The role of intermolecular vibrations and reorganization of a reaction system in tunneling reactions with H atom transfer. A Debye model for the medium

Mechanisms of temperature dependence of the rate constants for two types of solid-state tunneling chemical reactions, namely, transfer of an H atom between two molecules and intramolecular transfer, are analyzed. To this end, an analytical expression for the rate constant for tunneling atom transfer in solids is derived in the framework of a modified theory of nonradiative transitions. The mechanisms of the temperature dependence of the rate constant considered in this work include oscillations of the potential barrier to chemical reaction in intermolecular fluctuations and reorganization of the medium. The effect of pressure on the distance between reactants and on the frequency of intermolecular vibrations is taken into account. The theory developed is used to interpret experimental data on tunneling transfer of an H atom in two reactions: a) intramolecular hydrogen transfer in a matrix-isolated formic acid molecule entrapped in an argon crystal and b) H atom transfer from a fluorene molecule to an excited acridine molecule in a fluorene crystal. Dedicated to the 90th anniversary of the L. Ya. Karpov Institute of Physical Chemistry. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1073–1085, June, 2008.     

Pressure and temperature dependence of H-atom tunneling in the Debye approximation. Barrier preparation and media reorganization

In the frame of the radiationless transitions modified theory, the analytical expression of a rate constant of the chemical reaction with an atom tunneling is found for the case of a continuous spectrum of a phonon subsystem. Two mechanisms of temperature dependence of a rate constant are taken into account, the oscillations of the potential barrier of the reaction at the intermolecular vibrations and media reorganization. The simple expressions for temperature and pressure dependencies of a rate constant are obtained in the special case of lattice motion-the Debye model. The well-known Marcus expression for the rate constant of an electron transfer in the Debye phonon spectrum is deduced first. The pressure dependence of the reorganization energy of the media is derived. Comparison of the theoretical results with the literature experimental data on H-atom tunneling in the fluorene-acridine crystal, taking into account four promotive modes (translational, librational, and two low-frequency intramolecular modes at 95 and 238 cm(-1)) and the frequency dependence of the Grueneisen parameter, is fulfilled. Good agreement of the theory and experiments is observed.     

On the theory of the CO+OH reaction, including H and C kinetic isotope effects

The effect of pressure, temperature, HD isotopes, and C isotopes on the kinetics of the OH+CO reaction are investigated using Rice-Ramsperger-Kassel-Marcus theory. Pressure effects are treated with a step-ladder plus steady-state model and tunneling effects are included. New features include a treatment of the C isotope effect and a proposed nonstatistical effect in the reaction. The latter was prompted by existing kinetic results and molecular-beam data of Simons and co-workers on incomplete intramolecular energy transfer to the highest vibrational frequency mode in HOCO(*). In treating the many kinetic properties two small customary vertical adjustments of the barriers of the two transition states were made. The resulting calculations show reasonable agreement with the experimental data on (1) the pressure and temperature dependence of the HD effect, (2) the pressure-dependent (12)C(13)C isotope effect, (3) the strong non-Arrhenius behavior observed at low temperatures, (4) the high-temperature data, and (5) the pressure dependence of rate constants in various bath gases. The kinetic carbon isotopic effect is usually less than 10 per mil. A striking consequence of the nonstatistical assumption is the removal of a major discrepancy in a plot of the k(OH+CO)k(OD+CO) ratio versus pressure. A prediction is made for the temperature dependence of the OD+CO reaction in the low-pressure limit at low temperatures.     

Tunneling in the reaction of acetone with OH

Based on recent detailed quantum mechanical computations of the mechanism of the title reaction and, this paper presents kinetics analysis of the overall rate constant and its temperature dependence, for which ample experimental data are available for comparison. The analysis confirms that the principal channel is the formation of acetonyl radical + H(2)O, while the channel leading to acetic acid is of negligible importance. It is shown that the unusual temperature dependence of the overall rate constant, as observed experimentally, is well accounted for by standard RRKM treatment that includes tunneling. This treatment is applied at the microcanonical level, with chemically activated distribution of entrance species, i.e. using a stationary rather than a thermal distribution that incorporates collisional energy transfer and competition between the redissociation and exit channel. A similar procedure is applied to the isotopic reaction acetone-d6 + OH with equally satisfying results, so that the experimental temperature dependence of the KIE (kinetic isotope effect) is perfectly reproduced. This very good agreement between calculation and experiment is obtained without any fitting to experimental values and without any adjustment of the parameters of calculation.     

Small temperature dependence of the kinetic isotope effect for the hydride transfer reaction catalyzed by Escherichia coli dihydrofolate reductase

The H/D primary kinetic isotope effect (KIE) for the hydride transfer reaction catalyzed by Escherichia coli dihydrofolate reductase (ecDHFR) is calculated as a function of temperature employing ensemble-averaged variational transition-state theory with multidimensional tunneling. The calculated KIEs display only a small temperature dependence over the temperature range of 5 to 45 degrees C. We identify two key features that contribute to canceling most of the temperature dependence of the KIE that would be expected on the basis of simpler models. Related issues such as the isotope effects on Arrhenius preexponential factors, large differences between free energies of activation and Arrhenius activation energy, and fluctuations of effective barriers are also discussed.     

Proton-coupled electron transfer in soybean lipoxygenase

The proton-coupled electron transfer reaction catalyzed by soybean lipoxygenase-1 is studied with a multistate continuum theory that represents the transferring hydrogen nucleus as a quantum mechanical wave function. The inner-sphere reorganization energy of the iron cofactor is calculated with density functional theory, and the outer-sphere reorganization energy of the protein is calculated with the frequency-resolved cavity model for conformations obtained with docking simulations. Both classical and quantum mechanical treatments of the proton donor-acceptor vibrational motion are presented. The temperature dependence of the calculated rates and kinetic isotope effects is in agreement with the experimental data. The weak temperature dependence of the rates is due to the relatively small free energy barrier arising from a balance between the reorganization energy and the reaction free energy. The unusually high deuterium kinetic isotope effect of 81 is due to the small overlap of the reactant and product proton vibrational wave functions and the dominance of the lowest energy reactant and product vibronic states in the tunneling process. The temperature dependence of the kinetic isotope effect is strongly influenced by the proton donor-acceptor distance with the dominant contribution to the overall rate. This dominant proton donor-acceptor distance is significantly smaller than the equilibrium donor-acceptor distance and is determined by a balance between the larger coupling and the smaller Boltzmann probability as the distance decreases. Thus, the proton donor-acceptor vibrational motion plays a vital role in decreasing the dominant donor-acceptor distance relative to its equilibrium value to facilitate the proton-coupled electron transfer reaction.     

Secondary alpha isotope effects on deuterium tunneling in triplet o-methylanthrones: extraordinary sensitivity to barrier width

The rates of deuterium transfer in the photoenolization of triplet 1,4-dimethyl-10H-anthracen-9-one (1) with varying degrees of deuterium label in their methyl groups (1-d3, 1-d2, and 1-d) have been investigated as a function of temperature between 5 and 77 K. Measurable rate constants in the case of 1-d3 and 1-d2 were used to construct Arrhenius plots which illustrate the expected curvature and leveling off of rate constant versus temperature. The difference in tunneling rate constants of 1-d3 and 1-d2 yields a tunneling isotope effect, TIE = 2.4, which is attributed to the secondary alpha isotopic substitution. Density functional theory (DFT, B3LYP/6-31G*) calculations were carried out to obtain structural and energetic information for the H(D) transfer along the triplet state zero-point energy levels. The temperature dependence of the rate constants for each isotopologue was simulated with a model that considers the frequency of the C-D stretching mode and the quantum mechanical permeability determined from calculated energy parameters. The model suggests that a difference in barrier width of only 0.015 A between 1-d3 and 1-d2 leads to the observed 2-fold difference between tunneling rates.     

On Theoretical Treatments of Electronic Excitation Energy Transfer

In this paper, we review the generalized Forster-Dexter theory to treat photoinduced electronic energy transfer for a system in dense media and for an isolated system (i.e., a system in the collision-free condition). Instead of expressing the rate of energy transfer in terms of spectral overlap, the expression of the energy-transfer rate constant is obtained by evaluating a Fourier integral involved in the energy transfer rate constant using the saddle-point method. In this way, the energy-gap dependence, and the effect of temperature and the isotope effect on the energy transfer can be easily studied. The effect of bridge groups connecting between donor and acceptor chromophores on the intramolecular energy transfer is also studied.     

Pressure effects on enzyme-catalyzed quantum tunneling events arise from protein-specific structural and dynamic changes

The rate and kinetic isotope effect (KIE) on proton transfer during the aromatic amine dehydrogenase-catalyzed reaction with phenylethylamine shows complex pressure and temperature dependences. We are able to rationalize these effects within an environmentally coupled tunneling model based on constant pressure molecular dynamics (MD) simulations. As pressure appears to act anisotropically on the enzyme, perturbation of the reaction coordinate (donor-acceptor compression) is, in this case, marginal. Therefore, while we have previously demonstrated that pressure and temperature dependences can be used to infer H-tunneling and the involvement of promoting vibrations, these effects should not be used in the absence of atomistic insight, as they can vary greatly for different enzymes. We show that a pressure-dependent KIE is not a definitive hallmark of quantum mechanical H-tunneling during an enzyme-catalyzed reaction and that pressure-independent KIEs cannot be used to exclude tunneling contributions or a role for promoting vibrations in the enzyme-catalyzed reaction. We conclude that coupling of MD calculations with experimental rate and KIE studies is required to provide atomistic understanding of pressure effects in enzyme-catalyzed reactions.     

Tunneling transfer of atomic particles in chemical and biological reactions: The role of intermolecular vibrations and media reorganization

Various types of chemical and biological tunneling reactions in a condensed phase are discussed. The analytical expressions for the rate constants in different temperature ranges are given. Experimental data on such low-temperature processes as hydrogen transfer from a molecule to a radical between two molecules and intramolecular transformations are considered. Data on the kinetic isotope effect upon the transfer of atomic particles in the solid phase and biological liquids are presented. The effect pressure has on different tunneling reactions is also considered; where possible, experimental results are compared with theory.     

Some symmetry-induced isotope effects in the kinetics of recombination reactions

Symmetry-induced isotope effects in recombination and collision-induced dissociation reactions are discussed. Progress on understanding the anomalous isotope effects in ozone is reviewed. Then, calculations are performed for the simpler reaction xNe+yNe+H<-->xNeyNe+H, where x and y label either identical or different isotopes. The atomic masses in the model are chosen so that symmetry is the only difference between the systems. Starting from a single potential energy surface, the properties of the bound, quasibound, and continuum states of the neon dimer are calculated. Then, the vibration rotation infinite order sudden approximation is used to calculate cross sections for all possible inelastic and dissociative processes. A rate constant matrix that exactly satisfies detailed balance is constructed. It allows recombination to occur both via direct three-body collisions and via tunneling into the quasibound states of the energy transfer mechanism. The eigenvalue rate coefficients are determined. Significant isotope effects are clearly found, and their behavior depends on the pressure, temperature, and mechanism of the reaction. Both spin statistics and symmetry breaking produce isotope effects. Under most conditions the breaking of symmetry enhances the rates, but a wide spectrum of effects is observed; they range from isotope effects with a normal mass dependence to huge, mass-independent isotope effects to cancellation and even to reversal of the isotope effects. This is the first calculation of symmetry-induced isotope effects in recombination rates from first principles. The relevance of the present effects to ozone recombination is discussed.     

Quantum mechanics/molecular mechanics studies of triosephosphate isomerase-catalyzed reactions: effect of geometry and tunneling on proton-transfer rate constants

The role of tunneling for two proton-transfer steps in the reactions catalyzed by triosephosphate isomerase (TIM) has been studied. One step is the rate-limiting proton transfer from Calpha in the substrate to Glu 165, and the other is an intrasubstrate proton transfer proposed for the isomerization of the enediolate intermediate. The latter, which is not important in the wild-type enzyme but is a useful model system because of its simplicity, has also been examined in the gas phase and in solution. Variational transition-state theory with semiclassical ground-state tunneling was used for the calculation with potential energy surface determined by an AM1 method specifically parametrized for the TIM system. The effect of tunneling on the reaction rate was found to be less than a factor of 10 at room temperature; the tunneling becomes more important at lower temperature, as expected. The imaginary frequency (barrier) mode and modes that have large contributions to the reaction path curvature are localized on the atoms in the active site, within 4 A of the substrate. This suggests that only a small number of atoms that are close to the substrate and their motions (e.g., donor-acceptor vibration) directly determine the magnitude of tunneling. Atoms that are farther away influence the effect of tunneling indirectly by modulating the energetics of the proton transfer. For the intramolecular proton transfer, tunneling was found to be most important in the gas phase, to be similar in the enzyme, and to be the smallest in water. The major reason for this trend is that the barrier frequency is substantially lower in solution than in the gas phase and enzyme; the broader solution barrier is caused by the strong electrostatic interaction between the highly charged solute and the polar solvent molecules. Analysis of isotope effects showed that the conventional Arrenhius parameters are more useful as experimental criteria for determining the magnitude of tunneling than the widely used Swain-Schaad exponent (SSE). For the primary SSE, although values larger than the transition-state theory limit (3.3) occur when tunneling is included, there is no clear relationship between the calculated magnitudes of tunneling and the SSE. Also, the temperature dependence of the primary SSE is rather complex; the value of SSE tends to decrease as the temperature is lowered (i.e., when tunneling becomes more significant). For the secondary SSE, the results suggest that it is more relevant for evaluating the "coupled motion" between the secondary hydrogen and the reaction coordinate than the magnitude of tunneling. Although tunneling makes a significant contribution to the rate of proton transfer, it appears not to be a major aspect of the catalysis by TIM at room temperature; i.e., the tunneling factor of 10 is "small" relative to the overall rate acceleration by 10(9). For the intramolecular proton transfer, the tunneling in the enzyme is larger by a factor of 5 than in solution.     

Deep tunneling dominates the biologically important hydride transfer reaction from NADH to FMN in morphinone reductase

The temperature dependence of the primary kinetic isotope effect (KIE), combined temperature-pressure studies of the primary KIE, and studies of the alpha-secondary KIE previously led us to infer that hydride transfer from nicotinamide adenine dinucleotide to flavin mononucleotide in morphinone reductase proceeds via environmentally coupled hydride tunneling. We present here a computational analysis of this hydride transfer reaction using QM/MM molecular dynamics simulations and variational transition-state theory calculations. Our calculated primary and secondary KIEs are in good agreement with the corresponding experimental values. Although the experimentally observed KIE lies below the semiclassical limit, our calculations suggest that approximately 99% of the reaction proceeds via tunneling: this is the first "deep tunneling" reaction observed for hydride transfer. We also show that the dominant tunneling mechanism is controlled by the isotope at the primary rather than the secondary position: with protium in the primary position, large-curvature tunneling dominates, whereas with deuterium in this position, small-curvature tunneling dominates. Also, our study is consistent with tunneling being preceded by reorganization: in the reactant, the rings of the nicotinamide and isoalloxazine moieties are stacked roughly parallel to each other, and as the system moves toward a "tunneling-ready" configuration, the nicotinamide ring rotates to become almost perpendicular to the isoalloxazine ring.     

Proton-coupled hole transfer in X-irradiated doped crystalline cytosine.H2O

Following exposure to X-irradiation at low temperatures, the main reactions taking place in single crystals of cytosine monohydrate doped with minute amounts of 2-thiocytosine are hole transfer (HT) from the electron-loss centers to the dopant and recombination of oxidation and reduction products, assumedly by electron transfer. A huge deuterium kinetic isotope effect (KIE; >102-103) at 100 K, together with the kinetic curves obtained and density functional theory (DFT) calculations of equilibrium energy changes, indicates that these reactions proceed through a concerted proton-coupled electron/hole transfer where the proton transfer occurs between hydrogen-bonded cytosine molecules. The temperature dependence of these reaction rates between 10 and 150 K in normal and partially deuterated samples was investigated by monitoring the growth and decay of the various radical species over time using electron paramagnetic resonance (EPR) spectroscopy. By assuming a random distribution of the hole donors and acceptors in the crystals, the data are consistent with an exponential distance-dependent rate, giving a distance decay constant (beta) around 1 A-1 for the HT, which indicates that a long-range single-step superexchange mechanism mediates the charge transfer. The reactions undergo a transition from a slow, weakly temperature-dependent rate to an Arrhenius-type rate at 40-50 K, presumably being activated by excitation of low-frequency intermolecular vibrations that couple to the process. Below this transition temperature, the transfer probability might be dominated by temperature-independent nuclear tunneling. A similar beta value in both temperature regions suggests that hopping is not activated.     

Effect of pressure on the proton transfer rate from a photoacid to a solvent. 4. Photoacids in methanol

The pressure dependence of the excited-state proton dissociation rate constant of four photoacids, 2-naphthol-6,8-disulfonate (2N68DS), 10-hydroxycamptothecin (10-CPT), 5-cyano-2-naphthol (5CN2), and 5,8-dicyano-2-naphthol (DCN2), are studied in methanol. The results are compared with the results of the pressure dependence study we recently conducted for several photoacids in water, ethanol, and propanol. The pressure dependence is explained using an approximate stepwise two-coordinate proton transfer model. The increase in rate, as a function of pressure, manifests a strong dependence of proton tunneling on the distance which decreases with an increase of pressure between the two oxygen atoms involved in the process. The decrease in the proton transfer rate with increasing pressure reflects the dependence of the reaction on the solvent relaxation rate. We found that, for the relatively weak photoacids 2N68DS, 10-CPT, and 5CN2, the proton transfer rate constant increases by a factor of about 5-8 at a pressure of about 1.5 GPa. For a strong photoacid like DCN2, the rate increase was only by a factor of 2.     

Effect of temperature on excited-state proton tunneling in wt-green fluorescent protein

Steady-state emission and time-correlated single-photon counting (TCSPC) are used to measure the temperature dependence of the proton-transfer rate of wt-GFP in H2O and D2O. As the temperature decreases, the proton-transfer rate from the protonated form slows down. At about 80 K, the rate is about 10-fold slower than the rate at room temperature. At lower temperatures of 70 K down to 13 K (the lowest temperature studied), the rate of proton transfer is almost temperature independent. We explain the temperature dependence of the proton-transfer rate by an intermolecular vibration assisted tunneling mechanism. We attribute the specific intermolecular vibration to the oscillation of two oxygen atoms: the chromophore's phenol ring and the nearby water molecule. The kinetic isotope effect is about 5 and is almost temperature independent.     

Hydrogen tunneling in peptidylglycine alpha-hydroxylating monooxygenase

The temperature dependence of the primary and secondary intrinsic isotope effects for the C-H bond cleavage catalyzed by peptidylglycine alpha-hydroxylating monooxygenase has been determined. Analysis of the magnitude and Arrhenius behavior of the intrinsic isotope effects provides strong evidence for the use of tunneling as a primary catalytic strategy for this enzyme. Modeling of the isotope effect data allows for a comparison to the hydrogen transfer catalyzed by soybean lipoxygenase in terms of environmental reorganization energy and frequency of the protein vibration that controls the hydrogen transfer.     

Effect of pressure on a heavy-atom isotope effect of yeast alcohol dehydrogenase

Hydrostatic pressure causes a monophasic decrease in the (13)C primary isotope effect expressed on the oxidation of benzyl alcohol by yeast alcohol dehydrogenase. The primary isotope effect was measured by the competitive method, using whole-molecule mass spectrometry. The effect is, therefore, an expression of isotopic discrimination on the kinetic parameter V/K, which measures substrate capture. Moderate pressure increases capture by activating hydride transfer, the transition state of which must therefore have a smaller volume than the free alcohol plus the capturing form of enzyme [Cho, Y.-K.; Northrop, D. B. Biochemistry 1999, 38, 7470-7475]. The decrease in the (13)C isotope effect with increasing pressure means that the transition state for hydride transfer from the heavy atom must have an even smaller volume, measured here to be 13 mL.mol(-1). The pressure data factor the kinetic isotope effect into a semiclassical reactant-state component, with a null value of k(12)/k(13) = 1, and a transition-state component of Q(12)/Q(13) = 1.028 (borrowing Bell's nomenclature for hydrogen tunneling corrections). A similar experiment involving a deuterium isotope effect previously returned the same volume and null value, plus a pressure-sensitive isotope effect [Northrop, D. B.; Cho, Y.-K. Biochemistry 2000, 39, 2406-2412]. Consistent with precedence in the chemical literature, the latter suggested a possibility of hydrogen tunneling; however, it is unlikely that carbon can engage in significant tunneling at ambient temperature. The fact that the decrease in activation volumes for hydride transfer is equivalent when one mass unit is added to the carbon end of a scissile C-H bond and when one mass unit is added to the hydrogen end is significant and suggests a common origin.     

Nonadiabatic proton/deuteron transfer within the benzophenone-triethylamine triplet contact radical ion pair: exploration of the influence of structure upon reaction

The dynamics of proton transfer within a variety of substituted benzophenone-triethylamine triplet contact radical ion pairs are examined in the solvents acetonitrile and dimethylformamide. The correlation of the proton-transfer rate constants with DeltaG reveals an inverted region. The kinetic deuterium isotope effects are also examined. The solvent and isotope dependence of the transfer processes are analyzed within the context of the Lee-Hynes model for nonadiabatic proton transfer. Theoretical analysis of the experimental data suggests that the reaction path for proton/deuteron transfer involves tunneling, and the origin of the inverted region is attributed to a curved tunneling path.     

Effect of a complex formation on the calculated low-pressure rate constant of a bimolecular gas-phase reaction governed by tunneling

Many important bimolecular hydrogen-transfer processes that take place in the atmosphere proceed via a potential energy minimum (hydrogen-bonded complex) that precedes along the minimum energy path the unique saddle point of the reaction, the one corresponding to the hydrogen transfer. It is clear that the one-step low-pressure rate constant of such a reaction does not depend on the existence of any complex along the minimum energy path below the reactant if the reaction takes place by thermal activation over a transition state that lies quite above the reactants (for instance 10 kcal/mol). However, we have quantitatively shown in this article that the scenario notoriously changes if the reaction involves significant tunneling. In this work, we have theoretically calculated the rate constants and their temperature dependence for the reaction HO+HOH→HOH+OH by means of a canonical variational transition state theory and a canonical unified statistical theory (when necessary). Multidimensional tunneling effects have been included with a semiclassical transmission coefficient. Two kinds of modified potential energy surfaces (PESs), obtained from an original ab initio potential energy surface, previously calculated by us, have been used. The Eckart-modified PESs serve to model the hydrogen-abstraction profiles with no complexes along the path, while the Gaussian-modified PESs model the energy profiles with two complexes along the path symmetrically distributed at each side of the abstraction saddle point. Our results show that the existence of those complexes reduces the thickness of the classically forbidden region for energies below the adiabatic barrier, and then tunneling is promoted and the reaction is accelerated. The effect of the complex formation in several kinetic magnitudes, as the Arrhenius parameters and the kinetic isotope effect has also been analyzed. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 1685–1692, 1999