Simulations of the large kinetic isotope effect and the temperature dependence of the hydrogen atom transfer in lipoxygenase

Elucidating the role of nuclear quantum mechanical (NQM) effects in enzyme catalysis is a topic of significant current interest. Despite the great experimental progress in this field it is important to have theoretical approaches capable of evaluating and analyzing nuclear quantum mechanical contributions to catalysis. In this study, we use the catalytic reaction of lipoxygenase, which is characterized by an extremely large kinetic isotope effect, as a challenging test case for our simulation approach. This is done by applying the quantum classical path (QCP) method with an empirical valence bond potential energy surface. Our computational strategy evaluates the relevant NQM corrections and reproduces the large observed kinetic isotope effect and the temperature dependence of the H atom transfer reaction while being less successful with the D atom transfer reaction. However, the main point of our study is not so much to explore the temperature dependence of the isotope effect but rather to develop and validate an approach for calculations of nuclear quantum mechanical contributions to activation free energies. Here, we find that the deviation between the calculated and observed activation free energies is small for both H and D at all investigated temperatures. The present study also explores the nature of the reorganization energy in the enzyme and solution reactions. It is found that the outer-sphere reorganization energy is extremely small. This reflects the fact that the considered reaction involves a very small charge transfer. The implication of this finding is discussed in the framework of the qualitative vibronic model. The main point of the present study is, however, that the rigorous QCP approach provides a reliable computational tool for evaluating NQM contributions to catalysis even when the given reaction includes large tunneling contributions. Interestingly, our results indicate that the NQM effects in the lipoxygenase reaction are similar in the enzyme and in the reference solution reactions, and thus do not contribute to catalysis. We also reached similar conclusions in studies of other enzymes.     

Dissociative electron transfer in donor-peptide-acceptor systems: results for kinetic parameters from a density functional/polarizable continuum model

The main structural and electronic factors playing a role in intramolecular dissociative electron transfer of a simple donor-peptide-acceptor (D-peptide-A) model have been investigated by an integrated computational protocol based on the density functional theory, its time-dependent extension, and the polarizable continuum model. Our results allow us to elucidate the electronic states involved in the process and how they are perturbed by the orientation of the donor and the acceptor with respect to the peptide chain and by the presence of the solvent. We also report a semiquantitative estimation of the rate constant governing electron transfer obtained by a direct quantum mechanical evaluation of all the terms entering the kinetic expressions based on the Marcus theory and its extensions.     

The femtosecond dynamics of electron transfer in a modified photosynthesis reaction center: Quantum, classical, and kinetic analyses

The dynamics of electron transfer in a modified photosynthesis reaction center in which electron transfer from the bridge to the acceptor is blocked is considered. A microscopic model of the process is suggested. Within this model, the diabatic electronic states of the donor and bridge are described by one-dimensional displaced harmonic oscillators. The dynamics of the population of electronic states is calculated by the quantum method of wave packets and classical and kinetic modeling. The suggested model is used to study the qualitative dependence of the dynamics of electron transfer on the nonadiabatic interaction potential. The parameters of the model are determined by comparing the experimental and calculated absorption spectra of the product of electron transfer. It is shown that kinetic models can be used to approximately describe the dynamics of electron transfer in reaction centers. The boundaries of the applicability of the kinetic method are considered.     

Classical kinetic energy,quantum fluctuation terms and kinetic-energy functionals

We employ a recently formulated dequantization procedure to obtain an exact expression for the kinetic energy which is applicable to all kinetic-energy functionals. We express the kinetic energy of an N-electron system as the sum of an N-electron classical kinetic energy and an N-electron purely quantum kinetic energy arising from the quantum fluctuations that turn the classical momentum into the quantum momentum. This leads to an interesting analogy with Nelson’s stochastic approach to quantum mechanics, which we use to conceptually clarify the physical nature of part of the kinetic-energy functional in terms of statistical fluctuations and in direct correspondence with Fisher Information Theory. We show that the N-electron purely quantum kinetic energy can be written as the sum of the (one-electron) Weizsäcker term and an (N?1)-electron kinetic correlation term. We further show that the Weizsäcker term results from local fluctuations while the kinetic correlation term results from the nonlocal fluctuations. We then write the N-electron classical kinetic energy as the sum of the (one-electron) classical kinetic energy and another (N?1)-electron kinetic correlation term. For one-electron orbitals (where kinetic correlation is neglected) we obtain an exact (albeit impractical) expression for the noninteracting kinetic energy as the sum of the classical kinetic energy and the Weizsäcker term. The classical kinetic energy is seen to be explicitly dependent on the electron phase, and this has implications for the development of accurate orbital-free kinetic-energy functionals. Also, there is a direct connection between the classical kinetic energy and the angular momentum and, across a row of the periodic table, the classical kinetic energy component of the noninteracting kinetic energy generally increases as Z increases. Finally, we underline that, although our aim in this paper is conceptual rather than practical, our results are potentially useful for the construction of improved kinetic-energy functionals.     

Analysis of kinetic isotope effects for nonadiabatic reactions

Factors influencing the rates of quantum mechanical particle transfer reactions in many-body systems are discussed. The investigations are carried out on a simple model for a proton transfer reaction that captures generic features seen in more realistic models of condensed phase systems. The model involves a bistable quantum oscillator coupled to a one-dimensional double-well reaction coordinate, which is in turn coupled to a bath of harmonic oscillators. Reactive-flux correlation functions that involve quantum-classical Liouville dynamics for chemical species operators and quantum equilibrium sampling are used to estimate the reaction rates. Approximate analytical expressions for the quantum equilibrium structure are derived. Reaction rates are shown to be influenced significantly by both the quantum equilibrium structure and nonadiabatic dynamics. Nonadiabatic dynamical effects are found to play the major role in determining the magnitude of the kinetic isotope effect for the model transfer reaction.     

Theoretical study of the decomposition of BCl3 induced by a H radical

We report on a theoretical study of the gas-phase decomposition of boron trichloride in the presence of hydrogen radicals using ab initio energetic calculations coupled to TST, RRKM, and VTST-VRC kinetic calculations. In particular, we present an addition-elimination mechanism (BCl(3) + H → BHCl(2) + Cl) allowing for a much more rapid consumption of BCl(3) than the direct abstraction reaction (BCl(3) + H → BCl(2) + HCl) considered up to now. At low temperatures, T ≤ 800 K, our results show that a weakly stabilized complex BHCl(3) is formed with a kinetic law compatible with the consumption rate measured in the former experiments. At higher temperatures, this complex is not stable and then easily eliminates a chlorine atom. Our work also shows that a very similar mechanism, involving the same intermediate and sharing the same transition state, allows for the elimination of HCl. A dividing coefficient between these two elimination pathways is obtained from both a potential energy surface based statistical analysis and an ab initio molecular dynamics transition path sampling simulation. It finally allows partitioning of the global consumption rate of BCl(3) in terms of the formation of (i) BHCl(3), (ii) BHCl(2) + Cl through a H addition/Cl elimination mechanism, (iii) BCl(2) + HCl through a H addition/HCl elimination mechanism, and (iv) BCl(2) + HCl through direct abstraction.     

Fragment mode analysis and its application to the vibrational normal modes of boron trichloride-ammonia and boron trichloride-pyridine complexes

A method for expressing quantitatively the vibrational normal modes of a molecule in a basis set consisting of the normal vibrations (plus translations and rotations) of its constituent fragments is presented. The method is illustrated by describing the vibrational modes of BCl3-NH3 and BCl3-pyridine electron donor-acceptor complexes in terms of motions of BCl3 and either NH3 or pyridine. These complexes show examples of mixing between modes located on different fragments, mixing between modes of one fragment due to symmetry lowering, and the transformation of six fragment translations/rotations into vibrations of the complex. Although perturbation theory has been proposed to explain such examples of mode mixing, calculations imply that interactions between fragments of both complexes are too strong for perturbation theory to be generally applicable. In addition, the transformation of fragment rotations and/or translations into vibrations of the composite molecule will always occur and cannot be understood in detail by using perturbation theory. For the BCl3-pyridine complex, a band observed at 1107 cm(-1) is re-assigned as a combination of C-H in-plane bending and a ring-breathing mode of the pyridine fragment.     

Mechanism and kinetics of the reaction NO3 + C2H4

The reaction of NO(3) radical with C(2)H(4) was characterized using the B3LYP, MP2, B97-1, CCSD(T), and CBS-QB3 methods in combination with various basis sets, followed by statistical kinetic analyses and direct dynamics trajectory calculations to predict product distributions and thermal rate constants. The results show that the first step of the reaction is electrophilic addition of an O atom from NO(3) to an olefinic C atom from C(2)H(4) to form an open-chain adduct. A concerted addition reaction mechanism forming a five-membered ring intermediate was investigated, but is not supported by the highly accurate CCSD(T) level of theory. Master-equation calculations for tropospheric conditions predict that the collisionally stabilized NO(3)-C(2)H(4) free-radical adduct constitutes 80-90% of the reaction yield and the remaining products consist mostly of NO(2) and oxirane; the other products are produced in very minor yields. By empirically reducing the barrier height for the initial addition step by 1 kcal mol(-1) from that predicted at the CBS-QB3 level of theory and treating the torsional modes explicitly as one-dimensional hindered internal rotations (instead of harmonic oscillators), the computed thermal rate constants (including quantum tunneling) can be brought into very good agreement with the experimental data for the overall reaction rate constant.     

Primary kinetic isotope effects on hydride transfer from 1,3-dimethyl-2-phenylbenzimidazoline to NAD(+) analogues

Primary kinetic isotope effects (KIE) have been determined spectrophotometrically for the reaction of NAD(+) analogues (pyridinium, quinolinium, phenanthridinium, and acridinium ions) with 1,3-dimethyl-2-phenylbenzimidazoline in a 4:1 mixture of 2-propanol and water by volume at 25 degrees C. The values of KIE varied systematically from 6.27 to 4.06 as the equilibrium constant changed from around 10 to around 10(12). This is consistent with Marcus theory of atom transfer, assuming that there are no high-energy intermediates. Within this theory, the perpendicular effect is responsible for most of the change in KIE. The Marcus theory of atom transfer is consistent with a linear, triatomic model of the reaction. Perpendicular effects arise from the systematic decrease of bond distances and increase of bond orders in the critical complexes of the two related degenerate hydride transfer reactions as their C--H bonds become stronger. The parallel effect (Leffler--Hammond effect) is attenuated by the fairly high intrinsic barrier (lambda/4 is around 92 kJ/mol) and makes a smaller contribution to the change in the KIE.     

Bimolecular reactions of vibrationally excited molecules. Roaming atom mechanism at low kinetic energies

Quasiclassical trajectory calculations have been performed for the H + H'X(v) → X + HH' abstraction and H + H'X(v) → XH + H' (X = Cl, F) exchange reactions of the vibrationally excited diatomic reactant at a wide collision energy range extending to ultracold temperatures. Vibrational excitation of the reactant increases the abstraction cross sections significantly. If the vibrational excitation is larger than the height of the potential barrier for reaction, the reactive cross sections diverge at very low collision energies, similarly to capture reactions. The divergence is quenched by rotational excitation but returns if the reactant rotates fast. The thermal rate coefficients for vibrationally excited reactants are very large, approach or exceed the gas kinetic limit because of the capture-type divergence at low collision energies. The Arrhenius activation energies assume small negative values at and below room temperature, if the vibrational quantum number is larger than 1 for HCl and larger than 3 for HF. The exchange reaction also exhibits capture-type divergence, but the rate coefficients are larger. Comparisons are presented between classical and quantum mechanical results at low collision energies. At low collision energies the importance of the exchange reaction is enhanced by a roaming atom mechanism, namely, collisions leading to H atom exchange but bypassing the exchange barrier. Such collisions probably have a large role under ultracold conditions. The calculations indicate that for roaming to occur, long-range attractive interaction and small relative kinetic energy in the chemical reaction at the first encounter are necessary, which ensures that the partners can not leave the attractive well. Large orbital angular momentum of the primary products (equivalent to large rotational excitation in a unimolecular reaction) is favorable for roaming.     

Aqueous rhodium(III) hydrides and mononuclear rhodium(II) complexes

In aqueous solutions, as in organic solvents, rhodium hydrides display the chemistry of one of the three limiting forms, i.e. {Rh(I)+ H+}, {Rh(II)+ H.}, and {Rh(III)+ H-}. A number of intermediates and oxidation states have been generated and explored in kinetic and mechanistic studies. Monomeric macrocyclic rhodium(II) complexes, such as L(H2O)Rh2+ (L = L1 = [14]aneN4, or L2 = meso-Me6[14]aneN4) can be generated from the hydride precursors by photochemical means or in reactions with hydrogen atom abstracting agents. These rhodium(II) complexes are oxidized rapidly with alkyl hydroperoxides to give alkylrhodium(III) complexes. Reactions of Rh(II) with organic and inorganic radicals and with molecular oxygen are fast and produce long-lived intermediates, such as alkyl, superoxo and hydroperoxo complexes, all of which display rich and complex chemistry of their own. In alkaline solutions of rhodium hydrides, the existence of Rh(I) complexes is implied by rapid hydrogen exchange between the hydride and solvent water. The acidity of the hydrides is too low, however, to allow the build-up of observable quantities of Rh(I). Deuterium kinetic isotope effects for hydride transfer to a macrocyclic Cr(v) complex are comparable to those for hydrogen atom transfer to various substrates.     

Semiclassical quantum unimolecular reaction rate theory revisited

We describe a semiclassical quantum unimolecular reaction rate theory derived from the corresponding classical theory developed by Davis, Gray, Rice and Zhao (DGRZ). The analysis retains the intuitively useful mechanistic distinctions between intramolecular energy transfer and reaction, with the consequence that the semiclassical quantum theory version neglects some interference effects in the reaction dynamics. In the limiting case that intramolecular energy transfer is very fast compared to the rate of reaction we show that the DGRZ representation of the rate constant can be transformed, using the Weyl correspondence between quantum operators and classical variables, to the quantum flux–flux correlation function representation of the rate constant. In the more general case that the rate of intramolecular energy transfer influences the reaction dynamics, the semiclassical representation of the Wigner function for a classical system with both quasiperiodic and chaotic motion is used to obtain the reaction rate constant. Our analysis identifies the quantum analogue of the classical bottleneck to intramolecular energy transfer with the scars of unstable periodic orbits; it leads to a flux–flux correlation function representation of the rate constant for intramolecular energy transfer.     

Quantum calculations of the O(3P)+H2-->OH+H reaction

Quantum scattering calculations are reported for the O(3P)+H2(v=0,1) reaction using chemically accurate potential energy surfaces of 3A' and 3A" symmetry. We present state-to-state reaction cross sections and rate coefficients as well as thermal rate coefficients for the title reaction using accurate quantum calculations. Our calculations yield reaction cross sections that are in quantitative accord with results of recent crossed molecular beam experiments. Comparisons with results obtained using the J-shifting calculations show that the J-shifting approximation is quite reliable for this system. Thermal rate coefficients from the exact calculations and the J-shifting approximation agree remarkably well with experimental results. Our calculations also reproduce the markedly different OH(v'=0)/OH(v'=1) branching in O(3P)+H2(v=1) reaction, observed in experiments that use different O(3P) atom sources. In particular, we show that the branching ratio is a strong function of the kinetic energy of the O(3P) atom.     

Super-fermion representation of quantum kinetic equations for the electron transport problem

We discuss the use of super-fermion formalism to represent and solve quantum kinetic equations for the electron transport problem. Starting with the Lindblad master equation for the molecule connected to two metal electrodes, we convert the problem of finding the nonequilibrium steady state to the many-body problem with non-hermitian liouvillian in super-Fock space. We transform the liouvillian to the normal ordered form, introduce nonequilibrium quasiparticles by a set of canonical nonunitary transformations and develop general many-body theory for the electron transport through the interacting region. The approach is applied to the electron transport through a single level. We consider a minimal basis hydrogen atom attached to two metal leads in Coulomb blockade regime (out of equilibrium Anderson model) within the nonequilibrium Hartree-Fock approximation as an example of the system with electron interaction. Our approach agrees with exact results given by the Landauer theory for the considered models.     

Hydrogen atom vs electron transfer in catecholase-mimetic oxidations by superoxometal complexes. Deuterium kinetic isotope effects

Dioximato-cobalt(II), -iron(II) and -manganese(II) complexes (1)-(6), acting as functional catecholase and phenoxazinone synthase models, exhibit a deuterium kinetic isotope effect predicted by theory (k4H/k4D < or = 3) in the catalytic oxidative dehydrogenation of 3,5-di-tert-butylcatechol and 2-aminophenol by O2. KIEs in the range of (k4H/k4D approximately 1.79-3.51) are observed with (1) and (2) as catalysts, pointing to hydrogen atom transfer in the rate-determining step from the substrate hydroxy group to the metal-bound superoxo ligand. Less significant KIEs (1.06-1.20) are exhibited by catalysts systems (3)-(6), indicating that proton-coupled electron transfer is the preferred route in those cases.     

3-(Hetero)aryl-4-indolylamino-α-tetralones by diastereoselective internal redox cyclization: an "azaenamine" conjugate addition

(E)-3-(hetero)aryl-1-(2-((E)-(indolin-1-ylimino)methyl)phenyl)prop-2-en-1-ones 1 undergo 6-exo-trig cyclization reactions upon treatment with BF(3)·Me(2)S in dichloromethane at low temperature to give the tetralones 10 in good yield. This cyclization process can be considered to be an intramolecular Michael-type addition which is accompanied by an internal redox reaction as the indoline fragment is oxidized to indole with simultaneous hydrogen shift to nitrogen atom N1 and the α-carbon atom of the Michael system. The reactions at the iminic centers take place via umpolung of the classical carbonyl reactivity. The reaction is diastereoselective and affords exclusively 3,4-disubstituted α-tetralones 10 as trans-diastereomers. According to quantum chemical calculations the reactions take place under kinetic control with the trans-diastereomer being the kinetically favored product as it has the lower activation barrier compared to the cis-diastereomer.     

On the possibility of detecting low barrier hydrogen bonds with kinetic measurements

Recent experimental evidence has pointed to the possible presence of a short, strong hydrogen bond in the enzyme-substrate transition states in some biochemical reactions. To date, most experimental measures of these short, strong hydrogen bonds have monitored their equilibrium properties. In this work we show that kinetic measurements can also be used to detect the presence of short, strong hydrogen bonds. In particular, we find nontrivial differences among rate constant ratios of protonated to deuterated hydrogen bonds between strong and weak hydrogen bonds for proton transfer between donor-acceptor sites. We quantify this kinetic isotope effect by performing dynamical calculations of these rate constants by computing reactive flux through a dividing surface. This reactive flux is computed by evolving trajectories on an effective quantum mechanical potential energy surface.     

Curing kinetic study using a well-controlled multifunctional copolymer based on glycidyl methacrylate

The curing kinetics using a glycidyl methacrylate (GMA)-co-butyl acrylate (BA) statistical copolymer synthesized by atom transfer radical polymerization (ATRP) and a commercial linear diamine (Jeffamine^® D-230) was investigated in the temperature range between 50 and 100 °C. Isothermal experiments using differential scanning calorimetry (DSC) were performed to determine all the kinetics parameters, such as the reaction orders, the activation energy and the rate constants, based on an autocatalytic mechanism proposed by Kamal. The isoconversion method was used to evaluate the variation of the effective activation energy with the extension of the conversion that seems slightly decrease initially, and then increases as the cure reaction proceeds. In addition, dynamic kinetic parameters were calculated from non-isothermal experiments using the Kissinger and Ozawa methods. The resulting epoxy resin presents similar physical characteristics to some reported in the literature.     

Classical rotational and centrifugal sudden approximations for atom—molecule collisional energy transfer

The application of centrifugal and rotational sudden approximations to classical trajectory studies of rotational energy transfer in atom—molecule collisions to examined. Two different types of approximations are considered: a centrifugal sudden (CS) approximation, in which the orbital angular momentum is assumed to be constant during collisions, and a classical infinite order sudden (CIOS) approximation, in which the CS treatment is combined with an energy sudden approximation to totally decouple translational and rotational equations of motion. The treatment of both atom plus linear and nonlinear molecule collisions is described, including the use of rotational action-angle variables for the rotor equations of motion. Applications of both CS and CIOS approaches to rotational energy transfer in He + I₂ collisions are presented. We find the calculated CS and CIOS rotationally inelastic cross sections are in generally good agreement [errors of (typically) 10–50%] with accurate quasiclassical (QC) ones, with the CS results slightly more accurate than CIOS. Both methods are less accurate for small |Δj| transitions than for large |Δj| transitions. Computational savings for the CS and CIOS applications is about a factor of 3 (per trajectory) compared to QC. We also present applications using the CS method to rotational energy transfer in He, Ar, Xe + O₃ collisions, making comparisons with analogous QC results of Stace and Murrell (SM). The agreement between exact and approximate results in these applications is generally excellent, both for the average energy transfer at fixed impact parameters, and for rotationally inelastic cross sections. Results are better for He + O₃ and Ar + O₃ than for Xe + O₃, and better at low temperatures than at high. Since SM's quasiclassical treatment considered only total internal energy transfer without attempting a partitioning between vibration and rotation, while our CS calculation considers only rotational energy transfer, the observed good agreement between our and SM's cross sections indicates that most internal energy transfer in He, Ar, Xe + O₃ is rotational. The relation of this result to models of the activation process in thermal unimolecular rate constant determination is discussed.