Sason Shaik

P450 Enzymes: Their Structure, Reactivity, and Selectivity—Modeled by QM/MM Calculations

ion from camphor is affected by the choices made during setup.131 In this context, it should be noted that early QM/MM work on different P450cam intermediates and on different steps of the catalytic cycle employed separate setups that had been generated independently, which raises the question whether it is possible to handle the whole cycle with the same QM/MM setup. This is indeed the case: following a standard protocol that starts from the X-ray structure of the ferrous dioxygen complex and that involves careful assignment of protonation states and hydration, one can generate a common setup that gives QM/MM results for P450cam which are generally consistent with those obtained previously with individual setups.54 This confirms that setup issues can be resolved in a consistent manner if proper care is exercised. P450 Enzymes Modeled by QM/MM Calculations Chemical Reviews, 2010, Vol. 110, No. 2 955

How to Conceptualize Catalytic Cycles? The Energetic Span Model

A computational study of a catalytic cycle generates state energies (the E-representation), whereas experiments lead to rate constants (the k-representation). Based on transition state theory (TST), these are equivalent representations. Nevertheless, until recently, there has been no simple way to calculate the efficiency of a catalytic cycle, that is, its turnover frequency (TOF), from a theoretically obtained energy profile. In this Account, we introduce the energetic span model that enables one to evaluate TOFs in a straightforward manner and in affinity with the Curtin-Hammett principle. As shown herein, the model implies a change in our kinetic concepts. Analogous to Ohms law, the catalytic chemical current (the TOF) can be defined by a chemical potential (independent of the mechanism) divided by a chemical resistance (dependent on the mechanism and the nature of the catalyst). This formulation is based on Eyrings TST and corresponds to a steady-state regime. In many catalytic cycles, only one transition state and one intermediate determine the TOF. We call them the TOF-determining transition state (TDTS) and the TOF-determining intermediate (TDI). These key states can be located, from among the many states available to a catalytic cycle, by assessing the degree of TOF control (X(TOF)); this last term resembles the structure-reactivity coefficient in classical physical organic chemistry. The TDTS-TDI energy difference and the reaction driving force define the energetic span (δE) of the cycle. Whenever the TDTS appears after the TDI, δE is the energy difference between these two states; when the opposite is true, we must also add the driving force to this difference. Having δE, the TOF is expressed simply in the Arrhenius-Eyring fashion, wherein δE serves as the apparent activation energy of the cycle. An important lesson from this model is that neither one transition state nor one reaction step possess all the kinetic information that determines the efficiency of a catalyst. Additionally, the TDI and TDTS are not necessarily the highest and lowest states, nor do they have to be adjoined as a single step. As such, we can conclude that a change in the conceptualization of catalytic cycles is in order: in catalysis, there are no rate-determining steps, but rather rate-determining states. We also include a study on the effect of reactant and product concentrations. In the energetic span approximation, only the reactants or products that are located between the TDI and TDTS accelerate or inhibit the reaction. In this manner, the energetic span model creates a direct link between experimental quantities and theoretical results. The versatility of the energetic span model is demonstrated with several catalytic cycles of organometallic reactions.

Axial ligand tuning of a nonheme iron(IV)–oxo unit for hydrogen atom abstraction

The reactivities of mononuclear nonheme iron(IV)–oxo complexes bearing different axial ligands, [FeIV(O)(TMC)(X)]n+ [where TMC is 1,4,8,11-tetramethyl-1,4,8,11-tetraazacyclotetradecane and X is NCCH3 (1-NCCH3), CF3COO− (1-OOCCF3), or N3− (1-N3)], and [FeIV(O)(TMCS)]+ (1′-SR) (where TMCS is 1-mercaptoethyl-4,8,11-trimethyl-1,4,8,11-tetraazacyclotetradecane), have been investigated with respect to oxo-transfer to PPh3 and hydrogen atom abstraction from phenol OH and alkylaromatic CH bonds. These reactivities were significantly affected by the identity of the axial ligands, but the reactivity trends differed markedly. In the oxidation of PPh3, the reactivity order of 1-NCCH3 > 1-OOCCF3 > 1-N3 > 1′-SR was observed, reflecting a decrease in the electrophilicity of iron(IV)–oxo unit upon replacement of CH3CN with an anionic axial ligand. Surprisingly, the reactivity order was inverted in the oxidation of alkylaromatic CH and phenol OH bonds, i.e., 1′-SR > 1-N3 > 1-OOCCF3 > 1-NCCH3. Furthermore, a good correlation was observed between the reactivities of iron(IV)–oxo species in H atom abstraction reactions and their reduction potentials, Ep,c, with the most reactive 1′-SR complex exhibiting the lowest potential. In other words, the more electron-donating the axial ligand is, the more reactive the iron(IV)–oxo species becomes in H atom abstraction. Quantum mechanical calculations show that a two-state reactivity model applies to this series of complexes, in which a triplet ground state and a nearby quintet excited-state both contribute to the reactivity of the complexes. The inverted reactivity order in H atom abstraction can be rationalized by a decreased triplet-quintet gap with the more electron-donating axial ligand, which increases the contribution of the much more reactive quintet state and enhances the overall reactivity.

VALENCE BOND DIAGRAMS AND CHEMICAL REACTIVITY

A unified description of chemical reactivity is made possible with valence bond (VB) diagrams, such as those shown for the a simple case (only reactants and products must be considered) and a more complex system (an intermediate state also plays an important role; RC = reaction coordinate). Analysis of reactivity and mechanistic problems in organic and organometallic chemistry exemplifies the generality of the VB paradigm: in situ DNA repair, C-F and C-H bond activation, SRN 2c mechanism, stepwise versus concerted cycloaddition, and a lot more.

Charge-shift bonding and its manifestations in chemistry

Electron-pair bonding is a central chemical paradigm. Here, we show that alongside the two classical covalent and ionic bond families, there exists a class of charge-shift (CS) bonds wherein the electron-pair fluctuation has the dominant role. Charge-shift bonding shows large covalent-ionic resonance interaction energy, and depleted charge densities, and features typical to repulsive interactions, albeit the bond itself may well be strong. This bonding type is rooted in a mechanism whereby the bond achieves equilibrium defined by the virial ratio. The CS bonding territory involves, for example, homopolar bonds of compact electronegative and/or lone-pair-rich elements, heteropolar bonds of these elements among themselves and with other atoms (for example, the metalloids, such as silicon and germanium), hypercoordinated molecules, and bonds whose covalent components are weakened by exchange-repulsion strain (as in [1.1.1]propellane). Here, we discuss experimental manifestations of CS bonding in chemistry, and outline new directions demonstrating the portability of the new concept.

Exchange-enhanced reactivity in bond activation by metal–oxo enzymes and synthetic reagents

Reactivity principles based on orbital overlap and bonding/antibonding interactions are well established to describe the reactivity of organic species, and atomic structures are typically predicted by Hunds rules to have maximum single-electron occupancy of degenerate orbitals in the ground state. Here, we extend the role of exchange to transition states and discuss how, for reactions and kinetics of bioinorganic species, the analogue of Hunds rules is exchange-controlled reactivity. Pathways that increase the number of unpaired and spin-identical electrons on a metal centre will be favoured by exchange stabilization. Such exchange-enhanced reactivity endows transition states with a stereochemistry different from that observed in cases that are not exchange-enhanced, and is in good agreement with the reactivity observed for iron-based enzymes and synthetic analogues. We discuss the interplay between orbital- and exchange-controlled principles, and how this depends on the identity of the transition metal, its oxidation number and its coordination sphere.

Nature of the Fe-O2 bonding in oxy-myoglobin: effect of the protein.

The nature of the Fe-O2 bonding in oxy-myoglobin was probed by theoretical calculations: (a) QM/MM (hybrid quantum mechanical/molecular mechanical) calculations using DFT/MM and CASSCF/MM methods and (b) gas-phase calculations using DFT (density functional theory) and CASSCF (complete active space self-consistent field) methods. Within the protein, the O2 is hydrogen bonded by His64 and the complex feels the bulk polarity of the protein. Removal of the protein causes major changes in the complex. Thus, while CASSCF/MM and DFT/MM are similar in terms of state constitution, degree of O2 charge, and nature of the lowest triplet state, the gas-phase CASSCF(g) species is very different. Valence bond (VB) analysis of the CASSCF/MM wave function unequivocally supports the Weiss bonding mechanism. This bonding arises by electron transfer from heme-Fe(II) to O2 and the so formed species coupled then to a singlet state Fe(III)-O2(-) that possesses a dative sigma(Fe-O) bond and a weakly coupled pi(Fe-O2) bond pair. The bonding mechanism in the gas phase is similar, but now the sigma(Fe-O) bond involves higher back-donation from O2(-) to Fe(III), while the constituents of pi(Fe-O2) bond pair have greater delocalization tails. The protein thus strengthens the Fe(III)-O2(-) character of the complex and thereby affects its bonding features and the oxygen binding affinity of Mb. The VB model is generalized, showing how the protein or the axial ligand of the oxyheme complex can determine the nature of its bonding in terms of the blend of the three bonding models: Weiss, Pauling, and McClure-Goddard.

Kinetic-Quantum Chemical Model for Catalytic Cycles: The Haber−Bosch Process and the Effect of Reagent Concentration

A combined kinetic-quantum chemical model is developed with the goal of estimating in a straightforward way the turnover frequency (TOF) of catalytic cycles, based on the state energies obtained by quantum chemical calculations. We describe how the apparent activation energy of the whole cycle, so-called energetic span (delta E), is influenced by the energy levels of two species: the TOF determining transition state (TDTS) and the TOF determining intermediate (TDI). Because these key species need not be adjoining states, we conclude that for catalysis there are no rate-determining steps, only rate determining states. In addition, we add here the influence of reactants concentrations. And, finally, the model is applied to the Haber-Bosch process of ammonia synthesis, for which we show how to calculate which catalyst will be the most effective under specific reagents conditions.

Dihydrogen contacts in alkanes are subtle but not faint

Alkane molecules are held together in the crystal state by purportedly weak homonuclear R–H···H–R dihydrogen interactions. In an apparent contradiction, the high melting points and vaporization enthalpies of polyhedranes in condensed phases require quite strong intermolecular interactions. Two questions arise: ‘How strong can a weak C–H···H–C bond be?’ and ‘How do the size and topology of the carbon skeleton affect these bonding interactions?’ A systematic computational study of intermolecular interactions in dimers of n-alkanes and polyhedranes, such as tetrahedrane, cubane, octahedrane or dodecahedrane, showed that attractive C–H···H–C interactions are stronger than usually thought. We identified factors that account for the strength of these interactions, including the tertiary nature of the carbon atoms and their low pyramidality. An alkane with a bowl shape was designed in the search for stronger dihydrogen intermolecular bonding, and a dissociation energy as high as 12 kJ mol−1 is predicted by our calculations. Intermolecular non-polar H···H interactions between polyhedrane molecules may be as attractive as classical hydrogen bonds. A theoretical study identifies the chemical and structural factors that favour such attractive interactions.

A Valence Bond Modeling of Trends in Hydrogen Abstraction Barriers and Transition States of Hydroxylation Reactions Catalyzed by Cytochrome P450 Enzymes

The paper outlines the fundamental factors that govern the mechanisms of alkane hydroxylation by cytochrome P450 and the corresponding barrier heights during the hydrogen abstraction and radical rebound steps of the process. This is done by a combination of density functional theory calculations for 11 alkanes and valence bond (VB) modeling of the results. The energy profiles and transition states for the various steps are reconstructed using VB diagrams (Shaik, S. S. J. Am. Chem. Soc. 1981, 103, 3692-3701. Shaik, S.; Shurki, A. Angew. Chem. Int. Ed. 1999, 38, 586-625.) and the DFT barriers are reproduced by the VB model from raw data based on C-H bond energies. The model explains a variety of other features of P450 hydroxylations: (a) the nature of the polar effect during hydrogen abstraction, (b) the difference between the activation mechanisms leading to the Fe(IV) vs the Fe(III) electromers, (c) the difference between the gas phase and the enzymatic reaction, and (d) the dependence of the rebound barrier on the spin state. The VB mechanism shows that the active species of the enzyme performs a complex reaction that involves multiple bond making and breakage mechanisms by utilizing an intermediate VB structure that cuts through the high barrier of the principal transformation between reactants and products, thereby mediating the process at a low energy cost. The correlations derived in this paper create order and organize the data for a process of a complex and important enzyme. This treatment can be generalized to the reactivity patterns of nonheme systems and synthetic iron-oxo porphyrin reagents.