Absolute rate calculations for atom abstractions by radicals: energetic,structural and electronic factors

We calculate transition-state energies of atom-transfer reactions from reaction energies, electrophilicity indices, bond lengths, and vibration frequencies of the reactive bonds. Our calculations do not involve adjustable parameters and uncover new patterns of reactivity. The generality of our model is demonstrated comparing the vibrationally adiabatic barriers obtained for 100 hydrogen-atom transfers with the corresponding experimental activation energies, after correction for the heat capacities of reactants and transition state. The rates of half of these reactions are calculated using the Transition-State Theory with the vibrationally adiabatic path of the Intersecting-State Model and the semiclassical correction for tunneling (ISM/scTST). The calculated rates are within an order of magnitude of the experimental ones at room temperature. The temperature dependencies and kinetic isotope effects of selected systems are also in good agreement with the available experimental data. Our model elucidates the roles of the reaction energy, electrophilicity, structural parameters, and tunneling in the reactivity of these systems and can be applied to make quantitative predictions for new systems.     

Absolute rate calculations. Proton transfers in solution

The reaction path of the intersecting-state model is used in transition-state theory with the semiclassical correction for tunneling (ISM/scTST) to calculate the rates of proton-transfer reactions from hydrogen-bond energies, reaction energies, electrophilicity indices, bond lengths, and vibration frequencies of the reactive bonds. ISM/scTST calculations do not involve adjustable parameters. The calculated proton-transfer rates are within 1 order of magnitude of the experimental ones at room temperature, and cover very diverse systems, such as deprotonations of nitroalkanes, ketones, HCN, carboxylic acids, and excited naphthols. The calculated temperature dependencies and kinetic isotope effects are also in good agreement with the experimental data. These calculations elucidate the roles of the reaction energy, electrophilicity, structural parameters, hydrogen bonds, tunneling, and solvent in the reactivity of acids and bases. The efficiency of the method makes it possible to run absolute rate calculations through the Internet.     

Conformational analysis of the four 3-methyl-isopropylphenol isomers (thymols) by molecular orbital calculations and X-ray crystal structure determinations

PCILO calculations have been used in a conformational investigation of 3-methyl-x-isopropylphenols (thymol isomers), including a study of the barrier to internal rotation of substituents. The results of the calculations are in good agreement with those available from experimental crystal structure determinations, except for 3-methyl-6-isopropylphenol. For the latter the calculated most stable conformer cannot form a crystal with hexamers bonded by H bonds, as is determined by crystallography. The heights of the barriers to internal rotation of the substituents are compared with the available experimental data and discussed in terms of steric hindrance.     

Reactivity of haloethanes with hydroxyl radicals: Effects of basis set and correlation energy on reaction energetics

Ab initio calculations on fluoroethane reactions with the hydroxyl radical have been carried out at different levels of theory. The convergence of reaction barriers and reaction enthalpies has been systematically investigated with respect to the size and quality of the basis set and the treatment of correlation energy. The G2 and MP2 barrier heights and reaction enthalpies show the best agreement with the experimental data. The split valence basis sets of triple-zeta quality supplemented by diffuse and polarization functions are necessary to reproduce experimental values for barrier heights and reaction enthalpies at the MP2 level of theory. The full counterpoise correction was used to calculate the basis set superposition error for several standard basis sets, including polarization and diffuse functions. The smallest counterpoise corrections are associated with basis sets that contain polarization and diffuse functions, the diffuse functions being the most effective in reducing BSSE. However, in our case, the uncorrected barrier heights are in better agreement with experimental results than the counterpoise-corrected data. Thus, at the MP2 level of theory, which seems to be dictated for larger electronic systems of chemical interest, the optimal approach is to increase the basis set to the maximum size affordable and to use results without counterpoise corrections for the calculation of reaction barriers. A viable alternative is the use of G2 theory because its results for the barrier heights and reaction enthalpies are in excellent agreement with the experimental data. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1190–1199     

Infrared characterization of the HCOOH···CO2 complexes in solid argon: stabilization of the higher-energy conformer of formic acid

The complexes of formic acid (HCOOH, FA) with carbon dioxide are studied by infrared spectroscopy in an argon matrix. Two trans-FA···CO(2) and one cis-FA···CO(2) complexes are experimentally identified while the calculations at the MP2(full)/6-311++G(2d,2p) level of theory predict one more minimum for the cis-FA···CO(2) complex. The complex of the higher-energy conformer cis-FA with CO(2) is prepared by vibrational excitation of the ground-state trans-FA conformer combined with thermal annealing. The lifetime of the cis-FA···CO(2) complex in an argon matrix at 10 K is 2 orders of magnitude longer than that of the cis-FA monomer. This big difference is explained by the computational results which show a higher stabilization barrier for the complex. The solvation effects in solid argon are theoretically estimated and their contribution to the stabilization barriers of the higher-energy species is discussed. The relative barrier transmissions for hydrogen tunneling in the cis-FA···CO(2) complex and cis-FA monomer are in good agreement with the experimental decay rates.     

Alkali‐Metal‐Ion‐Assisted Hydrogen Atom Transfer in the Homocysteine Radical

Intramolecular hydrogen atom transfer (HAT) was examined in homocysteine (Hcy) thiyl radical/alkali metal ion complexes in the gas phase by combination of experimental techniques (ion‐molecule reactions and infrared multiple photon dissociation spectroscopy) and theoretical calculations. The experimental results unequivocally show that metal ion complexation (as opposed to protonation) of the regiospecifically generated Hcy thiyl radical promotes its rapid isomerisation into an α‐carbon radical via HAT. Theoretical calculations were employed to calculate the most probable HAT pathway and found that in alkali metal ion complexes the activation barrier is significantly lower, in full agreement with the experimental data. This is, to our knowledge, the first example of a gas‐phase thiyl radical thermal rearrangement into an α‐carbon species within the same amino acid residue and is consistent with the solution phase behaviour of Hcy radical.     

Theoretical study of the thermodynamics and kinetics of hydrogen abstractions from hydrocarbons

Thermochemical and kinetic data were calculated at four cost-effective levels of theory for a set consisting of five hydrogen abstraction reactions between hydrocarbons for which experimental data are available. The selection of a reliable, yet cost-effective method to study this type of reactions for a broad range of applications was done on the basis of comparison with experimental data or with results obtained from computationally demanding high level of theory calculations. For this benchmark study two composite methods (CBS-QB3 and G3B3) and two density functional theory (DFT) methods, MPW1PW91/6-311G(2d,d,p) and BMK/6-311G(2d,d,p), were selected. All four methods succeeded well in describing the thermochemical properties of the five studied hydrogen abstraction reactions. High-level Weizmann-1 (W1) calculations indicated that CBS-QB3 succeeds in predicting the most accurate reaction barrier for the hydrogen abstraction of methane by methyl but tends to underestimate the reaction barriers for reactions where spin contamination is observed in the transition state. Experimental rate coefficients were most accurately predicted with CBS-QB3. Therefore, CBS-QB3 was selected to investigate the influence of both the 1D hindered internal rotor treatment about the forming bond (1D-HR) and tunneling on the rate coefficients for a set of 21 hydrogen abstraction reactions. Three zero curvature tunneling (ZCT) methods were evaluated (Wigner, Skodje & Truhlar, Eckart). As the computationally more demanding centrifugal dominant small curvature semiclassical (CD-SCS) tunneling method did not yield significantly better agreement with experiment compared to the ZCT methods, CD-SCS tunneling contributions were only assessed for the hydrogen abstractions by methyl from methane and ethane. The best agreement with experimental rate coefficients was found when Eckart tunneling and 1D-HR corrections were applied. A mean deviation of a factor 6 on the rate coefficients is found for the complete set of 21 reactions at temperatures ranging from 298 to 1000 K. Tunneling corrections play a critical role in obtaining accurate rate coefficients, especially at lower temperatures, whereas the hindered rotor treatment only improves the agreement with experiment in the high-temperature range.     

Study of hydrogen-bonded clusters of 2-methoxyphenol–water

Various hydrogen-bonded clusters of 2-methoxyphenol (2MP) with water have been analyzed using ab initio methods and Atoms in Molecules (AIM) theory. The intramolecular hydrogen bond energy (and enthalpy) for 2MP was evaluated from two different methods. The results of rotational barriers method are in better agreement with experimental data. Binding energies, vibrational frequencies and geometrical parameters were examined and compared for these complexes. It was shown that in the most stable complex, water acts both as a donor and an acceptor. The “bifurcated” complex was shown to be relatively stable based on energy values. Atoms in Molecules and Natural Bond Orbital (NBO) analysis were used to confirm the existence of hydrogen bonds and to compare the strengths of them. The results obtained from quantum mechanical, AIM and NBO calculations are in agreement with each other.     

Tunneling molecular dynamics in the light of the corpuscular-wave dualism theory

This paper presents the experimental demonstration of the corpuscular-wave dualism theory. The correlation between the de Broglie wavelength related to the thermal motion and the potential barrier width and height is reported. The stochastic jumps of light atoms (hydrogen, deuterium) between two equilibrium sites A and B (identical geometry) occur via different pathways; one pathway is over the barrier (classical dynamics), and the other one is through the barrier (tunneling). On the over-the-barrier pathway, there are no obstacles for the de Broglie waves, and this pathway exists from high to low temperatures up to 0 K because the thermal energy is subjected to the Maxwell distribution and a certain number of particles owns enough energy for the hopping over the barrier. On the tunneling pathway, the particles pass through the barrier, or they are reflected from the barrier. Only particles with the energy lower than barrier heights are able to perform a tunneling hopping. The de Broglie waves related to these energies are longer than the barrier width. The Schr?dinger equation is applied to calculate the rate constant of tunneling dynamics. The Maxwell distribution of the thermal energy has been taken into account to calculate the tunneling rate constant. The equations for the total spectral density of complex motion derived earlier by us together with the expression for the tunneling rate constant, derived in the present paper, are used in analysis of the temperature dependence of deuteron spin-lattice relaxation of the ammonium ion in the deuterated analogue of ammonium hexachloroplumbate ((ND4)2PbCl6). It has been established that the equation CpTtun = EH (thermal energy equals activation energy), where Cp is the molar heat capacity (temperature-dependent, known from literature), determines directly the low temperature Ttun at which the de Broglie wavelength, lambdadeBroglie, related to the thermal energy, CpT, is equal to the potential barrier width, L. Above Ttun, the lambdadeBroglie wavelength related to the CpT energy is shorter than the potential barrier width and not able to overcome the barrier. The activation energy EH equals 7.5 kJ/mol, and therefore, the Ttun temperature for deuterons in ((ND4)2PbCl6 is 55.7 K. The agreement between the potential barrier width following from the simple geometrical calculations (L = 0.722 A) and de Broglie wavelength at Ttun (L = 0.752 A) is good. The temperature plots of the deuteron correlation times for (ND4)2PbCl6 reveal comparable values of the correlation times of the tunneling, (tau(T)), and over-the-barrier jumps (tau(H)) near 34.8 K. Matsuo, on the basis of the molar heat capacity study, found the first-order phase transition at this temperature.     

Temperature dependence of the kinetic isotope effects in thymidylate synthase. A theoretical study

In recent years, the temperature dependence of primary kinetic isotope effects (KIE) has been used as indicator for the physical nature of enzyme-catalyzed H-transfer reactions. An interactive study where experimental data and calculations examine the same chemical transformation is a critical means to interpret more properly temperature dependence of KIEs. Here, the rate-limiting step of the thymidylate synthase-catalyzed reaction has been studied by means of hybrid quantum mechanics/molecular mechanics (QM/MM) simulations in the theoretical framework of the ensemble-averaged variational transition-state theory with multidimensional tunneling (EA-VTST/MT) combined with Grote-Hynes theory. The KIEs were calculated across the same temperature range examined experimentally, revealing a temperature independent behavior, in agreement with experimental findings. The calculations show that the H-transfer proceeds with ～91% by tunneling in the case of protium and ～80% when the transferred protium is replaced by tritium. Dynamic recrossing coefficients are almost invariant with temperature and in all cases far from unity, showing significant coupling between protein motions and the reaction coordinate. In particular, the relative movement of a conserved arginine (Arg166 in Escherichia coli ) promotes the departure of a conserved cysteine (Cys146 in E. coli ) from the dUMP by polarizing the thioether bond thus facilitating this bond breaking that takes place concomitantly with the hydride transfer. These promoting vibrations of the enzyme, which represent some of the dimensions of the real reaction coordinate, would limit the search through configurational space to efficiently find those decreasing both barrier height and width, thereby enhancing the probability of H-transfer by either tunneling (through barrier) or classical (over-the-barrier) mechanisms. In other words, the thermal fluctuations that are coupled to the reaction coordinate, together with transition-state geometries and tunneling, are the same in different bath temperatures (within the limited experimental range examined). All these terms contribute to the observed temperature independent KIEs in thymidylate synthase.     

Predictive chemical kinetics: Density functional and hartree–fock calculations on free-radial reaction transition states

Density functional theory (DFT ) using gradient-corrected «nonlocal» functionals is used to calculated the thermochemistry and barrier heights for several types of peroxyl radical isomerizations currently being studied by kineticists. The calculations are generally in good agreement with experimental data, where such data are available. An important exception is that the O—H bond strengths in hydroperoxides are all predicted to be too weak by about 7 kcal/mol. The calculated reaction barriers are a few kcal/mol lower than the experimental estimates, but comparable in accuracy to the much more computationally expensive second-order Møller–Plesset (MP 2) predictions. Various theoretical methods converge on a 42 ± 2 kcal/mole barrier for CH₃OO → H₂CO + OH. The DFT calculations can be used to predict reaction barriers in cases where no reliable experimental data are available. The effects of the choice of basis set and correlation functional are explored. Improvements needed to make these calculations most valuable to the chemical kineticist are discussed. © 1994 John Wiley & Sons, Inc.     

Competition between covalent and noncovalent bond cleavages in dissociation of phosphopeptide-amine complexes

Interactions between quaternary amino or guanidino groups with anions are ubiquitous in nature and have been extensively studied phenomenologically. However, little is known about the binding energies in non-covalent complexes containing these functional groups. Here, we present a first study focused on quantifying such interactions using complexes of phosphorylated A(3)pXA(3)-NH(2) (X = S, T, Y) peptides with decamethonium (DCM) or diaguanidinodecane (DGD) ligands as model systems. Time- and collision energy-resolved surface-induced dissociation (SID) of the singly charged complexes was examined using a specially configured Fourier transform ion cyclotron resonance mass spectrometer (FTICR-MS). Dissociation thresholds and activation energies were obtained from RRKM modeling of the experimental data that has been described and carefully characterized in our previous studies. For systems examined in this study, covalent bond cleavages resulting in phosphate abstraction by the cationic ligand are characterized by low dissociation thresholds and relatively tight transition states. In contrast, high dissociation barriers and large positive activation entropies were obtained for cleavages of non-covalent bonds. Dissociation parameters obtained from the modeling of the experimental data are in excellent agreement with the results of density functional theory (DFT) calculations. Comparison between the experimental data and theoretical calculations indicate that phosphate abstraction by the ligand is rather localized and mainly affected by the identity of the phosphorylated side chain. The hydrogen bonding in the peptide and ligand properties play a minor role in determining the energetics and dynamics of the phosphate abstraction channel.     

Binding of phosphinate and phosphonate inhibitors to aspartic proteases: a first-principles study

Phosphinate and phosphonate derivatives are potent inhibitors of aspartic proteases (APs). The affinity for the enzyme might be caused by the presence of low barrier hydrogen bonds between the ligand and the catalytic Asp dyad in the cleavage site. We have used density functional theory calculations along with hybrid quantum mechanics/molecular mechanics Car-Parrinello molecular dynamics simulations to investigate the hydrogen-bonding pattern at the binding site of the complexes of human immunodeficiency virus type-1 AP and the eukaryotic endothiapepsin and penicillopepsin. Our calculations are in fair agreement with the NMR data available for endothiapepsin (Coates et al. J. Mol. Biol. 2002, 318, 1405-1415) and show that the most stable active site configuration is the diprotonated, negatively charged form. In the viral complex both protons are located at the catalytic Asp dyad, while in the eukaryotic complexes the proton shared by the closest oxygen atoms is located at the phosphinic/phosphonic group.     

Rate constants from the reaction path Hamiltonian. II. Nonseparable semiclassical transition state theory

For proton transfer reactions, the tunneling contributions to the rates are often much larger than thermally activated rates at temperatures of interest. A number of separable tunneling corrections have been proposed that capture the dependence of tunneling rates on barrier height and imaginary frequency size. However, the effects of reaction pathway curvature and barrier anharmonicity are more difficult to quantify. The nonseparable semiclassical transition state theory (TST) of Hernandez and Miller [Chem. Phys. Lett. 214, 129 (1993)] accounts for curvature and barrier anharmonicity, but it requires prohibitively expensive cubic and quartic derivatives of the potential energy surface at the transition state. This paper shows how the reaction path Hamiltonian can be used to approximate the cubic and quartic derivatives used in nonseparable semiclassical transition state theory. This enables tunneling corrections that include curvature and barrier anharmonicity effects with just three frequency calculations as required by a conventional harmonic transition state theory calculation. The tunneling correction developed here is nonseparable, but can be expressed as a thermal average to enable efficient Monte Carlo calculations. For the proton exchange reaction NH2 + CH4 <==> NH3 + CH3, the nonseparable rates are very accurate at temperatures from 300 K up to about 1000 K where the TST rate itself begins to diverge from the experimental results.     

Kinetic study of the reaction H2O2+H→H2O+OH by ab initio and density functional theory calculations

Theoretical investigations on the kinetics of the elementary reaction H₂O₂+H→H₂O+OH were performed using the transition state theory (TST). Ab initio (MP2//CASSCF) and density functional theory (B3LYP) methods were used with large basis set to predict the kinetic parameters; the classical barrier height and the pre-exponential factor. The ZPE and BSSE corrected value of the classical barrier height was predicted to be 4.1 kcal mol⁻¹ for MP2//CASSCF and 4.3 kcal mol⁻¹ for B3LYP calculations. The experimental value fitted from Arrhenius expressions ranges from 3.6 to 3.9 kcal mol⁻¹. Thermal rate constants of the title reaction, based on the ab initio and DFT calculations, was evaluated for temperature ranging from 200 to 2500 K assuming a direct reaction mechanism. The modeled ab initio-TST and DFT–TST rate constants calculated without tunneling were found to be in reasonable agreement with the observed ones indicating that the contribution of the tunneling effect to the reaction was predicted to be unimportant at ambient temperature.     

Mechanistic study and kinetic properties of the CF3CHO + Cl reaction

Theoretical investigations have been carried out on the mechanism and kinetics for the reaction of CF 3 CHO + Cl using duallevel direct dynamics method. The potential energy surface information was obtained at the MCQCISD/3//MP2/cc-pVDZ level and the kinetic calculations were done using variational transition state theory with interpolated single-point energy (VTST-ISPE) approach. The calculated results show that the reaction proceeds primarily via the H-abstraction channel, while the Cl-addition channel is unfavorable due to the higher barriers. The improved canonical variational transition-state theory (ICVT) with the small-curvature tunneling correction (SCT) was used to calculate the rate constants. The theoretical rate constants at room temperature are in general agreement with the experimental values. A three-parameter rate constant expression was fitted over a wide temperature range of 200-2000 K.     

The ground-state tunneling splitting of various carboxylic acid dimers

Carboxylic acid dimers in gas phase reveal ground-state tunneling splittings due to a double proton transfer between the two subunits. In this study we apply a recently developed accurate semiclassical method to determine the ground-state tunneling splittings of eight different carboxylic acid derivative dimers (formic acid, benzoic acid, carbamic acid, fluoro formic acid, carbonic acid, glyoxylic acid, acrylic acid, and N,N-dimethyl carbamic acid) and their fully deuterated analogs. The calculated splittings range from 5.3e-4 to 0.13 cm(-1) (for the deuterated species from 2.8e-7 to 3.3e-4 cm(-1)), thus indicating a strong substituent dependence of the splitting, which varies by more than two orders of magnitude. One reason for differences in the splittings could be addressed to different barriers heights, which vary from 6.3 to 8.8 kcal/mol, due to different mesomeric stabilization of the various transition states. The calculated splittings were compared to available experimental data and good agreement was found. A correlation could be found between the tunneling splitting and the energy barrier of the double proton transfer, as the splitting increases with increased strength of the hydrogen bonds. From this correlation an empirical formula was derived, which allows the prediction of the ground-state tunneling splitting of carboxylic acid dimers at a very low cost and the tunneling splittings for parahalogen substituted benzoic acid dimers is predicted.     

First principles study of the reaction of formic and acetic acids with hydroxyl radicals

The oxidation of formic and acetic acids with hydroxyl radicals was studied as a model for the oxidation of larger carboxylic acids using first principles calculations. For formic acid, the CBS-QB3 activation barriers of 14.1 and 12.4 kJ/mol for the acid and for the formyl channel, respectively, are within 3 kJ/mol of benchmark W1U values. Tunneling significantly enhances the rate coefficient for the acid channel and is responsible for the dominance of the acid channel at 298 K. At 298 K, tunneling correction factors of 339 and 2.0 were calculated for the acid and the formyl channel using the small-curvature tunneling method and the CBS-QB3 potential energy surface. The Wigner, Eckart, and zero-curvature tunneling methods severely underestimate the importance of tunneling for the acid channel. The resulting reaction rate coefficient of 0.98 x 10(5) m(3)/(mol x s) at 298 K is within a factor 2-3 of experimental values. For acetic acid, an activation barrier of 11.0 kJ/mol and a tunneling correction factor of 199 were calculated for the acid channel. Two mechanisms compete for hydrogen abstraction at the methyl group, with activation barriers of 11.9 and 12.5 kJ/mol and tunneling correction factors of 9.1 and 4.1 at 298 K. The resulting rate coefficient of 1.2 x 10(5) m(3)/(mol x s) at 298 K and branching ratio of 94% compare well with experimental data.     

Computational studies on the kinetics and mechanisms for NH3 reactions with ClOx (x = 0-4) radicals

Kinetics and mechanisms for NH3 reactions with ClOx (x = 0-4) radicals have been investigated at the G2M level of theory in conjunction with statistical theory calculations. The geometric parameters of the species and stationary points involved in the reactions have been optimized at the B3LYP/6-311+G(3df,2p) level of theory. Their energetics have been further refined with the G2M method. The results show that the H-abstraction process is the most favorable channel in each reaction and the barriers predicted in decreasing order are OClO > ClO > Cl > ClO3 > ClO4. All reactions were found to occur by hydrogen-bonding complexes; the rate constants for these complex metathetical processes have been calculated in the temperature range 200-2000 K by the microcanonical VTST and/or RRKM theory (for ClO4 + NH3) with Eckart tunneling and multiple reflection corrections. The predicted rate constants are in good agreement with the available experimental data.