3D-QSAR as a Tool for Understanding and ... - ACS Publications

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3D-QSAR as a Tool for Understanding and Improving Single-Site Polymerization Catalysts. A Review Victor L. Cruz,*,† Sonia Martinez,‡ Javier Ramos,† and Javier Martinez-Salazar† †

Biophym. Instituto de Estructura de la Materia, CSIC, Serrano 113-bis, 28006 Madrid, Spain Centro de Cálculo Cientı ́fico, Secretarı ́a General Adjunta de Informática (SGAI), CSIC, Pinar 19, 28006 Madrid, Spain

‡

ABSTRACT: This paper reviews the findings of quantitative structure−activity relationship (QSAR) studies focusing on single-site polymerization catalysts, with special attention paid to the use of 3D-QSAR tools. Such tools reveal the fine details of catalyst structure that may be correlated with polymerization activity or the properties of the synthesized polymer. The introduction of effective single-site polymerization catalysts, in addition to allowing scientists to synthesize new tailor-made polymers, has enabled a detailed theoretical analysis of the synthesis process. The benefits of single-site polymerization for theoretical studies include easy elucidation of the catalyst structure, a well-defined mechanism of action, and the fact that experiments can be systematically conducted on catalyst series featuring different substitution patterns. Using QSAR methods, experimental results can be related to theoretical measurements through statistical or chemometric tools. These tools have been extensively and successfully used in the field of drug design.

1. INTRODUCTION It is generally accepted in the fields of physics, chemistry, and biology that the intimate molecular structure of a molecule will determine its macroscopic properties. Many experimental and theoretical methodologies rely on this paradigm to understand the behavior of given molecular systems and thus develop new molecules with improved properties. Experimental studies in several fields have been based on high-throughput procedures designed to generate large quantities of experimental data. Then, using appropriate data mining tools, the corresponding structure−property relationships may be extracted.1−5 For instance, in the field of singlesite olefin polymerization catalysts, hundreds of polymerizations can be performed in a matrix of small vessels controlled by a robot. Each vessel is equipped with analytical tools that monitor different reaction variables and the properties of the resulting product.6 Some experiments have also addressed the performance of different catalysts.7 For example, the development of a Hf catalyst based on a pyridyl amine ligand for olefin polymerization by the Dow Chemical Co. was aided by results obtained using high-throughput screening technologies.8 Many research groups have explored the effects of experimentally modifying catalyst structure without the help of sophisticated and expensive high-throughput experimentation (HTE) equipment. The literature is replete with reports of this kind that offer information, usually qualitative, about the effects of different ligand composition on catalyst performance and polymer properties. Several studies have also theoretically addressed catalyst behavior during polymerization.9−14 Our group has actively contributed to this field with a number of computational studies.15−35 For this type of study, density functional theory (DFT) has allowed the treatment of polymerization catalyst © XXXX American Chemical Society

systems using the computational resources available at the time over the past 20 years. Here we review both experimental and theoretical studies designed to identify quantitative relationships between catalyst structure and behavior in olefin polymerization. These quantitative structure−activity relationship (QSAR) studies resemble those conducted in the field of drug design before the introduction of single-site catalysts.36−39 Today, the design of new drugs cannot be conceived without computational chemistry tools or, in other words, “in-silico” modeling. 3D-QSAR is among the most commonly used methods to design new more potent drugs against a specific target. The 3DQSAR method falls in the category of ligand-based design methods, since only information about the experimental bioactivity of a series of ligands is needed.40 This is the most common framework for the development of a more active drug. In the majority of cases, the detailed structure of a drug’s receptor is unknown. Despite knowledge of the primary sequence of millions of proteins, the 3D structures of only about 80000 of these proteins have been resolved, generally through X-ray diffraction or NMR techniques.41 Thus, many protein receptors have no known structure on which to base drug design. The rationale for ligand-based design methods is that ligand structure is the main factor related to the characteristic bioactivity of the target drug.42−47 It is assumed that all ligands target the same receptor and that they all interact with the same active site. Several techniques have been developed to examine such correlations, though rather than describing all available Received: July 22, 2013

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dx.doi.org/10.1021/om400721v | Organometallics XXXX, XXX, XXX−XXX

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Scheme 1. Ethylene Insertion and Propagation

Scheme 2. Proposed Polymerization Termination Mechanisms

ligand-based models, this review focuses on QSAR methods. These tools serve to assess correlations between experimentally measured activity and structural descriptors either obtained experimentally or calculated over a defined set of compounds or ligands with some expected activity. The literature contains over 17000 references to QSAR studies, mainly in the field of life sciences. Of these, some 4200 papers have examined the use of 3D-QSAR in drug design. The main difference between 3D-QSAR and QSAR is the nature of the structural descriptors used to obtain correlations. In QSAR, these descriptors are typically scalar numbers, whereas in 3DQSAR they are vectors or matrices corresponding to molecular fields defining the 3D properties of the system. The availability of 3D descriptors of molecular structure is one of the characteristics of 3D-QSAR considered most useful by drug designers.48 The models obtained using adequate chemometric tools enable scientists to examine in detail the molecular structure factors responsible for a given bioactivity. Single-site polymerization catalysis is a good framework for the application of 3D-QSAR tools, since the reaction

mechanism is well-known and, more importantly, the active sites of the catalysts have been well localized. As shown below, this is a remarkable advantage for the use of 3D-QSAR tools. A common outcome of single-site olefin polymerization is that the properties of the resulting polymer feature a narrow distribution around the mean in comparison to the much wider distribution observed for heterogeneous catalysis systems. This characteristic along with the uniqueness of the catalyst’s active site has prompted researchers to design new materials, focusing their attention mainly on catalyst structure.49 Special emphasis has been made almost in every QSAR study to search for correlations between structure and catalyst productivity. It is well-known that productivity is an overall experimental quantity including a series of individual steps and conditions which is characteristic of the polymerization process. However, it can be assumed that the variability exhibited by the polymerization productivity actually correlates with the catalyst structural variability in connection with the proposed polymerization mechanisms described below. B


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Scheme 3. 3D-QSAR Procedure

may also be characterized by the ligands surrounding its central metal atom. These ligands stabilize the central metal atom and build a specific steric environment around the atom. Collectively, the central metal atom, the growing chain, and the ligands attached to the metal atom constitute the geometry of the catalyst’s active site. The cocatalyst is another structural element that completes the catalyst complex.54 Its function is to activate the catalyst by partial dealkylation of the dialkyl precursor, leaving a vacant site at the central metal atom. The cocatalyst most commonly used for olefin polymerization is methylaluminoxane (MAO). However, the structure of MAO has still not been well determined, probably because of the mixture of oligomerization states obtained when MAO is formed in situ via the hydrolysis of methylaluminum. Cocatalyst structure plays a significant role in overall catalyst activity. The catalyst/cocatalyst forms a strong ion pair, the catalyst being the cationic species and the cocatalyst being negatively charged after methyl extraction. This ion pair may show strong interaction in the direction of the vacant site, hindering the olefin approximation and insertion process. In a nonpolar solvent, the ion pair will be tightly bonded, leaving the vacant site less accessible to the incoming monomer. In effect, it has been experimentally shown that polar solvents such as toluene are more effective for polymerization than, for example, the more hydrophobic solvent n-hexane. Hence, it should be ensured that the catalyst/cocatalyst interaction is sufficiently weak to allow coordination of the olefin to the central metal atom. Steric hindrance around the metal atom can be viewed as an important factor favoring ion pair separation, thus improving catalyst activity. This has been confirmed both experimentally and theoretically.21 In the sections below, catalyst/cocatalyst interactions are examined in terms of their effects on the interpretation of QSAR results. Prior to this, we describe the basic principles of the use of 3D-QSAR tools and the information they provide.

In fact, many other researchers also contemplate an equivalent assumption, as can be deduced from the large list of publications available in the literature regarding QSAR analysis of catalyst systems as collected in this review. The olefin polymerization mechanism of homogeneous catalysis originally proposed by Cossee and Arlman50,51 or Brookhart and Green52,53 is the generally accepted mechanism. The basic details of the system are shown in Scheme 1. The catalyst features a vacant coordination site and an aliphatic group bound to the central metal atom. In an initial step, the olefin approaches the central metal atom through the vacant site so that the double CC bond faces the electron-defective metal atom. In a subsequent step, the double bond is debilitated by the charge-transfer process of donation and back-donation between the bond and the metal atom. At the same time, weakening of the contiguous metal−alkyl bond causes elongation of the metal−Cα connection. Thus, in the transition state, a four-membered ring is formed by the metal atom, Cα, and both incoming ethylene C atoms. Finally, the metal atom bonds to the nearest ethylene C atom and the other ethylene C atom bonds to the Cα. The effective process is one insertion of an ethyl unit in the growing polymer chain. This process is repeated until a termination reaction occurs. The most accepted termination reactions are β-transfer to the monomer and β-hydrogen elimination11 (see Scheme 2). Both require activation of a H atom of Cβ for agostic interaction with the metal atom. The activated H can bind to one C atom of the incoming ethylene molecule, leaving the Cβ atom doublebonded to the Cα, which breaks its bond with the metal. The result is a vinyl-terminated polyolefin chain and an ethyl group bonded to the metal atom, which is able to initiate a new polymer chain. In contrast, the β-elimination mechanism involves hydride formation by direct bonding of Hβ to the metal atom, releasing a vinyl-terminated chain. Several studies have shown that the former β-hydrogen transfer to monomer mechanism is energetically more favorable than the β-hydrogen elimination procedure. According to these proposed mechanisms of single-site olefin polymerization, a series of common features can be derived independently of catalyst structure. Two of these features could be the central metal atom, which is the main factor responsible for the charge transfer processes that take place in each catalytic step, and the Cα atom of the growing alkyl chain, where insertion of a new ethylene unit occurs. In addition, the catalyst

2. 3D-QSAR TOOLS 3D-QSAR modeling combines chemical concepts and statistical tools in a framework of linear regression.55 The main goal of 3D-QSAR is to correlate molecular field descriptors for a set of well-defined chemical compounds with their activity or another property of interest. Molecular field descriptors are structural properties determined in a 3D grid of points defined around each molecule.56 For example, the steric C


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Figure 1. (a) Points used for the alignment rule. (b) Alignment of the training set molecules and cubic region used to calculate the 3D fields. H atoms have been omitted for clarity (image from ref 109).

field is assessed by placing a probe particle, usually an sp3 C atom, at each grid point and calculating the Lennard−Jones energy of interactions with all of the atoms of a particular molecule using parameters extracted from a force field. Other fields such as electrostatic interaction energy, molecular orbitals,57 and conceptual DFT local descriptors58,59 can also be used in 3D-QSAR models. In the simplest of cases, this type of modeling tries to correlate a dependent scalar variable with a large number of molecular field descriptors. In drug design, it is typical to start with tens of compounds for which some property/activity has been experimentally determined. This compound set is divided into two subsets: a training set comprising most of the compounds, used to derive the QSAR model, and a test set, used to assess the predictive capacity of the model. The main aspects of the 3D-QSAR method are explained in the following sections with the help of Scheme 3. 2.1. Molecular Alignment. The 3D descriptors are defined in a grid of points around the molecular structure (see the lattice structure represented in Scheme 3). The grid should be the same for all molecules to compare descriptors and infer their relationship with the dependent variable. The molecules themselves should be aligned in a rational manner so that the spatial distribution of descriptors has the same meaning for all molecules. Molecular alignment is critical for 3D-QSAR modeling,60 and any misalignment generally gives rise to a poor model. How to align molecules is a chemical question. In the field of drug design, a common skeleton is employed for all of the molecules used in the alignment. The pharmacophore, which is a set of chemical groups arranged as a defined 3D geometric pattern, provides a suitable skeleton.61−63 However, in singlesite catalysis, the active site is usually well defined and can offer the desired skeleton to build the alignment. For example, the active site of a metallocene catalyst for olefin polymerization has been well localized at the metal center. Thus, as a framework for molecular alignment, 3D-QSAR studies performed on metallocene catalysts have used the metal atom along with the aromatic ligand centroids and olefin chain initiator Cα atoms.64−67 Figure 1a indicates these points used to align the set of catalysts. The resulting alignment for a given case is provided in Figure 1b. The set of atoms or geometric characteristics used to align the compounds is known as the alignment rule.68

2.2. Molecular Fields. First, a region in space encompassing all the aligned molecules is defined. This definition consists of the upper and lower limits in each Cartesian coordinate and a grid spacing between points in each direction. The grid spacing and its dimensions define the number of points and the detail at which the molecular field is calculated. Fields that are too detailed contain a large number of points. This can be statistically dangerous because the chances of adding noise instead of signal to the model will increase with the number of points or descriptors considered. Conversely, a region that is too coarse could result in the loss of important information. Thus, the recommendation is to try different grid spacings. Spacings of 1 or 2 Å seem to achieve a good balance between sufficiently detailed information and statistical robustness.69 In principle, any structural property that can be assessed in a grid of points arranged around molecules is suitable for analysis. In the original comparative molecular field analysis (CoMFA) papers,56,70 steric and electrostatic fields were considered to explain the bioactivity of a selected set of catalysts. In Scheme 3, the molecular field is evaluated at each grid point and indicated in the columns of a table, in which the different compounds appear in the rows. This table is subsequently treated by statistical modeling to derive the QSAR equation. 2.3. Partial Least-Squares (PLS) Modeling. As commented on above, a dependent variable set is obtained containing tens of scalar values that we want to correlate with a descriptor space consisting of molecular fields determined on a grid of points around each molecule. We may therefore have thousands of these points (see the different columns in Scheme 3), each being a descriptor. Standard multivariate analysis methods cannot be used here because the descriptors are not independent from each other, giving rise to overfitted models. Wold’s group developed the partial leastsquares (PLS) procedure to deal with this type of data set.71 Basically, the PLS procedure consists of constructing linear combinations of descriptors, called latent variables (LV, see Scheme 3), with two characteristics: namely, they are mutually orthogonal and they fit to the dependent variable set. These LVs are equivalent to principal components in the sense that they are mathematical constructs able to explain most of the variance in the descriptor space. In principle, it is not intended that these LVs have physical meaning; they are only used in a suitable statistical manner to perform the regression analysis. The number of LVs that can be generated is as many as the number of dependent variables. However, only a few LVs will D


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descriptors. This expression can contain thousands of terms, one for each descriptor value at each grid point (see the final equation in Scheme 3). The practical way to analyze this long expression is through its graphical representation in molecular space. Considering that each term in the QSAR equation corresponds to a grid point, the different statistics obtained for each point can be plotted in the form of contour maps or isosurfaces on top of the molecular geometry. This representation allows the identification of molecular areas associated with a given statistical characteristic. The measure most recommended to represent explanatory power is the product of multiplying the QSAR equation coefficient at each grid point by the standard deviation of the molecular field at that point. On one hand, the coefficient gives an idea of the contribution of the given point to explain the observed activity/ property, and on the other hand, the standard deviation gives information about the variability of the molecular field values of all the compounds at that point. Logically, a low standard deviation means that the information contributed by one compound’s field at that point is indistinguishable from that provided by another compound’s field. Thus, the product of the coefficient times the standard deviation may be plotted in the form of isosurfaces, embedding values above or below a determined threshold on top of the molecular structures. In Figure 3, a map of the above product is shown for the steric field. The color convention is that green represents the more positive values of the coefficient times the standard deviation and yellow the more negative values. The interpretation of the map is that increasing the steric field in the green areas will improve the target activity/property. This could be achieved, for example, by introducing a larger group and thus more steric hindrance around that position. Conversely, the yellow areas indicate regions where additional steric hindrance will be detrimental for the catalyst’s activity. The different descriptors entering the QSAR equations can be represented simultaneously on the same molecular geometry to gain insight in the combined effect of those fields on the target property. For this combination to be useful, it is a common practice to represent, for example, the electrostatic field most prominent contributions in red and blue. The red areas would indicate where an increase in negative charge would contribute to enhance the measured property, whereas the blue areas would be associated with a constructive effect of positive charge on the dependent property. The perspective offered by the 3D techniques supposes an extra degree of specific information over the most traditional monodimensional QSAR models. The descriptors can be precisely located in the molecular 3D space in the form of isosurfaces, in contrast with the definition of scalar quantities built from simpler geometrical parameters which represents a global descriptor of each molecule. The joint graphical representation of the molecular structure and the QSAR information can be very intuitive for a chemist. 2.4.2. Predictive Power. The cross-validation procedure gives information about the predictive capacity of the model. The q2 regression coefficient is a very conservative statistic that may give an impression of how predictive a model is. Its values range from 1, which indicates excellent predictive power, to 0 or even negative values. In drug design, it is common practice to consider models with q2 values above 0.5, which is halfway between complete predictive capacity and no predictive power at all.

be sufficiently robust to obtain a meaningful regression. In principle, the more LVs used in the data fitting process, the better the correlation coefficient. Notwithstanding, there is a certain number of LVs above which improvement in the correlation coefficient is small and is achieved at the expense of adding complexity to the model. An appropriate number of LVs can be calculated by checking the predictive capacity of the models obtained using a different number of components. Predictive capacity can be measured using methods such as cross-validation, which involves the systematic elimination of one (leave one out, LOO) or some (leave some out, LSO) of the compounds in the training set and derivation of a model with the corresponding regression statistics to predict the eliminated compounds. The main statistics calculated are the cross-validated regression coefficient q2 and the predictive sum of squares (PRESS): N

PRESS =

∑ (Yobs,i − Ypred,i)2 i=1

q2 = 1 − PRESS/SSD

where Yobs,i and Ypred,i are the actual and predicted dependent variables, respectively, and SSD is the sum of the squared deviations of each dependent variable from the mean of all dependent variables. The final result of the cross-validation process is a table of q2 and PRESS values for each number of LVs considered. The model returning the highest q2 value and lowest PRESS value is the more suitable model, but we should select the model comprising the smallest number of LVs showing similar predictive capacity. Once the most significant number of LVs has been selected, the PLS procedure can be repeated without validation on all compounds. The fitting procedure will yield the known regression coefficient (r2) and a standard error of estimate (SEE). Figure 2 provides a typical plot of predicted vs actual dependent variables obtained for a training set of zirconocene catalysts. The model fit corresponds to an r2 value above 0.9. 2.4. Results Analysis. The models obtained using the PLS procedure have both explanatory and predictive power. 2.4.1. Explanatory Power. Explanatory or modeling power is conferred by the mathematical expression obtained for the relationship between the dependent variable and 3D

Figure 2. Experimental versus predicted activity plot. All values are expressed as logarithm units (image from ref 109). E


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Figure 3. Standard deviation times the 3DQSAR coefficient for the steric field mapped onto a selected catalyst (image from ref 109).

of commercial software. However, it has not yet been sufficiently tested to confirm its capacity being similar to that of the older software.

Despite the conservative nature of the cross-validation procedure, there is, however, a non-negligible possibility of chance correlations. Redundancy is the problem that will most compromise the cross-validation procedure. If several compounds in the test set show high correlation, the presence of a compound similar to one discarded in the LSO or LOO process will yield a predictive q2 value that is too optimistic. Obviously, the solution is to check redundancies prior to the PLS procedure and eliminate the redundant set. If redundancy is difficult to confirm, a useful tool may be the progressive scrambling procedure. Progressive scrambling72−75 is a technique that assesses the robustness of a cross-validated PLS model. It essentially scrambles the set of dependent variables across observations, so that the descriptor vectors corresponding to each compound are repaired at random with the dependent variables (activities in our case). If such a scrambled data set generates significant cross-validation statistics, some signal is being generated from random noise and the model should be abandoned. The final model can be used to predict the activity/property of any new untested compound that may not even be synthesized. The structure of the new molecule should be aligned following the alignment rule and the molecular fields calculated. Finally, the field values are entered in the QSAR equation, resulting in a predicted value for the target activity/ property. 2.5. Software Available for 3D-QSAR Studies. There are a number of software packages available for 3D-QSAR modeling in addition to the CoMFA module in the Sybyl package distributed by TRIPOS.76 Commercial software able to perform 3D-QSAR can be also found in the field-based QSAR module of the Schrodinger suite of programs.77 All of this software is very robust, and the underlying technology is well established, despite being black boxes closed to user modification. A main benefit of this software is that all steps of the 3D-QSAR procedure can be easily executed with the help of a user-friendly interface. Moreover, special descriptors such as those derived from conceptual DFT models can be easily imported into the procedure. There is also some software available to the public such as the recently published Open 3DQSAR package.78 This enables data manipulation similar to that

3. QSAR AND 3D-QSAR APPLICATIONS IN SINGLE-SITE POLYMERIZATION CATALYSIS The behavior of metallocene catalysts in the polymerization of ethylene and other α-olefins has been the focus of attention in the past 30 years. In the topic’s early days, Kaminsky and coworkers reported that the use of the (Cp)2ZrCl2 catalyst with MAO as cocatalyst yielded high amounts of polyethylene.79 Since then, many studies have addressed catalyst structure effects on catalyst activity and the properties of the final polymer. The following section provides an overview of some of these studies, classified according to the structural family of the catalyst. The aim of this overview is to point out the large amount of qualitative and QSAR studies in this area and how 3D-QSAR methodologies can be used to shed light on the effect of the catalyst structure on the catalyst activity. Figure 4 presents the general structure of the catalyst species reviewed in this paper. Each substituent described in that figure has an associated reference where the corresponding catalyst is studied. 3.1. Metallocene Catalysts: Bis-Cyclopentadienyl Type, Indenyl Type, and ansa-Metallocene Type. 3.1.1. Qualitative and QSAR Studies. The (Cp)2ZrCl2 catalyst family and its derivatives (CpR)2ZrCl2 have received much attention. Most studies in the field have examined the outcome of varying R in terms of steric or electronic effects on the cyclopentadienyl ring. Chien et al.80 examined (CpR)2ZrCl2/MAO systems (R = H, Me, Et, NM) for ethylene polymerization and concluded that both steric and electronic effects play a role in polymer chain propagation and catalyst decay. These authors indicated that single alkyl substituents in each Cp ring increased polyethylene production by enhancing electron donation during coordinated anionic propagation. The size of the substituent had the opposite effect in that it hindered monomer approach, so that very bulky substituents caused a reduction in catalyst activity. F


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Figure 4. Catalyst structures reported in this review. Superscript numbers correspond to references where the structure is included.

The activity order determined was (MeCp) 2 ZrCl 2 > (EtCp)2ZrCl2 > (NMCp)2ZrCl2 > Cp2ZrCl2. Single neomenthyl (NM) substituents in Cp rings increased polymerization activity through electronic effects. Any steric effect such as that of NM size was insufficient to significantly reduce activity relative to Cp2ZrCl2. However, in a study of (CpR)2ZrCl2/MAO catalyst (R = H, t Bu, Me3Si) systems, Nekhaeva et al.81 observed a lower activity of the tBu-containing catalyst in comparison to that of Cp2ZrCl2, due to the size of tBu. In contrast, when R = Me3Si, the activity of the system was increased over that noted for the use of Cp2ZrCl2. Thus, the activity tendency detected was (Me3SiCp)2ZrCl2 > Cp2ZrCI2 > (tBuCp)2ZrCl2. Considering the similar steric effects of R = tBu and R = Me3Si, the authors attributed the greater activity of the latter to electronic effects of the Si atom. This finding contradicts Chien’s conclusions:80 i.e., that polymerization rates for ethylene using (CpR)2ZrCl2 as catalyst increase with an increasing electron-donor effect of the R substituent in the cyclopentadienyl ring. Hence, it does not seem that most of the activity of this type of catalyst in

polymerization is conferred only by the electron effects of substituents in the Cp ring, and steric effects also need to be taken into account. Although the different studies tried to rationalize activities in terms of the electronic and steric effects of the catalyst, no efforts were made to quantify these effects. Mohring and Coville were the first to quantitatively assess the effect of a ligand on ethylene polymerization using this type of catalyst.82 The activity order observed for the (CpR)2ZrCl2/ethylalumoxane (EAO) systems examined (R = H, Me, Et, iPr, t Bu, SiMe3, CMe2Ph) was tBu > SiMe3 > Et > iPr > H > Me = CMe2Ph. These data were explained in terms of a quantitative combination of steric (measured as the cone angle with the metal atom as apex) and electronic (measured as different Hammett functions, H) parameters. The authors concluded that an increase in steric ligand size led to a small increase in polymerization activity, while an increase in ligand electrondonating capacity substantially increased catalytic activity. This electronic effect was estimated to approximately account for 80% of the activity change. The QSAR expression was G


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reduced 1-hexene incorporation in the polymer. However, the two split methyl substitution catalysts (R = 1,3-Me2, 1,2,4-Me3) showed a greater comonomer response than their di- and trisubstituted counterparts (R = 1,2-Me2, 1,2,3-Me3). The above results and those of several other studies in the field revealed that the influence of the ring substituent in (CpR)2ZrCl2 complexes in α-olefin polymerization reactions was also substantial.89 Numerous studies examining the effects of varying the R group have reported detectable changes in catalyst activity and polymer characteristics. The findings of these studies also indicate that the activity ordering for the same group of catalysts depends on the cocatalyst used.81,82 Thus, Yao et al. quantitatively evaluated the effects of several fluorinated borate cocatalysts (B(Ph-Fn)4−1 (n = 0−5)) in ethylene polymerization using Cp2ZrCl2 as the catalyst.90 Through the use of QSAR techniques, these authors concluded that the space around the metal center is important for activity and the potential energies of the Zr and B centers and their interaction energies did not play as great a role as spatial factors. In work performed by Mallin et al. on metallocene catalysts based on titanium, the effects of different substituents in titanocene catalysts used for ethylene polymerization were examined.91 The following order of activity was noted: Cp 2 TiCl 2 > (CpR)CpTiCl 2 > (CpR) 2 TiCl 2 (CpR = CpMe4iPr). These results indicate that the greater the steric bulk around the titanium metallocene, the lower the activity of these catalysts. More recently, several studies have addressed the influence of the metal center in the homopolymerization and copolymerization of different α-olefins using bis(cyclopentadienyl)zirconocene and -hafnocene complexes through the assessment of elementary chain propagation and termination reactions using a DFT method.92,93 Differences in activation energies for chain propagation and termination were found to be smaller for the zirconocene catalyst. In line with experimental observations, these studies have revealed that polymers produced using the zirconocene complex have molecular weights lower than those produced using the hafnocene complex. The effects of substituents in the Ti-based catalytic system (CpR)(CpR′)TiCl2/Et3Al2Cl3 (R = R′ = H, Me, Et, iPr, tBu, SiMe3, CMe2Ph, CO2Me and R = H, R′ = Me, tBu, SiMe3, CMe2Ph, CO2Me) for ethylene polymerization were also quantitatively assessed by Mohring et al.89 These authors found that the steric effect was responsible for activity ordering and only the unsubstituted catalysts and those with one small substituent exhibited high activity. The marked difference between these systems and their Zr analogues was ascribed to the smaller size of the Ti atom. From the above studies it can be deduced that both electronic and steric effects play a significant role in this type of reaction, yet no simple correlation exists between these factors and catalyst activity. Several attempts have been made to separate steric from electronic effects and to link some quantitative factor to a steric effect. Most of the data generated so far point to the existence of a steric threshold in metallocene catalysts, and once this threshold has been exceeded, both electronic and steric factors will come into play and affect catalyst activity.94 Other polymerization catalysts frequently used feature indenyl (Ind) or fluorenyl (Flu) rings as ligands instead of cyclopentadienyl (Cp) rings.

activity = 0.04(θ1) − 84.44(F )

where θ1 is the cone angle and F a Hammett parameter. Thus, the activity trend noted by Mohring differed from the trends reported by Chien (Me > Et > H) and Nekhaeva (SiMe3 > tBu). Such differences were attributed by Mohring to the different cocatalysts used. Rytter et al. also undertook a quantitative investigation of the catalytic activity of (CpR)2ZrCl2 (R = H, Me, 1,2-Me2, 1,3-Me2, 1-Me-2-Et, nPr, nBu, Me4, Me5).83 Through quantitative structure−activity relationship (QSAR) modeling, the propagation rate constant, obtained by kinetic modeling of the activity−time profile, was related to changes in 17 geometric and electronic descriptors derived from quantum chemical (QM) calculations on a transition state model for each catalyst. After exclusion of the 1-Me-2-Et catalyst as an outlier, the final model, with one principal component, indicated that the propagation rate constant was positively correlated with descriptors related to catalyst size (principal moment of inertia, radius of gyration, and the number of rotatable bonds) or with the partial charge on Zr and increasing Cp−Cp angle. Negative correlations were detected with the LUMO−HOMO energy gap and Zr−Hγ distance (r2 = 0.75 after leave-one-out crossvalidation). Subsequent to this, Coville et al. performed a study on ethylene polymerization using (CpR)2ZrCl2/MAO (R = H, Me, Et, iPr, tBu, SiMe3, CMe2Ph) catalysts.84 Following similar criteria used in a prior study on the same series but using EAO as cocatalyst,82 activities were ordered as follows: Et ≈ SiMe3 > i Pr > Me > H > tBu > CMe2Ph. When this rank order was compared to the order reported in their previous study, tBuand CMe2Ph-substituted complexes showed a lower activity than expected and this was attributed by the authors to intramolecular coordination of these substituents to the catalyst’s metal center, thus inhibiting the reaction. For the copolymerization of ethylene and 1-hexene, Möhring and Coville quantitatively explored the behavior of the same group of catalysts using EAO as cocatalyst.85 The steric and electronic factors assessed were the same as in their previous work.82 The electronic effect was again found to be dominant, accounting for around 87% of activity. However, both steric and electronic factors were responsible for the differences in activity observed between catalysts, and the reduction in activity produced by either steric or electronic parameters alone was insignificant. Further, the activity was markedly lower for homopolymerization than for copolymerization (except for R = H, for which the activity remained unchanged). Also, copolymerization activity decreased as the catalyst bulk increased. This can be explained by an increased difficulty for 1-hexene to approach a bulkier catalyst. However, the activity was also reduced for an increasing electron-donating capacity of the substituents. The authors proposed that electron-donating substituents stabilized the active cationic center and hence binding with 1-hexene could be improved. Rytter and co-workers also examined ethylene homopolymerization and ethylene/1-hexene copolymerization using methylsubstituted (RnC5H5−n)2ZrCl2/MAO catalytic systems (R = H, Me, 1,2-Me2, 1,3-Me2, 1,2,3-Me3, 1,2,4-Me3, Me4, Me5).86−88 In ethylene homopolymerization, lower activities were observed for Me4 and Me5, while in the ethylene/1-hexene copolymerization procedure, activities were relatively enhanced. When comonomer incorporation was examined, an increasing number of methyl substituents in the Cp ligand generally gave rise to H


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polymerization activity, as the relative stability of the cation is systematically increased. Finally, electron-donating substituents in the Cp′ ligand were observed to enhance the electron-donating capacity of the ligand, thus stabilizing the cation. Electron-withdrawing groups had the opposite effect. On comparison of these results with experimental observations it was concluded that electronwithdrawing substituents had a reducing effect on polymerization activity due to the stability of the cation. However, the effect of electron-donating substituents was less clear; although the stability of the cation is an important prerequisite, it was insufficient to produce an active catalyst. Although alkyl groups are weak electron donors, bulkier alkyl groups stabilized the cation more effectively at the cost of increasing steric hindrance. In a further study, the effect of the metal center in ethylene polymerization was examined along with the effect of the bridge structure of ansa-metallocene complexes activated by MAO.100 The catalytic systems tested were [(CH2)nC(C5H4)2MCl2] (M = Ti, Zr, Hf and n = 4−6), [(CH2)4Si(C5H4)2MCl2], and [Me2C(C5H4)2MCl2], where M = Ti, Zr. In a study by the same group,101 the effect of the bridge on activity was also explored in detail. It was observed that in all cases the titanocene catalysts exhibited much higher activities than the corresponding zirconocene and hafnocene analogues. Structure−activity relationship procedures revealed that the dimensions of the small carbon atom bridge were well-suited to the coordination requirements of the smaller titanium atom, while the dimensions of the large silicon atom bridge better matched the coordination requirements of the larger zirconium atom. Both of these bridged complexes achieved the least steric hindrance of the metal while retaining the stability of the metallocene compounds and showed higher activities than the unbridged or other ansa-metallocene complexes. The introduction of a cycloalkylidene or 1,1-silacyclopentylidene bridge, especially the bulky cycloheptylidene bridge, could improve the stability of the ansa-titanocenes and increase their activity for ethylene polymerization. The insertion of polypropylene was addressed using the catalytic system Me2Si(R-Ind)2ZrCl2/MAO, where R = H, Me.102 The results of this study indicated that, for the catalyst R = 2-Me, the activity was 8 times higher than that observed for the catalyst R = H, while the polymer molecular weight was 3 times higher. The activity order was in line with that detected by other authors and revealed that electron-donating groups increase the activity of the catalyst.99 However, to explain the significant differences noted between them, Franchini et al. designed a molecular study in which steric energy effects on the coordination of the propylene molecule were examined. The results suggested that the presence of the methyl group increases the propagation constant through a chain stationary insertion mechanism. The authors also concluded that, to obtain high activities overall, compromises in all of these factors seem to be inevitable and both electronic and steric factors should be considered. A recent study has examined the effect of an electrondonating fragment in the indenyl ligands of ansa-zirconocenes used for propylene homopolymerization and ethylene/ propylene copolymerization.103 The experimental homopolymerization results indicated a 20-fold increase in activity and a 3-fold increase in polymer molecular weight when a catalyst with a π-donating substituent was used. The same trend was recorded for the copolymerization process. According to the

In polymerization studies performed using R2ZrMe2/MAO (R = Cp, Ind, Flu) the order of catalyst activity was found to be Ind > Cp > Flu.95 The indenyl compound is more active than the cyclopentadienyl analogue due to its improved electrondonating capacity, whereas steric effects predominate for the Flu ligand. The effect of substituents in the indenyl rings has also been explored. Piccolrovazzi et al. determined the electronic effects of the substituents X = H, CH3, OCH3, F in the system (IndX)2ZrCl2/polymethylaluminoxane for ethylene polymerization.96 Electron-withdrawing-group (OCH3 and F) substitutions led to reductions in both activity and polymer molecular weight. For electron donors such as a methyl group, no significant changes were observed. Ethylene polymerization behavior has also been assessed for the series (1-R-Ind)2ZrCl2 (R = H, Me, Et, iPr, tBu, SiMe3, Ph, Bz, 1-naphthyl) and (2-R-Ind)2ZrCl2 (R = H, Me, Et, SiMe3, Ph, Bz, 1-naphthyl) with MAO as cocatalyst.97 The alkyl, aryl, and silyl substituents were chosen to cover a wide range of steric and electronic properties. Observed differences in activities were mainly attributed to steric effects of the substituents. In general, it was noted that substituents equal to or larger in size than iPr gave rise to poor polymerization activity. Catalysts with substituents at the C-1 position generally showed greater activity than those with substituents at C-2, and the larger the substituent, the more pronounced was this difference. The authors detected no correlation between activity and the Hammett parameter used as a measure of the electronic effects of the substituents. However, these authors concluded that electronic arguments must be considered, as catalyst activity may likely be explained through a combination of steric and electronic factors. Concerning ansa-metallocene-type catalysts, several research groups have examined the effects of several substituents at various positions of ring-bridged ligands on catalyst activity, chain length, and the stereo- and regioregularities of the resultant polymers. Factors related to the structure of a zirconocene catalyst, such as the structural rigidity and aperture and obliquity of its coordination gaps, have been attributed to play an important role in both catalyst activity and polymer properties for propylene polymerization.98 The influence of the ligand structures of 54 bridged zirconocene polymerization catalysts on the accessibility of the active reaction center has been assessed using the ab initio Hartree−Fock method.99 However, comparisons with experimental data were limited to qualitative trends due to dissimilar reaction conditions. The experimental order of activity, oneatom bridge > two-atom bridge, was explained by the more opened Cp−Cp angle in short-bridge complexes diminishing steric hindrance of the ligand. Silicon-bridged complexes conferred more activity to the catalyst than carbon-bridged complexes. Although the one-C-bridgef complex has a larger Cp−Cp angle than the Si-bridged complex, the Si-bridged complex shows a greater stability of the cation and improved shielding of the metal by the Cp ligand. It seems that these effects outweigh the ligand’s ability to enhance steric hindrance. On examination of the effects of the ancillary ligand, the experimental order of activity Cp < Thind (tetrahydroindenyl) < Ind may be explained by the relative stabilities of their cations, as variations in stericity are too small to explain this trend. The stability of the cation is strongly dependent on the aromaticity of the ancillary ligand. The introduction of further annelated aromatic rings leads to a considerable increase in I


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Figure 5. Standard deviation times the 3DQSAR coefficient for the steric field (top) and electrostatic field (bottom) mapped onto a selected catalyst of the ansametallocene set. Two viewpoints are shown for each field. The color codes and their meanings are explained in section 2.4.1.

catalyst structure on the polymerization process have been carried out on ethylene homopolymerization. In a first paper, the synthesis and testing at Repsol SA of a series of zirconocene catalysts bearing two types of aromatic ligands (cyclopentadienyl and indenyl) and different bridges between these ligands were described.64 This series was used for a 3D-QSAR study, which revealed steric field correlations with polymerization activity. The variation in polymerization activity data was successfully explained in terms of steric and electronic fields. The calculated model predicted that an increase in the Cp−Zr−Cp angle and/ or incorporation of bulky ligands would enhance catalytic activity. The effect of electronic interaction was confirmed by correlations found between activity and the LUMO molecular orbital and between activity and local softness. The model revealed that the arrangement of the aromatic ligands around the central metal atom as well as the chemical nature of the ligand (i.e., Cp or Ind) significantly contributes to explaining the variance shown by the experimental data. In a subsequent paper,67 the 3D-QSAR procedure was applied to a larger catalyst set using experimental data obtained by Kaminsky reported previously.107 The test set contained 25 compounds with different aromatic ligand substituents and different metals. The models constructed for the steric and electrostatic fields can be interpreted in terms of catalyst/ cocatalyst ion-pair interactions. Steric hindrance at specific positions and charge distribution around the aromatic ligands were correlated with increased activity. The explanation provided was the weakening of catalyst/cocatalyst interaction, leaving more space for the ethylene insertion reaction. Models including electronic-based descriptors such as LUMO and local softness108 indicate the enhanced influence on polymerization

authors of this study, the presence of an electron-donating fragment in the indenyl ligand stabilizes the alkylzirconocene cation and reduces the effective charge on the Zr atom. The latter is linked to a reduced likelihood of β-elimination termination reactions. Collectively, these findings would explain the molecular weight and activity results obtained. Dai et al.104 conducted QSAR studies on C(1)-bridged FluCp complexes of zirconium used in polypropylene polymerization, including nine catalysts with different bridges. Through molecular simulation these authors searched for a quantitative equation to relate the catalyst structure to its activity and argued that catalytic activity could be attributed to several structural factors. However, it is not clear which particular factors formed the QSAR equation. The prediction capacity of the equation was good. 3.1.2. 3D-QSAR Studies. Burkhardt and co-workers were the first to apply 3D-QSAR to the field of single-site catalysts in their pioneering work conducted on metallocene catalysts used to synthesize polypropylene polymers.105,106 These authors detected some correlation between the steric and electrostatic fields of a series of alkyl -substituted ansa-zirconocenes and observed DSC melting points. Surprisingly, to the best of our knowledge, this work was not continued. The use of 3D-QSAR for the study of single-site olefin polymerization catalysis has been made possible due to close collaboration between experimental and theoretical scientists. Experimentalists are aware of the importance of maintaining similar experimental conditions for all catalysts to ensure that the target property is mainly influenced by catalyst structure. All of the 3D-QSAR studies reported so far have been performed on ethylene polymerization because most of the systematic experimental studies regarding the influence of J


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molecular weight and catalyst volume can be also be directly observed in a bivariate plot. No clear interpretation was given for this correlation, but the analogy with the observed polymer molecular weight increase in supported metallocene-based catalysis was remarked upon. In a recent collaboration between the IEM-CSIC and URJC, a new zirconocene catalyst set containing aromatic substituents showing rac/meso stereochemistry was examined.109 Prior to the QSAR study, the most appropriate conformer set was selected in a conformational analysis. The best PLS model was selected, simultaneously considering both rac and meso isomers. The final model, obtained using a training set of 37 catalysts, included 87% steric and 13% electrostatic components. This result is compatible with previous QSAR models and stresses the steric influence cyclopentadienyl substituents have on catalyst activity. Owing to the high resemblance between conformers, the robustness of the model was assessed by a progressive scrambling procedure, which revealed a low redundancy level in the 3D descriptor set. 3.2. Iron-Based Catalysts. 3.2.1. Qualitative and QSAR Studies. Structure−activity relationships were examined for a set of 10 iron bis(arylimino) pyridine catalysts.110 The theoretical QSAR study revealed that the positions of the aryl groups in bis(arylimino) pyridyl complexes, iron− chloride distances, and the bond angles between the nitrogen atoms of the bis(imino)pyridine moiety played an important role in the activity of the catalysts. The resulting QSAR equation was formulated in terms of some geometrical parameters, d (bond distance), θ (bond angle), and φ (torsion angle), related to the catalyst structure:

activity of electron density redistribution at the metal active site due to the aromatic ligands. An additional link between experimental activity and electrostatic field was reported but had not been detected in the previous QSAR study. The reason for this discrepancy could be that the training set used in the first 3D-QSAR study contained no catalyst with substituents in the aromatic ring. Effectively, the presence of such substituents was essential to explain the influence of electrostatic interactions on polymerization activity. Cruz and co-workers conducted a study66 on a set of silyl ansa-zirconocenes including several cyclopentadienyl substituents that had been experimentally tested by Fajardo’s group at the Universidad Rey Juan Carlos (URJC). This group was able to confirm the positive correlation reported earlier between polymerization activity and the steric hindrance of cyclopentadienyl substituents. This finding is also consistent with the dependence observed between centroid−Zr−centroid angle and activity. In particular, the presence of two permethylated cyclopentadienyl rings gives rise to larger centroid−Zr− centroid angles, possibly due to cation−anion interaction weakening, which allows for more efficient olefin insertion. The steric component comprises over 90% of the CoMFA model for both catalyst activity and polymer molecular weight. Figure 5 shows the resulting CoMFA model containing the steric and electrostatic fields. The isosurfaces represented in the molecular structure correspond to the most prominent contributions made by these fields to explain the dependent variable behavior, in this case the activity. This picture illustrates the main results obtained with 3D-QSAR on metallocenes and discussed above. The steric field contribution to the resulting model becomes more than 90%. The corresponding plot of experimental versus predicted polymerization activity (Figure 6) illustrates the good correspondence between both sets, giving a correlation coefficient, r2, around 0.95.

activity = 18.51d − 18.49θ − 11.28φ + 15.61

Steric hindrance was shown to be the main factor modulating activation of the complex precursors. The derived simple structure−activity relationship was able to predict the activity of a catalyst test set reasonably well. 3.2.2. 3D-QSAR Studies. In a study conducted in collaboration with Repsol SA, a similar type of single-site catalyst was assessed using the results of well-controlled polymerization experiments performed on a series of bisiminopyridine iron complexes.65 Given the present uncertainty about the nature of the active species in this type of catalyst, dichloride precursor structures were also considered. A valid model was obtained correlating experimental polymer molecular weight with steric and electrostatic fields. This finding highlights the importance of intermolecular interactions in catalytic behavior, most probably between the catalyst and cocatalyst. The QSAR model was satisfactorily consistent with both other theoretical calculations and experimental observations. In particular, the steric effect seems to be the most important contributor, accounting for some 75% of the overall effect. The electrostatic model reinforces the idea that the catalyst/cocatalyst interaction affects polymerization behavior. The positive steric effect (green grid in Figure 7) occurs around the Si face, where a catalyst/cocatalyst interaction can compete against olefin complexation and insertion. In the same area, a negative charge increment (red grid in Figure 7) will be beneficial in terms of generating a product of higher molecular weight. In contrast, an increased steric contribution on the Re face will lead to lower molecular weights. In this region, an increased positive charge (blue grid in Figure 7) is correlated with a

Figure 6. Predicted versus actual logarithm of activity plot.

However, we noted some peculiarities of the QSAR models described in this work that were not encountered in previous studies. Increased steric bulk in the region defined by silicon bridge atom substituents was found to be beneficial in terms of generating greater polymer molecular weights. This finding is new, as previous 3D-QSAR studies did not consider sufficient variability in this molecular area. Positive correlation between K


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Figure 7. Standard deviation times the 3DQSAR coefficient for the steric field (top) and electrostatic field (bottom) mapped onto a selected bisiminopyridine iron catalyst. Two viewpoints are shown for each field. The color codes and their meaning are explained in section 2.4.1.

The correlation coefficient, r2, obtained in this case was 0.94.

higher polymer molecular weight. This region is mainly associated with polymerization chain transfer reactions. The resulting 3D-QSAR model containing steric and electrostatic field contributions gives a good correlation between experimental and calculated polymer molecular weights, as can be observed in Figure 8.

4. CONCLUSIONS AND PERSPECTIVES The initial discovery of single-site olefin polymerization catalysts opened an avenue to the synthesis of new materials whose composition could be better controlled in an effort to enhance their properties. Two essential features of single-site catalysts are their structure and mechanism of action. Knowledge of these two factors provides a magnificent opportunity to derive relationships between polymerization activity or polymer properties and catalyst structure. In effect, a large part of the literature is devoted to studies that have addressed these relationships. However, only a few such studies have used a more quantitative (i.e., QSAR) approach, in contrast with the overwhelming amount of work conducted in the field of drug design, in which QSAR forms part of the development process of a new drug. The work revised in this review highlights the major contribution of steric factors to the activity of many different kinds of catalyst systems. However, the information provided by the QSAR equation is often difficult to interpret, because the descriptors used are usually global quantities that reflect an overall property of catalyst structure. To overcome this limitation, the use of 3D-QSAR is proposed. Considering the whole set of 3D-QSAR models, it is clear that the steric field is the factor that best explains most polymerization activity. This observation has been made in practically every QSAR study. The 3D model can give additional information about which spatial locations are more sensitive to steric variations related to either polymerization

Figure 8. Predicted versus actual logarithm of polymer molecular weight plot. L


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Notes

activity or polymer molecular weight. In most studies, these regions have been linked to catalyst/cocatalyst interactions yet the cocatalyst structure is not generally taken into account. The reason for this is that, in most cases, the structure of the cocatalyst has not been well-defined and it is assumed that this structure will be the same for all systems and will therefore not contribute to any observed difference. We expect that adding the same cocatalyst structure to the catalyst geometry would add more noise than signal to the model because very small differences would be expected in the overall complex geometry. In fact, the differences in catalyst-cocatalyst interaction are governed by the catalyst structure itself should the cocatalyst structure remains constant. For example, bulky and/or negatively charged ligands could induce some additional separation of the ion pair. The arrangement of the catalyst/ cocatalyst complex is captured by the structural properties of the catalyst in this case. Another interesting issue that adds value to the 3DQSAR technique is that its predictive capacity can be used on other sets of catalysts tested under other experimental conditions. In such cases, only relative predictions can be made with respect to a reference compound, which could be a catalyst common to both the training and test sets. Further benefits of multidimensional QSAR techniques can be imported from the drug design to the single-site catalysis field by incorporating the latest developments.44,111 These include auto- and cross-correlation techniques to overcome the molecular alignment problem. We should stress that, to obtain useful quantitative relationships between structure and activity/property, care should be taken to keep the experimental conditions constant for the entire catalyst set to be tested. As for any systematic study aimed at analyzing the effect of one particular variable, it is desirable to keep constant the remaining set of variables. In any case, the statistical protocol used in 3D-QSAR is flexible enough to take into account additional variables other than those associated with the catalyst structure such as temperature, pressure, catalyst/cocatalyst ratio, etc. For convenience, these scalar variables could be loaded and weighted accordingly during the chemometric modeling procedure. The 3D-QSAR method may be very attractive for molecular modelers, but care should be taken to not produce overfitted models of experimental data through the use of a large number of molecular descriptors. A series of statistical techniques such as cross-validation, bootstrapping, and progressive scrambling are available to help construct reliable predictive models. 3D-QSAR correlations can be performed against dependent variables such as propagation constants. The resulting model would provide more specific information about the influence of molecular structure on the process associated with that kinetic parameter. We feel that 3D-QSAR models could be further improved by incorporating scalar descriptors such as experimental conditions (temperature, pressure, catalyst/cocatalyst ratio, etc.). As the ultimate goal of such studies, these models would be indispensable for the development of tailor-made catalysts and new materials.

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The authors declare no competing financial interest. Biographies

Dr. Victor Cruz obtained his Ph.D. at the Complutense University in Madrid in 1985. He worked in the R&D department of a multinational cosmetic company for 4 years. In 1989 he joined the Computer Center at the CSIC, beginning the constitution of the Computational Chemistry department. He moved in 2005 to the Biophym group of the Instituto de Estructura de la Materia-CSIC, with which he had been collaborating since the early 1990s. At that time, his research interest was to analyze, using chemometric tools, the structure−activity relationship for the catalysts in single-site olefin polymerization processes in close collaboration with Repsol SA, as the experimental reference. Currently, his research interest has moved to the exploration of the chemistry and physics of biomacromolecular systems using computational and theoretical approaches.

́ obtained her degree in Chemistry at the University of Sonia Martinez Valladolid and her Ph.D. degree at Complutense University, in Madrid, Spain. During her doctoral period at the Consejo Superior de ́ Investigaciones Cientificas (CSIC) she focused on the computational studies of organometallic catalysts for olefin polymerization. She also participated in some related projects in collaboration with Repsol SA. In 2005 she had a short stay at Prof. Morokuma’s group in Atlanta, GA, USA, where she focused on the ONIOM technique applied to

AUTHOR INFORMATION

dinitrogen hydrogenation reactions. She currently is working for the

Corresponding Author

*V.L.C.: e-mail, [email protected]; tel, +34915616800.

Altran consulting company as a Computational Chemistry consultant at the CSIC. M


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support through the Ramón y Cajal program, contract RYC2011-09585.

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REFERENCES

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Javier Ramos obtained degrees in Chemistry (Alcala University, 1998) and in Technical Engineering in Computer Systems (UNED, 2011). He received his Ph.D. from Alcala University in 2002, working on the study, by computer simulations, of olefin polymerization mechanisms using single-site catalysts, in collaboration with Repsol-YPF. Starting in 2005, he spent 2 years at Professor Theodorou’s laboratory at Athens University studying the melting properties of polyolefins as a function of their molecular architecture using Monte Carlo and molecular dynamics simulations. He was awarded with a Ramón y Cajal contract in 2012. At present, he is a hired researcher at the Structure of Matter Institute (CSIC) in Spain. His current research interests are modeling and simulation studies of both synthetic and biological macromolecular systems.

Prof. Javier Martinez-Salazar obtained his Ph.D. at the Autónoma University of Madrid in 1979 on the diffraction and viscoelasticity of polymers. Then he obtained a postdoctoral position at the group of Prof. Keller at the H.H. Wills Physics laboratory in Bristol, U.K., where he specialized in various aspects of Polymer Physics. He is a member of the EPF and he served as the representative of the Spanish polymer group in the period 1998−2010. He has earned numerous contracts with industries in the area of polyolefins, in particular with the Spanish Repsol, helping to build the well-known polymer chain of knowledge: from the design to the product. His main interest is now moving to physical aspects of the functionality of proteins. Presently he is Research Professor at the Institute for the Structure of the Matter, CSIC, in the group Biophym.

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ACKNOWLEDGMENTS This study received financial support from the CICYT (project MAT2012-36341). The authors thank the staff of the Secretaria General Adjunta de Informatica (SGAI-CSIC) and Centro de Supercomputacion de Galicia (CESGA) for technical support and computer time for the simulations. J.R. received financial N


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