A two transition state model for radical-molecule reactions: a case study of the addition of OH to C2H4

A two transition state model is applied to the study of the addition of hydroxyl radical to ethylene. This reaction serves as a prototypical example of a radical-molecule reaction with a negative activation energy in the high-pressure limit. The model incorporates variational treatments of both inner and outer transition states. The outer transition state is treated with a recently derived long-range transition state theory approach focusing on the longest-ranged term in the potential. High-level quantum chemical estimates are incorporated in a variational transition state theory treatment of the inner transition state. Anharmonic effects in the inner transition state region are explored with direct phase space integration. A two-dimensional master equation is employed in treating the pressure dependence of the addition process. An accurate treatment of the two separate transition state regions at the energy and angular momentum resolved level is essential to the prediction of the temperature dependence of the addition rate. The transition from a dominant outer transition state to a dominant inner transition state is predicted to occur at about 130 K, with significant effects from both transition states over the 10 to 400 K temperature range. Modest adjustment in the ab initio predicted inner saddle point energy yields theoretical predictions which are in quantitative agreement with the available experimental observations. The theoretically predicted capture rate is reproduced to within 10% by the expression [4.93 x 10(-12) (T/298)(-2.488) exp(-107.9/RT) + 3.33 x 10(-12) (T/298)(0.451) exp(117.6/RT); with R = 1.987 and T in K] cm3 molecules(-1) s(-1) over the 10-600 K range.     

Kinetics of CH + N2 revisited with multireference methods

The potential energy surface for the CH + N2 reaction was reexamined with multireference ab initio electronic structure methods employing basis sets up to aug-cc-pvqz. Comparisons with related CCSD(T) calculations were also made. The multireference ab initio calculations indicate significant shortcomings in single reference based methods for two key rate-limiting transition states. Transition state theory calculations incorporating the revised best estimates for the transition state properties provide order of magnitude changes in the predicted rate coefficient in the temperature range of importance to the mechanism for prompt NO formation. At higher temperatures, two distinct pathways make a significant contribution to the kinetics. A key part of the transition state analysis involves a variable reaction coordinate transition state theory treatment for the formation of H + NCN from HNCN. The present predictions for the rate coefficients resolve the discrepancy between prior theory and very recent experimental measurements.     

A two transition state model for radical-molecule reactions: applications to isomeric branching in the OH-isoprene reaction

A two transition state model is applied to the prediction of the isomeric branching in the addition of hydroxyl radical to isoprene. The outer transition state is treated with phase space theory fitted to long-range transition state theory calculations on an electrostatic potential energy surface. High-level quantum chemical estimates are applied to the treatment of the inner transition state. A one-dimensional master equation based on an analytic reduction from two-dimensions for a particular statistical assumption about the rotational part of the energy transfer kernel is employed in the calculation of the pressure dependence of the addition process. We find that an accurate treatment of the two separate transition state regions, at the energy and angular momentum resolved level, is essential to the prediction of the temperature dependence of the addition rate. The transition from a dominant outer transition state to a dominant inner transition state is shown to occur at about 275 K, with significant effects from both transition states over the 30-500 K temperature range. Modest adjustments in the ab initio predicted inner saddle point energies yield predictions that are in quantitative agreement with the available high-pressure limit experimental observations and qualitative agreement with those in the falloff regime. The theoretically predicted capture rate is reproduced to within 10% by the expression [1.71 x 10(-10)(T/298)(-2.58) exp(-608.6/RT) + 5.47 x 10(-11)(T/298)-1.78 exp(-97.3/RT); with R = 1.987 and T in K] cm3 molecule(-1) s(-1) over the 30-500 K range. A 300 K branching ratio of 0.67:0.02:0.02:0.29 was determined for formation of the four possible OH-isoprene adduct isomers 1, 2, 3, and 4, respectively, and was found to be relatively insensitive to temperature. An Arrhenius activation energy of -0.77 kcal/mol was determined for the high-pressure addition rate constants around 300 K.     

Reaction pathways and excited states in H(2)O(2)+OH-->HO(2)+H(2)O: a new ab initio investigation

The mechanism of the hydrogen abstraction reaction H(2)O(2)+OH-->HO(2)+H(2)O in gas phase was revisited using density functional theory and other highly correlated wave function theories. We located two pathways for the reaction, both going through the same intermediate complex OH-H(2)O(2), but via two distinct transition state structures that differ by the orientation of the hydroxyl hydrogen relative to the incipient hydroperoxy hydrogen. The first two excited states were calculated for selected points on the pathways. An avoided crossing between the two excited states was found on the product side of the barrier to H transfer on the ground state surface, near the transition states. We report on the calculation of the rate of the reaction in the gas phase for temperatures in the range of 250-500 K. The findings suggest that the strong temperature dependence of the rate at high temperatures is due to reaction on the low-lying excited state surface over a barrier that is much larger than on the ground state surface.     

Pronounced non-Arrhenius behaviour of hydrogen-abstractions from toluene and derivatives by phthalimide-N-oxyl radicals: a theoretical study

Abstraction of hydrogen atoms by pthalimide-N-oxyl radicals is an important step in the N-hydroxyphthalimide catalyzed autoxidation of hydrocarbons. In this contribution, the temperature dependency of this reaction is evaluated by a detailed transition state theory based kinetic analysis for the case of toluene. Tunneling was found to play a very important role, enhancing the rate constant by a factor of 20 at room temperature. As a result, tunneling, in combination with the existence of two distinct rotamers of the transition state, causes a pronounced temperature dependency of the pre-exponential frequency factor, and, as a consequence, marked curvature of the Arrhenius plot. This explains why earlier experimental studies over a limited temperature range around 300 K found formal Arrhenius activation energies and pre-factors that are 4 kcal mol(-1) and three orders of magnitude smaller than the actual energy barrier and the corresponding frequency factor, respectively. Also as a consequence of tunneling, substitution of a deuterium atom for a hydrogen atom causes a large decrease in the rate constant, in agreement with the measured kinetic isotope effects. The present theoretical analysis, complementary to the experimental rate coefficient data, allows for a reliable prediction of the rate coefficient at higher temperatures, relevant for actual autoxidation processes.     

Mechanism of a chemical classic: quantum chemical investigation of the autocatalyzed reaction of the serendipitous wöhler synthesis of urea

The detailed reaction pathways for the ammonium cyanate transformation into urea (W?hler's reaction) in the gas phase, in solution, and in the solid state have exhaustively been explored by means of first-principles quantum chemical calculations at the B3LYP level of theory using the 6-31G(d,p) basis set. This serendipitous synthesis of urea is predicted to proceed in two steps; the first step involves the decomposition of the ammonium cyanate to ammonia and isocyanic or cyanic acid, and the second one, which is the main reaction step (and probably the rate-determining step), involves the interaction of NH(3) with either isocyanic or cyanic acid. Several alternative pathways were envisaged for the main reaction step of W?hler's reaction in a vacuum involving the formation of "four-center" transition states. Modeling W?hler's reaction in aqueous solution and in the solid state, it was found that the addition of NH(3) to both acids is assisted (autocatalyzed) by the active participation of extra H(2)O and/or NH(3) molecules, through a preassociative, cooperative, and hydrogen-transfer relay mechanism involving the formation of "six-center" or even "eight-center" transition states. The most energetically economic path of the rate-determining step of W?hler's reaction is that of the addition of NH(3) to the C=N double bond of isocyanic acid, directly affording urea. An alternative pathway corresponding to the anti-addition of ammonia to the Ctbd1;N triple bond of cyanic acid, yielding urea's tautomer HN=C(OH)NH(2), seems to be another possibility. In the last case, urea is formed through a prototropic tautomerization of its enolic form. The energies of the reactants, products, and all intermediates along with the barrier heights for each reaction path have been calculated at the B3LYP/6-31G(d,p) level of theory. The geometry optimization and characterization of all of the stationary points found on the potential energy hypersurfaces was performed at the same level of theory.     

Theoretical determination of the rate coefficient for the HO2 + HO2 → H2O2+O2 reaction: adiabatic treatment of anharmonic torsional effects

The HO(2) + HO(2) → H(2)O(2) + O(2) chemical reaction is studied using statistical rate theory in conjunction with high level ab initio electronic structure calculations. A new theoretical rate coefficient is generated that is appropriate for both high and low temperature regimes. The transition state region for the ground triplet potential energy surface is characterized using the CASPT2/CBS/aug-cc-pVTZ method with 14 active electrons and 10 active orbitals. The reaction is found to proceed through an intermediate complex bound by approximately 9.79 kcal/mol. There is no potential barrier in the entrance channel, although the free energy barrier was determined using a large Monte Carlo sampling of the HO(2) orientations. The inner (tight) transition state lies below the entrance threshold. It is found that this inner transition state exhibits two saddle points corresponding to torsional conformations of the complex. A unified treatment based on vibrational adiabatic theory is presented that permits the reaction to occur on an equal footing for any value of the torsional angle. The quantum tunneling is also reformulated based on this new approach. The rate coefficient obtained is in good agreement with low temperature experimental results but is significantly lower than the results of shock tube experiments for high temperatures.     

Regular dynamics in transition states with flat saddles

In the vicinity of a transition state, the dynamics is constrained by approximate local invariants of the motion even if the potential energy surface is anharmonic. The concept of local regularity near a saddle point is investigated in the framework of classical mechanics. The dynamics along the reaction coordinate decouples locally into a reactive mode and several bounded degrees of freedom. The partial energy stored in the unbounded mode is adiabatically invariant. Starting from a purely harmonic situation at the saddle point, anharmonicity coefficients are observed to come into play in a sequential way in the laws of motion. In most cases, each kind of anharmonic coefficient can be related to a particular feature of the potential energy surface or of the reaction path. These regularities account for previous classical trajectory calculations by Berry and co-workers, who observed that for flat saddles (i.e., those characterized by a low value of the modulus of the imaginary frequency), trajectories become temporarily collimated and less chaotic during passage through the transition state.     

Quantum capture, adiabatic channel, and classical trajectory study of the high pressure rate constant of the reaction H+O2-->HO2 between 0 and 5000 K

Limiting high pressure rate constants for the recombination reaction H+O(2)-->HO(2) are modeled between 0 and 5000 K on an ab initio potential. Quantum capture theory is employed for the temperature range from 0 to about 1 K, while classical trajectory calculations are suitable for covering temperatures above about 200 K. The intermediate temperature range is analyzed by adiabatic channel capture theory. The system is characterized by transition-state switching from outer transition states in the long-range-C(6)R(6) potential to inner transition states in the range of a "shoulder" of the potential. The limiting high pressure rate constants from the trajectory calculations are sufficient for comparison with the experimental data which are available over the range from 300 to 900 K. Specific rate constants k(E,J) for HO(2) dissociation are also given and analyzed with respect to internal consistency with capture cross sections.     

Mechanism and kinetics properties for the reaction: Chloroethane with atomic O (P)

In this paper, we present direct dynamics calculations for the multiple-channel reaction of CH₃CH₂Cl with atomic O (³P) in a wide temperature range (200–3000 K), based on canonical variational transition state theory including small curvature corrections. Four distinct saddle points, one for α-abstraction and three for β-abstraction, have been located for this reaction. The potential energy surface information has been calculated at the MP2/6-311G(d,p) level. The energies along the minimum energy path have been further improved by single-point energy calculations at the G3MP2 level. In the β-abstraction channel, Jahn–Teller effect has been found. Changes of geometries, generalized normal-mode vibrational frequencies, and potential energies along the reaction paths for all channels have been discussed and compared. The calculated total rate constants match the available experimental values reasonable well over the measured temperature range. The results show the variational effect can be negligible and the small curvature tunneling contribution plays an important role for the calculation of the rate constant. At low temperature α-abstraction may be the major reaction channel, while β-abstraction will have more contribution to the whole reaction rate as the temperature increase.     

New insights into the mechanism of proton transfer to hydride complexes: kinetic and theoretical evidence showing the existence of competitive pathways for protonation of the cluster [W3S4H3(dmpe)3]+ with acids

The reaction of the hydride cluster [W3S4H3(dmpe)3]+ (1, dmpe = 1,2-bis(dimethylphosphanyl)ethane) with acids (HCl, CF3COOH, HBF4) in CH2Cl2 solution under pseudo-first-order conditions of excess acid occurs with three kinetically distinguishable steps that can be interpreted as corresponding to successive formal substitution processes of the coordinated hydrides by the anion of the acid (HCl, CF3COOH) or the solvent (HBF4). Whereas the rate law for the third step changes with the nature of the acid, the first two kinetic steps always show a second-order dependence on acid concentration. In contrast, a single kinetic step with a first-order dependence with respect to the acid is observed when the experiments are carried out with a deficit of acid. The decrease in the T1 values for the hydride NMR signal of 1 in the presence of added HCl suggests the formation of an adduct with a W-H...H-Cl dihydrogen bond. Theoretical calculations for the reaction with HCl indicate that the kinetic results in CH2Cl2 solution can be interpreted on the basis of a mechanism with two competitive pathways. One of the pathways consists of direct proton transfer within the W-H...H-Cl adduct to form W-Cl and H2, whereas the other requires the presence of a second HCl molecule to form a W-H...H-Cl...H-Cl adduct that transforms into W-Cl, H2 and HCl in the rate-determining step. The activation barriers and the structures of the transition states for both pathways were also calculated, and the results indicate that both pathways can be competitive and that the transition states can be described in both cases as a dihydrogen complex hydrogen-bonded to Cl- or HCl2(-).     

Structure effects of benzene hydrogenation studied with sum frequency generation vibrational spectroscopy and kinetics on Pt(111) and Pt(100) single-crystal surfaces

Sum frequency generation (SFG) surface vibrational spectroscopy and kinetic measurements using gas chromatography have identified at least two reaction pathways for benzene hydrogenation on the Pt(100) and Pt(111) single-crystal surfaces at Torr pressures. Kinetic studies at low temperatures (310-370 K) show that benzene hydrogenation does not proceed through cyclohexene. A Langmuir-Hinshelwood-type rate law for the low-temperature reaction pathway is identified. The rate-determining step for this pathway is the addition of the first hydrogen atom to adsorbed benzene for both single-crystal surfaces, which is verified by the spectroscopic observation of adsorbed benzene at low temperatures on both the Pt(100) and Pt(111) crystal faces. Low-temperature SFG studies reveal chemisorbed and physisorbed benzene on both surfaces. At higher temperatures (370-440 K), hydrogenation of benzene to pi-allyl c-C(6)H(9) is observed only on the Pt(100) surface. Previous single-crystal studies have identified pi-allyl c-C(6)H(9) as the rate-determining step for cyclohexene hydrogenation to cyclohexane.     

Theoretical examination of Mg(2+)-mediated hydrolysis of a phosphodiester linkage as proposed for the hammerhead ribozyme

The hammerhead ribozyme is an RNA molecule capable of self-cleavage at a unique site within its sequence. Hydrolysis of this phosphodiester linkage has been proposed to occur via an in-line attack geometry for nucleophilic displacement by the 2'-hydroxyl on the adjoining phosphorus to generate a 2',3'-cyclic phosphate ester with elimination of the 5'-hydroxyl group, requiring a divalent metal ion under physiological conditions. The proposed S(N)2(P) reaction mechanism was investigated using density functional theory calculations incorporating the hybrid functional B3LYP to study this metal ion-dependent reaction with a tetraaquo magnesium (II)-bound hydroxide ion. For the Mg(2+)-catalyzed reaction, the gas-phase geometry optimized calculations predict two transition states with a kinetically insignificant, yet clearly defined, pentacoordinate intermediate. The first transition state located for the reaction is characterized by internal nucleophilic attack coupled to proton transfer. The second transition state, the rate-determining step, involves breaking of the exocyclic P-O bond where a metal-ligated water molecule assists in the departure of the leaving group. These calculations demonstrate that the reaction mechanism incorporating a single metal ion, serving as a Lewis acid, functions as a general base and can afford the necessary stabilization to the leaving group by orienting a water molecule for catalysis.     

The kinetics and mechanism of aqueous cleavage of imide bond in 5, 5-diethyl barbituric acid (5, 5-diethyl-2,4,6-(1H, 3H) pyrimidinetrione) in a highly alkaline medium

The kinetic study of alkaline hydrolysis of 5, 5-diethyl barbituric acid has been carried out at various [O H] and different temperatures ranging from 85–95°C. The reaction follows an irreversible first-order consecutive reaction path of the type \documentclass{article}\pagestyle{empty}\begin{document}${\rm A}\buildrel{{k1{\rm obs}}}\over\longrightarrow{\rm B}\buildrel{{k2{\rm obs}}}\over\longrightarrow$\end{document} X under pseudo-first-order kinetic conditions. A, B, and X represent for 5, 5-diethyl barbituric acid, diethyl malonuric acid, and ammonia, respectively. The pH-rate profiles obtained at three different temperatures reveal distinct phases which are attributed to a change in rate-determining step with change in [O H]. On the basis of the observed data, a possible mechanism has been discussed.     

Calculation of the anharmonic effect on the main reactions referring to ethylbenzene combustion mechanism

About 11 reactions related to ethylbenzene are studied in this paper using transition state theory. The YL method proposed by Yao and Lin is utilized to calculate the anharmonic and the harmonic rate constants in these reaction processes in the temperature range of 300–4,000 K, energy diagram and the temperature dependence of the rate coefficients are also presented. The calculations indicate that the harmonic rate constants are larger than the anharmonic rate constants in most cases. Especially, there is a temperature junction between the high and low relationship between the anharmonic and harmonic rate constants in several reactions. Furthermore, the calculated values are in good agreement with other theoretical ones within the allowable error. Finally, the kinetic parameters and the thermodynamic parameters are calculated. To sum up, it can be concluded that the anharmonic effect in these reactions is very significant and cannot be ignored.     

Kinetic study of the hexacyanoferrate (III) oxidation of dihydroxyfumaric acid in acid media

The kinetics of the hexacyanoferrate (III) oxidation of dihydroxyfumaric acid to hexacyanoferrate (II) and diketosuccinic acid was looked into within the 0.04 to 5.3 M HCl acidity range under different temperatures, ionic strengths, and solvent permittivity conditions. The kinetic effect of alkali metal ions, transition metal impurities, and substrate concentrations have also been analyzed. The observed inhibition effect brought about by addition of the reaction product, hexacyanoferrate (II), is a sign of a complex mechanism. The rate constants remained essentially unchanged up to 1 M HCl, diminished between 1.0 and 3.0 M HCl, and rose above 3.0 M HCl. Depending on the medium acidity, three mechanisms can be put forward, which involve different kinetically active forms. At low acidity, the rate-determining step involves a radical cation and both the neutral and the anion substrate forms are equally reactive ( k 1 = k 2 = 2.18 +/- 0.05 M (-1) s (-1), k -1 = 0.2 +/- 0.03). When the medium acidity is boosted, the rate-determining step involves the neutral dihydroxyfumaric acid and two hexacyanoferrate (III) forms. In the intermediate region the rate constant diminished with rising [H (+)] ( k' 1 = 0.141 +/- 0.01 and k' 2 = 6.80 +/- 0.05). Specific catalytic effect by binding of alkali metal ions to oxidant has not been observed. In all instances it was assessed that the substrate decomposition is slow compared to the redox reaction.     

Ethanol reforming on Co(0001) surfaces: a density functional theory study

A computational study using density functional theory is carried out to investigate the reaction mechanism of ethanol steam reforming on Co(0001) surfaces. The adsorption properties of the reactant, possible intermediates, and products are carefully examined. The reaction pathway and related transition states are also analyzed. According to our calculations, the reforming mechanism primarily consisting of dehydrogenation steps of ethanol, ethoxy, methanol, methoxy, and formic acid, is feasible on Co(0001) surfaces. It is also found that the reaction of formaldehyde yielding formic acid and hydrogen may not be an elementary reaction. The dehydrogenation of ethoxy possesses the highest barrier and is accordingly identified as the rate-determining step.