A Density Functional Study of the Completion of the Methane

8452

J. Phys. Chem. B 2001, 105, 8452-8460

A Density Functional Study of the Completion of the Methane Monooxygenase Catalytic Cycle. Methanol Complex to MMOH Resting State Harold Basch,*,†,‡ Djamaladdin G. Musaev,*,† and Keiji Morokuma*,† Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory UniVersity, Atlanta, Georgia 30322, and Department of Chemistry, Bar Ilan UniVersity, Ramat Gan 52900, Israel ReceiVed: February 14, 2001; In Final Form: June 26, 2001

In the final stage of the hydroxylation of methane to methanol by the methane monooxygenase (MMO) enzyme, a binuclear iron-methanol complex (II), expels the methanol and restores the resting state (RS) FeIII-FeIII form of the hydroxylate (MMOH) component to complete the catalytic cycle. The overall process, II f RS, can include protonation, addition of water, expulsion of methanol, and ligand rearrangement, all in an unknown order of occurrence. A model previously applied successfully to describe the hydroxylation mechanism that produces II is used here with the density functional theory to examine a series of intermediate structures and reaction steps to find the lowest-energy reaction path for II f RS. Two different groups of structures and reaction steps are considered; those involving proton transfer from the protein/environment to the complexes (group A) and those that are charge neutral with consideration of internal hydrogen atom migration among the oxygen ligands of the diferric complexes (group B). The lowest-energy paths for group A were found to be paths II - CH3OH f III + H+ f VII + H2O f IX, II - CH3OH f III + H2O f V + H+ f IX, and II + H+ f VI - CH3OH f VII + H2O f IX, with overall reaction energies of -19.9 (9A) and -35.0 (11A) kcal/mol. The methanol dissociation step gives a small thermodynamic barrier to all these mechanisms. In group B, the preferred reaction path is II + H2O f IV f X {or XI} - CH3OH f XII, as well as II - CH3OH f III + H2O f V f XII, with reaction energies of -15.7 (9A) and -18.8 (11A) kcal/mol. The IX and XIII structures have similar geometries and can be identified with the RS of MMOH, depending on its actual charge. The 11A structures are consistently more stable than their 9A counterparts, as expected for FeIII-FeIII complexes, and the II f RS process will proceed entirely on the 11A energy surface.

I. Introduction cycle1

The methane monooxygenase (MMO) catalytic for the hydroxylation of methane can be arbitrarily divided into four quadrants, as shown in Scheme 1. In quadrant I, the resting MMOHox FeIII-FeIII state undergoes a two-electron reduction by the reductase (MMOR) component of the enzyme to an FeIIFeII complex. This change is accompanied by shifts in the amino acid and solvent ligands surrounding and bridging the binuclear iron catalytic center. X-ray crystal structures of both the oxidized and reduced forms have been published.2 The most extensive modeling of these two complexes has been presented by Freisner et al.3 In the second quadrant, the FeII-FeII moiety reacts with O2 to form bridging peroxyl FeIII-FeIII complex P, which cascades through a series of structural transformations and O-O activation to give the intermediate Q complex with an FeIV(µO)2FeIV-centered diamond structure core.1,4,5 In the third quadrant, Q reacts with CH4 through a series of transition states and intermediate structures to give an FeIII-FeIII-methanol complex. This part of the reaction path has been described by Siegbahn and co-workers,6 Hoffmann and co-workers,7 us,8,9 and Yoshizawa and co-workers.10 Finally, in the fourth quadrant, the methanol complex expels methanol and finds its way back to the original FeIII-FeIII resting state (RS) to complete the catalytic cycle. In this work, we examine possible intermediate complexes and a series of fourth-quadrant transformations and * Corresponding author. † Emory University. ‡ Bar Ilan University.

structures that may bring the methanol complex back to the initial RS form of the active site MMOH component in the catalytic cycle. It should be noted that in traversing various stations (equilibrium and transition state structures) on the entire reaction path cycle, the overall spin state of the binuclear iron complex can vary because of the changes in metal oxidation states. We4,8 and others5,6 have identified two important ferromagnetic spin states: 9A with MS ) 8/2 and 11A with MS ) 10/2. The latter is expected to be lower in energy for FeIII-FeIII centers, and the 9A should be lower for FeII-FeII and FeIV-FeIV combinations. Thus, a curve crossing of spin states is expected in each of the first three quadrants, but no such crossing is anticipated in the fourth quadrant studied here. Despite these considerations, all systems here were studied for both the 9A and 11A states. The structural model used is the same as was successfully applied to describe the Q and CH4 reaction. Compound Q, structure I in Figure 1, has two bidentate bridging carboxylate groups, the two bridging oxo ligands, and an additional pair of H2O and NH2 groups on each Fe atom to complete its first coordination sphere. The complex is charge neutral. The particular choice of this model, as well as the consistent use of ferromagnetic spin coupling in the calculations, has been explained in detail previously.4,8,11 Here, one should note that recently Friesner and co-workers12 have published their studies of the mechanism of C-H activation reaction {Q + CH4} using a very large model including about 100 atoms. Their findings and conclusions are

10.1021/jp010573d CCC: $20.00 © 2001 American Chemical Society Published on Web 08/08/2001

Methane Monooxygenase Catalytic Cycle

J. Phys. Chem. B, Vol. 105, No. 35, 2001 8453

SCHEME 1: Proposed Mechanism of Hydrocarbon Hydroxylation by MMOH

nearly quantitatively same as those of our previous paper8 that used the same small model we are using here. They confired our previous conlcusions that that the reaction of compound Q with the methane molecule proceeds via the “bound-radical” mechanism with a rate-determinig transition state corresponding to the H-atom abstraction by the bridging oxo ligand. This demonstrates the usefulness of our small model used in this and previous papers. Direct methane attack on structure I at one of the bridging oxo ligands has been found to give the lowest energy reaction path. Methane can approach from either the NH2 or H2O side in this simplified model. Previously, we have studied 8,13 the both N side (NH2 side) and O side (H2O side) pathways of the methane C-H bond activation process. However, since in the actual enzyme the N side is blocked by protein and only O side pathway is accessible,2,14 here we consider the formation of methanol only on the O side. The resultant methanol complex II is also given in Figure 1. As seen in this figure, the methanol does not occupy the bridging site, but rather, has moved out to a second coordination sphere beyond the bidentate carboxylate ligands which are pinned back opposite the other bridging oxo (O2) ligand. Methanol is also hydrogen-bonded by its oxygen atom (O1) to a water ligand hydrogen and is attracted to a carboxylate oxygen atom by its methyl hydrogen. The ground state of this complex is calculated to be a high-spin state, 11A. Its 9A state is calculated to be 12.6 and 9.6 kcal/mol higher in energy at the SBK (the valence double-ζ basis set for light atoms (H,C,N,O) with no polarization function; see below) and SBK* (SBK basis set with polarization function for the light atoms; see below) basis sets, respectively. The binding energy of methanol was calculated to be 8.1 or 9.2 kcal/mol (9A or 11A) with the SBK basis set, which decreased to 4.0 or 3.7 kcal/ mol, respectively, as the basis set was improved to SBK*. Considering the possible alternative stabilization of methanol by surrounding solvent, the straightforward conclusion would be that there is only a small barrier for the dissociation of methanol from the binuclear Fe complex II after its formation in the hydroxylation process. The methanol complex II, which has been discussed in detail previously,13 is the starting point for our investigation of the fourth quadrant processes. II. Method of Calculation Density functional theory (DFT) with the hybrid B3LYP exchange-correlation potential15 was used for all the calculations reported here. The basis set labeled as SBK adopts the StevensBasch-Krauss effective core potentials (ECP) and the standard 31G, CEP-31, and (8s8p6d/4s4p3d) basis sets for H, (C, O, and

N), and Fe atoms, respectively.16 All structures were gradient optimized using analytically calculated Hessian to ensure convergence to equilibrium geometries. Single-point energies were calculated for the final structures using the SBK* basis set, which consists of the above SBK basis set plus a set of d-type polarization functions with exponents of 0.75 and 0.85, respectively, on all the O and C atoms. The Gaussian 98 package17 was used for all the calculations. All the molecular geometries (II-XIV) in Figure 1 were initially constructed as having only first coordination sphere ligands around the Fe atoms. In some cases, the optimized equilibrium structure shows one or more of the ligands having moved out to the second (or outer) coordination sphere. There were some equilibrium structures that showed proton transfer between the NH2- and H2O ligands to give NH3 and OHligands, respectively. This was considered an artificial result of the simplified model used here and rejected. In one case, an anion-like [H-O..H..O-H] hydrogen-bond system was formed from the interaction of an H2O and an OH- ligand on different Fe atoms. This strongly stabilized structure was also considered to be unrealistic and irrelevant to the processes considered here. III. Results and Discussion The calculated intermediates and reaction paths, with the energetics, in the fourth quadrant are sketched in Scheme 2. This diagram should be very useful in following the discussion. All the optimized structures are shown in Figure 1. In Table 1, we have presented the calculated total energies and energy differences between the 11A and 9A states of all structures. Tables 2 and 3 show the Mulliken atom spin populations and energies, respectively, of individual reaction steps. The Supporting Information include the Cartesian coordinates of all calculated complexes. First, we should note once again that the ground states of all calculated structures, except structure V, are a high-spin 11A state, and their 9A state lies significantly higher (from 6 to 25 kcal/mol at the SBK* level) in energy (see Table 1). In sipte of that below, we will discuss both 11A and 9A states for the sake of completeness of our results. In case of complex V, the ground state is found to be the 9A state, and the 11A state lies higher by 8.8 and 7.6 kcal/mol at the SBK and SBK* levels, respectively. We believe that the stabilization of the 9A state of structure V over 11A is a result of migration of one of the H atoms of the terminal water molecule to the NH2 ligand located on Fe1, which is an artifact and does not represent the reality. The series of processes, which ultimately leads back to the FeIII-FeIII resting state after the hydroxylation reaction, begins

8454 J. Phys. Chem. B, Vol. 105, No. 35, 2001

Basch et al.

Figure 1. Calculated geometries of the possible intermediates (distances in Å, angles in deg) of conversion of the methanol complex FeIII(µ-O)(HOCH3)FeIII (II) to the bis(µ-hydroxy)-diiron complex FeIII(µ-OH)2FeIII (XIII) and (µ-hydroxy)(µ-hyrdo)-diiron complex FeIII(µ-OH)(µ-OH2)FeIII (IX). Numbers for the 9A state are without parentheses, while those for the 11A state are in parentheses.

with the methanol complex II and can proceed to structure III (Figure 1), where methanol has already dissociated:

II f III + CH3OH

(1)

Like the methanol complex II, this structure has two fivecoordinate Fe atoms in ostensibly equivalent coordination environments. However, the 9A and 11A states of III differ in their spin population distributions on the metal atoms. As seen in Table 2, 11A has approximately four unpaired spins on each

Fe atom. The remaining two spins are distributed on the ligands, with 0.67e on the bridging oxo ligand. In an symmetric geometry like III, the spin populations should also be symmetric. For an FeIII-FeIII complex with spin (2S + 1) ) 11, this can be realized by having five unpaired spins on each Fe atom. For 9A, however, there is an additional spin-pairing. This pairing have character of either intra-atomic on an Fe atom which is destabilizing, interatomic between Fe atoms which should be weak, interatomic between an Fe and an oxo atom, or a mixture of various



SCHEME 2: Calculated Mechanism of Conversion of the Methanol Complex FeIII(µ-O)(hoch3)FeIII (II) to the Bis(µ-hydroxy)-diiron Complex FeIII(µ-OH)2FeIII (XIII) and (µ-hydroxy)(µ-hyrdo)-diiron Complex FeIII(µ-Oh)(µ-OH2)FeIII (IX)a

a

Energies with the SBK* basis set are shown for 9A and 11A (in parentheses).

TABLE 1: Calculated Total Energies (in au) and the Energy of the 9A State Relative to That of the 11A (in kcal/mol, Given in Italics after Slash) of the Structures Presented in Figure 1 and Related Molecules SBK structures

9A

H2 H2O H3O+ H8O4 H9O4+ CH3OH II III + CH3OH III IV V VI VII VIII IX X XI XII XIII XIV

-1.174416 -17.152524 -17.440732 -68.693671 -69.067816 -23.985069 -419.705161/12.6 -419.690475/12.7 -395.707188/11.5 -436.905318/11.8 -412.922958/-8.8 -420.118203/21.9 -396.119348/12.2 -437.304993/18.0 -413.276880/30.3 -436.900341/10.0 -436.898439/12.3 -412.907352/17.5 -412.893151/14.3 -412.896002/7.2

SBK* 11A

9A

11A

-17.172189

-419.725300 -419.710683 -395.725497 -436.924126 -412.908878 -420.153033 -396.138757 -437.333616 -413.325113 -436.916199 -436.918090 -412.935312 -412.915863 -419.907358

characters. The Fe-O interatomic coupling, if localized to only one Fe-O pair, will stabilize that Fe-O bond by enhancing its bonding character. The single strengthened Fe-O bond introduces an electronic asymmetry between the two Fe atoms which can be seen by the 9A state having about three and four spins, respectively, on the two Fe atoms. Thus, one Fe-oxo bond is

-24.016795 -419.868969/9.6 -419.857098/13.1 -395.845783/10.5 -437.071307/12.1 -413.064657/-7.6 -420.269219/21.0 -396.248952/12.1 -437.467952/18.6 -413.421366/25.6 -437.072900/8.4 -437.063930/11.9 -413.049454/12.6 -413.041471/11.7 -413.037692/6.1

-419.884205 -419.877962 -395.862457 -437.090667 -413.052480 -420.302718 -396.268274 -437.497640 -413.462181 -437.086284 -437.082942 -413.069485 -413.060098 -413.047346

shorter than the other in 9A, and the shorter bond involves the Fe atom with the smaller number of spins. These charateristics are actually seen in the 9A state of complex III as well as of the methanol complex II. Thus in III, the 11A electronic and geometric structures are symmetric, but the 9A geometry is “distorted” by the asymmetry in the electronic charge and spin


Basch et al.

TABLE 2: Mulliken Atomic Spin Densities of the Structures II-VI 9A

11A

structure

qa

Fe1

O

Fe2

Fe1

O

Fe2

II III IV V VI VII VIII IX X XI XII XIII XIV

0 0 0 0 +1 +1 +1 +1 0 0 0 0 0

2.76 2.81 2.93 3.06 4.08 4.13 4.12 4.08 4.16 4.15 4.15 4.16 4.16

0.35 0.38 0.41 0.39 0.15 0.11 0.12 0.11 0.23 0.17 0.10 0.20 -

4.08 4.06 4.08 4.08 2.61 2.67 2.62 2.71 2.88 2.90 2.73 2.92 2.71

4.08 4.10 4.11 4.12 4.15 4.12 4.15 4.14 4.15 4.15 4.14 4.15 4.16

0.66 0.67 0.62 0.66 0.21 0.23 0.22 0.21 0.22 0.24 0.21 0.25 -

4.10 4.10 4.10 4.07 4.11 4.12 4.11 4.12 4.16 4.14 4.16 4.15 4.13

a

Charge on the structure.

TABLE 3: Calculated Energies (in kcal/mol) of the Reactions 1-15 SBK*

SBK reaction

9A

11A

9A

11A

(1) II f III + CH3OH (2) II + H2O f IV (3) IV f V + CH3OH (4) III + H2O f V (5) II + _Η+_f_VI (6) III + H+ f VII (7) IV + H+ f VIII (8) V + Η+f IX (9) VI f VII + CΗ3ΟΗ (10) VIII f IX + CH3OH (11) VI + Η2Ο f VIII (12) VII + Η2Οf IX (13) IV f X (14) IV f XI (15) X f XII + CH3OH (16) XI f XII + CH3OH (17) V f XII (18) XII f XIII (19) XII f XIV

8.1 -29.9 31.8 -6.2 -24.4a -23.8a -16.0a -21.5a 8.7 27.0 -21.5 -3.1 3.1 4.3 5.0 3.8 -23.7 8.9 7.1

9.2 -29.1 18.9 -19.4 -33.6a -24.5a -22.2a -26.4a 18.3 14.8 -17.6 -21.2 5.0 3.8 -2.6 -1.4 -16.6 12.2 17.5

4.0 -18.9 25.2 2.3 2.2 18.7 -16.7 -0.1 -1.0 4.6 4.2 -1.5 -22.0 5.0 7.4

3.1 -21.5 13.4 -11.2 11.1 11.7 -14.3 -13.6 2.8 4.8 0.0 -2.1 -10.7 5.9 13.9

a

Using H9O4+ and H8O4.

distributions. It should also be noted that the intra-atomic coupling character on the Fe atom is probably responsible for 9A being overall less stable than 11A in these systems. As noted above, methanol dissociation from II, reaction 1, is calculated to be energetically low. There are, however, competing processes. The conversion of one of the bridging oxo atoms in Q to a loosely attached methanol in structure II leaves a coordination position available on at least one Fe atom. An interesting question is whether an adventitious (solvent) water molecule will fill the available ligand site to form the methanol complex with an additional water molecule, before the methanol dissociates. The optimized structures of such complexes, IV, are shown in Figure 1. The binding energies for the process

II + H2O f IV

(2)

are found to be very large in the SBK basis and ∼9 kcal/mol less in the SBK* basis set, at an average ∼20 kcal/mol exothermic for the two spin states (Table 3). This is a much larger binding energy for the water molecule than would be expected based on the methanol binding. Examination of structures IV for its 9A and 11A states shows that they are somewhat different. Complex IV (9A) is a cooperatively bonded

methanol-water dimer in a second coordination sphere around an essentially III core, with the methanol hydrogen atom interacting with a carboxylate oxygen at 1.659 Å, one of its oxygen atoms hydrogen bonded (1.524 Å) to the solvent water hydrogen, and the water oxygen attached to the ligand water hydrogen at 1.456 Å. Besides these short O...H distances, the strength of the H bonds in IV (9A) can also be gauged by the larger water O-H bond lengths (1.030 Å to 1.045 Å) for the participating hydrogen atoms. The other O-H bonds on both these water molecules are reduced ∼0.975 Å from the usual ∼0.985 Å, showing their incipient hydroxy form as the H bond networked hydrogens are stretched by being attracted to other oxygen atoms. Similar structural features are found also for the methanol complexes II. Complex IV in the 11A state, on the other hand, has the added water molecule bound to Fe1 and a second sphere methanol. One of the ligand waters is H-bonded (1.624 Å) to a carboxylate oxygen which is now detached from Fe1. This oxygen is hydrogen bonded to the methanol hydrogen (1.743 Å), and the methanol oxygen is also H-bonded to a hydrogen atom (1.489 Å) of the solvent water molecule. The structural features common to complexes II and IV are (1) methanol prefers to be an outer-sphere ligand, perhaps for steric repulsion reasons, and (2) the binuclear FeIII core prefers five-coordination (5C) for each Fe atom and will even detach a carboxylate oxygen from Fe to make room for a different ligand, water in this case. Monodentate carboxylate ligands have been observed in the X-ray crystal structures1 of both the oxidized (resting) and reduced states of MMOH, without the methanol, of course. The similar, relatively large binding energies found for 9A and 11A states of IV show the flexibility of the binuclear Fedicarboxylate core of these complexes. Direct water binding to an Fe, with the detachment and hydrogen bonding to a carboxylate oxygen atom in 11A, has the same energetic weight as that of the outer-sphere networked additional water molecule in 9A. Since the reaction energy for eq 2 shown in Table 3 does not take into account any solvation of the added water molecule, reaction 2 must be even less exothermic in the protein environment than calculated here as a gas-phase process. Even so, the synergistic effect of binding both the methanol and the water molecules is clear. The Fe atom spin populations show the usual behavior for 9A and 11A states of IV (Table 2), and the two Fe-oxo bond distances behave accordingly; they are very similar for 11A and smaller (1.798 Å) for the Fe-oxo bond distance involving the Fe atom that has the ∼3 spins in 9A. The next step could be the dissociation of the methanol molecule from IV to form V:

IV f V + CH3OH

(3)

As seen in Figure 1, in V (9A) one carboxylic oxygen is detached from Fe1 atom and H-bonded with a water hydrogen. V (11A), on the other hand, shows two outer-sphere water molecules, hydrogen-bond-networked between a water ligand on Fe1 and a carboxylate O atom bound to Fe2. The latter has no innersphere water molecules and is, therefore, only four-coordinate. The low coordination does not affect the spin populations which remain at ∼4 spins/Fe atom. Structure V(9A) showed a tendency for proton transfer from a water ligand to a NH2 group on the same metal center (Fe1) to form metal bound NH3 and H2O. This is, certainly, something that cannot happen in the real enzyme with histidine groups, which are represented in this model by NH2 ligands. Therefore, we will discard V (9A) from our further discussions.



The SBK* endothermicity for reaction 3 is high for both V spin states (Table 3). For 11A, the reaction is strongly (13.4 kcal/ mol) uphill. Dissociating the methanol in the presence of the added water molecule takes 4-6 times more energy than without it (reaction 1). These results suggest that reaction 3, and any mechanism that depends on it, can be ruled out as too high in energy. An alternative route from II to V is for II to first lose the methanol to give III, reaction 1, and for III to add a water molecule to form V in reaction 4:

III + H2O f V

(4)

In the SBK* columns, Table 3 shows that although the first of these two steps is mildly endothermic, the reaction energy of eq 4 slightly increases (9A), or more than balances (11A), the endothermicity of eq 1. The net result of the two paths [1 + 3 or 2 + 4] is the same; II f V is 6.3 kcal/mol energetically uphill (9A) or 8.1 kcal/mol exothermic (11A). An ubiquitous motif of the FeIII-FeIII and FeII-FeII X-ray structures is a bridging hydroxo group, which could be formed by two different processes: (A) by external protonation of the bridging oxo ligands and (B) by the internal protonation via H migration from the terminal water ligands to the bridging oxo ligands. Here, we will investigate both of these processes. Let us to start our discussions with the possible elemetary reactions corresponding to the external protonation mechanism. In general, here we should discuss four different protonation reactions:

II + H+ f VI

(5)

III + H+ f VII

(6)

IV + H+ f VIII

(7)

V + H+ f IX

(8)

Also, it should be noted that the protonation is difficult to evaluate energetically. Certainly, any protonation of an oxygen atom in a charge neutral system will be very exothermic. The protonation of the complex II, III, IV, and V has to be balanced by the deprotonation of solvent, amino acid, or wherever the proton comes from. For the purposes of such a calculation, we assumed the balancing process to be the deprotonation of H9O4+ to give H8O4 + H+, using published18 lowest-energy structures for H9O4+ and H8O4. The resulting deprotonation energy in the SBK basis is 234.8 kcal/mol. Protonation of the bridging oxo group of complex IV leads to complex VIII, reaction 7, which will, of course, carry a charge of +1. Both the 9A and 11A structures have all the ligand groups in the first coordination sphere of both Fe atoms, but with one of the carboxylate oxygen atoms detached from the Fe1 atom in both spin states. The methanol is almost monodentate bonded to Fe2 in 9A, but to Fe1 in 11A. The significance of this switch is not clear, since the spin populations on the iron atoms for both spin states (Table 2) are normal. In any event, the methanol oxygen is not far from the other Fe atom in both spin states; 2.465 Å to Fe1 in 9A and 2.991 Å to Fe2 in 11A. The Fe atoms, therefore, are effectively six-coordinate in 9A, but Fe2 in 9A is closer to five-coordinate. The bridging oxo is now a hydroxide group. In 9A, the bridging Fe--O(H) distance is shorter than Fe1-O(H), possibly because of the less crowded coordination sphere with the larger Fe2-O(methanol) distance. However, the Fe2-O(H) distance is also smaller in 9A, where

Fe2 is six-coordinate, in this case perhaps, because of greater spin pairing; here Fe2 has the smaller spin population of ∼3. The calculated reaction energy of (7) relative to H9O4+ + IV dissociation limit gives -16.0 kcal/mol for 9A and -22.2 kcal/mol for 11A (Table 2). These are reasonable numbers, but the uncertainty remains of how to treat processes where the charges on the reacting and product species are changing, in the absence of a reliable solvation model and without some knowledge of the origin of the proton in the enzymatic system. Protonation of II leads to forms of the complex VI, reaction 5. Structure VI, presented in Scheme 2, look similar for the 9A and 11A states. In both cases, a carboxylic oxygen is lifted from Fe1 and doubly hydrogen bonded to a (Fe1)-water hydrogen atom and the methanol hydrogen. In the 9A structure, the methanol oxygen is bound to both Fe atoms, while in 11A, it is attached only to Fe1. This is part of the general trend that 9A structures tend to be more compact than 11A, perhaps because of the higher spin pairing in the former, although for all the structures in Table 2 the 11A state is more stable than 9A. The calculated reaction energy of eq 5 relative to the H9O4+ + II dissociation limit gives -24.4 kcal/mol for 9A and -33.6 kcal/ mol for 11A (Table 3). Protonation of the complex III leads to the structure VII, reaction 6, which has the simple geometry of a bridging hydroxyl group with five-coordinate Fe atoms and +1 charge. All the core ligands (H2O, NH2, HCO2) are inner-shell-bound to the Fe atoms. This is another example of the strength of outershell binding on the stability of the complexes. A similar situation was found in reaction 4, where V (11A) has two secondshell water molecules. The protonation energy (relative to H9O4+ + III) of III is calculated to be -23.8 and -24.5 kcal/mol for the 9A and 11A states, respectively. The last protonation reaction to discuss is the reaction 8, where protonation of the V leads to the complex IX. In the 9A state, structure IX has the additional water molecule bound almost exclusively to Fe1, making the latter 6C and Fe2 essentially 5C, with a long (3.06 Å) water-Fe2 distance. The bridging hydroxyl has a longer bond length to Fe2 than to Fe1, where the latter has the ∼3 unpaired spins. There are no hydrogen bonds in the 9A state structure IX. In contrast, in the 11A state structure IX has the additional water molecule hydrogen bonded between the water ligand on Fe1 (1.487 Å) and the carboxylic oxygen (2.046 Å), also on Fe1. This water oxygen is at a closest O-Fe distance of 3.605 Å from Fe1. The calculated reaction energy of eq 8 relative to the H9O4+ + V dissociation limit is -26.2 kcal/mol for 9A and -26.9 kcal/ mol for 11A (Table 3). As seen in Scheme 2, in general, products of the reactions 6 and 8, complexes VII and IX, could also be reached via eliminating loosely bound methanol molecule from the complexes VI and VIII, respectively:

VI f VII + CH3OH

(9)

VIII f IX + CH3OH

(10)

However, both reactions are calculated to be energetically unfavorable: reaction 9 is endothemic by 2.2 and 11.1 kcal/ mol for the for the 9A and 11A states, respectively. Reaction 10 is endothermic by 18.7 and 11.7 kcal/mol for the 9A and 11A states, respectively. Meantime, structures VIII and IX could be also reached via coordinating water molecule to the complexes VI and VII, respectively:


Basch et al.

VI + H2O f VIII

(11)

VII + H2O f IX

(12)

The water coordination energies are calculated to be -16.7 and -14.3 kcal/mol for reaction 1 and -0.1 and -13.6 kcal/mol for reaction 12, at their 9A and 11A states, respectively. Let us summarize this section about II f IX reaction paths with protonated species (group A). As shown in Scheme 2, there are six different paths for II f IX, with different orders of CH3OH elimination, H2O addition, and protonation. Any path going through any highly endothermic step, 3 or 10, will be be unfavorable. The other three paths is as follows: path 1 + 6 + 12, II f III f VII f IX, path 1 + 4 + 8, II f III f V f IX, and path 5 + 9 + 2, II f VI f VII f IX; are all energetically feasible. For all these three preferable paths, the methanol dissociation step is a rate-determining for entire process. Note that the terminal structures IX have a bridging hydroxyl and added water molecule. The latter either straddles Fe1 and Fe2 very asymmetrically (9A), being essentially bound to Fe1 and giving 5C and 6C Fe atoms, or is in a second-shell hydrogen-bonded network (11A). Within the present model and protonated structures, IX (11A) can be identified with the FeIIIFeIII RS complex in MMOH. An alternative approach to the external protonation processes studied above is the internal H migration processes leading to only charge neutral complexes (group B). This framework has been also used by Freisner and co-workers3 in considering both the FeIII-FeIII and FeII-FeII forms, which are separated by a two-electron reduction. Thus, protonation of the bridging oxo in IV (still containing the methanol) would require that the proton comes from within the complex: either from the hydrogen bond network within protein, or from one of the water/glutamate ligands coordinated to Fe centers and hydrogen-bond-neworked with solvent molecules. If the methanol is bound to only one of the Fe atoms, as is usually found, then there are two resultant possibilities here, leaving either Fe1 (structure X) or Fe2 (structure XI) with a bonded terminal OH instead of a water and a bridging hydroxide. The corresponding reactions are

IV f X

(13)

IV f XI

(14)

The optimized structures are, generally, very similar, with all the ligands bound in the first coordination sphere and the Fe atoms being five- or six-coordinate. Complex XI in 9A state (Figure 1) looks very much like VIII, with a dangling carboxylate oxygen doubly hydrogen bonded to the Fe2-bound methanol hydrogen (1.505 Å) and a hydrogen atom belonging to an Fe1-connected water molecule (1.560 Å). The terminal hydroxide that came from deprotonating one of the coordinated water molecules is bound to Fe2 with a short Fe-O distance of 1.815 Å, leaving Fe2 without any attached waters. This hydroxide sits trans to the Fe2-OH(bridging) bond in nearoctahedral coordination and the bridging Fe2-OH bond distance (2.013 Å) is longer than Fe1-OH(bridging), although Fe2 has the smaller (∼3) spin population. A strong trans effect in such binuclear Fe complexes has also been reported by Siegbahn.5 Thus, although Fe-OH bonds are expected to be longer than FedO, the Fe-OH(bridging) bond length in 9A seems not to be determined solely by the FeTO(bridging) bond spin pairing that increases the bond order and, consequently, shortens the bond length.

Complex X in the 9A state, on the other hand, has the methanol attached to Fe1 and hydrogen bonded to the dangling carboxylate oxygen atom, with no additional H bonds. Here Fe1 is six-coordinate with the terminal Fe-OH bond. The two Fe-OH bonds on Fe1 are cis to each other, and again, the terminal Fe-OH bond distance is a short 1.838 Å. Looking ahead to the X and XI structures at their 11A state where the terminal Fe-OH bond lengths are almost ∼0.1 Å longer than for the corresponding 9A equilibrium geometries, the spin pairing on one of the Fe atoms in the 9A state could also involve these terminal Fe-OH bonds since the lower-spin population Fe atom also has the terminal OH ligand in both XI(9A) (Fe2) and X (9A) (Fe1). Complex X in 11A looks just like X in 9A, with the same distribution of ligands, H bond, and Fe coordination spheres. Thus, Fe1 is six-coordinate, and Fe2 is five-coordinate with no Fe2-O(methanol) bond. On the other hand, XI in 11A differs from XI in 9A, in the former having a normal bond Fe1O(methanol) bond length and a noninteracting Fe2-O(methanol) distance (3.137 Å) while the latter has the shorter Fe2O(methanol) bond (2.136 Å) and an interacting Fe1-O(methanol) 2.444 Å distance. As noted above, the 11A Fe-OH(terminal) bond lengths are ∼0.05-0.08 Å longer than those in 9A. The Fe-OH (bridging) bond lengths in the 11A complexes are also somewhat larger than in 9A. The SBK* energetics of processes 13 and 14, listed in Table 2, show that the transfer of a proton from a terminally coordinated water to the Fe1-O-Fe2 bridging oxo position is very mildly endothermic or even minutely exothermic. Reaction 13 to give structures X is somewhat more favored, especially in the SBK* basis. Overall, the energetic differences between 13 and 14 are small, and we will continue with both XI and X, keeping all the complexes on the reaction path charge neutral. A reasonable next step is to dissociate the methanol

X f XII + CH3OH

(15)

XI f XII + CH3OH

(16)

to give structures XII in Figure 1. The geometries for 9A and states of XII are similar, with both Fe atoms being fivecoordinate and a second coordination shell water molecule doubly hydrogen bonded to a ligand water molecule hydrogen atom bound to Fe1 and the oxygen atom of the terminal OH group on Fe2. Again, the 9A Fe-OH bond lengths are consistently shorter than those in 11A. Reactions 15 and 16 (Table 2) are also calculated to be mildly endothermic or exothermic. In the SBK* basis, process 16 starting from structure XI is favored. The X f XI rearrangement energy is 5.6 (9A) and 2.1 (11A) kcal/mol. Combining 13 + 15 and 14 + 16 gives the IV f XII + CH3OH process as 3.2 and 2.7 kcal/mol, respectively, for the 9A and 11A states, irrespective of the path through X or XI. These are small endothermic energy values (SBK*) and, therefore, plausible reaction paths. Structures XII are actually one member set of states (9A and 11A) belonging to a family of structurally isomeric complexes which differ in the type and distribution of the oxygen groups (oxo, hydroxyl, water) in the bridging and terminal positions around the Fe atoms. For example, structures XII can also be derived from V by transferring a proton from a terminal water ligand to the bridging oxo position, in analogy to reactions 13 and 14. Table 2 shows that 11A

V f XII

(17)

is very exothermic. Thus, both path (2 + 13)/(14 + 15)/(16)



through II f IVf X/XI f XII and path 2 + 4 + 17 through II f IIIf Vf XII lead energetically downhill to XII by (SBK*) 15.7 kcal/mol (9A) or 18.6 kcal/mol (11A). Here the 11A path is more exothermic by ∼3 kcal/mol. Since II in 11A is already (SBK*) 9.6 kcal/mol more stable than II in 9A, the 11A path is even more energetically favored. Another member of this (V, XII) structurally isomeric family is XIII, where a water proton is transferred from the added water molecule in XII to the terminal hydroxide to initially form double bridging hydroxides. Alternately, XIII can be derived from V by transferring a proton from water to the bridging oxo group. The terminal oxygen ligands now on the Fe atoms are all water molecules (Figure 1). Equilibrium structures XIII resemble the Q complexes, except with hydroxy groups replacing the bridging oxy atoms. Here, in XIII, the Fe centers are both 6C. The process:

XII f XIII

(18)

is found to be endothermic, showing that the XII structures are the more stable isomeric form relative to XIII (Table 2). Since reaction 17 is more exothermic than reaction 18, V f XIII is also exothermic. In this family series, there is one more combination of hydroxy and water ligands, that which initially distributes one terminal hydroxide group on each Fe atom and two water bridging groups (XIV). The optimized geometries for XIV are shown in Figure 1 Geometries of the 9A and 11A states of XIV are similar. Instead of the initial terminal hydroxide and bridging water groups, one water and one hydroxide from each metal center form a hydrogen bond across the Fe1 and Fe2 gap. The bidentate bridging carboxylic acid groups bulge outward to an allow optimum energetic arrangement of the water/hydroxide H-bond. This bend precludes additional bridging of the Fe atoms by another water molecule. The Fe centers in XIV are both fivecoordinate. XIV is also less stable than XII so that

XII f XIV

(19)

is endothermic (Table 2) by (SBK*) 7.4 (9A) or 13.9 (11A) kcal/ mol. Thus, as noted above and seen in Scheme 2, two charge neutral paths from the methanol complex (II), involving the addition of an adventitious water molecule followed by hydrogen atom migration (where CH3OH elimination can take place either before or after the process), leads to structure XII with a lowenergy barrier. Complex XII has one bridging hydroxyl group and a second sphere water molecule connecting terminal water and hydroxyl ligands on the two metal centers and 5C Fe atoms. Within the framework of the charge neutral model complexes (group B) examined here, structure XII can be identified with the FeIII-FeIII resting state RS of MMOH. IV. Summary and Conclusions The last stage in the oxidation of methane to methanol by the hydroxylase component of the MMO enzyme involves the conversion of the diferric methanol complex to the original FeIII-FeIII resting state (RS) form to complete the catalytic cycle. Using density functional theory and model compounds, we have here examined a series of intermediate structures and reaction steps that can be involved in the closing stage reaction path. Starting from the methanol complex (II), the processes involve, in various orders of occurrence, bridging site protonation, addition of water, dissociation of methanol, and rearrangement of ligands. Two different possibilities are evalu-

ated: one involving protonation from an external source (group A) and the other involving hydrogen atom transfer among oxygen ligands within the diferric complexes (group B). In the latter group, all the structures are charge neutral. The possible reaction paths examined here are summarized in Scheme 2. The cube consisting of structures II to IX represents the external protonation pathways (group A) leading to structure IX, which is identified as RS of the catalytic cycle. The upper square followd by the right-hand tilted square in Scheme 2 represents internal hydrogen atom migration pathways (group B) leading to structure XIII, another RS structure. The guiding principle in choosing the preferred paths in each group is that the thermodynamic barrier (endothermicity) should be small (if any) along the entire reaction path. Generally, the methanol dissociation process is the only or main endothermic step in all the mechanisms, and therefore, its reaction energy should be favorable for the optimum paths. In group A, these and other considerations lead to two lowest energy paths: II - CH3OH f III + H+ f VII + H2O f IX, II - CH3OH f III + H2O f V + H+ f IX, and II + H+ f IV - CH3OH f VII + H2O f IX. The methanol dissociation step gives a small thermodynamic barrier to all these mechanisms. In group B the same considerations give the preferred reaction paths II + H2O f IV f X {or XI} - CH3OH f XII, as well as II - CH3OH f III + H2O f V f XII. Complexes IX or XII are identified with the FeIII-FeIII resting state RS of MMOH within the model structures used here, depending on the charge of RS. The general similarity between the path A and path B terminal structures reinforces the conclusion that the correct end-point geometries have been found. The preferred paths for group A is (SBK*) calculated to be 19.9 (9A) and 35.0 (11A) kcal/mol exothermic. The exact values will depend on how protonation energies are handled in the protein environment. In this study, the DFT calculated deprotonation energy of H9O4+ (to H8O4) of 234.8 kcal/mol was subtracted from the simple energy difference between protonated and unprotonated species. Since this balancing solvation energy is common to all the group A paths, no mechanism is prejudiced by the solvation uncertainty. The reaction energy for the optimal path B mechanism is -15.7 (9A) and -18.8 (11A) kcal/mol. For both preferred A and B paths, the 11A state is more exothermic, on top of the initially lower energy of the II 11A state relative to II 9A. Therefore, the II f RS process will take place on the 11A energy surface. Acknowledgment. H.B. acknowledges the Visiting Fellowship from the Emerson Center. The present research is in part supported by a grant (CHE-9627775) from the National Science Foundation. Acknowledgment is made to the Cherry L. Emerson Center of Emory University for the use of its resources, which is in part supported by a National Science Foundation grant (CHE-0079627) and an IBM Shared University Research Award. Acknowledgment is also made for generous support of computing time at Bar Ilan University Computer Center and US National Center for Supercomputing Applications (NCSA). Supporting Information Available: The Cartesian coordinates of all calculated structures. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Waller, B. J.; Lipscomb, J. D. Chem. ReV. 1996, 96, 2625, and references therein. (b) Shu, L.; Nesheim, J. C.; Kauffmann, K.; Munck, E.;

8460 J. Phys. Chem. B, Vol. 105, No. 35, 2001 Lipscomb, J. D.; Que Jr., L. Science 1997, 275, 515. (c) Solomon, E.; Brunold, T. C.; Davis, M. I.; Kemsley, J. N.; Lee, S.-K.; Lehnert, N.; Neese, F.; Skulan, A. J.; Yang, Y.-S.; Zhou, J. Chem. ReV. 2000, 100, 235, and references therein. (2) (a) Rosenzweig, A. C.; Fredrick, C. A.; Lippard, S. J.; Nordlund, P. Nature 1993, 366, 537. (b) Rosenzweig, A. C.; Nordlund, P.; Takahara, P. M.; Fredrick, C. A.; Lippard, S. J. Chem. Biol. 1995, 2, 409. (3) Dunietz, B. D.; Beachy M. D.; Cao, Y.; Whittington, D. A.; Lippard, S. J.; Friesner, R.A. J. Am. Chem. Soc. 2000, 122, 2828. (4) (a) Torrent, M.; Musaev, D. G.; Morokuma, K.; Basch, H. J. Phys. Chem. B 2001, 105, 4453. (b) Torrent, M.; Mogi, K.; Basch, H.; Musaev, D. G.; Morokuma, K. J. Phys. Chem. B. 2001, in press. (5) Siegbahn, P. E. M. Inorg. Chem. 1999, 38, 2880. (6) Siegbahn, P. E. M.; Crabtree, R. H. J. Am. Chem. Soc. 1997, 119, 3103-3113. (7) Yoshizawa, K.; Ohta, T.; Yamabe, T.; Hoffmann, R. J. Am. Chem. Soc. 1997, 119, 12311. (8) Basch, H.; Mogi, K.; Musaev, D. G.; Morokuma, K. J. Am. Chem. Soc. 1999, 121, 7249. (9) Basch, H.; Musaev, D. G.; Mogi, K.; Morokuma, K. J. Phys. Chem. A. 2001, 105, 3615. (10) Yoshizawa, K.; Ohta, T.; Yamabe, T. Bull. Chem. Soc. Jpn. 1998, 71, 1899. (11) Morokuma, K.; Musaev, D. G.; Vreven, T.; Basch, H.; Torrent, M.; Khoroshun, D. V. IBM J. Res. DeV., in press. (12) Gherman, B. F.; Dunietz, B. D.; Whittington, D. A.; Lippard, S. J.; Friesner, R. A. J. Am. Chem. Soc. 2001, 123, 3836. (13) Basch, H.; Musaev, D. G.; Morokuma, K. J. Phys. Chem. B, to be submitted.

Basch et al. (14) (a) Whittington, D. A.; Lippard, S. J. In ACS Symposium Series; Hodgson, K. O.; Solomon, E. I.; Eds.; American Chemical Society: Washington D. C., 1998. (b) Willems, J.-P.; Valentine, A. M.; Gurbiel, R.; Lippard, S. J.; Hoffman, B. M. J. Am. Chem. Soc. 1998, 120, 9410. (15) (a) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (b) Becke, A. D. Phys. ReV. A 1988, 38, 3098-3100. (c) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785. (16) (a) Stevens, W. J.; Basch, H.; Krauss, M. J. Chem. Phys. 1984, 81, 6026. (b) Stevens, W. J.; Krauss, M.; Basch, H.; Jasien, P. G. Can. J. Chem. 1992, 70, 612. (17) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, Revision A.7; Gaussian, Inc.: Pittsburgh, PA, 1998. (18) (a) For H8O4: Muller-Dethlefs, K.; Hobza, P. Chem ReV. 2000, 100, 143. (b) For H9O4+: Hodges, M. P.; Wales, D. J. Chem. Phys. Lett. 2000, 324, 279.

A Density Functional Study of the Completion of the Methane

Recommend Documents