Published: September 20, 2011 r2011 American Chemical Society 12017 dx.doi.org/10.1021/jp2062332 | J. Phys. Chem. A 2011, 115, 12017–12024 ARTICLE pubs.acs.org/JPCA Force Field Parametrization and Molecular Dynamics Simulation of Flexible POSS-Linked (NHC; Phosphine) Ru Catalytic Complexes Amirhossein Ahmadi, † Carl McBride, †,‡ Juan J. Freire,* ,† Anna Kajetanowicz, § Justyna Czaban, § and Karol Grela § † Departamento de Ciencias y Tecnicas Fisicoquímicas, Facultad de Ciencias, Universidad Nacional de Educacion a Distancia, Senda del Rey 9, 28040 Madrid, Spain § Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland ’ INTRODUCTION Computational techniques offer the opportunity to explore many aspects of the behavior of molecular systems. In the present work, we have investigated the possibility of using molecular simulations in the study of particularly complex structures that act as catalysts in important organic chemistry reactions. Olefin metathesis is a remarkable topic in current chemistry because it is a very efficient and elegant method of formation of CdC double bonds. 14 It is widely used not only in small-scale laboratory research chemistry, but also in large-scale industrial production. 5 Metathesis owes its unique role in modern organic chemistry to well-defined Ru-based (pre)catalysts. Replacement of a phosphine ligand with a N-heterocyclic carbene (NHC) ligand in Grubbs first generation catalysts (Gru I) 6 leads to NHC-based second generation catalysts (Gru II, Ind II, Ind II 0 ) that typically display better thermal stability and activities compared to first generation catalysts (Figure 1). 7 Although the metathesis (pre)catalysts have been successfully designed for stability, 8 functional group tolerance, 9 activity, 10 and selectivity, 11 enabling metathesis methodology to be broadly applied, this methodology does have some drawbacks. One of the most arduous tasks is the difficulty associated with the separation of the desired product(s) from the ruthenium catalysts, although they are typically used in small quantities, usually 15 mol %. This inconvenience prevents the wide employment of metathesis Figure 1. Examples of Grubbs (Gru) and indenylidene (Ind) type ruthenium catalysts. Generation two includes saturated and unsaturated mesityl-substituted (SImes and IMes) NHC rings. Received: July 1, 2011 Revised: September 16, 2011 ABSTRACT: In recent years, N-heterocyclic carbene (NHC) or phospine groups have been put forward as candidate catalysts ligands for olefin metathesis reactions to be performed using multistep methods. Some of these proposed ligands contain polyhedral oligomeric silsesquioxane (POSS) structures linked to NHC rings by means of alkyl chains. Some important properties for the prediction of catalytic activity, such as the theoretically defined buried volume, are related to the confor- mational characteristics of these complex ligands that can be studied through molecular dynamics simulations. However, the chemical structure of resulting catalytic complexes usually contains atoms or groups that are not included in the common forcefields used in simulations. In this work we focus on complexes formed by a catalytic metal center (Ru) with both phospine and POSS-linked NHC groups. The central part of the complexes contain atoms and groups that have bonds, bond angles, and torsional angles whose parameters have not been previously evaluated and included in existing force fields. We have performed basic ab initio quantum mechanical calculations based on the density functional theory to obtain energies for this central section. The force field parameters for bonds, bond angles, and torsional angles are then calculated from an analysis of energies calculated for the equilibrium and different locally deformed structures. Nonbonded interactions are also conveniently evaluated. From subsequent molecular dynamics simulations, we have obtained results that illustrate the conformational characteristics most closely connected with the catalytic activity.
Transcript
Published: September 20, 2011
r 2011 American Chemical Society 12017 dx.doi.org/10.1021/jp2062332 | J. Phys. Chem. A 2011, 115, 12017–12024
ARTICLE
pubs.acs.org/JPCA
Force Field Parametrization and Molecular Dynamics Simulation ofFlexible POSS-Linked (NHC; Phosphine) Ru Catalytic ComplexesAmirhossein Ahmadi,† Carl McBride,†,‡ Juan J. Freire,*,† Anna Kajetanowicz,§ Justyna Czaban,§ andKarol Grela§
†Departamento de Ciencias y T�ecnicas Fisicoquímicas, Facultad de Ciencias, Universidad Nacional de Educaci�on a Distancia,Senda del Rey 9, 28040 Madrid, Spain§Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
’ INTRODUCTION
Computational techniques offer the opportunity to exploremany aspects of the behavior of molecular systems. In the presentwork, we have investigated the possibility of using molecularsimulations in the study of particularly complex structures thatact as catalysts in important organic chemistry reactions.
Olefin metathesis is a remarkable topic in current chemistrybecause it is a very efficient and elegant method of formation ofCdC double bonds.1�4 It is widely used not only in small-scalelaboratory research chemistry, but also in large-scale industrialproduction.5 Metathesis owes its unique role in modern organicchemistry to well-defined Ru-based (pre)catalysts. Replacementof a phosphine ligand with a N-heterocyclic carbene (NHC)ligand in Grubbs first generation catalysts (Gru I)6 leads toNHC-based second generation catalysts (Gru II, Ind II, Ind II0)that typically display better thermal stability and activitiescompared to first generation catalysts (Figure 1).7
Although the metathesis (pre)catalysts have been successfullydesigned for stability,8 functional group tolerance,9 activity,10 andselectivity,11 enabling metathesis methodology to be broadlyapplied, this methodology does have some drawbacks. One of themost arduous tasks is the difficulty associated with the separationof the desired product(s) from the ruthenium catalysts, although
they are typically used in small quantities, usually 1�5 mol %.This inconvenience prevents the wide employment of metathesis
Figure 1. Examples of Grubbs (Gru) and indenylidene (Ind) typeruthenium catalysts. Generation two includes saturated and unsaturatedmesityl-substituted (SImes and IMes) NHC rings.
Received: July 1, 2011Revised: September 16, 2011
ABSTRACT: In recent years, N-heterocyclic carbene (NHC)or phospine groups have been put forward as candidate catalystsligands for olefin metathesis reactions to be performed usingmultistep methods. Some of these proposed ligands containpolyhedral oligomeric silsesquioxane (POSS) structures linkedto NHC rings by means of alkyl chains. Some importantproperties for the prediction of catalytic activity, such as thetheoretically defined buried volume, are related to the confor-mational characteristics of these complex ligands that can bestudied through molecular dynamics simulations. However, thechemical structure of resulting catalytic complexes usuallycontains atoms or groups that are not included in the commonforcefields used in simulations. In this work we focus oncomplexes formed by a catalytic metal center (Ru) with both phospine and POSS-linked NHC groups. The central part of thecomplexes contain atoms and groups that have bonds, bond angles, and torsional angles whose parameters have not been previouslyevaluated and included in existing force fields. We have performed basic ab initio quantum mechanical calculations based on thedensity functional theory to obtain energies for this central section. The force field parameters for bonds, bond angles, and torsionalangles are then calculated from an analysis of energies calculated for the equilibrium and different locally deformed structures.Nonbonded interactions are also conveniently evaluated. From subsequent molecular dynamics simulations, we have obtainedresults that illustrate the conformational characteristics most closely connected with the catalytic activity.
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reactions in pharmaceutical synthesis, wherein permitted levelsof such metallic contaminants are very low (for example, only5 ppm or below a total of 20 ppm if two or more are present fororal administration of members of the platinum group [Pt, Pd, Ir,Rh, Ru, and Os]).12 Because even multistep methods, incorpor-ating double purification on silica gel and treatment with acti-vated carbon,13 fail to reach an acceptable level of rutheniumimpurities, new techniques concerning separation are a subject ofinterest for many researchers.14
In previous work by some of the authors, the feasibility ofconnecting a second generation indenylidene catalyst with twoPOSS (polyhedral oligomeric silsesquioxane) moieties (for anexample, see Figure 2) was explored. A catalyst of this typeshould be active and stable and, additionally, because of its bulkysubstituents, should be easily separated after reaction via filtra-tion through polymeric membranes. However, although we wereable to obtain the desired catalyst, the yield was very low (around10%). Moreover, an activity test in the ring closing metathesisreaction of diethyl diallylmalonate gave rather poor results.These observations prompted us to study the optimal lengthof the linker between the aromatic ring and the POSS moiety.Different alkyl chain lengths imply different sizes of the sub-stituents close to the catalytic center and a different degreeof flexibility, which may have consequences for the catalyticactivity.
The main purpose of this paper is to establish the basis forperforming adequate numerical calculations that can help in theunderstanding and prediction of the catalytic performance ofthese types of flexible complexes. A precise theoretical predictionof such features can only be carried out using the help ofmolecular simulations; in particular, using molecular dynamics(MD). This technique is able to describe the dynamic trajectoryof the structure by solving classical mechanical equations.15,16
Given an array of atoms and a distribution of velocities (the latterassociated to the system temperature), these equations are ableto produce new positions and new velocities. These equations arenumerically solved using a simulation time step sufficiently smallso that forces can be considered to be constant and determinedby the potential energy defined by the given set of atomiccoordinates.
To proceed with this iterative numerical scheme, a potentialenergy depending on the atomic coordinates should be consid-ered. According to the molecular mechanics approach, differentfunctions are defined to describe interactions between differentatoms and atomic groups. Essentially, the parameters defineequilibrium values and force constants for bonds and bondangles. Changes in torsional angles, which are directly relatedwith the molecular flexibility, are also considered and they aredescribed bymeans of adequate functions, having several maximaand minima to represent energy barriers. Moreover, van der
Waals and electrostatic interactions between atoms are describedthrough relatively simple functions. All of this information iscontained in the so-called force field files.17
In this work, we make use of the PCFF force field.18 PCFF is amember of a consistent family of second generation force fields.They have been parametrized considering a wide range ofexperimental properties for organic compounds containinghydrogen, carbon, nitrogen, oxygen, sulfur, phosphorus, halogenatoms and their ions, alkali metal cations, and several biochemi-cally important divalent metal cations. However, PCFF (or anyother similar force fields19) does not contain some of theimportant information needed for the definition of the centralpart of the complexes considered in this work. In particular, itdoes not contain information about the parameters correspond-ing to the carbene atom in the NHC ring or how to describe thesomewhat loosely bonded structure around the metal atom.
To rectify this paucity of force field data for the region ofinterest, our approach has been to perform basic quantummechan-ics calculations on this central section. An energy minimizationis first carried out to determine its equilibrium constants. Theresults are then compared with bibliographic experimental datacorresponding to similar structures. Further calculations provideresults for the energies corresponding to different locally de-formed configurations. These results are then fitted to obtain thedifferent new parameters. These parameters are then added tothe standard PCFF force field, and subsequently, MD simula-tions of the catalytic complex structures immersed in an organicsolvent are carried out. The analysis of the results allows us toinvestigate some structural differences in the central part of thecomplex due to its bulky outer parts and also provides someconclusions concerning conformational characteristics that mayaffect their catalytic performance.
’METHODOLOGY
We have made use of the Materials Studio (MS) software suitfor some of the steps involved in the present study.20 The MSgraphic module “Visualizer” has been employed to build thedifferent complex structures. Quantum mechanics calculationsare performed for the energy by means of the module “DMol3”.This module allows us to perform an ab initio calculation basedon the density functional theory for the electronic structure andenergy for organic and inorganic molecules. Because the feasi-bility of this calculation strongly depends on the number ofatoms involved, we have restricted ourselves to the study of thecomplex central part (Figure 3) containing the atomic featuresthat need to be parametrized.
In DMol3, some different methodological options can beconsidered. We have undertaken a preliminary study to deter-mine the ability of the different options available in DMol3 to
Figure 2. Complex with alkyl chain links of three carbons.
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predict the well-known parameters corresponding to the struc-ture of simple alkyl molecules (bond lengths and angles and,particularly, the description of the potential energy correspond-ing to their torsional barriers). This verification has been carriedout using the same procedures that have been subsequently usedto study the complexes as described below. It reveals the need touse a gradient-corrected method (GC-PW91) in which allelectrons are included,21,22 considering a second set of valenceatomic orbitals and a polarization d-function on all nonhydrogenatoms (in the DMol3module, this corresponds to the DNDbasisset). We should note that the functional density theory has beenpreviously employed to obtain other force field parameters ofsome molecules.23
However, because the original PCFF schemeswere largely basedon the HF/6-31G* functional,18 we have performed a detailedcomparison between the energy results obtainedwithDMol3 (withthe indicated specifications) and the PCFF forcefield for differentvalues of the main torsional angle of the n-butane molecule. Wehave verified that both sets of data are similar (see Figure 4). Thisseems to validate the use of the chosen functional and algorithm.It is important to estimate the contribution of the nonbondedinteractions separately from the rest of the interactions,24 sincerepulsions between nonbonded atoms (hydrogen and carbon
atoms separated by four or five bonds) are not taken into accountin the definition of the PCFF torsional barrier function (thoughthey are reflected in the quantum calculations). However, theserepulsive regions are not relevant from a simulation point of view,since they are implemented via nonbonded interactions. Thus, adirect fit of the DMol3 results to the PCFF torsional functiondata in the region of the minima should provide us with anadequate description of the torsional barrier.
An initial geometry minimization yields an equilibrium struc-ture for the central section of the molecule. This structure isshown in Figure 3. It should be noted that in most Grubbsstructures the X-ray data25,26 show that hydrogens in the methinegroup are located in the plane formed by chlorine and Ru atoms.This type of discrepancy may be due to steric effects associatedwith the presence of bulky substituents. Further calculations areperformed for different deformed configurations of the centralstructure. Because we are focusing on specific features within amany atom structure, we have not carried out a general study interms of normal coordinates,23,27 but have restricted our energycalculations to a number of locally deformed configurations ofbond distances or angles. (In the case of bond and torsional anglevariations each particular deformation may involve several con-tributions). The results corresponding to different values of bonddistances, bond angle values or torsional angles are fitted toexpressions to describe these features included in the PCFFforcefield. In particular one has the following expressions
Vb ¼ kbðb� beqÞ2 ð1Þfor bond length, b, and
Vθ ¼ kθðθ� θeqÞ2 ð2Þfor bond angle θ (in radians). The subscript eq denotes theequilibrium value. See Figures 5 and 6 for illustrations of the fitscarried out to determine the parameters for bonds and bondangles.
For the torsional barriers, we use the function
VΦ ¼ kΦ½1 þ cosðmΦ� δÞ� ð3Þfor the barrier corresponding to torsional angle Φ (m is thenumber of minima and δ is a phase angle). The different ki
Figure 4. Variation of the potential energy, VT, with the torsional anglefor n-butane. Solid line, ab initio calculations; symbols, PCFF calcula-tions (total energy); dotted line, torsion barrier contribution; VΦ, alsofrom PCFF.
Figure 3. Optimized central part of the complex.
Figure 5. Fit of the DMol3 results for the energy variation with thecarbene�Ru distance to eq 1. Black squares, theoretical results; circleand spline line, eq 1 with the parameters shown in Table 2.
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parameters are constants associated to the simplest description offorces.
The van der Waals interactions between atoms i and j at Rdistance are expressed as
VVDWðrÞ ¼ εij½2ðrijv=rÞ9 � 3ðrijv=rÞ6� ð4Þwith the combination rules
rijv ¼ ½ðriiv Þ6 þ ðrjjv Þ6�1=6=21=6 ð5Þ
εij ¼ 2ðεiiεjjÞ1=2ðriiv rjjv Þ3=½ðriiv Þ6 þ ðrjjv Þ6� ð6ÞIt is worth stating that, from the point of view of performing
molecular simulations, it is important to have precise informationabout the equilibrium values. Our equilibrium results can becompared with bibliographic data obtained from X-ray experi-ments for similar model structures.25,26,28 This comparison isshown in Table 1. It can be verified that our bond length resultsare remarkably close to the experimental data. Some largerdifferences are found for the angles centered on the metal atom,which, for the model molecules, try to adapt to the presenceof more bulky substituents in the plane perpendicular to thephosphine�Ru�carbene axis. Therefore, this axis shows agreater deviation from linearity than in the case of our centralstructure. Also, the angles formed by the Ru atom and perpendi-cular atoms clearly depend on the substituents (significantasymmetries can be noticed in the experimental data correspond-ing to the different model structures). Therefore, we concludethat our calculations for the simplified central structure of thecomplex yield reasonable values of bond lengths and bond angles.
A very precise determination of the bond length and bondangle force constants, kb and kθ, is not quite so critical (actually,some simplified descriptions go as far as to use totally rigid bondsand angles). For the description of torsional barriers we haveperformed a full range sweep of the torsional angle values(in most cases, several torsional angles are coupled in a singleatom displacement). As in the case of butane, we have tried todiscern the cases where abnormal increases of energy along thebarrier are due to the presence of strong repulsive interactionsbetween nonbonded atoms, only performing fits to the energies
corresponding to the unaffected range of angles. The nonbondedinteractions should be computed separately from the rest of thecontributions.24 Fortunately, the disposition of atoms in thecentral part of this simplified central structure (particularly thealmost colinear carbene�Ru and Ru�P bonds) avoids anysignificant presence of nonbonded interactions. Actually, the abinitio calculated variations of energy are always compatible withreasonable values of the torsional force constants.
Figure 7 shows the fit corresponding to some coupled torsionson bonds involving the complex metal atom. The new torsionalbarrier parameters correspond to mainly rigid parts of themolecule. Therefore, the most relevant parameters to determineare the locations and the number of barrier minima (the flexibleparts of the structure, particularly the alkyl chain links, containgroups whose interactions are fully described in the originalPCFF forcefield.) These parameters are summarized in Table 2.
As we explained above, we do not expect dramatic changes inthe properties of these complexes due to nonbonded interactionsin the region surrounding the Ru atom. However, PCFF does notinclude parameters for the Ru atom and some van der Waalspotential-well values previously reported for Ru and similarmetals,24,29 are an order of magnitude smaller than the valuesof εii shown in the PCFF file included in MS for Pd, Pt and othertransition metals. For these reasons, we have performed anindependent evaluation, using the GC-PW91 functional.21,22
To this end, we have calculated the interaction energies betweenthese metal centers and an inert Ar atom, which is employed as atest particle.30 (The potential for Ar�Ar interactions obtained
Table 1. Comparison between our Theoretical Results forBond Lengths (in Å) and Bond Angles (in Degrees) for theCentral Structure and Experimental Data Obtained fromDiffraction Experiments.a
Figure 6. Fit of the DMol3 results for the energy variation with thecarbene�Ru�P bond to eq 2. Black squares, theoretical results; circleand spline line, eq 2 with the parameters shown in Table 2.
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from experiments are closely reproduced by the aforementionedfunctional as provided in the software, whereas a similar repro-duction for other noble gases would require a further nonimple-mented parametrization.31) The metal parameters are thenderived from fits of the results to eq 4. We have verified thatthe εij parameters for the Pd�Ar and Pt�Ar interactionsobtained with this fitting procedure differ by less than 10% fromthose predicted applying the PCFF values and combination rules.Therefore, it seems apparent that the applied method canprovide an adequate estimate of the van der Waals εij parameterfor this type of atom. Performing a similar calculation for theinteraction between Ru and Ar and comparing the results withthose corresponding to the Pd�Ar and Pt�Ar cases, we havefinally arrived at the van der Waals parameters of Ru that areshown in Table 2. These results are consistent with the range ofparameter values exhibited by other transition metals in thePCFF file.
The MD simulations are prepared following several steps.First, we build the whole molecular structure with the toolscontained in the graphical MS platform. In particular, we con-sider the unsaturated (NHC; phospine) complex shown inFigure 2 with links formed by an alkyl chain of 3 carbons (n = 3)and similar structures with n = 5 and 7. At this stage, charges forthe structure are calculated by using the charge equilibrationmethod.32 We have verified that these results are close to thoseprovided by our previous ab initio calculations for the centralregion. Charge values corresponding to the most significantcentral atoms are also incorporated in Table 2.
Next, we build a simulation box having periodic boundaryconditions using the MS module “Amorphous Cell”. AmorphousCell uses different simulation techniques and an initial minimiza-tion to create an initial configuration having a reasonably lowenergy. Our systems are constituted by a single complex structureplus 170 organic solvent (dichloromethane) molecules containedin a box that has cubic periodic boundary conditions. The volumeof this initial box is fixed so that density is about 70% of the
expected real density at room temperature. Subsequently we run ashort MD simulation for each system using the MS module“Discover”. This simulation provides some output files neededfor the final MD simulation runs, which are described below.
A difference with respect to the DMol3 module is that bothAmorphous Cell and Discover make use of a standard forcefield(such as PCFF). The introduction of our new set of molecularparameters in this procedure cannot be easily carried out byfollowing the procedures implemented in the MS software. How-ever, similar structures can be run by using conveniently modifiedmolecules.Here these temporary structuralmodifications consist in
Table 2. Selection of New Parameters Incorporated to theForce Field that are Related to the Special Features Present inthe Complex Central Structure
bond beq (Å) kb (kcal/mol/ Å2)
Ru�carbene 2.084 140
Ru�P 2.42 85
Ru�Cl 2.39 110
Ru�C 1.85 300
N�C (ring) 1.385 380
carbene�N 1.358 470
P�C 1.839 220
bond angle θeq (�) kθ (kcal/mol/rad2)
carbene�Ru�P 176 25
carbene�Ru�Cl 88 75
carbene�Ru�C 91 60
Cl�Ru�Cl 147 23
Cl�Ru�C 106.5 27
Ru�carbene�N 128 35
carbene�N�C(ring) 91 60
N�C(ring)�C(ring) 106 90
C�Ru�P 92.6 40
Cl�Ru�P 90.4 55
N�carbene�Ru 128 35
torsion angle kΦ (kcal/mol/rad) m δ (�)
N�carbene�Ru�P 0.7 2 0
N�carbene�Ru�C 0.7 2 180
N�carbene�Ru�Cl 0.7 2 180
carbene�Ru�P�C 0.13 3 180
C�Ru�P�-C 0.13 3 0
Cl�Ru�P�C 0.13 3 0
carbene�Ru�C�H 0.9 2 180
*�C(ring)�C(ring)�* 4.07 2 0
*�N�C(ring)�* 2.25 2 0
*�carbene�N�* 2.25 2 0
Nonbonded Interactionsvan der Waals εii (kcal/mol) rν
ii (Å)
Ru 3 2.9
highest charges for central atoms i qi
Ru 0.372
carbene in NHC ring 0.25
Cl �0.43
Figure 7. Fit of the DMol3 results for the energy variation with thetorsional angle N�carbene�Ru�P to eq 3. Black squares: theoreticalresults. Circle and spline line: eq 3, with the combined contributions ofthe N�carbene�Ru�P, N�carbene�Ru�Cl, and N�carbene�Ru�Cl barrier parameters shown in Table 2 (the coupled variation ofthe torsional angle associated with a second N atom in the NHC ring isalso included).
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substituting theRu atomby hexavalent S and bonding an additionalH to the carbene atom in the NHC ring.
For the MD simulation of the real systems, we use the opensource molecular dynamics software DL-POLY.33 This softwareoffers total flexibility when it comes to incorporating newforcefield parameters. Moreover, we have verified that its use inLinux platforms is consistently more efficient from a computa-tional point of view (the simulations being about 2�3 timesfaster when using the same number of parallel processors).
In DL-POLY, all the forcefield parameters to be used for thedifferent molecular mechanics elements of a given system(bonds, bond angles, torsional angles, and nonbonded inter-actions) should be explicitly specified one by one in differentinput lines. This can be a problem for systems where the numberof such elements is large (in our structure several thousandtorsional angles have to be defined). To circumvent this problem,we have written a bespoke Linux shell script. This script detectsall the elements system that are needed to be parametrized fromthe output connectivity file of MS Discover (the “mdf” file).Subsequently, the script reads the corresponding parametersfrom a forcefield file (in our case, an extension of the PCFFforcefield file in which we have incorporated our new para-meters) and writes the corresponding input “FIELD” file for DL-POLY.We have also written another Linux script that transformsthe MD output file containing the system coordinates fromDiscover (“car” file) into the input “CONFIG” input file in theformat required to run the DL-POLY simulations. Beforeexecuting these Linux scripts, we have reversed the aforemen-tioned temporary changes in the structures that were incorpo-rated solely for the purpose of preparing and performing theshort initial MD simulation with theMSmodules. These changesare limited to a couple of atoms so any structural deformationsthey cause are easily corrected after running a fewMD simulationsteps with the real structures.
The MD simulations with DL-POLY are performed in threesteps. First, a preliminary equilibration run of 1 ns is performed atthe initial lower density, maintaining constant volume andconstant room (298 K) temperature (NVT). The lower densityfacilitates a fast equilibration. This is followed by a further 1 nssimulation at constant pressure (NPT) which yields a systemwith density close to the real density for this system. Then finallya 5 ns production simulation is performed for the real densitysystem at constant volume. In all cases we use a 1 fs simulationtime-step. The analysis of the results is carried out by calculatingdifferent properties included in the trajectory data form theproduction run, frames or “snapshots” being saved every 25 ps.
’ANALYSIS OF RESULTS
We have analyzed different conformational characteristics ofthe complexes. First of all, we have investigated the results forknown bond lengths and bond angles along the trajectories.Most mean values for bonds and angles remain very close tothe equilibrium values introduced in the force field (obtained,as previously mentioned, from a simplified central structure).However, we observe a noticeable increment in the Ru�carbeneand Ru�P distances, both growing by approximately 0.1 Å. Thisgrowth seems to alleviate tensions introduced by the presence ofthe bulky branches attached to the NHC rings. It should be notedthat the constants for these particular bonds in the complex areparticularly small compared with typical covalent bonds, so thatthese greater deformations can be allowed. Table 3 contains the
mean quadratic radius of gyration of the complex and also themean distance between the Ru atom and the center of masses ofthe POSS cages. We can observe the expected increase of thesequantities with the link alkyl chain length (number of carbons, n)for the n = 3 and 5 cases. However, differences are smaller whencomparing the n = 5 and the n = 7 (for which a slight decrease ofthe radius of gyration can actually be observed). This suggeststhat the n = 3 link is mainly rigid, while the new bondsincorporated in the n = 5, 7 links lead to a considerably higherdegree of flexibility.
We have also determined the orientation between an axisassociated with the central part of the complex (carbene�P line)and the main chain axis of a potentially reactive molecule(propene) introduced into the system as a probe. The results,shown in Figure 8, demonstrate random orientations along thetrajectory. Therefore, the probe molecule is able to rotate freelyso that, in principle, the best orientation for a reaction can easilybe accessed.
We have also focused on the dynamic orientation of the twonormalized vectors connecting the Ru atoms with both POSScages 1 and 2, v1 and v2, characterized by the auto- and cross-correlation functions
CiðτÞ ¼ ÆviðtÞ:viðτ þ tÞæt=ÆviðtÞ:viðtÞæt ð7Þand
CPðτÞ ¼ ÆPðtÞPðτ þ tÞæt=ÆP2ðtÞæ ð8Þwith
PðtÞ ¼ v1ðtÞ:v2ðtÞ ð9ÞThe autocorrelation functions Ci(τ) exhibit a decay time of lessthan 1.5 ns (see Figure 9 for n = 3). Therefore, it is shown that the
Table 3. Structural Results for the Complex
alkyl chain length, n radius of gyration (Å2) Ru�POSS mean distance
3 11.23 ( 0.05 12.1 ( 0.1
5 12.98 ( 0.06 14.0 ( 0.2
7 12.58 ( 0.07 14.9 ( 0.3
Figure 8. Orientation (angle α) of the carbene�P axis in the complexrelative to the axis formed by the two terminal C atoms of a probepropane molecule. The trajectory frames were saved every 25 ps.
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molecule has completely reoriented over this period, which isconsistent with our use of 5 ns of simulation trajectory. The cross-correlation (Figure 10), however, exhibits a rather dynamicallyrigid structure, where both vectors maintain their mutual orienta-tions, close to antiparallel, during the simulation trajectory.
The buried volume is a useful property to predict the usefulnessof a metal ligand complex for catalytic purposes.34 It measures thespace occupied by the ligand in the first coordination sphere of themetal center. To calculate this property, we define a sphere ofradius R centered on the metal atom. We construct a tridimen-sional mesh of cubic elements of volume, s3, whose centers arewithin the sphere. We assume that all these elements are inside thesphere (the number of elements should be high enough so thatdifferences due to the incorrect assignment of the elementscontaining the surface as elements inside or outside the spherecan be neglected). Next we check whether the center of eachelement is within the Bondi radius (third column in Table 1 ofref 34) of any atom in the ligand, thus, defining if this element isoccupied or free. The buried volume is calculated as the percentageof occupied elements. Because our structures are flexible, thiscalculation should be averaged over all the trajectory frames.
For our calculation, we use the value R = 3.0 Å. The results arecontained in Table 4.We consider three sets of results. In the firstset we only take into account the atoms attached to the NHC.These numbers can be compared with results obtained forsimpler rigid NHC ligands. They show a greater occupiedvolume for the intermediate case, correlated with the previouslydiscussed changes in size and flexibility. However, the longeralkyl link tends to reduce the occupied volume. It seems that theextra flexibility in these links allow for a better accommodation ofthe bulky POSS cages. Our data are slightly higher to thosepreviously reported for ligands with other relatively bulkysubstituents with simpler chemical structures that were reportedto show34 percentages of buried volume ranging from 19 to 27%,see second column in Table 2 of ref 34. Therefore, the presenceof the alkyl links and POSS cages do not seem to impose furthersteric restrictions with respect to accessibility.
The second set of results corresponds to the buried volumesimultaneously due to both the NHC ring ligand and thesubstituents attached to Ru (two chlorine atoms and a =CH2
group). Obviously, it has a higher value but it seems to have asmaller dependence of the alkyl chain length, being slightlygreater for the intermediate (n = 5) alkyl chain link. We havealso evaluated the simultaneous occupied volume of the wholecomplex structure around the Ru atom, before the reaction takesplace. This reaches a significantly high value (about 75%) anddoes not show any significant variation with the link chain length.Because Ru, NHC-ring carbene, phosphorus, and the twochlorine atoms adopt an approximately planar configuration,the remaining free volume should be obviously located in theplane opposite to the =CH2 substituent, see Figure 3.
In summary, our methodological implementation of differentcomputational techniques has been able to provide some im-portant quantitative data on the conformational characteristicsrelated with the catalytic activity of a family of complexes formedby a metal and ligands with a relatively complex chemical.Naturally, this methodology can be applied to studies of othersimilar systems.
Present Addresses‡Departamento de Quimica Fisica I, Facultad de CienciasQuimicas, Universidad Complutense de Madrid, 28040 Madrid,Spain.
’ACKNOWLEDGMENT
This work has been supported by Project CP-FP 214095-2“HiCat” of the 7th framework programme of the EuropeanCommission. J.J.F. also acknowledges Grant CTQ2010-16414of the MICINN (Spain), and Grant P2009/ESP-1691 of the
Figure 9. Self-correlation of the vectors (crosses and circles) joining theRu atom with the center of the POSS cages.
Figure 10. Cross-correlation of the vectors joining the Ru atom withthe center of the POSS cages.
Table 4. Results for the Buried Volume
alkyl chain
length, n
% buried volume
by NHC
ring ligand
% buried volume
by NHC ring
and substituents
% buried volume by
NHC ring, phosphine,
and substituents
3 27 ( 3 50 ( 3 76 ( 1
5 32 ( 2 54 ( 2 76 ( 1
7 27 ( 3 50 ( 2 75 ( 1
12024 dx.doi.org/10.1021/jp2062332 |J. Phys. Chem. A 2011, 115, 12017–12024
The Journal of Physical Chemistry A ARTICLE
CAM (Spain). We are grateful to Dr. D. Wolf and Dr. C. Azap,Evonik Industries, for helpful discussions on the calculationof properties within the framework of the HiCat project, andProf. S. Pricl, University of Trieste, for her useful indications onparameter calculations.
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