Cundari Th.R. -- Computational Organometallic Chemistry-0824704789

FIGURE 10 Structures of (a) (S,S)-C2H4(4,5,6,7-tetrahydro-1-indenyl)2ZrCl2 and

(b) (S,S)-C2H4(indenyl)2ZrCl2. (Redrawn from Ref. 166.)

found using molecular mechanics. This lack of energy discrimination can be understood by realizing that the catalyst has no symmetry because of the puckering of the indenyl rings. Since there is no ability for the catalyst to discriminate between the two different faces of the olefin, an atactic polymer should, and does, result.

Modifications to (S,S)-C2H4(4,5,6,7-tetrahydro-1-idenyl)2ZrCl2 were undertaken in order to probe the catalyst for those structural features that give rise to good differentiation between olefin faces (54). Rappe´ and coworkers found that a methyl group in position 4 of the indenyl ring (see Fig. 10) should increase stereoselectivity by inducing unfavorable steric interactions. From molecular mechanics calculations, this structure was found to increase the energy difference between transition states by 1 kcal/mol for the third insertion (as opposed to the 5 kcal/mol calculated earlier) (54). Rappe´ concluded that steric congestion occurs in the space that leads to the syndiotactic defect. However, if a methyl group was placed in position 3 of the indenyl ring, an atactic polymer was produced, because the energy difference between transition states for the third insertion was almost zero (54).

Morokuma and coworkers attempted a similar approach to understand both regioand stereoselectivity of ansa metallocene catalysts (55). Ab initio methods

were again used to determine the structure and energies of the transition states to ethylene insertion. Molecular mechanics was used to determine the effect of methyl substituents on olefins and cyclopentadienyl rings on the regioand stereoselectivity of Ziegler–Natta polymerization. Molecular mechanics using MM2 was carried out using a pseudoatom for Zr. Minimal conformational searching was employed, and only the substrate was energy-minimized (55). From this limited model, the authors found that primary insertion with one methyl group on the cyclopentadienyl ring was 3 kcal/mol lower than secondary insertion. The authors concluded that steric effects were responsible for the unfavorable energy.

A slightly different approach to modeling ansa metallocenes is to use an iso or sec-butyl group to represent the growing polymer chain (56–64). Guerra and coworkers modeled both Ti and Zr complexes using methods and parameters obtained from the literature (65–72). Crystal structures for the titanium-based systems were used to set up the zirconium systems. The Zr–C(alkyl) bond length

˚ ˚

was set to 2.28 A and the Zr–C(olefin) bond length to 2.30 A (by analogy with the Ti complexes) and all aromatic hydrogens were allowed to bend 10° out of plane. Energy maps were calculated as a function of M–C(alkyl) and M–C(ole- fin) bond rotations. Relative energies between complexes with re and si coordinated faces were generated. Molecular mechanics models were found to agree with experimental findings on the racemic system. In addition, secondary insertions were directed by interactions between the methyl group on the olefin and the cyclopentadienyl and indenyl ligands.

A number of other specific studies were found in the literature concerning Ziegler–Natta polymerization (see Table 1). In essence, all studies followed paths analogous to those illustrated in this section. To summarize: The discriminating step in the mechanism is the orientation of olefin insertion. This orientation can be analyzed by modeling simple complexes, with both re and si faces of the olefin coordinated, and then looking for energy differences between the re and si complexes. By looking at energy differences between re and si complexes, any errors introduced in the method are averaged out.

5. MODELING OF ZEOLITES

Thus far in this chapter we have concentrated on homogeneously catalyzed transformations, which have grown in popularity in industry over the past decade (73). Heterogeneously catalyzed transformations are still very popular in industry and deserve attention (44). Interest in zeolites as heterogeneous catalysts has grown recently, largely because of their ability to discriminate between different molecular shapes. Molecular mechanics has been used largely to identify specific sites for guest molecule adsorption in the zeolite channels. In this section, we shall consider some of the challenges involved in the molecular mechanics modeling of host/guest interactions in zeolites.

Location of aromatic molecules in zeolites has attracted much interest (74). Using a customized modeling code, ZEOLITHENERGIE, Fuess and coworkers have calculated the positions of aromatics in zeolite Y (75). More importantly, the methodology outlined has been adapted to many different hosts and guests (see Table 1). Their calculation takes place in seven steps:

1.Interaction energies are calculated between one guest molecule and the zeolite lattice. Considering only a single guest molecule in the zeolite models the case of infinite dilution.

2.No distinction is made between the zeolite T-sites (Si and Al). All are treated as 75% Si and 25% Al. For example, zeolite NaY is modeled with a Si/Al ratio of 3.0.

3.Because the zeolite system is so large, it is very difficult to model all interactions using a conventional force field such as MM2. Instead, the zeolite cage and guest molecule are held rigid, and the structure is minimized considering only nonbonded interactions.

4.Nonbonded energy, φtot, is calculated as the sum of Leonnard–Jones and electrostatic interactions:

In this equation, Bαβ characterizes short-range repulsion between atoms α and β, Cαβ characterizes the dispersive interaction between α and β, and r is the internuclear distance. All parameters used in the study of Fuess and coworkers are reported in Ref. 75.

5.Hydrogen bonding is ignored.

6.Internal adsorption energy, ∆Uads, is calculated by a Boltzmann weight of φtot summed at constant temperature, T:

ν

7.A three-dimensional grid is defined in an asymmetric zeolite unit, and the guest molecule is placed in the center of the grid. The orientation of the molecule is optimized by a Monte Carlo procedure: First a 0.25-

orientations per grid point.

Using the method just outlined, it has been argued that preferred adsorption

sites depend on the nature of cations and hydrogen bonding possibilities in zeolite Y (76). The adsorption of benzene in HxZSM-5, HxAlxSi96 xO192, has been studied

because of the importance of ZSM-5 as a shape-selective commercial catalyst (76). Molecular mechanics has revealed that there are four different orientations of the benzene molecule in the zeolite channel: one with the aromatic plane perpendicular to the [010] channel axis, two with the aromatic plane parallel to the channel axis, and one intermediate. To come to these conclusions Mentzen and coworkers used a Buckingham potential to minimize the energy of the benzene molecule in the zeolite (76). Mentzen and coworkers also noted the importance of starting with a good set of positional parameters for the zeolite, which are usually obtained from X-ray or neutron diffraction studies.

One important goal of molecular modeling is to be able to predict molecular behavior in order to save time and money. In zeolite chemistry, for example, it would be advantageous to be able to predict which zeolite would be optimal for a given transformation. Consider 2,6-diisopropyl naphthalene (DIPN) and 2,7- diisopropyl naphthalene: solid acid catalysts tend to produce a mixture of these two isomers, which requires costly separation. If a zeolite catalyst with appropriate channel size were used, then only the desired 2,6-isomer could be formed. Workers have turned to molecular mechanics to determine which zeolite will best catalyze the selective production of 2,6-DIPN (77). Using Insight II, Horsley and coworkers used molecular graphics to determine that zeolite L has pores so large that they cannot distinguish between the 2,6- and 2,7-isomers of DIPN. On the other hand, mordenite selectively adsorbs 2,6-DIPN (77). With parameters from the literature (78), Horsley and coworkers modeled mordenite and zeolite L using Discover.

To determine which of the two isomers, 2,6-DIPN or 2,7-DIPN, was better adsorbed by the zeolite, the interaction energy along the general diffusion pathway was calculated (77). The diffusion path was defined by a series of points along the channel axis. Using a strong harmonic potential, the sorbate was constrained to lie a fixed distance from the extremes, and the zeolite lattice was fixed in the crystallographically determined structure. The sorbate was then energy-

˚

minimized, moved by 0.2 A, and reminimized. This process was repeated until the sorbate was at the end of the section of channel. A plot of energy as a function of distance was used to determine the energy barrier as the sorbate moved through the zeolite. For mordenite, 2,6-DIPN showed an energy barrier of 4 kcal/mol, whereas the 2,7-isomer showed 18 kcal/mol (77). These results were in agreement with the molecular graphics visualizations.

Simple energy minimization did not result in reasonable results for the zeolite L system: areas of severe strain were noted, which were not visible in the molecular graphics analysis. As the sorbate moved through the channels in zeolite L, the isopropyl groups were caught on bits of zeolite. Horsley and co-

workers added a Monte Carlo step to their procedure: the sorbate was added to the channel, a Monte Carlo conformational search was carried out, then the lowest energy structure was used for the energy calculation. The results showed that zeolite L could not distinguish between 2,6- and 2,7-diisopropyl naphthalene.

Recently a new force field for the modeling of Faujasite-type zeolites has been reported (79). This force field was developed to address a deficiency in the approaches mentioned earlier: the new force field models the Si and Al atoms explicitly, as opposed to the T-model, in which the Si/Al ratio is held constant. Jaramillo and Auerbach note that the T-model is acceptable when the guest molecule is reasonably far from the zeolite T-sites. However, when the guest molecule is an ion, for example, Na , then there is a small distance between guest and T- sites, requiring the Si and Al sites to be modeled explicitly. Partial charges, which are reported in the paper, were used for the zeolite potential (on Si, Al, both types of oxygen, and Na) (79). Both flexible and rigid frameworks were used to model the positions of sodium cations in the zeolite using a Buckingham potential (Eq. 4). Jaramillo and Auerbach developed a program, Clazyx, to convert computed coordinated into cationic sites, which can be compared with experiment. Barriers between sites were modeled using molecular dynamics at 1000 K with 1-fs time steps. The new force field was able to reproduce experimental cation positions, site occupancies, and vibrational frequencies.

Molecular mechanics has also been used to study skeletal isomerization of 1-butene to isobutene (80), olefin selectivity in fluid catalytic cracking using ZSM-5, zeolite Y, mordenite and β (81), carbon–sulfur bond cleavage over zeolite Y (82), and the location of naphthalene and 2-methylnaphthalene in HZSM- 5 (83). In all cases, a methodology similar to those described earlier were adopted (75,77).

6.APPLICATIONS OF MOLECULAR MODELING TO CATALYSTS IN INDUSTRY

Several companies make use of different levels of molecular modeling of catalytic processes. In this section we present some of the work by Shell Chemical Company and BP Amoco Chemicals. Because of propriety issues, we present an overview of some of the work that pertains to this chapter.

6.1. Shell Higher Olefin Process (SHOP)

Shell Chemical Company has developed a method in which ethylene is oligomerized to higher α-olefins using a nickel-based catalyst (84). The ligands, shown in Figure 11, are chelating O- and P-donors.

Shell uses computational chemistry because ligand synthesis is costly (in terms of both time and money), experimental results can be ambiguous, and the

FIGURE 13 Formation of branched versus internal olefins from the insertion of 1-butene into the growing polymer chain. Notice that the branched/internal ratio depends on how the olefin binds to the metal. (Redrawn from Ref. 87.)

6.2. Molecular Modeling at BP Amoco Chemicals

Work at BP Amoco Chemicals is based on the philosophy that the design and improvement of products is practically achieved in three steps: 1) reading the literature, garnering ideas, and brainstorming, 2) testing the best ideas using molecular modeling, and then 3) confirming the computational results with laboratory work. BP Amoco Chemicals’ scientists have successfully used computational chemistry in many projects, one of which is the single-site catalyst model (88).

In the polypropylene catalyst shown in Figure 14, an isotactic-atactic block copolymer can be formed by rotation of one ring relative to the Zr-centroid axis. (For descriptions of polymer stereochemistry, see Fig. 9.) The isospecific rac rotomer of the catalyst gives rise to the isotactic block, while the aspecific meso form gives rise to the atactic block (Fig. 14). Using UFF (4) and RFF (85,86) (as well as ab initio methods and DFT), the workers were able to confirm experimental evidence (89,90) that the indenyl substituent, R in Figure 14, could influence the equilibrium between the rac and meso rotomers. Using RFF the workers were able to successfully predict the relative amount of isotactic and atactic blocks in the polymer and to correlate that with R.

In addition to modeling polypropylene formation, scientists at BP Amoco Chemicals have successfully used computations to model desulfurization of light naphtha, flue gas multicomponent equilibria, methane-to-methanol conversion, and oxygen scavenging films.