rC H complex starting at T s0 K and during which temperature was allowed to2 3 2 2 4˚evolve freely. The initial geometry had a short Ru–P bond length of 1.86 A as a way of introducing excess energy in this bond. The snapshots show that a pure metathesis reaction is

observed. This is more clearly illustrated in the graph in which the time evolution of the C –C and the internal ethylene C5C distance are displayed.methyl ethylene


to exhibit reactivity, the higher activity of themonophosphine system compared to bisphos-

w xphine complexes reported by Dias et al. 4 canbe understood. We stress that we have alsofound that the bisphosphine is active, whichalso agrees with the experimental data. Finally,the fact that ruthenium–carbene complexesbased on sterically crowded phosphines giveshigher metathesis activity, can be rationalizedby their intrinsically more labile Ru–P bonds asindicated by longer Ru–P bond lengths.

Acknowledgements

Mr. Wick Kortenoeven is gratefully acknowl-edged for making the high-quality colour fig-ures.

References

w x Ž .1 R. Car, M. Parrinello, Phys. Rev. Lett. 55 1985 2471–2474.w x2 R.J. Meier, G.H.J. VanDoremaele, S. Iarlori, F. Buda, J. Am.

Ž .Chem. Soc. 116 1994 7274–7281.w x3 M. Reinhold, J.E. McGrady, R.J. Meier, J. Chem. Soc.,

Ž .Dalton Trans. 1999 487.w x4 E.L. Dias, S.T. Nguyen, R.H. Grubbs, J. Am. Chem. Soc.

Ž .119 1997 3887.w x Ž .5 P. Cossee, J. Catal. 3 1964 80–88.w x Ž .6 M. Brookhart, M.L. Green, J. Organomet. Chem. 250 1983

395–408.w x7 S. Iarlori, F. Buda, R.J. Meier, G.H.J. VanDoremaele, Mol.

Ž .Phys. 87 1996 801.w x8 B.B. Coussens, F. Buda, H. Oevering, R.J. Meier,

Ž .Organometallics 17 1998 795.w x9 O.M. Aagaard, R.J. Meier, F. Buda, J. Am. Chem. Soc. 120

Ž .1998 7174.w x Ž .10 J.P. Perdew, Phys. Rev. B 33 1986 8822.w x Ž .11 A. Becke, J. Chem. Phys. 96 1992 2155.w x12 K.J. Ivin, J.C. Mol, Olefin Metathesis and Metathesis Poly-

merization, Academic Press, San Diego, 1997.

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