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Name of Principal Investigator:

Stephen D. Williams

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Title of Proposed Project:

A Density Functional Theory Study of Rhodium Dimer Homogeneous Catalysts

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(a) Technical Summary:

Density Functional Theory DFT) methods will be used to investigate some of the electronic and steric effects that may influence the selectivity of some rhodium dimer catalysts for the formation of cyclopropanes via catalytic carbene insertion reactions. The catalysts of interest are Rh2L4 where L is an acetamide with a bulky substituent on the amide nitrogen atom. The calculations on these molecules have been preceded by calibrations consisting of DFT calculations on some rhodium carboxylate dimers for which a great deal of experimental and theoretical results exist.

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(b) Non-technical Summary:

The production of compounds that include the cyclopropyl group (three CH2 groups joined to form a three membered ring) is a difficult but important process. It is particularly important in the manufacture of insecticides that are highly effective and that also have very low toxicity for mammals. The formation cyclopropyl groups is promoted by catalytic molecules that include Rh-Rh single bonds. The structure of these catalytic molecules can influence the structure of the cyclopropyl groups that they can form. This influence, or control of the catalytic reaction is very important but is not very well understood. This project is a study of these catalytic molecules that will improve our understanding, in a quantitative fashion, of some of the factors that can influence the structure of the cyclopropyl products that these reaction produce. This may ultimately lead to new, more effective, safer, and less expensive agents to control insect pests.

3. Technical Proposal

a. Problem Description:

Many rhodium(II) complexes are potent catalysts for a variety of important types of chemical reactions, including hydrogenations, carbene insertions, oxidation & hyroformylation, and photochemical processes[1]. This proposal is concerned with the carbene insertion reactions. The rhodium (II) carboxylate dimers (Rh2L4, where L is the conjugate base of a carboxylic acid such as acetate or formate) are typical catalysts for carbene insertions. A particularly important reaction of this type is the insertion of a carbene into a carbon - carbon double bond to form a cyclopropyl group. The relative orientation of the carbene and the groups on the double bond determine whether the cyclopropyl group will have cis or trans stereochemistry. In some cases the cis isomer is the desired product, and in others the trans isomer is of interest. Control of this stereochemistry is a significant problem and is the focus of this project. An important example of a system where this stereochemical control is vital is the pyrethroid insecticides. These compounds have very low toxicity for mammals but are highly toxic for insects. The active site of these molecules is a substituted cyclopropyl group that must be cis for the compound to be effective. The project will answer the following question: "What can Density Functional Theory (DFT) say about the properties of a rhodium dimer catalyst that may influence the stereochemistry of cyclopropyl groups that can be formed with the catalyst?"

b. Objectives:

Rhodium dimer catalysts have been relatively well studied. The carboxylates in particular have been the subject of extensive experimental and theoretical study[2]. Experimental studies have used such diverse techniques as ESR spectroscopy[3], vibrational and NMR spectroscopy[4], UV-VIS spectroscopy[5], X-ray crystallography[6], and photoelectron spectroscopy[7]. Theoretical studies of these and related compounds have included CASSCF methods[8], extended CNDO[9], ab initio SCF[10], and many Xalpha-SW calculations[11]. It has been suggested that enhanced selectivity in the stereochemistry of cyclopropyl products may be obtained if one or more carboxylate ligands is replaced with an amide[12]. This provides a new site (on the N atom) where a bulky substituent may be placed, thus allowing steric as well as electronic factors to influence the course of the insertion reaction. The goal of this study is to use DFT methods to investigate the influence of these amide ligands on the electronic properties of the complexes, and on the interactions of the complexes with some rather simple carbenes. This should provide some new insights into the control of the stereochemistry in these catalytic reactions.

c. Technical Approach:

It is anticipated that the ligands in a rhodium dimer catalyst may influence the selectivity of the catalyst through both electronic and steric effects. If the dimer has a preferred orientation for its binding to the carbene, then the direction of approach of the carbene to a double bond will also be constrained. This can have a large influence on the distribution of the products in the catalytic reaction. In this project the preferred orientation(s) of a carbene bound to the dimer will be investigated. The investigation will use DFT methods (and specifically Dgauss and possibly Dmol) for three reasons: 1) Unlike Gaussian 94, Dgauss includes high quality basis sets for Rh. 2) Dgauss and Dmol are both significantly faster and make better use of CRAY vector hardware than Gaussian. 3) It is known that electron correlation effects are important in the electronic structure of compounds with metal-metal bonds, and is particularly important when there are multiple metal metal bonds[13]. With Hartree-Fock based methods, the least expensive method for including electron correlation is the MP2 method; the cost of this method increases with the fifth power of the number of electrons in the system. All modern DFT methods include correlation effects to some extent, but their cost only increases with the cube of the number of electrons. Since the smallest molecule in this study has about 200 electrons and the largest about 540 electrons, the much improved cost scaling for DFT is very important to this project. DFT methods are known to be useful for investigations of rhodium dimers. An early controversy related to these compounds was the nature of the Rh-Rh bond: it is short enough in the acetate and formate complexes that multiple bonding is a real possibility. This issue was finally resolved by the Xalpha calculations of Norman et al[11]. which convinced all researchers in the area that the bond was in fact a single bond. This is also consistent with the recent relativistic Xalpha calculations of Stranger et al[11]. Since Xalpha methods may be regarded as an early DFT method[14] that lacks an electron correlation potential, DFT methods have long played an important role in the study of these compounds. The catalysts whose selectivity is of interest here are ones where the ligands are amides, perhaps with large N atom substituents.

The previous project, for which this proposal is a renewal, has shown that with Dgauss, the best structures for the formate and acetate complexes were obtained with geometry optimizations using the LDF method and the DZVP basis set (see the attached summary report for more details.) In the proposed project some of these results will be compared with the newer (and better?) basis sets available in Dgauss 3.0. Since the inclusion of density gradient corrections was shown to lead to poor structures (at a significantly higher cost), only LDF methods will be used in this study. Some effort will also be made to investigate what sort of numerical basis set in Dmol will be needed to reproduce the Dgauss results. If (as is anticipated) Dmol can reproduce these results at lower cost, then it may be used for a majority of the work proposed here. The most important result of the previous project is that the adduct of a singlet carbene to one of these rhodium dimer catalysts has a bent Rh-Rh-C linkage; this is absolutely critical to the prediction of stereochemistry and has not been noted in the only previous study[12] of computed structures of carbene adducts in these materials, which used an unusual combination of molecular mechanics and extended Hückel calculations. A typical structure for such a complex:carbene adduct is shown in the second figure attached to the summary report (section 7). The new basis sets and codes (Dmol) will be checked to see if they also reproduce this bent linkage.

It is important to note that the complex and carbene orbitals which are responsible for the bent linkage are qualitatively very similar when computed with a variety of methods. Solid renderings of some of these orbitals are shown in the first figure in the summary report. The approximate compositions (and hence shapes) and relative energies of these orbitals are the essentially the same if DFT or HF methods are used. They have been computed with LDF/DZVP, LDF-BP/DZVP, LDF-BLYP/DZVP, rhf/sto-3g, rhf/3-21g, rhf/lanl2dz, svwn/3-21g (a DFT method in Gaussian 94), and extended Hückel (in Hyperchem) methods. The energy ordering and shapes of the rhodium complex orbitals (these calculations were done for the formate complex, at the LDF/DZVP geometry) are qualitatively the same for all of these methods except extended Hückel, for which the energy ordering is quite different. Hence it seems unlikely that the computed bonding for the carbene adducts will be radically different when calculated with a new basis set in Dgauss, or with Dmol, but completeness demands that some of these calculations be done.

The specific compounds of interest will be complexes where the ligands are acetamide, N-phenyl-acetamide, and possibly N-pentafluorophenyl-acetamide. The first will be used because it is smaller and the calculations will be cheaper than for the others; it will also be used to judge the effects of the N for O substitution in the ligand. The latter two will be of interest since the phenyl and pentafluorophenyl groups are large and will cause some steric effects. The carbenes to be investigated are :CH2 because it is small and cheap to compute, and :CHCOOEt because experimental data exists for this more stable carbene interacting with these catalysts. The later carbene is also large enough so that it will show steric effects with the bulky ligands.

Some of the steric effects have been studied. The last figure in the summary report compares steric effects for :CH₂ bonded to either rhodium acetate or rhodium acetamide. The energy scaling (vertical scale factor) is the same for the potential energy scans, so the larger gradient and curvature for the amide complex case suggests that the extra H atoms in this complex are already exerting some steric effects. These figures are also slightly deceptive. They do not represent relaxed potential scans, where all of the geometric parameters for the adduct except for the fixed angles for the carbene would be optimized. Instead these surfaces represent DFT energies for completely rigid molecules (all coordinates fixed for each point.) Thus, the shallow minima associated with the bent Rh-Rh-C linkage do not appear in these surfaces. It is anticipated that similar scans with the bulkier ligands and/or with the larger carbenes will show more dramatic steric effects.

In addition to extending and completing the steric effect studies, an attempt will be made to model the transition state for the addition of a carbene to a C=C double bond. Initially this will focus on the carbene insertion reaction without the catalyst. When this much simpler transition state is understood, efforts will be made to also include the effect of the catalyst in the reaction. If this is successful, the results from this part of the study will provide very compelling evidence for the mechanism of steric control in this reaction, as well as high quality suggestions for what may be done to modify that control.

d. Justification of resources requested:
Dgauss and Dmol have been optimized to run on CRAY vector hardware, so flyer is an appropriate platform for using these codes. While Gaussian 94 has probably not been optimized for the CRAY to quite the extent that Dgauss has, it requires such a large amount of cpu and scratch disk space that flyer is an appropriate platform for it as well. While Gaussian and Dmol do not require any special user interface, Dgauss does require the use of Unichem as a front and rear end processor. Unichem runs only on SGI hardware and there are no SGI machines at ASU. Hence Unichem will be run, using its x-windows option, on hawksbill on the NCSC workstation cluster, from ASU. By the time the allocation committee considers this proposal, AVS will be running on a DEC workstation in ASU's chemistry department. This will be used for visualization of results from Dmol calculations, similar to those included in this proposal for Unichem calculations. Since none of the important codes to be used for this project, and none of the hardware for running these codes, are available locally at ASU, this project requires the use of code and hardware at NCSC.

There are 3 metal complexes of interest to this study: the ligands in these complexes are: acetamide, phenylacetamide, and pentafluorophenylacetamide. The complexes have 214, 374, and 534 electrons respectively. Since the DFT calculation costs scale with the cube of the number of basis functions, which is approximately proportional to the number of electrons, the calculation costs (compared to the acetamide complex) increase by a multiplicative factor of 5.3 and 15.5 respectively. A complete geometry optimization using the local density method in Dgauss for the acetamide complex: estercarbene adduct required about 20 hours of cpu. This suggests that the time required for the larger complexes may be in excess of 100 hours of cpu. This can be reduced by first performing optimizations on the molecular fragments, then putting the molecule (catalyst:carbene adduct) together, then doing an optimization. This strategy was required for an optimization of the large carbene bonded to the acetamide complex. Experience suggests that an optimization of the phenylacetamide carbene adduct will require about 60 hours of cpu. Only single point calculations of the pentafluorophenylacetamide complexes will be attempted. These will require an additional 40 hours of cpu. Transition state searches will be carried out for smaller complexes (formate complex initially), but will be more time consuming to carry out. They will also require calculation of vibrational frequencies. I estimate about 60 hours of cpu will be required for these calculations. With 15 hours of cpu included as a cushion for various mistakes, this makes the total request 175 hours of cpu. The permanent disk requirements (on flyer) are rather modest, since the output files will be transferred to ASU for permanent storage as they are generated. Disk requirements on the cluster are larger, since a single set of restart files for a Dgauss optimization will require almost 40 Mbytes. The calculations on the complex with the pentafluorophenylacetamide ligand will be held to the end of the funding period; these will be attempted only if there significant amount of time left over.

e. Previous Supercomputing Experience:

The principal investigator has been using the facilities at NCSC since the center first opened. In addition, he has been a temporary user of the facilities at the San Diego Supercomputing Center, and the Pittsburgh Supercomputing Center. He has been using DFT codes at NCSC for over two years, and has many years of experience with several versions of the Gaussian package. He has written and made NCREN (then called CONCERT) presentations on new features in Gaussian 92. These were in Tech Talk, and NCREN in late summer, 1992. He has taught courses on computational chemistry that have included the use of NCSC facilities. He has participated in NCSC's UFE program on computational science, both as a student and as an instructor.

1. References:

1. T. R. Felthouse, Progress in Inorg. Chem. 29, 73, (1982).
2. E. B. Boyer and S. D. Robinson, Coord. Chem. Rev. 50, 109, (1983).
3. T. Kawamura, K. Fukamachi, T. Sowa, S. Hayashida, and T. Yonezawa, J. Amer. Chem. Soc. 103, 364, (1981); T. Kawamura, H. Katayama, H. Nishikawa, and T. Yamabe, J. Amer. Chem. Soc. 111, 8156, (1989).
4. V. M. Miskowski, T. P. Smith, T. M. Loehr, and H. B. Gray, J. Amer. Chem. Soc. 107, 7925, (1985); C. D. Garner, M. Berry, and B. E. Mann, Inorg. Chem. 23, 1500, (1984).
5. J. W. Trexler Jr., A. F. Schreiner, and F. A. Cotton, Inorg. Chem. 27, 3265, (1988); M. Y. Chavan, T. P. Shu, X. Q. Lin, M. Q. Ahsan, J. L. Bear, and K. M. Kadish, Inorg. Chem. 23, 4538, (1984); T. Sowa, T. Kawamura, T. Shida, and T. Yonezawa, Inorg. Chem. 22, 56, (1983); L. Dubicki, and R. L. Martin, Inorg. Chem. 9, 673, (1970).
6. G. G. Christoph, and Y. B. Koh, J. Amer. Chem. Soc. 101, 1422, (1979); J. L. Bear, C. L. Yao, L. M. Jui, F. J. Capdevielle, J. D. Korp, T. A. Albright, S. K. Kang, and K. M. Kadish, Inorg. Chem. 28, 1254, (1989); F. A. Cotton, and T. R. Felthouse, Inorg. Chem. 20, 5843, (1981); Y. B. Koh, and G. G. Christoph, Inorg. Chem. 18, 1122, (1979).
7. G. A. Rizzi, M. Casarin, E. Tondello, P. Piraino, and G. Granozzi, Inorg. Chem. 26, 3406, (1987).
8. R. Wiest, A. Strich, and M. Benard, New J. Chem. 15, 801, (1991).
9. H. J. Freund, B. Dick, and G. Hohlneicher, Theoret. Chimica Acta (Berl.), 57, 181, (1980).
10. H. Nakatsuji, Y. Onishi, J. Ushio, and T. Yonezawa, Inorg. Chem. 22, 1623, (1983); H. Nakatsuji, J. Ushio, K. Kanda, Y. Onishi, T. Kawamura, and T. Yonezawa, Chem. Phys. Lett. 79, 299, (1981).
11. J. G. Norman Jr., and H. J. Kolari, J. Amer. Chem. Soc. 100, 791, (1978); F. A. Cotton, and X. Feng, Inorg. Chem. 28, 1180, (1989); J. G. Norman Jr., G. E. Renzoni, and D. A. Case, J. Amer. Chem. Soc. 101, 5262, (1979); B. E. Bursten, and F. A. Cotton, Inorg. Chem. 20, 3042, (1981); G. A. Rizzi, M. Casarin, E. Tondello, P. Piraino, and G. Granozzi, Inorg. Chem. 26, 3406, (1987); R. Stranger; G. A. Medley; J. E. McGrady; J. M. Garrett; T. G. Appelton, Inorg. Chem. 35, 2268 (1996).
12. M. P. Doyle, W. R. Winchester, J. A. A. Hoorn, V. Lynch, S. H. Simonsen, and R. Ghosh, J. Amer. Chem. Soc. 115, 9968, (1993).
13. M. B. Hall, Polyhedron, 6, 679, (1987).
14. D. A. Case, Annual Reviews in Physical Chemistry, page 151, (1982).

Summary Report

Problem Statement: Rhodium (II) dimer complexes are important catalysts for a variety of reactions. This project focused on one of these reactions: the insertion of a singlet carbene into a carbon-carbon double bond to form a cyclopropane ring. The resulting cyclopropyl group can have dramatic biological effects, especially in the pyrethroid insecticides which have very low toxicity for mammals and birds, but very high toxicity for insects. The purpose of this project was to investigate the factors that influence the stereochemistry of cyclopropanes produced using these important materials via the use of density functional theory (DFT). The catalyst stabilizes the singlet carbene by forming catalyst : carbene complex that is an intermediate for the insertion reaction. The electronic and geometric properties of this intermediate play a large role in determining the stereochemistry of the product.

The project has three parts: 1) Calibration of method. There are several different DFT methods that might be used for this work; they differ in terms of basis set, treatment of density gradients, and cost. These methods were compared by computing values (particularly geometric values) that can be compared with experiment. The rhodium (II) formate and acetate complexes were chosen for this part of the study as they have known crystal structures. 2) Electronic effects. The chosen method was used to find optimized structures for the adduct of a singlet methylene carbene with several Rh complexes, including the acetate and acetamide complexes. For this small carbene, it is expected that the structure will be determined largely by purely electronic factors. 3) Steric effects. The methylene carbene is replaced by larger carbenes that are more typical of the ones used in experimental studies, and/or the amide H atom is replaced by a more bulky substituent. The differences between structures found in 2 and 3 are likely to be due to purely steric effects.

Results: Calibration: The largest basis set available for Rh in Dgauss 2.3 is the DZVP basis set; this was used in all of the Dgauss work. LDF, BP, and BLYP methods were investigated for the structures of the aquo formate and acetate complexes. These methods differ in treatment of electron density gradient and in cost. The LDF method (no gradient corrections) were cheapest, with the BP calculations 10% to 30% more expensive, and the BLYP method 100% to 500% more expensive to run. The results (for bond lengths in Å) are:

Species	Parameter	Known	LDF	BP	BLYP
Formate
	Rh-Rh	2.38	2.386	2.419	2.437
	Rh-O	2.03	2.027	2.086	2.118
	Rh-O (axial)	2.45	2.232	2.318	2.361
Acetate
	Rh-Rh	2.386	2.383	2.415	2.442
	Rh-O	2.036	2.030	2.089	2.124
	Rh-O (axial)	2.310	2.306	2.442	2.44

Clearly, the LDF computed structures are in best agreement with experiment; hence the LDF/DZVP method was used for the rest of the project. The fact that these were also the cheapest calculations is a very nice bonus.

Electronic Effects: The basic electronic structure of these complexes has been known for some time. The metal-metal bonding may be described in simple terms as sigma2pi4delta2pi*4delta*2 giving an overall metal-metal single bond. When forming a singlet carbene adduct, the initial description of the bonding will involve donation from the carbene HOMO into the complex LUMO and back donation from a filled complex orbital into the carbene LUMO. The orbitals most likely to be involved in this bonding are shown in the first attached figure. The complex LUMO has cylindrical symmetry, so any preferred orientation must come from the back donation. Several energy minima have been found for carbene adducts with these complexes. They are ALL characterized by a strongly bent Rh-Rh-C linkage, with an angle near 160; a typical structure is shown in the second figure. This suggests that the back donation occurs via the complex HOMO; overlap between this orbital and the carbene LUMO will be enhanced by off-axis bonding. This result is new, and is probably the most important so far in the project. Control of the reaction product (cyclopropane) stereochemistry requires that one side of the carbene be different from the other and the non-symmetrical structure for the adduct satisfies this requirement very nicely.

Steric Effects: Much remains to be done to investigate the steric effects that may influence the course of the carbene insertion reaction. Some results have been obtained, however. The last attached figure compares the energy of a carbene adduct to the acetate or acetamide complex as a function of the carbene orientation. The energy scales are the same for these plots; the geometric parameters are defined in the previous figure. Clearly the range of positions accessible for the carbene is significantly more limited for the acetamide adduct, due the steric effects of the N bonded H atoms. Further study is expected to show more pronounced steric effects for larger carbenes and bulkier N substituents.

This project is not complete. This summary report is attached to a renewal proposal for more time to complete the investigation of the steric effects, and to characterize the transition state for the complex mediated addition of a carbene to a C=C double bond.

So, far the major value of this work is the electronic effect result: the adduct of a carbene to the complex is NOT symmetrical.

Non-Technical Summary

The cyclopropyl group (three carbon atoms bonded to form a three membered ring) is difficult to synthesize, but has considerable biological significance. The pyrethrin insecticides, which are highly toxic for insects but have little effect on most other animals, are based on a cyclopropyl group. The biological effects of the group depend on the relative orientation of the other atoms bonded to the carbons; this relative orientation is the stereochemistry of the ring. It is the control of this stereochemistry that is the challenging aspect of making these rings.

Rhodium (II) dimers are powerful catalysts the synthesis of cyclopropyl groups. They do this by holding a CH₂ group (a carbene) in place so that it can add to a C=C double bond to form the cyclopropyl group. The stereochemistry of the resulting ring is controlled by the relative orientation of the carbene and the double bond; these catalysts are stereo-selective because they can restrict this relative orientation. They can, therefore, promote the formation of rings with two groups on the same side (cis) or on opposite sides (trans) of the ring.

The purpose of this project was to use density functional theory (DFT) to investigate the behavior of these catalysts. What is it about the distribution of electrons in these catalysts that causes them to be selective? What can be done to them to make them promote the trans product? What can be done to make them promote the cis product? Getting the answers to these questions requires a significant amount of computation: a typical job might run at about 400 million operations per second for 20 or more hours.

The answers are not all in yet, however, the project has yielded one very important result so far. Control of the product cyclopropyl ring's stereochemistry requires that one side of the carbene be different from the other side, so that it can approach and add to the double bond in one orientation and not the other. This project has shown that when the carbene bonds to the catalyst the Rh-Rh-C bond angle is bent. This implies that one side of the carbene is close to the catalyst, so that only the other side of the carbene can approach and add to a double bond. This is a purely electronic effect; it has nothing to do with crowding from other atoms in the catalyst. It is this effect that allows these catalysts to be selective in the type of cyclopropyl rings they form.

Applications:

There are significant industrial applications of this work. Rhodium is an extraordinarily expensive metal. Anything that can be done to make more efficient or more selective catalysts based on this metal will improve the quality and lower the cost of compounds manufactured using rhodium based catalysts. This project suggests that the selectivity of rhodium dimer catalysts for cyclopropanation reactions is fundamentally and electronic effect; efforts to improve these catalysts should focus on the distribution of the electrons within the catalysts.

There probably are not government or public policy implications of this work.

6) Education:

There are two different ways this project has affected education at Appalachian State University.

I teach second semester physical chemistry; for most chemistry majors at Appalachian this course is the only significant introduction to quantum mechanics and its applications to chemistry that they see. I have included a computational chemistry project as part of this course for several years. This year (spring 1996) I applied for a set of class accounts on hawksbill and flyer that the students used with unichem for their projects. There were several semi-empirical MO projects, one ab initio MO project, and several DFT projects. This part of the course was quite successful (copies of the student papers are available from Marcie Tolley). I would not have attempted to include the ab initio and DFT methods (or used any NCSC facilities for that matter) if I had not had the research experience that I have had using these codes.

A second and equally important educational aspect of this project is in undergraduate research. Tony Whittington, who has now graduated from ASU, completed most of the calculations in the calibration part of this project; he used close to 100 hours (YMP) of to produce his results. Some of these results are summarized in the table in section 2 of this report. Tony has told me that on some of his job interviews the interviewers were surprised to learn that an undergraduate had so much experience using supercomputers.

7) Optimization:

This study was performed using Dgauss, a third party code for DFT work supported by NCSC. I did not attempt to modify or improve this code. It is a moderately well vectorized code that, for most of my jobs, runs at about 500 Mflops on the T90.