Transition State Modeling for Catalysis - American Chemical Society

Chapter 4

Transition States in Catalysis and Biochemistry Margareta R. A . Blomberg and Per E . M . Siegbahn

Downloaded by COLUMBIA UNIV on August 7, 2012 | http://pubs.acs.org Publication Date: April 8, 1999 | doi: 10.1021/bk-1999-0721.ch004

Department of Physics, University of Stockholm, Box 6730, S-113 85 Stockholm, Sweden

Three different examples are given from recent applications where transition states for catalytic processes are obtained. The size of the model systems range from 15 to 40 atoms and transition metals are present. The first example is a model study of homogeneous alkane activation. In the reaction be tween nickel cations and n-butane, it is shown that an unusual type of multi-center transition states determine the fractions of different elimination products. The second example is con cerned with methane hydroxylation in methane monooxygenases (MMO) present in microorganisms termed methanotrophs. The H-atom abstraction from methane is studied using a dinuclear iron model complex. Thefinalexample is the substrate mech anism ofribonucleotidereductase (RNR), transforming RNA nucleotides into DNA nucleotides. In the present survey of recent work concerned with studies of chemical reac tions, three different examples will be described. In all of these the determi nation of transition states is the key problem. The examples serve to show possibilities and limitations of present approaches. For many years the accu racy of the methods used was the main limitation, but this is no longer true for the present type of problems rel 12 ating to reaction mechanisms. In the present work the D F T (Density Functional Theory) method termed B3LYP is used (1). For benchmark tests of this method comprising 55 common first and second row molecules performed using slightly larger basis sets than used here (£), an average absolute deviation compared to experiments of 2.2 kcal/mol was obtained for the atomization energies, of 0.013 A for the bond distances and of 0.62 degrees for the bond angles. The present accuracy should be almost as

© 1999 American Chemical Society

In Transition State Modeling for Catalysis; Truhlar, D., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1999.

49


50 high as in this benchmark test and should be enough to discriminate between different reaction mechanisms. Instead, the main limitation is now the size of the system that can be treated. This means that one has to be careful in selecting proper models for the real situation. Since the most realistic approach is to start out by performing a calculation on an isolated gas phase model, the actual environment also has to be considered before the final answer is reached. The exception to this rule is, of course, when gas phase reactions of reasonably small systems are studied. In the first example given here, the reaction between nickel cations and butane, the simplest case of a direct comparison to gas phase experiments is discussed. This example is chosen to point out the possibility to make detailed evaluations of the accuracy of calculated potential surfaces by direct compar isons to experiments. It also shows the complexity of even seemingly simple reactions where the models chosen are known to be the best possible. In con trast, for the other two examples taken from biochemistry, an accurate modeling of the true situation is one of the major problems. This is particularly true for the first example of methane activation by methane monooxygenase (5), where even the metal complex directly involved in the reactions is too big to be a useful first model. The second problem, concerned with the R N R substrate reaction (4), is simpler in this respect and all residues directly involved could eventually be included in the model. In general for biochemical reactions, also the effects of the surrounding protein environment should be taken into consideration. This was done in the R N R substrate case but, as will be shown, for properly chosen models these effects can be kept very small. Computational Details Methods and basis sets. A l l calculations were made using the GAUSSIAN94 program (5). The calculations were performed in several steps. First, an optimization of the geometry was performed using the B3LYP method (1). Double zeta basis sets were used in this step (the LANL2DZ set of the Gaussian94 program). In the second step the energy was evaluated for the optimized geometry using very large basis sets including diffuse functions and with two polarization functions on each atom (the 6-311+G(2d,2p) basis sets). The final energy evaluation was also performed at the B3LYP level. A l l energies discussed below include zero-point vibrational effects. These were calculated using all electron basis sets of essentially double zeta quality. For the N i + butane reaction, the zero-point vibrational effects were calculated at the B3LYP level, while for M M O and R N R Hartree-Fock results, scaled by 0.9, were used. A l l transition states are characterized by having only one imaginary frequency. In the R N R calculations dielectric effects from the surrounding protein were calculated at the optimized structures, using the Self-Consistent Reaction Field (SCRF) method. In the present study the self-consistent isodensity polarized continuum model (SCI-PCM) was used. In this method the solute cavity is determined from a surface of constant charge density around the solute molecule. The dielectric constant of the protein is the main empirical parameter of the +


51


model and it was chosen to be equal to 4 in line with previous suggestions for proteins. This choice has recently been found to give very good agreement with experiment for two different electron transfer processes in the bacterial photosynthetic reaction center (6). In the present case where neutral models are chosen throughout, the dielectric effects are found to be extremely small. Localisation of transition states. A major part of the studies discussed here is spent on the determination of relevant transition states. To some extent the procedure to find the transition states requires chemical intuition and each problem has its own solution, but there are some technical points which are quite general and could be useful to mention. In some of the present systems the final models used are quite large, particularly for the biochemical problems. One useful general experience here is that the local structure of a transition state for a particular reaction is usually quite independent of the size of the system. Therefore, to obtain a good starting point the model should first be made as small as possible. The second useful technical point is that freezing procedures should be extensively used to approach the transition state. Following some assumed reaction path, the positions of some key atoms should be fixed at different intervals and all other coordinates optimized until a barrier region is located. At this stage, a Hessian matrix should be calculated to be used for the final localisation of the transition state. Since Hessian matrices are expensive to obtain, it is useful to try to use as simple methods and as small basis sets as possible. Even Hessians obtained at the Hartree-Fock level using minimal basis sets can be quite adequate. Once the transition state has been determined for the smallest possible model, the molecular model should be extended by adding all necessary parts of the system that might affect the energy. Even though these extensions may be necessary for the final accurate energetic results, they normally do not modify the structure and character of the transition states very much. Environmental effects from e.g. a surrounding protein can simply be added on afterwards since it is very unusual that they will affect the structures significantly, at least when the present type of neutral models are used. In this way, transition states can today be obtained for systems with up to 50 atoms using the methods described above. Examples of such cases will be given in the subsections below. Results +

N i and Butane. A n important long-term goal is to understand the funda mental mechanisms of homogeneous catalysis involving transition metal com plexes. A n attractive route in this direction is to study the reactions of the sim plest model systems, the naked metal atoms, in the gas phase. This approach has been used by both experimentalists and theoreticians, creating a useful meeting point for the different techniques, and in particular makes it possible to obtain a thorough evaluation of the accuracy of calculated potential energy surfaces. Below we summarize the preliminary results from a recent study of the reaction between naked nickel cations and n-butane (7). The purpose of


52 this study is to combine energies, geometries, and vibrational frequencies from quantum chemical calculations on all key reaction intermediates and transition states to build a detailed statistical rate model for the N i + n-C4H4 reaction. Such a model would provide absolute time scales for complex fragmentation and time-dependent branching fractions that are directly comparable to experimen tal results (7). In the present chapter we report some of the main features of the calculated potential surfaces. The results from molecular beam experiments on this reaction can be summarized such that at 0.2 kcal/mol collision energy, and after 6 fis, 63 % C H elimination, 1 % C H elimination, 26 % H elimination, and 11 % NiC4Hi" complexes are observed (#). Nickel cations and n-butane form an electrostatic complex, NiC4Hi" , cal culated to be bound by 32 kcal/mol relative to ground state reactants ( N i , D plus n-C4H4), see Fig. 1. The elimination reaction paths from this electro static complex can start with either C-C activation or C - H activation. Earlier experimental work on alkane activation by transition metal cations has been interpreted in terms of this initial C-C or C-H insertion as the rate-limiting step, and the subsequent step has been expected to be a /3-hydrogen or /9-alkyl migration, followed by a three-center, reductive elimination of H or alkane. In contrast, the present calculations show that both C-H and C-C activation have low barriers, well below (12-15 kcal/mol) the separated reactants. Furthermore, the highest potential energy along the paths to H or alkane activation occurs at intriguing multi-center transition states (7). These involve concerted motion of several atoms along a segment of the reaction path connecting each insertion in termediate to the corresponding exit-channel ion-induced-dipole complex. Sim ilar results have previously been obtained for the reaction between n-propane and different transition metal cations (9,10). In ref. 7 it is shown that, both H and C H elimination from n-butane, can occur via either an initial C - C , or an initial C-H insertion. However, the subsequent multi-center transition states are found to be substantially lower for the reaction paths that start with C-C bond activation, and therefore we restrict the present discussion only to those reactions. The calculated potential surfaces for the reaction paths initiated by insertion of N i into a C-C bond of n-butane are shown in Fig. 1. From this figure it can be seen that the main differences between the reactions appear at the multi-center transition states that follow the C-C insertions, and as will be discussed below, the ordering of the multi-center transition states agree with the experimentally observed yields of the different elimination products. From the central C-C insertion product, N i ( C H ) 2 , two different multicenter transition states are possible, MCTS1 and MCTS2. In MCTS1, which gives the lowest barrier, 11 kcal/mol below the separated reactants, a hydro gen atom moves directly from one ethyl group to the other, finally leading to the Ni(C H4)(C He) electrostatic complex. From this complex ethane can be eliminated, see Fig. 1, and in the molecular beam experiment this is the most abundant elimination product, 63 % yield. In MCTS2, shown in Fig. 2, one hy drogen atom from each ethyl group leaves and directly forms H , finally leading +

2

6

4

2

0

0


+

2

2

2

2

2

6

+

2

5

+

2

2

2


53


20.0

o o 5a

0.0

e?

-2o.o

—i

MCTS3 MCTS2 MCTS1

a o -a Ni(C H ) 4

NKC^HZ + C ^ +

10

r

-40.0

J(C H ) 3

6

+ +

CH_

Ni(C H ) + H +

2

Ni(C H )(C H ^ 2

4

2

Ni(C H )(CH )

+

3

6

4

6/

4

2

2

/

1-'

-60.0 0.0 Reaction coordinate —> Figure 1: 11-C4H10.

+

Calculated potential energy surfaces for C-C insertion of N i into

1.449A

\

/

1.635A \ ""2.180A

1.663A

1.596A /

\ * '

2.017A

2.194A''

*2.014A

MCTS2

+

Figure 2: Structure of one of the optimized multi-center transition states for N i + n-C4Hio discussed in the text. The arrows indicate the imaginary vibrational mode. +

to the N i ( C H ) H electrostatic complex. This reaction path has the second lowest barrier, 6 kcal/mol below the separated reactants, and subsequently H 2

4

2

2

2


54 can be eliminated, see Fig. 1, yielding the second most abundant elimination product, 26 % yield in the molecular beam experiment. From the terminal C-C insertion product, N i ( C H ) ( C H 7 ) , one possible multi-center transition state, MCTS3, has been investigated. In this transition state a hydrogen atom moves directly from the ethyl group to the methyl group. This reaction path, thus yielding the Ni(C He)(CH4) electrostatic complex, gives the third lowest barrier, 2 kcal/mol below the separated reactants and it can finally lead to methane elimination, see Fig. 1. The experimental yield of the methane elimination product is only 1 %. In conclusion, the calculations are in good agreement with the experimental observations, giving a qualitatively correct distribution of the possible elimina tion products. However, the quantitative assessment of the calculated potential surface, in particular the height of the rate determining barriers, will have to await the more detailed comparisons between experiment and theory based on the statistical rate modeling in progress (7). Furthermore, the calculations give a new interpretation of the experimental results, in terms of an unusual type of multi-center transition states as the rate-limiting step. +

3

3

+


3

Methane Monooxygenase ( M M O ) . Methane monooxygenases are a group of enzymes which convert methane to methanol via a monooxygenase pathway in which the dioxygen molecule is activated via reduction : CH + 0 4

2

+ N A D H + H+ —> C H O H + H 0 + NAD+ 3

2

(1)

The X-ray structure of the 251 kD hydroxylase from M. capsulatus (11), has a dinuclear iron center bridged by a hydroxide, a glutamate, and an acetate from the buffer, where waters are expected to be bound in vivo. The terminal ligands are mostly oxygen derived but there is also a histidine ligand on each iron center. Experiments have indicated that the active species in the reaction with methane, commonly denoted compound Q, probably has bridging fi-oxo groups and with both irons having oxidation state IV (12,13). The complex is diamagnetic. To model this compound, a complex with only oxygen derived ligands was adopted for simplicity. Ferromagnetic coupling is furthermore used to simplify the calculations. The first part of the study of methane activation by M M O is to optimize the structure of compound Q without methane, see Fig. 3. The geometry obtained after a B3LYP optimization was quite surprising. First, both iron centers are only five coordinated. In fact, models with 6-coordinated starting structures for the optimization, quickly rearrange to adopt 5-coordination. The second, and perhaps even more surprising feature, is that the two oxo groups are asymmetrically placed between the Fe atoms so that the two Fe-0 (oxo) bond lengths for each metal are substantially unequal. The short Fe-0 distances are found to be 1.74 and 1.77 A and the long distances 2.00 and 2.05 A. This is very different from what is known from similar structures, most notably Mn(III) dimeric complexes. After this work was finished a striking confirmation of this structure appeared (14) > New E X A F S data on intermediate Q of M M O was interpreted in terms of an Fe(IV)-(/a-0) -Fe(IV) diamond core structure 2



55

1.020A

1.382A

9

Figure 3: Optimized structure of the A model of compound Q. with asymmetric bridging oxo groups, essentially identical with the intermediate proposed here. Fe-0 (oxo) distances of 1.77 A and 2.05 A were reported. Even though ferromagnetic coupling and simple water and hydroxyl ligands are used, a structure is thus obtained from the calculations which in the most critical region for the chemistry is almost identical to the true structure. The structure of compound Q can be regarded as being derived from an octahedron, but showing strong Jahn Teller (JT) distortions. The J T axis, along which the M - L bonds are elongated, is not the axis normal to the M-(/x-0) -M plane, as in the known Mn(III) cases, but is the axis defined by the long M-oxo bond and the vacant site trans to it; this vacancy can be interpreted as an extreme case of J T distortion leading to the departure of the H2O ligand, assisted by the relatively strong second sphere hydrogen bonding that it can engage in when no longer bound to iron. The four short M-L bonds are in the plane normal to the J T axis. Of these four short bonds, one is formed to a bridging oxo. Since the simple model of the reactant complex of M M O is so well in line with experimental information, the results for the methane activation reaction should also be interesting. The resulting transition state is shown in Fig.4. It should first be noted that the starting guess for the optimization was actually a four-center transition state with a rather short Fe-C distance, but at convergence 2



56

the character of the transition state is very clearly one of a pure abstraction. With the identification of the transition state structure for the methane re action, explanations for the main experimental results can be suggested. First, the large K I E (Kinetic Isotope Effect) for the reaction (12,13), is clearly consis tent with the type of transition state shown in Fig.4. There is a large zero-point effect for the reaction barrier and for the same reason, there is also a large K I E . The calculated K I E for C D at 298.15 °K is 8.0, which is somewhat larger than the experimental value, indicating that the real transition state could be a little bit tighter with more bonding towards the metal. Quite recently, new experi ments by Nesheim and Lipscomb (15) have led to much larger K I E values for the methane reaction than the previous ones. For C D H a value of 9 was found in close agreement with the calculated value. However, for CH4:CD an even larger value of 19 was measured. Large effects of tunneling were suggested to rationalize these large K I E values. Tunneling effects are not accounted for in the present simple estimate of the K I E value. The second main experimental result, 65 % retention of configuration with 4

2

2

4


57 chiral ethane, is in apparent contradiction with the formation of a nearly free methyl radical in the transition state of Fig.4. A reasonable explanation could be that after the transition state is passed, an Fe-CH bond is very rapidly formed. The calculations actually confirm that the most stable product of the methane activation indeed has an Fe-CH3 bond, although a quite weak one with a bond strength of 9 kcal/mol. The final structure on the methane reaction pathway is the methanol product which is quite stable by 40.3 kcal/mol with respect to the starting reactants. The rather simple model used for the present calculations is thus able to explain the main experimental results. At present, calculations are in progress to study this reaction further with more realistic models including all the actual residues of the first coordination sphere. The results obtained to date essentially confirm the picture described above.


3

R N R Substrate Reaction. D N A differs chemically from R N A in two major respects. First, its nucleotides contain 2'-deoxyribose residues (DNA nucleotides) rather than ribose residues (RNA nucleotides). Secondly, D N A contains the base thymine whereas R N A contains uracil. The enzymes that catalyze the set of reactions required for the first of these transformations, see scheme 1, are named Ribonucleotide Reductases (RNR). The present knowledge of R N R has been summarized in recent reviews (16,17). The E. coli R N R is an a/?2 tetramer that can dissociate into two catalytically inactive homodimers, R l and R2. The X-ray structures of both R l (18,19) and R2 (20) have been determined. The reactions leading to substrate conversion can be described in the following way. A n Fe(II)-dimer in R2 is first oxidized, probably to a bis-/ioxo Fe(IV)-dimer, which then is reduced in two steps probably by abstracting two hydrogen atoms from surrounding residues to become a resting Fe(III)dimer complex. In the reduction process a Tyrl22 radical is produced, which can be stored for long periods waiting for the substrate to arrive 30 A away in R l . When the substrate arrives, the radical character will move along a hydrogen bonded chain from Tyrl22 to Cys439 at the substrate site in R l . The substrate reactions are then catalyzed by the Cys439 radical in a process where two other cysteines and probably also a glutamate participates. The leading experimental model for the substrate reactions has been given by Stubbe (21). 2

Scheme 1

HO

OH

HO

H

RNA

DNA

nucleotide

nucleotide



58

DNA nucl.

Reaction coordinate

Figure 5: Energy-diagram for the transformation from the R N A to the D N A nucleotide. The calculations show that the apparently simple transformation in scheme 1 goes over several steps. The computed energy diagram is shown in Fig.5. The rate limiting step is the fourth one, where a rather stable keto intermediate is at tacked. After considerable experimentation a transition state was found, shown in Fig.6. There are some important aspects of this transition state that should be noted here. First, the attack on the keto group is a complex concerted action where Cys225 and Glu441 are mainly involved but where also the involvement of Asn437 is significant. This type of cyclic transition state is found in many other standard transformations common in enzyme reactions. In a simplified picture, the reaction can be described as a proton transfer from Cys225 via a water molecule and Glu441 to the keto oxygen, and a simultaneous attack of the cysteine anion on the carbon of the keto group. It is extremely important to note that in spite of this description in terms of ions, the model chosen is neutral. The choice of neutral models for this type of reaction is quite different from what is normally done, for example using molecular mechanics models, and the present modeling is therefore controversial at the present stage. How ever, the calculations definitely show that this is a strongly concerted process and any attempt to divide this process into separate attacks using ionic models does not work. There are several important implications of this finding. The main one is that since the model is neutral the effects of the surrounding protein should be very small. Using a dielectric continuum model with a cavity shaped



59

Figure 6: Optimized transition state structure for cysteine attack on ribose C3' in the R N R substrate reaction. after the molecule and a dielectric constant equal to four, the effects of the surrounding protein were found to be truly negligible. The effect on the barrier for the reaction shown in Fig.6 is only 0.9 kcal/mol and the effect on the endothermicity is even smaller with 0.4 kcal/mol. In many other enzyme reactions studied recently the same observation is made that neutral gas phase models give a very good description of the reaction. The consistency of the model is in these reactions demonstrated by the small effects found by simple models of the surrounding and, of course, the reasonable agreement with experimental facts available. Conclusions It has been shown that if appropriate procedures are used rather complicated transition states for systems containing up to 50 atoms can be obtained. It is furthermore shown that the accuracy of the calculated energy profiles should be good enough to discriminate between different possible reaction mechanisms in both homogeneous catalysis and biochemistry.


60


Literature Cited 1. Becke, A. D. Phys. Rev. 1988, A38, 3098; Becke, A. D. J. Chem. Phys. 1993, 98, 1372; Becke, A. D. J. Chem. Phys. 1993, 98, 5648. 2. Bauschlicher, C.W.,Jr; Ricca, A.; Partridge, H.; Langhoff, S.R., in Recent Advances in Density Functional Methods, Part II, Ed. D.P. Chong, p. 165 (World Scientific Publishing Company, Singapore, 1997). 3. Siegbahn, P.E.M.; Crabtree, R.H. J. Am. Chem. Soc. 1997, 119, 3103. 4. Siegbahn, P.E.M., submitted. 5. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; Head-Gordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 94 Revision B.2; Gaussian Inc.: Pittsburgh, PA, 1995. 6. Blomberg, M.R.A.; Siegbahn, P.E.M.; Babcock, G.T., submitted. 7. Yi,S.S.; Blomberg, M.R.A.; Weisshaar, J.C., to be published. 8. Noll, R.J.; Weisshaar, J.C. J. Am. Chem. Soc. 1994, 116, 10288. 9. Yi, S.S.; Blomberg, M.R.A.; Siegbahn, P.E.M.; J.C. Weisshaar J. Phys. Chem. A 1998, 102, 395. 10. Holthausen, M.C.; Fiedler, A.; Schwarz, H.; Koch, W. J. Phys. Chem. 1996, 100, 6236, Holthausen, M.C.; Koch, W. J. Am. Chem. Soc. 1996, 118, 9932, Holthausen, M.C.; Koch, W. Helv. Chim. Acta 1996, 79, 1939. 11. Rosenwieg, A.C.; Frederick, C.A.; Lippard, S.J.; Nordlund, P. Nature 1993, 366, 537. 12. Feig, A.L.; Lippard, S.J. Chem. Rev. 1994, 94, 759. 13. Wallar, B.J.; Lipscomb, J.D. Chem. Rev. 1996, 96, 2625. 14. Shu, L.; Nesheim, J.C.; Kauffmann, K.; Munck, E.; Lipscomb, J.D.; Que, Jr., L. Science 1997, 275, 515. 15. Nesheim, J.C.; Lipscomb, J.D. Biochemistry 1996, 35, 10240. 16. Sjöberg, B.M. Structure 1994, 2, 793, Sjöberg, B.-M. Structure and Bonding 1997, 88, 139. 17. Gräslund, A.; Sahlin M. Annu. Rev. Biophys. Biomol. Struct. 1996, 25, 259. 18. Uhlin, U.; Eklund, H. Nature 1994, 370, 533. 19. Eriksson, M.; Uhlin, U.; Ramaswamy, S.; Ekberg, M.; Regnström, K.; Sjöberg, B.-M.; Eklund, H. Structure 1997, 5, 1077. 20. Nordlund, P.; Sjöberg, B.-M.; Eklund, H. Nature 1990, 345, 593. 21. Stubbe, J. Biol. Chem. 1990, 265, 5330; Mao, S.S.; Holler, T.P.; Yu, G.X.; Bollinger, J.M.; Booker, S.; Johnston, M.I.; Stubbe, J. Biochemistry 1992, 31, 9733.


Transition State Modeling for Catalysis - American Chemical Society

Recommend Documents