A compelling experimental test of the hypothesis that enzymes have evolved to enhance quantum mechanical tunneling in hydrogen transfer reactions: the beta-neopentylcobalamin system combined with prior adocobalamin data

An intriguing but controversial hypothesis has appeared that "The optimization of enzyme catalysis may entail the evolutionary implementation of chemical strategies that increase the probability of tunneling and thereby accelerate the reaction rate" (Kohen, A.; Klinman, J. P. Acc. Chem. Res. 1998, 31, 397). Restated, enzymes may have evolved to enhance quantum mechanical tunneling by coupling to protein low nu modes that squeeze the reacting centers together in, for example, their H(*) atom abstraction reactions. Such a putative "protein squeezing" mechanism would enhance hydrogen quantum mechanical tunneling by reducing the barrier width. An alternative hypothesis is that enzymes do not enhance tunneling, but simply exploit the same amount of tunneling present in their enzyme-free solution reactions, if those reactions occur. A third, conceivable hypothesis is that enzymes might even inadvertently decrease the amount of tunneling as an undesired result of increasing the barrier width while reducing the barrier height. Testing these hypotheses experimentally requires the extremely rare event of being able to measure the amount of tunneling both in the enzyme system and in a very similar if not identical reaction in enzyme-free solution. This has been accomplished experimentally in only one prior case, our recent study of AdoCbl (coenzyme B(12)) and 8-Meo-AdoCbl undergoing enzyme-like H(*) abstraction reactions (Doll, K. M.; Bender, B. R.; Finke, R. G. to J. Am. Chem. Soc. 2003, in press). The data there reveal no change in the level of tunneling within or outside of the enzyme in comparison to the best literature data for an AdoCbl-dependent enzyme, methylmalonyl-CoA mutase. However, that first system suffers from two limitations: the measurement of the KIE (kinetic isotope effect) data in a nonenzymic 80-110 degrees C temperature range; and lower precision data than desired due to the HPLC-MS method required for one of the KIE analyses. These limitations have now been overcome by the synthesis, then thermolysis and KIE study vs temperature of the H(*) abstraction reaction of beta-neopentylcobalamin (beta-NpCbl) in ethylene glycol-d(0) and ethylene glycol-d(4). This is the first experimental test of Klinman's hypothesis using KIE data obtained at enzyme-relevant temperatures. The key data obtained are as follows: deuterium KIEs of 23.1 +/- 3.0 at 40 degrees C to 39.0 +/- 2.3 at 10 degrees C; an activation energy difference E(D) - E(H) of 3.1 +/- 0.3 kcal mol(-)(1); and a pre-exponential factor ratio A(H)/A(D) of 0.14 +/- 0.07. Moreover, our now three sets of data (NpCbl; AdoCbl; 8-MeOAdoCbl) are shown to lie on the same ln KIE vs 1/T linear plot yielding a set of enzyme-temperature-relevant, high-precision KIE, E(D) - E(H), and A(H)/A(D) data over a relatively large, 110 degrees C temperature range. Significantly, the enzyme-free solution KIE, E(D) - E(H), and A(H)/A(D) are identical within experimental error to those for methylmalonyl-CoA mutase. This finding leads to the conclusion that there is no enzymic enhancement of the tunneling in at least this B(12)-dependent enzyme. This B(12) enzyme does, however, exploit the same (unchanged) level of tunneling measured for the nonenzymic, Ado(*) solution H(*) abstraction reaction. A discussion is presented of the still open question of if this first experimental finding, of "no enzymic enhancement of tunneling" in one B(12)-dependent enzymic system, is likely to prove more general or not.     

Double hydrogen tunneling revisited: the breakdown of experimental tunneling criteria

Formic acid dimer was chosen as a model system to investigate synchronous double proton transfer by means of variational transition state theory (VTST) for various isotopically modified hydrogen species. The electronic barrier for the double proton transfer was evaluated to be 7.9 kcal/mol, thus being significantly lower than it was determined in previous studies. The tunneling probabilities were evaluated at temperatures from 100 up to 400 K and typical Arrhenius behavior with enhancement by tunneling is observed. When comparing the transmission factors kappa in dependence of the mass of the tunneling hydrogen, it was found that there are two maxima, one at very low masses (e.g., 0.114 amu, corresponding to the muonium entity) and one maximum at around 2 amu (corresponding to deuterium). With the knowledge of the VTST-hydrogen transfer rates and the corresponding tunneling corrections, various tunneling criteria were tested (e.g., Swain-Schaad exponents) and were shown to fail in this reaction in predicting the extent of tunneling. This finding adds another aspect in the ongoing "Tunneling-Enhancement by Enzymes" discussion, as the used tunneling criteria based on experimental reaction rates may fail to predict tunneling behavior correctly.     

Time- and space-summation studies of the diffusion equation: experimental test of the ergodic hypothesis

One-atom detection techniques have been used to test the equality between time and ensemble averages, following a gedanken experiment on the diffusion of atoms suggested by Einstein and Fürth. Experimental results confirmed that a system of freely diffusing atoms was ergodic.     

The first triple thiol-thiolate hydrogen bond versus triple diselenide bond that bridges two metal centers

Treatment of fac(S)-[Rh(aet)3] (aet = 2-aminoethanethiolate) with aqueous HBF4 in air led to the protonation at coordinated thiolato groups to give a rhodium(III) dimer, [{Rh(aet)2(Haet)}{Rh(aet)(Haet)2}](BF4)3 ([1](BF4)3). On the other hand, similar treatment of fac(Se)-[Rh(aes)3] (aes = 2-aminoethaneselenolate) produced a dinuclear rhodium(III) complex, [Rh2(selenocystamine)3](BF4)6 ([2](BF4)6), because of the autoxidation of coordinated selenolato groups by air. The crystal structures of [1](BF4)3, DeltaDelta-[1](BF4)3, and [2](BF4)6 were determined by X-ray crystallography. In [1]3+ two RhIII octahedrons are connected through a strong triple thiol-thiolate S-H...S hydrogen bond, while two RhIII octahedrons are directly joined by a triple diselenide bond in [2]6+. The cyclic voltammetry indicated that in acidic media the RhIII center in fac(Se)-[Rh(aes)3] is more easily oxidized to RhIV than that in fac(S)-[Rh(aet)3], which is responsible for the formation of coordinated diselenide bonds.     

An evolved gas analysis study of the reduction of nickel oxide by hydrogen

The reduction of NiO by H₂ was followed by conventional thermogravimetry and a new evolved gas analysis approach which follows the course of the reaction by measuring the H₂O content of the gas stream. Excellent correspondence is observed between the two techniques for simultaneous measurements. Heating rates between 0.5 and 10° min^–1 shift the temperature of the reaction as does changing the surface area of the NiO. These shifts are discussed in terms of the Neel temperature (T _N) of NiO and the thermal history of the sample. No correlation between reaction rate andT _N is observed under dynamic conditions. Preheating the sample in vacuum at 130° has a marked effect on shape of the DTG and EGA curves.

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Zusammenfassung Die Reduktion von NiO durch H₂ wurde durch konventionelle Thermogravimetrie und eine neue Analyse des entwickelten Gases untersucht, welche den Reaktions-ablauf durch Messung des H₂O-Gehalts des Gasstromes verfolgt. Eine ausgezeichnete Übereinstimmung beider Techniken wird bei simultanen Messungen beobachtet. Aufheizgeschwindig keiten zwischen 0.5 und 10° min^–1 verschieben die Temperatur der Reaktion und verändern die Oberfläche des NiO. Diese Verschiebungen werden auf Grund der Neel-Temperatur (T _N) des NiO und der thermischen Vergangenheit der Probe erörtert. Unter dynamischen Bedingungen wird keine Korrelation zwischen der Reaktionsgeschwindigkeit undT _N beobachtet. Das Vorwärmen der Probe im Vakuum bei 130° zeigt einen deutlichen Einfluß auf die Form der DTG und EGA Kurven.

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() ( ), H₂O . . 0.5 10° , . (T _N) . T _N. 130° - -.

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Presented at the 11th Annual NATAS Meeting, New Orleans, LA, Oct. 19–21, 1981.

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The authors are grateful to Mr. F. Schrey for measurements of the surface area.     

Quantum chemical calculation of the barrier for tunneling of hydrogen in hydrogen abstraction from methane by methyl

An adiabatic reaction path for hydrogen abstraction from methane by methyl is computed by quantum chemical methods and then symmetrized by properly defining the reaction coordinate. The theoretical barriers are then fitted with the barriers defined by the parabolic and Eckart functions. Rate constants for the hydrogen and deuterium-abstraction processes via tunneling at low temperatures are then computed.     

Importance of anharmonicity, recrossing effects, and quantum mechanical tunneling in transition state theory with semiclassical tunneling. A test case: the H2 + Cl hydrogen abstraction reaction

The hydrogen abstraction reaction from H2 by the Cl atom is studied by means of the variational transition state theory with semiclassical tunneling coefficients on the BW2 potential energy surface. Vibrational anharmonicity and coupling between the bending modes are taken into account. The occurrence of trajectories that recross the transition state is estimated by means of the canonical unified statistical method and by classical trajectories calculations. Different semiclassical methods for tunneling calculations are tested. Our results show that anharmonicity has a small but nonnegligible effect on the thermal rate constants, recrossing can be neglected, and tunneling is adequately described by the least-action approximation, and less successfully by the large-curvature version 3 approximation. However, the large-curvature version 4 and small-curvature approximations lead to a severe underestimation of tunneling. Thermal rate constants calculated using transition state theory including anharmonicity and tunneling agree very well with accurate quantal thermal rate constants over a wide temperature range, although the improvement over the harmonic transition state theory with the microcanonically optimized semiclassical tunneling approximation (based on version 3 of the large-curvature tunneling method) used in a previous study of this reaction is only marginal.     

Inelastic tunneling spectroscopy of gold-thiol and gold-thiolate interfaces in molecular junctions: The role of hydrogen

It is widely believed that when a molecule with thiol (S-H) end groups bridges a pair of gold electrodes, the S atoms bond to the gold and the thiol H atoms detach from the molecule. However, little is known regarding the details of this process, its time scale, and whether molecules with and without thiol hydrogen atoms can coexist in molecular junctions. Here, we explore theoretically how inelastic tunneling spectroscopy (IETS) can shed light on these issues. We present calculations of the geometries, low bias conductances, and IETS of propanedithiol and propanedithiolate molecular junctions with gold electrodes. We show that IETS can distinguish between junctions with molecules having no, one, or two thiol hydrogen atoms. We find that in most cases, the single-molecule junctions in the IETS experiment of Hihath et al. [Nano Lett. 8, 1673 (2008)] had no thiol H atoms, but that a molecule with a single thiol H atom may have bridged their junction occasionally. We also consider the evolution of the IETS spectrum as a gold STM tip approaches the intact S-H group at the end of a molecule bound at its other end to a second electrode. We predict the frequency of a vibrational mode of the thiol H atom to increase by a factor ～2 as the gap between the tip and molecule narrows. Therefore, IETS should be able to track the approach of the tip towards the thiol group of the molecule and detect the detachment of the thiol H atom from the molecule when it occurs.     

The first experimental evidence of room-temperature magnetocaloric effect in fullerenes

Journal of Thermal Analysis and Calorimetry - The aim of the study was the first characterization of fullerenes, organic molecular solids without a d or f metal/ion, as paramagnets with the...     

The widespread occurrence of enzymatic hydrogen tunneling,andits unique properties,lead to a new physical model for the origins of enzyme catalysis

The investigation of C-H bond activation by enzymes over the past several decades has revealed a plethora of deviations from semi-classical kinetic models. Although the early enzymatic results were interpreted in the context of a tunneling correction, the emergent properties are now seen to be largely incompatible with this type of analysis as well. This chapter introduces some of the experimental data that form the basis for our present understanding. A vibronically nonadiabatic model, that has a number of features in common with the Marcus treatment for electron transfer, offers a robust physical picture for the hydrogen tunneling behavior seen in both native enzymes and in enzymes that have been perturbed either by site-specific mutagenesis or by perturbation of the reaction conditions. Native enzymes under optimal conditions most commonly show behavior that requires a heavy atom donor-acceptor distance that is in the range of 2.7 Å. This compression beyond van der Waals distances is proposed to arise from the process of enzymatic conformational sampling. The absence of any evolutionary driving force to optimize tunneling for deuterium transfer (natural abundance < 0.02%), together with the frequent observation that the enthalpic barrier for deuterium transfer is the same or very similar to that for protium transfer, leads to the proposal that tunneling is a consequence of a generic property of enzyme function in which overall protein flexibility enables the generation of active sites that can be quite compressed.     

Coherent tunneling of proton in the intramolecular hydrogen bond of crystalline bromo-hydroxyphenalenone at low temperature

Infrared absorption spectra of 5-bromo-9-hydroxyphenalenone were measured and analyzed in detail as a function of temperature. An intense and broad peak at 83 cm⁻¹ occurring in the protonated crystal, but not in the deuterated analog, arises from the coherent tunneling motion of the hydrogen in the intramolecular hydrogen bond. Strong temperature dependence of the frequency and width of the tunneling peak determined by fitting the Gaussian or Lorentzian peak shape function is reproduced well by three-parameter functions representing the thermal population of the excited state of the tunneling proton.     

Kinetic isotope effect in hydrogen transfer arising from the effects of rotational excitation and occurrence of hydrogen tunneling in molecular systems

Hydrogen kinetic isotope effect with values of alpha identical with ln(kH/kT)/ln(kD/kT)>3.3 which are generally ascribed to quantum tunneling of hydrogen are shown to arise in O+HCl(DCl,TCl) reactions due to the effects of rotational excitation on the distribution of encounters with the critical dividing surface. At higher rotational excitations these distributions are shifted towards the regions of the critical dividing surface with low barrier energies which can lead to a large enhancement of the barrier crossing. This effect depends strongly on the hydrogen isotope involved in the reaction and, at some temperatures, gives rise to alpha much larger than 3.3. It can be readily seen that the effect should arise also in condensed molecular systems, due to internal rotations or other vibrations "perpendicular" to the reaction coordinate.     

The importance of tunneling in the first hydrogenation step in ammonia synthesis over a Ru(0001) surface

The hydrogenation of nitrogen (N(ads)+H(ads)-->NH(ads)) on metal surfaces is an important step in ammonia catalysis. We investigate the reaction dynamics of this hydrogenation step by time independent scattering theory and variational transition state theory (VTST) including tunneling corrections. The potential energy surface is derived by hybrid density functional theory on a model cluster composed of 12 ruthenium atoms resembling a Ru(0001) surface. The scattering calculations are performed on a reduced dimensionality potential energy hypersurface, where two dimensions are treated explicitly and all others are included implicitly by the zero-point correction. The VTST calculations include quantum effects along the reaction coordinate by applying the small curvature tunneling scheme. Even at room temperature (where ruthenium already shows catalytic activity) we find rate enhancement by tunneling by a factor of approximately 70. Inspection of the reaction probabilities shows that the major contribution to reactivity comes from the vibrational ground state of the reactants into vibrationally excited product states. The reaction rates are higher than determined in previous studies, and are compatible with experimental overall rates for ammonia synthesis.     

The reduction of ferricyanides and a sensitive test for the detection of hydrogen peroxide

Yellow zinc ferricyanide is reduced by heating to white zinc ferrocyanide by hydrogen peroxide in the presence of zinc sulphate and sodium, acetate. Copper ferricyanide, however, is reduced to brown copper ferrocyanide at room temperature, by means of hydrogen peroxide in the presence of copper sulphate and sodium acetate. The latter reaction can be applied for the detection of extremely small quantities of hydrogen peroxide both in a test tube (2.5 γ in 1 ml) and as a spot test (0.5 to 1 γ).     

Analysis of the first thermal response test in Algeria

Ground source heat pumps (GSHPs) mean attractive heating and cooling systems. Optimum design of a borehole heat exchanger (BHE), as the outer part of a GSHP heating system, requires knowledge of the thermal properties of the soil. Those data, the effective thermal conductivity of the soil λ_eff and the average temperature of the soil T ₀ enable us to determine the necessary number and depth of boreholes. The determination of thermal conductivity of the soil in laboratory experiments does not usually coincidence with the data under in situ conditions. Therefore, an in situ method of experimental determination of these parameters, thermal response testing (TRT) is used primarily for in situ determination of design data for BHEs. In this study, which was the first TRT in Algeria (Tlemcen site), the purpose was to determine the effective ground thermal conductivity. Measured data were evaluated by the line source model. Used method and performed evaluation are presented for a borehole drilled in clay, silt, and sand. The resulting effective ground thermal conductivity was 1.364 W/m K and the borehole thermal resistance was 0.18 K/(W/m).     

An experimental test of the double solubility rule

Vapor pressures, fusion (H_fus), and sublimation (H_s) enthalpies are reported ford, dl-2,3-dibromobutane-1,4-diol, andd,dl-dimethyl 2,3-diacetyltartrate. Values of 8.1, 7.04, 6.9, and 6.6 kcal/mol for H_fus were measured by differential scanning calorimetry and values of 28.4, 27.3, 26.2, and 25.5 kcal/mol (not corrected to 25) were calculated for H_s from the temperature dependence of vapor pressure, respectively. The vapor pressure ofdl-2,3-dibromobutane-1,4-diol, which crystallizes as a conglomerate, exceeds the vapor pressure of thed form by more than a factor of 2 over the temperature range studied. The ratio of vapor pressures ofdl- andd-dimethyl 2,3-diacetyltartrate, which crystallizes as a racemic compound, is approximately 1.5.     

The contribution of quantum mechanical tunneling to the 1,2-hydrogen rearrangement of methylbromocarbene

The rate constants for the 1,2-hydrogen rearrangement of methyl- and methyl-d₃-bromocarbene have been determined as a function of temperature. The Arrhenius plots are curved, and the intermolecular isotope effect is small and may increase with increasing temperature. We believe that although the rearrangement proceeds classically at high temperatures, as suggested by theory, quantum mechanical tunneling contributes significantly to the reaction at low temperatures. Alternative explanations are presented and discussed.