To date, from a theoretical point of view, probably this is the most investigated organometallic reaction. This chapter covers the elementary steps which are relevant to the polymerization of olefins with group 4 catalysts, and special emphasis is dedicated to systems with a substituted biscyclopentadienyl-based ligand, or with a monocyclopentadienylamido-based ligand the so-called constrained geometry catalysts, CGC of Figure 1, since these are the most investigated the mono-Cp systems to a less extent and the ones of possible industrial relevance.
In particular, we will focus on the elementary steps which compose the propagation reaction. Nevertheless, in the final sections we will briefly report about these points. It is well established that the active polymerization species is an alkyl cation where the alkyl group is the polymeric growing chain. Therefore, one or both of the two are removed when the active catalyst is formed. The metallocene equatorial belt is in the yz plane, and the axis is along the z axis. Of the five frontier orbitals, the most important to the following discussion are the three low-lying and orbitals reported in Figure 2.
All three orbitals have significant extent in the yz plane, which corresponds to the plane defining the equatorial belt of the metallocene. The orbital is chiefly in character, while the two orbitals in addition to contribution from the and orbitals contain s and contributions. The orbital resembles a orbital and is directed along the y axis, while the orbital is the highest in energy between the three orbitals, and points along the z axis. BP86 calculations we performed on the fragment confirm this framework. The mechanism generally accepted for olefin polymerization catalyzed by group 3 and 4 transition metals is reported in Figure 3, ands it is named after Cossee .
It substantially occurs in two steps; i olefin coordination to a vacant site; ii alkyl migration of the growing chain to the olefin. Green, Rooney and Brookhart [30, 31] slightly modified this mechanism with the introduction of a stabilizing interaction which would facilitate the insertion reaction. The key features of the insertion mechanism are that the active metal center must have an available coordination site for the incoming monomer, and that insertion occurs via chain migration to the closest carbon of the olefin double bond, which undergoes cis opening with formation of the new metalcarbon and carbon-carbon bonds.
Consequently, at the end of the reaction the new Mt—chain is on the site previously occupied by the coordinated monomer molecule.
We will start with the species prior olefin coordination Section 3. This result was explained by a reduced steric pressure of the L ligands which favors the onaxis geometry bonded to a big metal at the bottom of the triad. Moreover, the energy of the orbital which is responsible for on-axis bonding increases along the triad, and therefore the preference for the off-axis geometry is enhanced . When the models include the more representative Cp rings, the results obtained with different methods are contradictory. Morokuma and co-workers suggested Olefin Polymerization by Early Transition Metals 29 that the off-axis orientation of the methyl group in the crystalline structure could be due to the presence of the negative counterion.
With the methyl group off-axis, a better electrostatic interaction between the two charged ions could be obtained. The value of the Cp—Mt—Cp bending angle is another key factor that influences the relative stability of the on- and off-axis geometries . The GVB calculations of Goddard and co-workers showed that the onaxis geometry is favored by larger values, due to an increased steric pressure of the Cp rings on the group, which clearly favors the on-axis geometry.
Since a systematic study of this point is still missing, we investigated the performances of different computational approaches through geometry optimizations of the species with different pure and hybrid DFT functionals, and at the HF and MP2 level of theory. The main geometrical parameters are reported in Table 1. With the exception of the HF structure, in all cases the bond is bent away from the local symmetry axis. When this deviation is larger, no agostic interactions were found, whereas to smaller values of the angle see Figure 4 a interaction is associated.
We always found these two minimum energy situations. Differently, at the HF level we only found one structure of minimum energy, with the bond perfectly aligned to the symmetry axis, and with no signs of agostic interactions. In all cases, the preferred geometry corresponds, by roughly 1. Finally, single point CCSD T calculations on the B3LYP geometries predict that the two structures are of substantially the same energy, since the geometry is preferred by 0.
These conclusions are in agreement with all the precedent studies which indicated that whatever geometry is favored, the potential energy surface for this swing motion of the Zr—C bond in the equatorial belt of the metallocene is relatively flat. In the CGC catalysts, where the steric pressure of one of the Cp ligand is missing, off-axis geometries are more favored. This detailed analysis substantially confirms the previous BP86 studies of Ziegler .
As for group III metallocenes, Goddard , Ziegler [38, 45] and coworkers found on-axis geometries for the ,  and  species. The preferential on-axis geometry for all the neutral Sc species was ascribed to the higher s orbital contribution to bonding for group 3 metals with respect to group 4 metals. As an alkyl group longer than a simple methyl group is to the metal atom, the situation is different due to the possible formation of and bonds. With group 4 metallocenes, all authors substantially found a slightly off-axis geometry in the presence of a interaction. As for the species, to test the performance of different computational approaches we performed geometry optimizations with different pure and hybrid DFT functionals, and at the HF and MP2 level of theory of the species.
The main geometrical parameters are reported in Table 2. This result is consistent with the calculations reported in Table 1 for the system, where the MP2 geometry resulted in the largest values of the angle.
However, all the methodologies concord on the presence of a rather strong interaction, since the Zr—H2 distance is in the range 2. The BP86 functional results in the stronger agostic interaction shortest Zr—H2 distance. To check for the flatness of the potential energy surface relative to the swing motion of the Zr—C bond in the equatorial belt of the metallocene, we performed a geometry optimization at the B3LYP level, with the angle fixed at The optimized structure resulted to be only 0. Finally, it is clear that the presence of a or a bond favor offaxis geometries, since the on-axis geometry would push the C atom which participates in the agostic interaction towards the Cp rings.
The electronics behind olefin coordination to group 4 cationic species was studied in details by Marynick, Morokuma and co-workers [33, 47]. Their analysis indicated that olefin coordination is due to in-phase interactions between the olefin orbital with metal orbitals corresponding to the mainly, and to one lobe of the orbitals of Figure 2. Since group 4 cations contain metals, no back-bonding from the metal to the olefin orbital is present.
Several authors calculated the olefin uptake energy to olefin-free group 4 bis-Cp and mono-Cp polymerization catalysts. For neutral scandocenes, the interaction between the olefin and the metallocene is reduced due to the absence of the favorable electrostatic cation-olefin interaction [43, 50]. Also in these cases the olefin uptake is a barrierless process, unless bulky ligands as rings are considered . The substantially lower uptake energy Olefin Polymerization by Early Transition Metals 33 values calculated in the presence of alkyl groups longer than methyl are ascribed to the presence of a or interaction that stabilizes the olefin-free metallocene.
To examine systematically the performances of different computational approaches in evaluating geometry and energetics related to the coordination of olefins to group 4 catalysts, we performed geometry optimizations with different pure and hybrid DFT functional, and at the HF and MP2 level of theory, of the complex. The main geometrical parameters are reported in Table 3. Since two different geometries were found for the species, for each methodology we considered the approach of ethene to the metal atom to both the geometries reported in Table 1. As for the olefin-free species, two different geometries can be localized.
The Zr—H distances and the angle in the structures with a interaction are rather similar, whatever methodological approach is used. In all cases the olefin is unsymmetrically coordinated to the metal atom, with the ethene C atom closest to the group roughly 0. The MP2 uptake energy, instead, is remarkably higher, These results indicate that BSSE corrections must be considered for realistic olefin binding energies. Recent studies have shown that they modify substantially the olefin-coordination energetics.
Therefore, it is reasonable to expect similar solvent and olefin coordination energies. With regard to the presence of the counterion, it has to be considered that it is the species which coordinates more strongly to the metallocene, due to its negative charge.see url
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Solvent effects, usually accounted for with continuum models, reduce the energy required to dissociate the ion-pair , but still it remains a highly endothermic process. Very similar conclusions were obtained by Ziegler and co-workers, which modeled ethene and toluene as solvent coordination to the and systems coordinated . Their calculations clearly indicated that the olefin-bound intermediate is only a shallow minimum energy situation. Along this line, Ziegler and co-workers performed static and dynamic BP86 simulations of the ethene insertion into the ion-pair, and found that olefin coordination occurs with a large barrier .
Finally, the uptake energy values only represent a contribution to the total free energy of coordination. In fact, an always unfavorable uptake entropy has to be accounted for.
Whether the metal-olefin complex is a real chemical species, or the olefin undergoes direct insertion into the metal-carbon bond has been a matter of debate for many years. However, some experimental studies of the last years established that such species do exist , although as transient species.
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Moderately stable olefin adducts have been obtained when the olefin is tethered to the metal  or to the Cp ligands . Upper bounds to the olefin uptake energy can be obtained by measurements of the processes in fluxional allyl derivatives of group 3  and group 4  metallocenes. The insertion reaction of a coordinated olefin into the Mt—C where Mt is a group 4 metallocene, or a model of it, has been the subject of several theoretical studies [26, , , 43, 46, 47, 49, 71].
All authors agree that the insertion reaction occurs through a slipping of the olefin towards the first C atom of the growing chain, and that the four centers transition state assumes an almost planar geometry. For a model based on the analogous group 3 system, the transition state is only slightly more advanced relative to the one for the cationic zirconocene [43,50]. The electronics behind the insertion reaction is generally explained in terms of a simple three-orbitals four-electrons scheme.
Hoffmann and Lauher early recognized that this is an easy reaction for complexes, and the relevant role played by the olefin orbital in determining the insertion barrier . According to them, the empty orbital of the olefin can stabilize high energy occupied d orbitals of the metal in the olefin complex, but this stabilization is lost as the insertion reaction approaches the transition state. The net effect is an energy increase of the metal d orbitals involved in the back-donation to the olefin orbital.
In agreement with Hoffmann and Lauher, for systems the lowest unoccupied molecular orbital LUMO of the olefin complex see Figure 7 chiefly corresponds to a bonding metal-olefin interaction. To quantify this point, Ziegler and co-workers compared the insertion barrier for ethene insertion into the cationic and neutral systems. The insertion barrier for the neutral system is roughly 20 times higher than the insertion barrier for the cationic system . Finally, it is worth noting that Hoffmann and Ziegler predicted that and complexes can be suitable polymerization catalysts if other ligands can accept the d electrons in orbitals orthogonal to the olefin orbital —which 38 Luigi Cavallo corresponds to a reduction of the relevance of the interaction— [26, 72], while Ziegler also noted that if the occupied metal d orbitals are lower in energy, e.
The presence of a favorable interaction which stabilize the transition state is another point of convergence between various authors [, 39, 46, 49, 50, 73, 74]. Before continuing, it is worth noting that a short distance indicative of a interaction is almost inevitable as the orbital of the C atom of the growing chain bonded to Zr tilts away from the Zr—C axis to be oriented towards the closest C atom of the olefin, giving rise to the bonding interactions with the olefin itself.
According to Janiak, the stabilization becomes important through an increase in electron deficiency of the metal, that switches from a formally Zr in the olefin-coordinated reactant, to the formally Zr in the insertion product .
Similar ideas were developed by Grubbs and Coates, who also made a nice relationship between the hyperconjugative stabilization by atoms of substrate undergoing nucleophilic substitution reactions in organic chemistry, and the agostic stabilization by atoms in ZieglerNatta catalysis . Regarding the height of the insertion barrier, the situation is much more controversial, since pure density functionals and some MP2 calculations suggest that this a barrierless reaction, or it occurs with a negligible barrier.
For instance, the static BP86 calculations of Ziegler and co-workers on the reaction of ethene with the system predicts a barrier of 0. Ahlrichs and co-workers investigated the system and found a considerable energy barrier and a transition state only without inclusion of electron correlation . At the MP2 level, they found that the insertion reaction occurs on a very flat, downhill potential energy surface. However, the basis set they used basis functions was not particularly extended, and this can influence the MP2 energetics. When group 3 metals are considered, the situation is rather similar, since for ethene insertion on the static DFT calculations of Ziegler and co-workers predicted almost negligible insertion barriers, Olefin Polymerization by Early Transition Metals 39 the particular level of theory, and that larger basis sets were needed for accurate RQCISD calculations.
However, for the Ti system they also calculated an insertion barrier of 1. First principles molecular dynamics simulations also resulted in processes with low free energy barriers. However, they also warned that quite longer simulation times were needed for quantitative predictions . Since the situation about the height of the insertion barrier is not so clear, we performed a systematic comparison of the performances of different computational approaches in determining insertion barriers and geometries, with the aim to offer a further contribution to the discussion.
The main geometrical parameters of the transition state for the insertion reaction of ethene into the Zr—C bond of the species are reported in Table 4. The latest transition state is predicted by the simple HF theory, at a distance of 2. As reasonable, to longer C1—C2 distances in the transition state correspond shorter and longer Zr—C1 and Zr—C3 distances which correspond to the Zr—C which are going to be broken and formed, respectively.
All the transition states are characterized by the presence of a strong interaction, with Zr—Hl distances around 2. The only exception is represented by the HF transition state which shows a longer Zr—Hl distance, around 2. With regard to the insertion barriers, the BP86 and BPW91 functionals predict extremely low barrier, around 0. The BnLYP functionals predict relatively higher insertion barriers, and the higher is the amount of HF exchange the higher is the insertion barrier. The HF predicts a remarkably high and unrealistic barrier At the MP2 level the insertion barrier is 2. The BP86 geometry we calculated is very similar to that calculated by Ziegler and co-workers for the same system, although in their geometry optimizations the BP86 gradient corrections were not included.
Olefin Polymerization by Early Transition Metals 41 Firstly, inclusion of polarization functions on the C and H atoms of the reactive groups and reduces considerably the insertion barrier compare runs 1 and 2 as well as runs 6 and 7 and seems to be mandatory. Instead, inclusion of polarization functions on the ancillary ligand has a negligible effect on the calculated insertion barrier compare runs 2 and 3 as well as runs 7 and 8. Extension of the basis set on the reactive groups lowers further the insertion barrier compare runs 7 and 9.
Finally, the extension of the active orbitals space to include all the occupied orbitals reduces sensibly the insertion barrier compare runs 3 and 4. In Table 5 the insertion barrier at levels of theory higher than MP2 are also reported runs The insertion barriers reported in Table 5 can be used to obtain a further approximation of the insertion barrier. The authors remarked that these barriers are certainly overestimated, since inclusion of polarization functions on the C and H atoms, and geometry optimizations at the MP2 level reduced the insertion barrier for the Ti system to 3.
As for the final state after the insertion step, all authors do agree that the interaction occurring in the transition state evolves into a one. Moreover, the is usually predicted to correspond to the kinetic product that, through a conformational rearrangement of low energy, could evolve into the thermodynamic product [33, 34, 36, 37, , 46, 71]. The frontside insertion requires a rearrangement of the growing chain from a to an orientation.
This barrier was predicted to be rather low. Once the growing chain adopts a geometry, the insertion is almost barrierless according to the BP86 calculations of Ziegler , lower than 2. As for the backside approach, the insertion can occur without any particular rearrangement. The last authors investigated the same reaction path with the analogous system also.
This mechanism involves a two-monomer transition state, where the entering of a new monomer unit triggers the insertion of the already complexed monomer. Specific calculations to support this model are not available. A clear experimental estimate of the intrinsic reaction barrier to olefin insertion is still missing. Very recent NMR experiments of Casey and co-workers on the propene insertion into the Y—C of the neutral group 3 system resulted in a of With regards to the mono-Cp CGC catalysts, the BP86 static and dynamic calculations of Ziegler and co-workers on the ethene reaction with the system indicated that interconversion between geometries with different agostic interactions and is rather easy.
Ethene coordination to the preferred olefin-free species is likely to lead to the most stable olefin-bound species. The insertion reaction occurs after a rearrangment of the growing chain from a to a geometry. The static energy barrier they calculated for the insertion reaction is 4.
All the calculations reported above indicate that the insertion reaction is a rather easy process, and usually underestimate the experimental apparent propagation barrier. The aspects regarding olefin coordination were discussed in Section 3. Their calculations clearly indicated that the ethene-bound intermediate is only a shallow minimum energy situation along the reaction coordinate, when the counterion is considered, and the insertion barrier raises from 7.
Along this line, Ziegler and co-workers performed static and dynamic BP86 simulations of the ethene insertion into the ion-pair . In the olefin-free ion-pair the ethyl group which simulates the growing chain shows no agostic interactions with the Zr atom. Ethene coordination occurs from the side opposite to the anion, in agreement with the simulations of the CGC-catalysts of Lanza et al. After olefin coordination, which occurs with a large barrier, the insertion step has a low energy barrier.
The overall barrier, from separated reactants to the transition state, was calculated to be The last results described are a strong indication that any computer modeling of the activity of early transition metal catalysts for the polymerization of olefins probably requires the inclusion of the counterion in the simulations.
In this section we will focus on the origin of the regioselectivity of the insertion reaction primary vs. Before continuing, it has to be noted that the energy difference between the secondary and primary propene insertion, can be considered composed by two main contributions, electronic and steric. The steric contribution to due to steric interaction between the monomer, the growing chain and the ligand skeleton, was modeled successfully through simple molecular mechanics calculations , and was reviewed recently [11,24].
For this reason in the following we will focus only on the electronic contribution to Olefin Polymerization by Early Transition Metals 45 Regarding the origin for the electronic preference for primary versus secondary propene insertion, the ab initio calculations of Morokuma and coworkers on approximated transition state geometries for primary and secondary propene insertion into the Ti—methyl of the system indicated that secondary propene insertion was disfavored by 4.
The latter is essentially stabilized by favorable electrostatic attraction and less serious exchange repulsion, in agreement with the experimental results and the Markovnikov rule of organic chemistry. Their Mulliken analysis on the transition state for ethene insertion into the Ti—methyl indicated that the ethene C atom that is going to be bonded to the metal atom is more negatively charged relatively to the ethene C atom that is going to be bonded to the methyl group. Thus, they argued that the additional methyl group of the propene would give a more favorable electrostatic interaction with the C atom of the olefin closer to the methyl group than to the metal atom.
That is, primary insertion is favored over secondary insertion. Moreover, in the transition state for the secondary insertion, the propene methyl group is closer to the additional metal ligands than for primary insertion, causing a larger exchange repulsion. To confirm these conclusions with more realistic models, we performed BP86 calculations on the primary and secondary propene insertion into the of the system. The transition states for primary and secondary propene insertion are reported in Figure Firstly, the presence of the methyl group of the propene molecule does not modify substantially the geometry of the transition state, which remains substantially planar, and both of them are stabilized by a strong interaction.
However, the transition state occurs slightly earlier in the primary than in the secondary propene insertion, as evidenced by the slightly less formed C—C bond in the transition state for the primary insertion. The length of the breaking Zr—C bond is the same in both transition states, whereas the forming Zr—C bond is considerably longer in the transition state leading to secondary propene insertion.
This results confirms the pioneering conclusions of Morokuma and co-workers, and are in substantial agreement with the high preference experimentally observed for primary propene insertion with group 4 metallocenes. Since every propene insertion, whatever its orientation, creates a new stereogenic center, the catalyst stereospecificity which defines the stereoregularity or tacticity of the polymer produced is determined by the stereochemical relationship between the stereogenic carbon atoms in the polymer chain.
Multiple insertions of the same enantioface produce a polymer chain with chiral centers of the same configuration, i. Multiple insertions of alternating enantiofaces produce a polymer chain with chiral centers of alternating configuration, i. Random enantioface insertions produce a polymer chain with no configurational regularity, i. A necessary but not sufficient prerequisite for models of catalysts for the stereospecific polymerization of 1-olefins polymerization, is the stereoselectivity of each monomer insertion step.
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The possible origin of stereoselectivity in this class of systems was investigated through simple molecular mechanics calculations [11, 14, 24, 32, 52, , ]. Since molecular mechanics cannot be used to calculate the energy of transition states, suitable models were adopted.
These models are extremely similar to the complex with an orientation of the growing chain rather similar to that adopted when a interaction is present. They were often called pre-insertion intermediates because the insertion transition state could be reached from these intermediates with a minimal displacement of the reacting atoms. All the molecular modeling studies performed indicate that for group 4 metallocenes independently of their structure and symmetry , when a substantial stereoselectivity is calculated for primary monomer insertion, this is not due to direct interactions of the of the chiral metallocene with the monomer.
Instead, the origin of stereoselectivity is connected to a chiral orientation of the growing chain determined by its interactions with the of the chiral metallocene. It is the chirally oriented growing chain which discriminates between the two prochiral faces of the propene monomer. In short, the stereoselectivity is mainly due to non-bonded energy interactions of the methyl group of the chirally coordinated monomer with the chirally oriented growing chain.
According to the scheme of Figure 12, in the framework of a regular chain-migratory mechanism the and some symmetric metallocenes lead to iso- and syndiotactic polymers, respectively. In fact, for the symmetric systems the same propene enantioface is enchained at each 48 Luigi Cavallo insertion step, whereas for the symmetric systems there is a regular alternation of the propene enantioface which is enchained.
The molecular mechanics calculations used to develop this mechanism of stereoselectivity assume the applicability of the Hammond postulate to this case i. The validity of these assumption is confirmed by the large amount of experimental results which have been rationalized with this kind of calculations [11, 12, 14, 24]. Nevertheless, in this final section we present a quantum mechanics validation of this mechanism through full DFT localization of the transition states for the insertion reaction of propene into the Zr-isobutyl bond of two typical stereospecific homogeneous catalysts.
The first system is based on the racemic-dimethylsilyl-bisindenyl zirconocene, with a symmetry of coordination of the aromatic ligand, and the actual catalyst leads to a highly isotactic polymer. The second system is based on the dimethylsilylcyclopentadienylfluorenyl zirconocene, with a symmetry of coordination of the aromatic ligand, and the corresponding catalyst leads to a highly syndiotactic polymer. In the transition state of Figure 13a the growing chain is pushed away from the bulky bis-indenyl ligand, and is oriented in a uncrowded part of space, whereas in the transition state of Figure 13b the growing chain interacts repulsively with the indenyl group on the left.
Both transition states present an anti orientation of the methyl group of the reacting propene molecule and of the atom as well as the following of the growing chain, i. Transition states with a cis orientation of the propene methyl group and of the growing chain i. The repulsive interactions between the growing chain and the in the structure of Figure 13b are at the origin of the energy difference between the two diastereoisomeric transition states. In fact, the structure reported in Figure 13a is calculated to be 3.
According to the mechanism of migratory insertion of Figure 12, in the successive insertion step the relative coordination position of the growing chain and of the propene molecule are switched. However, due to the symmetry of the catalysts they are identical and thus at each insertion step the same enantioface of the propene is inserted. That is, an isotactic 50 Luigi Cavallo polymer is produced. Incidentally, for the R,R coordination of the bisindenyl ligand as in Figures 13a and 13b the insertion of the re enantioface is favored.
Of course, for the S,S coordination of the bis-indenyl ligand the insertion of the si enantioface is favored. The models for the syndiospecific catalyst coordinate to a Zr atom a propene molecule, an isobutyl group simulating a primary growing chain and the bridged dimethylsilyl-cyclopentadienylfluorenyl In this case the coordination of the is achiral.
The metal atom, instead, is chiral after coordination of the monomer and of the growing chain, since four different ligands are coordinated to it, and the standard Cahn-IngoldPrelog CIP nomenclature can be used . In the transition state of Figure 14a the growing chain is pushed away from the bulky fluorenyl group, and is oriented in a uncrowded part of space, whereas in the transition state of Figure 14b the growing chain interacts repulsively with the fluorenyl group.
As for the transition states leading to an isotactic polymer, both transition states of Figure 14 present an anti orientation of the methyl group of the reacting propene molecule and of the growing chain. Again, the repulsive interactions between the growing chain and the in the structure of Figure 14b is at the origin of the energy difference between the two diastereoisomeric transition states. In fact, the structure reported in Figure 14a is calculated to be 2. Due to the symmetry of the catalyst this corresponds to have enantiomeric transition states and thus there is a regular alternance in the insertion of the two enantiofaces of the propene.
That is, a syndiotactic polymer is produced. Incidentally, for the R configuration at the metal atom as in Figures 14a and 14b the insertion of the re enantioface is favored. Of course, for the S configuration at the metal the insertion of the si enantioface is favored. In the framework of the regular chain migratory mechanism of Figure 12, the enantioface selectivities we have calculated for the and catalysts of Figures 13 and 14, explain the iso- and syndiospecificity experimentally found for the corresponding real catalysts .
New polymeric materials with new properties have been discovered, and the fields of applications of these catalysts are expanding continuously. In the last years an impressive understanding of the relationship between the catalysts-structure and the properties of the produced polymer has been achieved. Computational chemists certainly gave a strong contribution, and in the previous sections we reported about the status of the art in the field, and we showed the major contributions gave by a molecular modeling approach.
It is now possible to model successfully the whole propagation process, and very important details of it, as the regio- and stereoselectivity of the insertion step. Nevertheless, there is still much work to do in this field. In the next years we will probably arrive to dynamically simulate the whole polymerization process in the presence of the counterion and of explicit solvent molecules. As for the experimental issues which have been not rationalized yet computationally, we remark that still it is not easy to model the relative activity of different catalysts, and even to predict if a certain catalyst will show any activity at all.
Moreover, copolymerizations still represent an untackled problem. However, considering the pace at which the understanding of once obscure facts progressed it is not difficult to predict that also these challenges will be positively solved. Minima were localized by full optimization of the starting structures, while the transition states for the insertion reaction were approached through a linear transit procedure which started from the olefin-coordinated intermediate. Full transition state searches were started from the structures corresponding to the maximum of the energy along the linear transit paths.
The real nature of these structures as first order saddle points was confirmed by frequency calculations which resulted in only one imaginary frequence. Geometry optimizations were performed at different level of theory. Single point coupled cluster calculations with inclusion of single, double and perturbatively connected triple excitations, CCSD T [, ], were performed on the B3LYP geometries. With regard to the basis set, the all electrons MIDI basis set of Huzinaga was used on the Zr atom , while the valence basis set agumented with a polarization function p on the H atoms and pure d functions on the C and Si atoms of Ahlrichs, denoted as SVP , was used on all the atoms.
The polarization functions, were also included on all the atoms of the ligand. For all the H, C and Si atoms of the ligand the G basis set was used. If not explicitly stated, the MP2  and CCSD T calculations were performed within the frozen core approximation, which corresponds to exclude the 1s orbital of the C atoms, the orbitals up to 2p on the Si atom, and the orbitals up to 3d on the Zr atom from the active orbitals space. To investigate the effect of the basis set on the MP2 insertion barrier we performed a series of single-point MP2 where we utilized also the valence basis of Ahlrichs with no polarization functions, denoted as SV, and the G basis set agumented with a polarization function p on the H atoms and cartesians d functions on the C , denoted as G d,p [,], The calculations relative to the regioselectivity and stereoselectivity of the propene insertion reactions Sections 4 and 5 were performed with the Amsterdam Density Functional ADF package .
STO basis sets were used for silicon 3s,3p , carbon 2s,2p and hydrogen 1s , augmented with a single 3d, 3d, and 2p function, respectively ADF basis set III. The inner shells on zirconium including 3d , silicon including 2p , and carbon 1s , were treated within the frozen core approximation.
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Nobel Lectures in Chemistry, ; Elsevier, , pp 6. Nobel Lectures in Chemistry, ; Elsevier, , pp Tetrahedron , 8, Organometallics , 13, Macromolecules , 15, New York, ; Vol. Luigi Cavallo Lauher, J. Brookhart, M; Green, M. Organometallics , 17, Organometallics , 14, Organometallics , 20, Organoemtallics , 14, Polyhedron , 7, Macromolecules , 31, Download e-book for kindle: Metal Catalysed Reactions in Ionic Liquids: Steel Catalysed Reactions in Ionic beverages is the 1st non-edited publication with reference to steel catalyzed reactions in ionic drinks to hide the literature from its origins till early The sequence constitution and Bonding publishes serious experiences on subject matters of study curious about chemical constitution and bonding.
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