Rate-promoting vibrations and coupled hydrogen-electron transfer reactions in the condensed phase: a model for enzymatic catalysis

A model is presented for coupled hydrogen-electron transfer reactions in condensed phase in the presence of a rate promoting vibration. Large kinetic isotope effects (KIEs) are found when the hydrogen is substituted with deuterium. While these KIEs are essentially temperature independent, reaction rates do exhibit temperature dependence. These findings agree with recent experimental data for various enzyme-catalyzed reactions, such as the amine dehydrogenases and soybean lipoxygenase. Consistent with earlier results, turning off the promoting vibration results in an increased KIE. Increasing the barrier height increases the KIE, while increasing the rate of electron transfer decreases it. These results are discussed in light of other views of vibrationally enhanced tunneling in enzymes.     

Hydrogen-abstraction reactivity patterns from A to Y: the valence bond way

"Give us insight, not numbers" was Coulson's admonition to theoretical chemists. This Review shows that the valence bond (VB)-model provides insights and some good numbers for one of the fundamental reactions in nature, the hydrogen-atom transfer (HAT). The VB model is applied to over 50 reactions from the simplest H + H(2) process, to P450 hydroxylations and H-transfers among closed-shell molecules; for each system the barriers are estimated from raw data. The model creates a bridge to the Marcus equation and shows that H-atom abstraction by a closed-shell molecule requires a higher barrier owing to the additional promotion energy needed to prepare the abstractor for H-abstraction. Under certain conditions, a closed-shell abstractor can bypass this penalty through a proton-coupled electron transfer (PCET) mechanism. The VB model links the HAT and PCET mechanisms conceptually and shows the consequences that this linking has for H-abstraction reactivity.     

Performance of the correlation consistent composite approach for transition states: a comparison to G3B theory

The correlation consistent composite approach (ccCA) was applied to the prediction of reaction barrier heights (i.e., transition state energy relative to reactants and products) for a standard benchmark set of reactions comprised of both hydrogen transfer reactions and nonhydrogen transfer reactions (i.e., heavy-atom transfer, SN2, and unimolecular reactions). The ccCA method was compared against G3B for the same set of reactions. Error metrics indicate that ccCA achieves "chemical accuracy" with a mean unsigned error (MUE) of 0.89 kcal/mol with respect to the benchmark data for barrier heights; G3B has a mean unsigned error of 1.94 kcal/mol. Further, the greater accuracy of ccCA for predicted reaction barriers is compared to other benchmarked literature methods, including density functional (BB1K, MUE=1.16 kcal/mol) and wavefunction-based [QCISD(T), MUE=1.10 kcal/mol] methods.     

Evidence for concerted pathways in ion-pairing coupled electron transfers

Ion-pairing with electro-inactive metal ions may change drastically the thermodynamic and kinetic reactivity of electron transfer in chemical and biochemical processes. Besides the classical stepwise pathways (electron-transfer first, followed by ion-pairing or vice versa), ion-pairing may also occur concertedly with electron transfer. The latter pathway avoids high-energy intermediates but a key issue is that of the kinetic price to pay to benefit from this thermodynamic advantage. A model is proposed leading to activation/driving force relationships characterizing such concerted associative electron transfers for intermolecular and intramolecular homogeneous reactions and for electrochemical reactions. Contrary to previous assertions, the driving force of the reaction (defined as the opposite of the reaction standard free energy), as well as the intrinsic barrier, does not depend on the concentration of the ion-pairing agent, which simply plays the role of one of the reactants. Besides solvent and intramolecular reorganization, the energy of the bond being formed is the main component of the intrinsic barrier. Application of these considerations to reactions reported in recent literature illustrates how concerted ion-pairing electron-transfer reactions can be diagnosed and how competition between stepwise and concerted pathways can be analyzed. It provided the first experimental evidence of the viability of concerted ion-pairing electron-transfer reactions.     

Electron transfer versus proton transfer in gas-phase ion/ion reactions of polyprotonated peptides

The ion/ion reactions of several dozen reagent anions with triply protonated cations of the model peptide KGAILKGAILR have been examined to evaluate predictions of a Landau-Zener-based model for the likelihood for electron transfer. Evidence for electron transfer was provided by the appearance of fragment ions unique to electron transfer or electron capture dissociation. Proton transfer and electron transfer are competitive processes for any combination of anionic and cationic reactants. For reagent anions in reactions with protonated peptides, proton transfer is usually significantly more exothermic than electron transfer. If charge transfer occurs at relatively long distances, electron transfer should, therefore, be favored on kinetic grounds because the reactant and product channels cross at greater distances, provided conditions are favorable for electron transfer at the crossing point. The results are consistent with a model based on Landau-Zener theory that indicates both thermodynamic and geometric criteria apply for electron transfer involving polyatomic anions. Both the model and the data suggest that electron affinities associated with the anionic reagents greater than about 60-70 kcal/mol minimize the likelihood that electron transfer will be observed. Provided the electron affinity is not too high, the Franck-Condon factors associated with the anion and its corresponding neutral must not be too low. When one or the other of these criteria is not met, proton transfer tends to occur essentially exclusively. Experiments involving ion/ion attachment products also suggest that a significant barrier exists to the isomerization between chemical complexes that, if formed, lead to either proton transfer or electron transfer.     

A Monte Carlo simulation of free energy relationships for the electron transfer reaction between Fe+ and Fe2+ in water

A free energy barrier ΔF^≠ = 174.2 kJ/mol for the self-exchange electron transfer reaction model Fe⁺/Fe²⁺ in water has been calculated by combining Monte Carlo simulations and the statistical perturbation theory. We have shown that, even for those electron transfer reactions that present a very high free energy barrier of activation, the free energy curve behaves parabolically versus the reaction coordinate, which justifies the quadratic expression for the activation free energy done by Marcus.     

Dynamical arrest of electron transfer in liquid crystalline solvents

We argue that electron transfer reactions in slowly relaxing solvents proceed in the nonergodic regime, making the reaction activation barrier strongly dependent on the solvent dynamics. For typical dielectric relaxation times of polar nematics, electron transfer reactions in the subnanosecond time scale fall into nonergodic regime in which nuclear solvation energies entering the activation barrier are significantly lower than their thermodynamic values. The transition from isotropic to nematic phase results in weak discontinuities of the solvation energies at the transition point and the appearance of solvation anisotropy weakening with increasing solute size. The theory is applied to analyze experimental kinetic data for the electron transfer kinetics in the isotropic phase of 5CB liquid crystalline solvent. We predict that the energy gap law of electron transfer reactions in slowly relaxing solvents is characterized by regions of fast change of the rate at points where the reaction switches between the ergodic and nonergodic regimes. The dependence of the rate on the donor-acceptor separation may also be affected in a way of producing low values for the exponential falloff parameter.     

Non-exponentiality in electron transfer kinetics: Static versus dynamic disorder models

Non-exponential electron transfer kinetics in complex systems are often analyzed in terms of a quenched, static disorder model. In this work we present an alternative analysis in terms of a simple dynamic disorder model where the solvent is characterized by highly non-exponential dynamics. We consider both low and high barrier reactions. For the former, the main result is a simple analytical expression for the survival probability of the reactant. In this case, electron transfer, in the long time, is controlled by the solvent polarization relaxation—in agreement with the analyses of Rips and Jortner and of Nadler and Marcus. The short time dynamics is also non-exponential, but for different reasons. The high barrier reactions, on the other hand, show an interesting dynamic dependence on the electronic coupling element,V _el.     

The theory of electron transfer reactions: what may be missing?

Molecular dynamics simulations are presented for condensed-phase electron transfer (ET) systems where the electronic polarizability of both the solvent and the solute is incorporated. The solute polarizability is allowed to change with electronic transition. The results display notable deviation from the standard free energy parabolas of traditional ET theories. A new three-parameter ET model is applied, and the theory is shown to accurately model the free energy surfaces. This paper presents conclusive evidence that the traditional theory for the free energy barrier of ET reactions requires modification.     

The <Emphasis Type="Italic">Saunders-Bell</Emphasis> Analysis of Tunnel Effects in Reactions with Kinetic Isotope Effects

Summary. The primary kinetic isotope effects of deuterium were investigated in 22 hydrogen and deuterium transfer reactions, including enzymatic and nonenzymatic hydride transfer reactions, elimination reactions, and reactions catalyzed by enzymes lipooxygenase, amine dehydrogenase, and methylmalonyl-CoA mutase. In each case, the Saunders-Bell analysis was applied to calculate the tunnel effects and the corresponding thermodynamic parameters. The Saunders-Bell analysis was effective in 14 cases out of 22. A high degree of correlation was found between the barrier factor, the tunnel factor, and the entropy factor among all reactions studied. From this, a general relationship between the three factors was derived, based on the Saunders-Bell analysis of the Bell equation; the Saunders-Bell analysis is valid within certain limits of the barrier factor. This general relationship is universally valid for all hydrogen/deuterium transfer reactions in nature with moderate tunneling, when the Saunders-Bell analysis applies.     

The Saunders-Bell Analysis of Tunnel Effects in Reactions with Kinetic Isotope Effects

The primary kinetic isotope effects of deuterium were investigated in 22 hydrogen and deuterium transfer reactions, including enzymatic and nonenzymatic hydride transfer reactions, elimination reactions, and reactions catalyzed by enzymes lipooxygenase, amine dehydrogenase, and methylmalonyl-CoA mutase. In each case, the Saunders-Bell analysis was applied to calculate the tunnel effects and the corresponding thermodynamic parameters. The Saunders-Bell analysis was effective in 14 cases out of 22. A high degree of correlation was found between the barrier factor, the tunnel factor, and the entropy factor among all reactions studied. From this, a general relationship between the three factors was derived, based on the Saunders-Bell analysis of the Bell equation; the Saunders-Bell analysis is valid within certain limits of the barrier factor. This general relationship is universally valid for all hydrogen/deuterium transfer reactions in nature with moderate tunneling, when the Saunders-Bell analysis applies.     

A model VBCI calculation on the state correlation diagram for radical abstraction and addition reactions

State correlation diagrams for radical reactions are calculated from potential energy surfaces for the model process A−B+C→A+B−C including the H−H+H reaction of three one-electron atoms with ab initio valence bond configuration interaction in a minimal 1s basis. Effects of substituents are simulated by a variation of the nuclear charges. Qualitative predictions derived from the diagrams agree well with recent experimental and advanced theoretical data. In general, the reaction barrier and the geometry of addition and abstraction reactions depend strongly on the reaction enthalpy, but there are marked exceptions if charge transfer states of the reactants have particularly low energies. Received: 8 November 1996 / Accepted: 5 March 1997     

On gas phase alpha-effects. 1. The gas-phase manifestation and potential SET character

The possibility of a gas-phase alpha-effect has been explored for the methyl transfer from methyl formate to hydroxide, hydroperoxide, and ethoxide by computing barrier heights at the HF/6-311++G(2df,2p) level of theory. The alpha-nucleophile (hydroperoxide) is found to have a lower barrier than the gas-phase-acidity-matched normal nucleophile (ethoxide) by 3.6 kcal/mol, offering evidence for a gas phase alpha-effect. A Shi-Boyd analysis for these reactions indicates that there is more single-electron-transfer character in the hydroperoxide transition state than for either hydroxide or ethoxide, further bolstering the existence of a gas-phase alpha-effect and the appropriateness of the Hoz model for the alpha-effect.     

Modified electron transfer model for excitation functions of the type M + RX → MX + R and M+ + RX− (M = alkali,R = alkyl group,X = halogen) and M′ + N2O → MO* + N2 (M′= Ba OR Sm)

A one-dimensional model is described for the excitation functions of reactions that are initiated by an electron transfer at close range. The process is governed by a barrier in the entrance channel, the abortive reflection of trajectories at higher energies and by the competition of an adiabatic and a diabatic channel for the reactive flux. The model is fitted to measured cross sections for the (K.Rb)+CH₃I, K+C₂H₅Br and (Ba.Sm)÷ N₂O reactions and the electron transfer cross section for K+CH₃I → K⁺ + CH₃I^- is successfully predicted from the fitting parameters of the reactive channel.     

Peculiarities and paradoxes of photoinduced electron transfer reactions

Many chemical reactions involve the electron transfer stage. The kinetics of photoinduced electron transfer reactions is commonly considered in terms of either the transition state theory as preliminary thermally activated reorganization of the medium and reactants (necessary for degeneracy of the electronic levels of the reactants and the products) or nonradiative quantum transitions, which do not require preliminary activation and are observed in the exoergic region. A new approach to the kinetics of such reactions that has been proposed recently considers a substantial reduction of the barrier in the contact reactant pair due to strong electronic interaction and takes into account the intermediate formation of a charge transfer complex. This approach has explained many well-known important features of electron transfer reactions that are inconsistent with the first two theories.     

Nucleophilic attack on phosphate diesters: a density functional study of in-line reactivity in dianionic, monoanionic, and neutral systems

A density functional study of the hydrolysis reaction of phosphodiesters with a series of attacking nucleophiles in the gas phase and in solution is presented. The nucleophiles HOH, HO-, CH3OH, and CH3O- were studied in reactions with ethylene phosphate, 2'3'-ribose cyclic phosphate and in their neutral (protonated) and monoanionic forms. Stationary-point geometries for the reactions were determined at the density functional B3LYP/6-31++G(d,p) level followed by energy refinement at the B3LYP/6-311++G(3df,2p) level. Solvation effects were estimated by using a dielectric approximation with the polarizable continuum model (PCM) at the gas-phase optimized geometries. This series of reactions characterizes factors that influence the intrinsic reactivity of the model phosphate compounds, including the effect of nucleophile, protonation state, cyclic structure, and solvent. The present study of the in-line mechanism for phosphodiester hydrolysis, a reaction of considerable biological importance, has implications for enzymatic mechanisms. The analysis generally supports the associative mechanism for phosphate ester hydrolysis. The results highlight the importance for the reaction barrier of charge neutralization resulting from the protonation of the nonbridging phosphoryl oxygens and the role of internal hydrogen transfer in the gas-phase mechanism. It also shows that solvent stabilization has a profound influence on the relative barrier heights for the dianionic, monoanionic, and neutral reactions. The calculations provide a comprehensive data set for the in-line hydrolysis mechanisms that can be used for the development of improved semiempirical quantum models for phosphate hydrolysis reactions.     

Tunneling Assists the 1,2‐Hydrogen Shift in N‐Heterocyclic Carbenes

At room temperature, 1,2‐hydrogen‐transfer reactions of N‐heterocyclic carbenes, like the imidazol‐2‐ylidene to give imidazole is shown to occurr almost entirely (>90 %) by quantum mechanical tunneling (QMT). At 60 K in an Ar matrix, for the 2, 3‐dihydrothiazol‐2‐ylidene→thiazole transformation, QMT is shown to increase the rate about 10⁵ times. Calculations including small‐curvature tunneling show that the barrier for intermolecular 1,2‐hydrogen‐transfer reaction is small, and QMT leads to a reduced rate of the forward reaction because of nonclassical reflections even at room temperature. A small barrier also leads to smaller kinetic isotope effects because of efficient QMT by both H and D. QMT does not always lead to faster reactions or larger KIE values, particularly when the barrier is small.     

Ultrafast deactivation processes in aminopyridine clusters: excitation energy dependence and isotope effects

Fast excited-state relaxation in H-bonded aminopyridine clusters occurs via hydrogen transfer in the excited state. We used femtosecond pump-probe spectroscopy to characterize the excited-state reaction coordinate. Considerable isotope effects for partially deuterated clusters indicate that H-transfer is the rate-limiting step and validate ab initio calculations in the literature. A nonmonotonous dependence on the excitation energy, however, disagrees with the picture of a simple barrier along the reaction coordinate. An aminopyridine dimer serves as a model for Watson-Crick base pairs, where similar reactions have been predicted by theory.     

Inner-sphere activation barrier in reactions of electron transfer complex ions with asymmetric deformation of metal-ligand bonds

Summary An analysis has been made of the effects on the magnitude of the activation barrier from distortion of the configuration of a regular octahedron of the ligand skeleton in reactions of electron transfer between octahedral complexes of metals. The results obtained in numerical estimates of the magnitude of the barrier have been compared with the values calculated within the framework of the symmetric deformation model.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2441–2446, November, 1981.The author wishes to thank A. M. Kuznetsov for discussion of this work and for valuable comments.     

Regioselectivity of aliphatic versus aromatic hydroxylation by a nonheme iron(II)-superoxo complex

Many enzymes in nature utilize molecular oxygen on an iron center for the catalysis of substrate hydroxylation. In recent years, great progress has been made in understanding the function and properties of iron(IV)-oxo complexes; however, little is known about the reactivity of iron(II)-superoxo intermediates in substrate activation. It has been proposed recently that iron(II)-superoxo intermediates take part as hydrogen abstraction species in the catalytic cycles of nonheme iron enzymes. To gain insight into oxygen atom transfer reactions by the nonheme iron(II)-superoxo species, we performed a density functional theory study on the aliphatic and aromatic hydroxylation reactions using a biomimetic model complex. The calculations show that nonheme iron(II)-superoxo complexes can be considered as effective oxidants in hydrogen atom abstraction reactions, for which we find a low barrier of 14.7 kcal mol(-1) on the sextet spin state surface. On the other hand, electrophilic reactions, such as aromatic hydroxylation, encounter much higher (>20 kcal mol(-1)) barrier heights and therefore are unlikely to proceed. A thermodynamic analysis puts our barrier heights into a larger context of previous studies using nonheme iron(IV)-oxo oxidants and predicts the activity of enzymatic iron(II)-superoxo intermediates.