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

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specific molecular mechanics models for a single class of catalyst, often confining the study to one reaction type containing a single type of catalyst (2).

We have four goals for this chapter: 1) present an overview of the steps commonly employed to study organometallic catalysis, 2) show how the principles underlying molecular mechanics methods are applied to three specific examples (stereoselectivity in asymmetric hydrogenation, olefin polymerization, and host/guest interactions in zeolites), 3) briefly illustrate the practical applications of molecular modeling to catalysts used in industry, and 4) present a limited survey of the literature to illustrate how different workers have applied molecular mechanics to the study of properties of catalysts of importance to organometallic chemists.

2. WHERE TO BEGIN

2.1.Force Field Parameterization

Before we can model any catalytic process, we need to have at our disposal some molecular mechanics code and a well-parameterized force field. A general overview of molecular mechanics is presented in Chapters 2 and 3. In essence, molecular mechanics computes the energy required to deform a molecule from its ideal, ‘‘strain-free’’ geometry. Broadly speaking, there are two different types of molecular mechanics code: programs that are based on empirically assigned parameters for each type of bond and bond angle, and programs that assign molecular mechanics parameters based on rules. Parameter-based code, for example, MM2 (3), explicitly assigns a force constant and equilibrium value to all bond lengths, angles, torsion angles, and van der Waals interactions in the molecule. Rule-based code, for example, the Universal Force Field, UFF (4), derives these parameters from rules based on ‘‘normal’’ distances and angles. For example, a normal bond distance is the sum of covalent radii of the connected atoms. In the UFF a strain-free bond distance, rij (Eq. 1), between atoms i and j is given by the sum of covalent radii, ri rj, with corrections for electronegativity, rEN (Eq. 2) and bond order rBO (Eq. 3):

rij ri rj rEN rBO							(1)
rEN	ri rj(√χi		√χj)2				(2)
	(χiri χjrj)
rBO λ(ri rj) ln (n)							(3)

In Eqs. (2) and (3), χ is electronegativity, n is the bond order, and λ is a parameter. Another example of a rule-based force field is VALBOND, from the Landis group.

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There are many different pieces of code available for molecular mechanics, ranging from the simple, such as MM2, to the elaborate, such as Cerius2, SYBYL, Spartan, and HyperChem. The code chosen for a particular model of catalytic processes depends on two factors: (1) the complexity of the system that is to be studied, and (2) the amount of computer expertise available. Complicated structures, such as surfaces and zeolites, generally require specialized software packages for their visualization; typically workers use commercial code with perhaps minor modifications. Simpler systems, such as modeling vanadium oxo species, are amenable to study using simpler codes, such as MM2, that are customized to suit the specific needs of the research group. It should be noted that the various available packages employ different force assumptions and some force fields are more suitable to one kind of application than to another (see Chapter 2).

A good molecular mechanics model is only as good as the parameters or theory upon which it is based (5). Equilibrium geometrical parameters, such as distances, angles, and torsion angles, are usually found from crystallographic data. Traditionally, force constants are found from either spectroscopic data or quantum mechanical calculations (see Chapter 2). It is customary to assume that the metal-independent parameters for the organic portion of the organometallic complex are the same as the parameters found in any molecular mechanics code optimized for organic compounds. Once we have a set of parameters, we generally compute a structure and then carry out a point-by-point comparison between the computed and experimentally determined structure, usually an X-ray crystal structure. An alternative to the point-by-point comparison of computed and experimental structures, recently proposed by Cundari, is to use genetic algorithms or neural networks to compare the computed structure with many crystal structures in order to optimize the parameter set (6,7).

2.2. The Mechanism

Mechanisms in organometallic chemistry can be quite complicated and are often matters of considerable controversy (8–10). However, there is usually one step in the mechanism that enables us to get a handle on the problem we wish to solve. For example, when we look at Ziegler–Natta polymerization we shall see that the face of the olefin that coordinates to the metal determines the stereochemistry of the polymer. In this case, the molecular mechanics model focuses on the differences in energy between the two different coordination modes of the olefin. In general, a molecular mechanics model needs to focus on the step in the mechanism that gives rise to the interesting, or surprising, chemistry. Most often, we model a single step in a mechanism to determine the outcome of the reaction. The issue is to determine the rate-determining step in the mechanism and model that step. However, there may be pre-equilibria that also play a role in the reac-

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tion, so we tend to model the rate-determining step along with any pre-equilibria that may be important. Since mechanisms are often not known with certainty, we must be careful in our interpretation of results.

2.3.Conformers and Conformational Searching

In the experimental laboratory, we deal with moles of substances. On the computer, we often look at a single structure or a small set of structures. It is important to realize that there may be an entire ensemble of conformers that can participate in a reaction. Computational chemists take one of two approaches to the problem of multiple conformations: (1) carry out conformational searches as efficiently and exhaustively as feasible, or (2) study a model of the system in which there are as few conformational degrees of freedom as possible.

There are two general approaches to the search of the conformational space of a molecule: systematic and stochastic. Systematic approaches generate a conformational grid in which all torsion angles in the molecule are varied yielding many conformers. Consequently, systematic searches are feasible only with molecules that contain a few rotatable bonds. Random, or stochastic, searches often use Monte Carlo–type algorithms in which all torsion angles in the molecule are varied in a random manner, usually simultaneously. Efficient conformational searching is essential to developing a reliable computational model of any system. The topic of conformational searching is usually discussed in most texts on molecular modeling (11–13). In addition to these ‘‘traditional approaches,’’ molecular dynamics and genetic algorithms are currently being used to search the conformational space of molecules (11–13).

Once we have established the focus question we wish to address and have the appropriate molecular mechanics code, force field, and parameter set, we can begin our computations. In the next three sections we look, in detail, at two homogeneous systems and one heterogeneous system. We begin with homogeneous asymmetric hydrogenation in which molecular mechanics addresses the question of how stereochemistry is transferred from the ligand to the substrate. Then we look at homogeneous Ziegler–Natta olefin polymerization to examine the use of molecular mechanics in determining the stereochemistry of a growing polymer chain. Finally, we look at the shape selectivity of zeolites as an example of heterogenous catalysis. At the end of this chapter, we present two tables summarizing other applications of molecular mechanics to organometallic catalysis. For convenience and ease of use, we include the software and force field used as well as the location of parameters and the problem studied.

3. HYDROGENATION

Olefin hydrogenation has been known since 1966, when Wilkinson and coworkers reported the homogeneous hydrogenation of olefins by rhodium catalysts (see

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FIGURE 1 Wilkinson’s catalyst, [Rh(PPh3)3Cl].

Fig. 1 for catalyst structure) (14–16). Since its discovery, homogeneous hydrogenation has grown and is not limited to olefins as substrates. Shortly after the discovery of homogeneous olefin hydrogenation, it became apparent that by modifying the ligands from PPh3 to a chiral ligand, stereoselective homogeneous hydrogenation became possible. Only low enantiomeric excesses, ee’s,* were achievable in the initial studies. However, moving to bidentate chiral ligands (Fig. 2) resulted in a dramatic increase in ee.

Molecular mechanics modeling of the asymmetric hydrogenation must begin with the mechanism of the reaction. When the prochiral olefin binds to the catalyst containing chiral bidentate phosphine, two possible diastereomers result: one with the re face and one with the si face of the olefin coordinated to the metal (Fig. 3). Work in the Halpern and Brown laboratories has shown that the observed enantiomeric product cannot result from the diastereomer observed in solution (17–20). Thus, the minor diastereomer, which cannot be observed, must be responsible for the dominant chiral product. Any molecular mechanics model of the asymmetric hydrogenation reaction must explain how the minor diastereomer reacts faster than the major.

To effectively model the asymmetric hydrogenation reaction, we must look at the mechanism carefully. The first step involves the displacement of solvent and the coordination of the enamide to produce the two diastereomers (Fig. 3) (17–20). It appears as though the enamide-coordinated diastereomers are in rapid equilibrium with each other through the solvento species (Fig. 4). This square planar rhodium(I) cation is then attacked by dihydrogen to form an octahedral rhodium(III) complex (Fig. 4). Hydrogen then inserts into the Rh–C bonds, and the product is reductively eliminated (Fig. 4). From a molecular mechanics standpoint we have three entities to model: the square planar rhodium(I) solvento species and the two intermediates (square pyramidal dihydrogen complex and the octahedral dihydride).

In order to model the square planar rhodium(I) complex we need to realize that the positions trans to the diphosphine may not be equivalent, since the diphosphine is chiral. Consider the [(diphosphine)Rh(norbornadiene)] as a model for the solvento species. In order to distinguish between the nonequivalent phosphorus atoms, we label them Pa and Pb. Each olefin is 90° from one phosphorus atom

* Enantiomeric excess is defined as % R enantiomer % S.

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FIGURE 2 Example of an asymmetric hydrogenation catalyst, [(S,S-CHIRA- PHOS)Rh(nobornadiene)] . The norbornadiene ligand is used to represent the coordination of solvent molecules.

and 180° from the other. It is very difficult to model a structure in which one interaction has two different equilibrium bond angles. There are two approaches in the literature to the problem: 1) assign the P atoms different labels (Pa and Pb) and then define each interaction uniquely (this results in a significant increase in the number of parameters) (21–23), and 2) redefine the potentials, creating a more general force field (24). Once we have decided upon an appropriate force field, we need to turn our attention to modeling an η2-bonded olefin.

In molecular mechanics a chemical bond is considered to be composed of two spheres attached by a spring. Modeling of M-olefin systems presents a simple problem: Where do we anchor the metal? (Strictly speaking, the metal should be anchored to the center of the olefin CCC bond, but there is no atom at the CCC centroid to anchor the metal.) One approach is to bond the metal to both carbon atoms in the olefin. This creates a metallocycle, which is not a realistic model for olefin binding. An alternate approach is to define a pseudoatom (an atom with

FIGURE 3 Structures of [(S,S-CHIRAPHOS)Rh(MAC)] (MAC is methyl (Z)-α- acetamidocinnamate; see Fig. 6). Notice that (a) has the re face of the olefin coordinated to the Rh, whereas (b) has the si olefin face coordinated.

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FIGURE 4 Attack of dihydrogen on the two diastereomers of [(S,S-CHIRA- PHOS)Rh(MAC)] . Notice that the two diastereomers of [(S,S-CHIRAPHOS) Rh(MAC)] are in equilibrium via the solvento species. After hydrogen attacks the square planar rhodium(I) complex, an octahedral rhodium(III) dihydride is formed. (Redrawn from Ref. 32.)

zero van der Waals radius and zero force constants) in the CCC centroid and then bond the pseudoatom to the metal. However, if the pseudoatom interrupts the bonding, then the two halves of the olefin rotate with respect to each other and physically unrealistic results emerge (Fig. 5). One resolution is to place a pseudoatom at the centroid of the CCC bond but to leave the C–C bond intact (23). Thus, we generate a single point of attachment of the olefin to the metal, but we do not interrupt the C–C connectivity. A similar approach has been used for the molecular mechanics modeling of cyclopentadienyl ligands (25–28).

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FIGURE 5 Bonding models for an η2-olefin interaction. (a) Shows the actual bonding in the complex, (b) a molecular mechanics model of the metallocycle, (c) shows how the two halves of the olefin can rotate relative to each other if a pseudoatom, D, interrupts the bonding, and (d) shows a molecular mechanics model that is used in the literature. (From Ref. 23.)

Now that we have the ability to bond olefins and enamides to the rhodium, we are in a position to be able to model asymmetric hydrogenation. Using CHEMX,* Brown and Evans modeled a series of [(diphosphine)Rh(dehydroamino acid)] complexes (29). CHIRAPHOS was used as the chiral diphosphine with ethyl (Z)-α-acetamidocinnamate (EAC) as the substrate (Fig. 6). The structures of interest were assembled from fragments derived from X-ray crystal struc-

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tures. Hydrogens were added at standard 1.08-A distances. Only the van der Waals energy was minimized, using TORMIN in COSMIC molecular modeling package,† assuming the P–Ph torsional barriers were insignificant. Brown and Evans noted that the energy difference between the re and si diastereomers was small enough to lie within the computational limits of accuracy. However, they concluded that the main difference between diastereomers occurs in the nonbonded interaction between α-ester group and the aryl groups on the phosphorus atoms of the diphosphine.

With the geometries of the diastereomers established, Brown and Evans then modeled the addition of H2 to Rh (29). Four different pathways for hydrogen attack were considered, two for each diastereomer. The hydrogen was placed

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1.60 A from the metal and the van der Waals energy minimized. Sterically impossible structures were eliminated, and the resulting two diastereomers showed a large energy difference (42.2 kcal/mol). The high-energy diastereomer contained a significant nonbonded interaction between ester and P–Ph group, whereas the low-energy diastereomer did not. Finally, these workers calculated an energy surface for the attack of dihydrogen on the metal. The major and minor diastereomers were found to respond quite differently to the addition of dihydrogen. Sub-

* CHEMX was reported to be available from Dr. K. Davies and associates, Molecular Design, Oxford, UK. See Ref. 29.

† COSMIC and TORMIN were reported to be available from Dr. J. G. Venter, Smith Kline and French, Welwyn Garden City, See Ref. 29.

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FIGURE 6 Structure of ethyl (Z)-α-acetamidocinnamate (EAC).

sequent to this paper, Landis and coworkers have approached the same problem from a quantum mechanical perspective, yielding results that are more sound from a theoretical perspective.

Bosnich and coworkers analyzed asymmetric hydrogenation using molecular graphics with MODEL-MMX* (30). Dihydrogen addition to both major and minor diastereomers was analyzed for the [(S,S-CHIRAPHOS)Rh(EAC)] complex. (EAC is ethyl-N-acetyl-α-aminocinnamate.) As with the Brown approach (29), Bosnich considered only van der Waals terms in the computation of energies and the partial minimization of the complexes using the method reported by Davies and Murrall (31). The crystal structure of the major diastereomer was used for input, and eight dihydride structures were analyzed (Fig. 7). Only two of the eight possible trajectories gave feasible energies for dihydrogen attack at the metal. Calculations agreed with experiment in that the computed low-van- der-Waals-energy structures contained the correct alignment about the M–H and M–olefin bonds for product formation.

In 1993 Landis began a detailed study of the asymmetric hydrogenation reaction (32). In this work, he analyzed the structural features of the catalyst that give rise to high enantioselectivity. In particular, he focused on methyl (Z)-α- acetamidocinnamate (MAC) as the substrate with DIPAMP, CHIRAPHOS, and DIPH as phosphines (Fig. 8). In addition to the prochiral MAC substrate, Landis also included norbornadiene as a test substrate to develop the methodology. In the molecular mechanics calculations, Landis used a modified SHAPES force field (24) within CHARMM (33). Electrostatics were included using Rappe´ and Goddard’s QEq method (34). Inclusion of electrostatics was found not to alter results significantly. Finally, the conformational space of the molecule was sampled by using a constrained grid-search technique.

The differential equilibrium constant for the binding to form the two diastereomers (using MAC as the substrate) is reported to decrease from about 30

* MODEL-MMX was reported to be obtained from Clark Still modified by K. Steliou, University of Montreal. MMX, developed by K. Gilbert and J. J. Gajewski, Indiana University, was obtained through Serena Software.

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FIGURE 7 Dihydrogen attack trajectories for the major and minor diastereomers of [(diphosphine)Rh(enamide)] studied by Bosnich and coworkers (30). In this figure the enamide is represented by coordinated O and olefin and the diphosphine by the coordinated phosphorus atoms. (Redrawn from Ref. 30.)

to 10 to 1 on moving from CHIRAPHOS to DIPAMP to DIPH (18,35). For [(CHIRAPHOS)Rh(MAC)] , Landis found a diastereomeric energy difference of 2.3 kcal/mol using molecular mechanics (32). Changing the diphosphine from CHIRAPHOS to DIPH, a 1.3-kcal/mol energy difference between diastereomers was computed (as compared with 0.3 kcal/mol reported in the literature). These results suggest that the margin of error involved in this methodology is about 1 kcal/mol. Finally for the DIPAMP complex, a 0.4-kcal/mol energy difference between diastereomers was computed (as opposed to the experimental ∆H of 1.4 kcal/mol).

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FIGURE 8 Structures of DIPMAMP, CHIRAPHOS, and DIPH. (Redrawn from Ref. 32.)

Since enantioselectivity in this reaction is a result of the energy difference between the diastereomeric transition states after H2 is added, Landis modeled the addition of H2 to the diastereomers of the CHIRAPHOS and DIPAMP complexes with MAC as the substrate. Landis posed a simple question: Is there a significant barrier to hydrogen attack at the Rh center that can be modeled by molecular mechanics? In the first study Landis found that all possible attack trajectories allowed almost strain-free attack of dihydrogen (molecular mechanics barriers were less than 3 kcal/mol) (32). In a subsequent study, a better picture of the reaction coordinate was generated using DFT and quantum mechanical models, which are outside the scope of this chapter.

Several other workers have used different force fields to model enantioselective hydrogenation to different substrates (see Table 1). For example, Schwalm and coworkers approached the enantioselective hydrogenation of α-ketoesters using AMBER (36) from within MACROMODEL (37,38). Mortreux and coworkers have used CAChe (39) augmented with MM2 (3) to model asymmetric hydrogenation of ketopantolactone (40). Ruiz has used Cerius2 (41) with the Universal Force Field (4) to model hydrogenation using Rh and Ir complexes of rigid dithioethers as ligands and acrylic acids (42).