Transition State Theory Rate Constants Research Articles

Rate Constants for the Hydrogen Abstractions in the OH-Initiated Oxidation of Glycolaldehyde. A Variational Transition-state Theory Calculation

The reaction between the OH radical and glycolaldehyde has been theoretically studied for the first time. By means of preliminary MP2(FC)/6-31G*, B3LYP/6-31G*, CBS-Q, G2, and G3 electronic structure calculations, two main processes have been determined, CH2OHCHO + OH → CH2OHCO + H2O and CH2OHCHO + OH → CHOHCHO + H2O, in clear agreement with experimental data. Then the variational transition-state theory rate constants with multidimensional tunneling corrections (when necessary) (VTST-MT) have been calculated using dual-level interpolation algorithms. The theoretical rate constant for the global process at 298 K of 3.83 × 10-11 cm3 molecule-1 s-1 is in reasonable agreement with the experimental value. In the temperature range 100−350 K, we predict a clear inverse dependence of the global rate constant on temperature.

Activation barriers and rate constants for hydration of platinum and palladium square-planar complexes: an ab initio study.

In the present work, an ab initio study on hydration (a metal-ligand replacement by water molecule or OH- group) of cis- and transplatin and their palladium analogs was performed within a neutral pseudomolecule approach (e.g., metal-complex+water as reactant complex). Subsequent replacement of the second ligand was considered. Optimizations were performed at the MP2/6-31+G(d) level with single-point energy evaluation using the CCSD(T)/6-31++G(d,p) approach. For the obtained structures of reactants, transition states (TS's), and products, both thermodynamic (reaction energies and Gibbs energies) and kinetic (rate constants) characteristics were estimated. It was found that all the hydration processes are mildly endothermic reactions-in the first step they require 8.7 and 10.2 kcal/mol for ammonium and chloride replacement in cisplatin and 13.8 and 17.8 kcal/mol in the transplatin case, respectively. Corresponding energies for cispalladium amount to 5.2 and 9.8 kcal/mol, and 11.0 and 17.7 kcal/mol for transpalladium. Based on vibrational analyses at MP2/6-31+G(d) level, transition state theory rate constants were computed for all the hydration reactions. A qualitative agreement between the predicted and known experimental data was achieved. It was also found that the close similarities in reaction thermodynamics of both Pd(II) and Pt(II) complexes (average difference for all the hydration reactions are approximately 1.8 kcal/mol) do not correspond to the TS characteristics. The TS energies for examined Pd(II) complexes are about 9.7 kcal/mol lower in comparison with the Pt analogs. This leads to 10(6) times faster reaction course in the Pd cases. This is by 1 or 2 orders of magnitude more than the results based on experimental measurements.

Kinetic Monte Carlo Study of Competing Hydrogen Pathways into Connected (100), (110), and (111) Ni Surfaces

Hydrogen mobility upon and pathways into connected surfaces of a fcc metal, using the Ni (100), (110), and (111) faces as a model, are examined through computational methods. Our interest is in finding the time scale for an initial H-atom population density deposited on the surface to reach an equilibrium surface and sublayer distribution, and to understand the H dynamics in the region of Ni surface steps. The activation energies for H mobility from site-to-site are determined using a realistic potential energy function, and a set of 232 transition state theory rate constants governs the H-hopping model. A handful of the TST rate constants are compared favorably to very accurate calculations of rate constants for the same potential using a 3-d quantum mean field method. The set of TST rate constants are used in a kinetic Monte Carlo solution of the rate equations for surface hopping and surface penetration to complete the picture. We find that fast diffusion of H atoms occurs on all of the Ni surfaces with H atoms rapidly exchanging surfaces via both concave and convex step edges, and leaving the less stable (111) face. We examine the time scale for the approach to equilibrium for the H atoms on both the surfaces and sublayers. The effect of convex step edges vs the effect of direct terrace penetration for the H atoms is examined, and we find that at temperatures below about 1000 K the H-atom penetration at convex step edges becomes the favored pathway to the subsurface. As the H atoms flow via the step edges to the sublayer, a transient cycling current of H-atom probability is set up near the step edge, which fades away as equilibrium is reached.

The Pitzer Free Rotor Model for Nondegenerate Modes: Application to the Long-Range Behavior of Halogen Radical Reactions with Substituted Olefins

While the Pitzer model had been used in the past with great success for degenerate internal motions, e.g., transitional bending motions in the recombination of hydrogen and methyl radicals, simpler models are often used in the treatment of nondegenerate modes, such as the transitional bending motions in the recombination reaction of hydrogen and choloromethyl radicals. In this work, highly detailed analysis of the Pitzer free rotor treatment for nondegenerate internal motions is presented. The addition reaction of a chlorine radical with 1,1,-dichloroethylene is used here for illustrative purposes. The reaction proceeds in two steps: the reactants reach a bridged intermediate that can dissociate back to reactants or yield the •C2H2Cl3 adducts. Only the long-range part of the reaction was investigated in this paper. Electronic structure calculations were performed at the UQCISD(T)/6-31G**//UMP2/6-31G** level of theory, and canonical variational transition state theory rate constants were computed. In conclusion, it is shown that two different pathways lead to the bridged intermediate. Consideration of the forward and backward rate constants demonstrated that the more direct route to the bridged intermediate is favored kinetically.

N[bond]C(alpha) bond dissociation energies and kinetics in amide and peptide radicals. Is the dissociation a non-ergodic process?

Dissociations of aminoketyl radicals and cation radicals derived from beta-alanine N-methylamide, N-acetyl-1,2-diaminoethane, N(alpha)-acetyl lysine amide, and N(alpha)-glycyl glycine amide are investigated by combined density functional theory and Møller-Plesset perturbational calculations with the goal of elucidating the mechanism of electron capture dissociation (ECD) of larger peptide and protein ions. The activation energies for dissociations of N[bond]C bonds in aminoketyl radicals decrease in the series N[bond]CH(3) > N-CH(2)CH(2)NH(2) >> N[bond]CH(2)CONH(2) approximately N[bond]CH(CONH(2))(CH(2))(4)NH(2). Transition state theory rate constants for dissociations of N[bond]C(alpha) bonds in aminoketyl radicals and cation-radicals indicate an extremely facile reaction that occurs with unimolecular rate constants >10(5) s(-1) in species thermalized at 298 K in the gas phase. In neutral aminoketyl radicals the N[bond]C(alpha) bond cleavage results in fast dissociation. In contrast, N[bond]C(alpha) bond cleavage in aminoketyl cation-radicals results in isomerization to ion-molecule complexes that are held together by strong hydrogen bonds. The facile N[bond]C(alpha) bond dissociation in thermalized ions indicates that it is unnecessary to invoke the hypothesis of non-ergodic behavior for ECD intermediates.

A high level theoretical investigation of the N2O4→2 NO2 dissociation reaction: Is there a transition state?

The N2O4→2 NO2 dissociation reaction was investigated at a high level of theory using the couple cluster with all single and double excitations and connected triples [CCSD(T)] and complete active space self-consistent field approaches, and the cc-pVDZ, aug-cc-pVDZ, and cc-pVTZ basis sets. Only at the coupled cluster level a first-order saddle point was found connecting reactant and products. Collectively, structural, vibrational, and thermodynamic data for the three stationary points represent the best theoretical description of this reaction system to date, and are in good agreement with available experimental results. Unimolecular transition state theory rate constants (k∞) were also evaluated at 250, 298.15, and 350 K. At the CCSD(T)/cc-pVTZ level of calculation these results are 0.62×101, 1.90×103, and 1.66×105 s−1, respectively. Known experimental results at 298 K vary from 1.7×105 to 1.0×106 s−1. Including an estimate for basis set superposition error, we predict ΔH2980 for the dissociation reaction to be 12.76 kcal/mol (Expt. 13.1–13.7 kcal/mol).

Anharmonic effects on the transition state theory rate constant

Accurate rovibrational levels for HCN up to 24 349 cm−1 above the bottom of the vibrational well and vibrational levels at the saddle point of the HCN/HNC isomerization reaction up to 32 809 cm−1 above the saddle point have been computed and used to obtain partition functions over the temperature range 200–2500 K. Under the rigid-rotor approximation, the rovibrational partition function for HCN is found to be exactly separable into vibrational and rotational contributions to first order. Two approximate approaches, second-order perturbation theory and simple perturbation theory, the latter of which obviates the need for a direct summation over energy levels, are shown to yield vibrational partition functions for HCN and at the saddle point that agree with the accurate values within 2%. In contrast, the usual harmonic approximation leads to errors of up to 24% in the individual partition functions, resulting in differences of between 3.5% and 6.5% in conventional transition state theory rate constants calculated with harmonic versus anharmonic vibrations.

Comparison of transition state theory rate constants for internal conformational motion with those obtained from molecular dynamics simulations

The results of molecular dynamics (MD) simulations are compared to transition state theory estimations for formation of conformational defects in a polymer crystal. The rates of conformational defect formation and destruction are obtained in terms of a distribution over possible conformational states. The rate constant obtained by this method, when normalized by the number of possible defect sites, is independent of the size of the system, in apparent contrast with the results of MD simulations. The difference is interpreted in terms of the effective temperature of the MD calculation.

Hydride transfer in liver alcohol dehydrogenase: quantum dynamics, kinetic isotope effects, and role of enzyme motion.

The quantum dynamics of the hydride transfer reaction catalyzed by liver alcohol dehydrogenase (LADH) are studied with real-time dynamical simulations including the motion of the entire solvated enzyme. The electronic quantum effects are incorporated with an empirical valence bond potential, and the nuclear quantum effects of the transferring hydrogen are incorporated with a mixed quantum/classical molecular dynamics method in which the transferring hydrogen nucleus is represented by a three-dimensional vibrational wave function. The equilibrium transition state theory rate constants are determined from the adiabatic quantum free energy profiles, which include the free energy of the zero point motion for the transferring nucleus. The nonequilibrium dynamical effects are determined by calculating the transmission coefficients with a reactive flux scheme based on real-time molecular dynamics with quantum transitions (MDQT) surface hopping trajectories. The values of nearly unity for these transmission coefficients imply that nonequilibrium dynamical effects such as barrier recrossings are not dominant for this reaction. The calculated deuterium and tritium kinetic isotope effects for the overall rate agree with experimental results. These simulations elucidate the fundamental nature of the nuclear quantum effects and provide evidence of hydrogen tunneling in the direction along the donor-acceptor axis. An analysis of the geometrical parameters during the equilibrium and nonequilibrium simulations provides insight into the relation between specific enzyme motions and enzyme activity. The donor-acceptor distance, the catalytic zinc-substrate oxygen distance, and the coenzyme (NAD(+)/NADH) ring angles are found to strongly impact the activation free energy barrier, while the donor-acceptor distance and one of the coenzyme ring angles are found to be correlated to the degree of barrier recrossing. The distance between VAL-203 and the reactive center is found to significantly impact the activation free energy but not the degree of barrier recrossing. This result indicates that the experimentally observed effect of mutating VAL-203 on the enzyme activity is due to the alteration of the equilibrium free energy difference between the transition state and the reactant rather than nonequilibrium dynamical factors. The promoting motion of VAL-203 is characterized in terms of steric interactions involving THR-178 and the coenzyme.

A Quantum Chemical and TST Study of the OH Hydrogen-Abstraction Reaction from Substituted Aldehydes: FCHO and ClCHO

In the present study, ab initio methods have been used to study the OH hydrogen-abstraction reaction from two substituted aldehydes: FCHO and ClCHO. A complex mechanism in which the overall rate depends on the rates of two competitive reactions, a reversible step where a reactant (or prereactive) complex is formed, followed by the irreversible hydrogen abstraction to form the products, is corroborated. This mechanism was previously shown to describe accurately the kinetics of the OH hydrogen-abstraction reaction from formaldehyde and acetaldehyde. Classical transition state theory (TST) rate constants calculated with tunneling corrections, assuming an unsymmetrical Eckart barrier, agree very well with experimental upper bound values. Activation energy barriers and enthalpies of reaction have been estimated through CCSD(T) single point calculations using MP2 geometries and frequencies and the 6-311++G(d,p) basis set.

Molecular Mechanics for Chemical Reactions: A Standard Strategy for Using Multiconfiguration Molecular Mechanics for Variational Transition State Theory with Optimized Multidimensional Tunneling

Multiconfiguration molecular mechanics (MCMM) is an extension of molecular mechanics to chemically reactive systems. This dual-level method combines molecular mechanics potentials for the reactant and product configurations with electronic structure Hessians at the saddle point and a small number of nonstationary points to model the potential energy surface in the reaction swath region between reactants and products where neither molecular mechanics potential is valid. The resulting semiglobal potential energy surface is used as input for dynamics calculations of tunneling probabilities and variational transition state theory rate constants. In this paper, we present a standard strategy for applying MCMM to calculate rate constants for atom transfer reactions. In particular, we propose a general procedure for determining where to calculate the electronic structure Hessians. We tested this strategy for a diverse test suite of six reactions involving hydrogen-atom transfer. It yields reasonably accurate rat...

Anharmonic Semiclassical Variational Transition-State Theory Rate Constant Model for H Atom Association with Different Sites on the Diamond {111} Surface

Canonical variational transition-state theory (CVTST) rate constants, for H atom association to terrace and ledge sites on the diamond {111} surface, are calculated using anharmonic energy levels for the transitional modes orthogonal to the reaction path. The reaction path and transitional modes, required for the calculation, are defined by the reaction path Hamiltonian. A separable Einstein−Brillouin−Keller (EBK) semiclassical quantization model is used to determine anharmonic energy levels for the transitional modes. The free energy, calculated from these anharmonic levels, has multiple maxima along the reaction path, which become more pronounced as the temperature is increased. CVTST association rate constants, calculated from the highest maxima, are somewhat larger than the harmonic CVTST rate constants. A canonical unified statistical theory (UST), which incorporates the effect of the multiple free energy maxima and minima, gives association rate constants in remarkably good agreement with those determined from quasiclassical trajectory calculations. The rate constant for the terrace site is significantly larger than those for the ledge sites. The multiple maxima and minima in the free energy curve result from strong couplings between the transitional bending and surface modes, which changes the eigenvectors for the transitional modes as the reactive system moves along the reaction path. This work illustrates the possible importance of coupling between transitional and conserved modes in VTST calculations for barrierless association reactions.

Capability of LEPS Surfaces to Describe the Kinetics and Dynamics of Non-Collinear Reactions

The popular LEPS surface for collinear reaction paths and a simple bent surface yielding a nonlinear saddle point geometry were used to examine the capability of the LEPS surfaces in describing the kinetics and dynamics of systems with noncollinear reaction paths. The parameters calculated for the atom−diatom Cl + ClH reaction include geometries, vibrational frequencies, and curvatures (to estimate the tunneling effect) along the reaction path, as well as variational transition-state theory rate constants and kinetic isotope effects. The collinear LEPS and the bent surfaces for this triatomic system show similar behavior, so similar behavior in noncollinear polyatomic reactions may be expected, with the consequence of saving time and computational effort.

Ab initio study on the dynamical properties of the hydrogen abstraction reaction NH 2 + OH → NH + H 2 O

The geometry of the transition state of the title reaction was optimized at the unrestricted Hartree–Fock, the spin-unrestricted second-order Moller–Plesset, and the spin-unrestricted quadratic configuration interaction with all single and double substitutions levels of theory. The changes in the geometry, the bound vibrational modes, and the potential energy along the minimum energy path are discussed. Variational transition-state theory rate constants calculated with the tunneling and curvature effect correction agree very well with the experimental values.

Theoretical Studies on the Reaction Path Dynamics and Variational Transition-State Theory Rate Constants of the Hydrogen-Abstraction Reactions of the NH(X3Σ-) Radical with Methane and Ethane

The ground-state imidogen radical, NH(X{sup 3}{Sigma}{sup {minus}}), has received a great deal of attention in recent years because it is an important chain carrier in the combustion of energetic materials. The hydrogen-abstraction reactions of the radical NH(X{sup 3}{Sigma}{sup {minus}}) with methane and ethane have been studied by using ab initio molecular orbital theory and the canonical variational transition-state theory. The geometries of the reactants, transition states, and products were optimized at the UHF, UMP2, UMP4(sdq), and UQCISD levels of theory, and the forward and reverse reaction potential barriers were calculated accurately at the UQCISD/6-311+G(3df,2p) and Gaussian 2 levels. The reaction paths were calculated by the intrinsic reaction coordinate theory at the UMP2/6-311G{sup **} level. The changes of the geometries and generalized normal-mode vibrational frequencies along the IRC were discussed. The energy profile along the IRC was further improved by the Gaussian 2 method. The forward and reverse reaction rate constants for the temperature range from 300 to 2000 K were evaluated by the conventional transition-state theory and the canonical variational transition-state theory with a small curvature tunneling correction. The theoretical rate constants of the forward and reverse reactions are all in good agreement with the experimental ones in the measuredmore » temperature range.« less

Ab initio ground potential energy surface, VTST and QCT study of the O(3P)+CH4(X 1A1)→OH(X 2Π)+CH3(X 2A2″) reaction

An ab initio study of the ground potential energy surface (PES) of the O(3P)+CH4→OH+CH3 reaction has been performed using the second- and fourth-order Mo/ller–Plesset methods with a large basis set. A triatomic analytical ground PES with the methyl group treated as an atom of 15.0 a.m.u. has been derived. This PES has been employed to study the kinetics [variational transition state theory (VTST) and quasiclassical trajectory (QCT) rate constants] and dynamics (QCT method) of the reaction. The ab initio points have also been used directly to calculate the VTST rate constant considering all atoms of the system. The best VTST methods used lead to a good agreement with the experimental rate constant for 1000–2500 K, but QCT rate constant values are about one-third the experimental ones for 1500–2500 K. The cold QCT OH(v=0) rotational distribution arising from the simulation of the reaction with O(3P) atoms produced in the photodissociation of NO2 at 248 nm is in good agreement with experiment, while the very small QCT OH(v=1) population obtained is consistent with measurements. The triatomic PES model derived in this work may be used in studies of the kinetics and dynamics under conditions where the methyl group motions are not strongly coupled to the motions leading to reaction.

An analytical potential energy surface of the HClF (2A′) system based on ab initio calculations. Variational transition state theory study of the H+ClF→F+HCl, Cl+HF and F+HCl→Cl+HF reactions and their deuterium isotope variants

In this work we have carried out abinitio electronic structure calculations on the ground (2A′) potential energy surface (PES) involved in the H(2S)+ClF and the F(2P)+HCl reactions. Transition states and van der Waals minima have been characterized and have been used along with a grid of approximately 3400 abinitio [PUMP2/6-311G(3d2f,3p2d)] points to derive an analytical PES. The global root-mean-square deviation of the fit (2.66 kcal mol-1) is within the range of the estimated abinitio accuracy. The saddle-point energies of this fitted PES were locally scaled to reproduce the thermal rate constants at 300 K of these reactions considering the H isotope. Calculated variational transition state theory rate constants with the inclusion of a microcanonical optimized multidimensional tunneling correction are in good accord with experiments at different temperatures, both for reactions with H and D isotopes. A small H/D kinetic isotope effect is predicted to have a similar extension (kH/kD≈1–2) for the three reactions depending on the temperature and according to the available experimental results.

Variational transition state calculation of the rate constants for the N( 4S u)+O 2(X [formula omitted])→NO(X 2Π)+O( 3P g) reaction and its reverse between 300 and 5000 K

An improved analytical fit of the ground (2A′) potential energy surface (PES) involved in the N+O 2→NO+O reaction and its reverse has been derived. This PES leads to variational transition state theory (VTST) rate constants that are in agreement with the experimental data of both reactions. The substantial improvement achieved for the forward reaction suggests that the new analytical PES should be more adequate than the earlier ones to describe this system.

Activated diffusion of benzene in NaY zeolite: Rate constants from transition state theory with dynamical corrections

We calculated transition state theory and exact rate coefficients for benzene jumps in Na-Y zeolite between 150 and 500 K. This is the first exact flux correlation function rate calculation for a non-spherical molecule inside a zeolite. We calculated rates for jumps between SII and W sites, located near Na ions in 6-rings and in 12-rings windows, respectively. Partition function ratios were calculated using Voter’s displacement vector method. A general Arrhenius behavior is observed over the whole temperature range for all processes. The activation energies are close to the difference between the minimum energies in the sites, and between the sites and the transition states. The calculated prefactors present reasonable values around 1012–1013 s−1, in good agreement with nuclear magnetic resonance relaxation experiments. We were not able to decompose the prefactors into simple vibrational and entropic components, and therefore a complete calculation of the rate constant seems necessary to obtain reliable values. In three of the four types of motions investigated, the transition state theory rate constant is approximately equal to the more exact correlation function rate constant. However, in the case of the W→W jump, transition state theory is qualitatively wrong. This is due to the fact that the minimum energy path from one W site to another is very unstable and intersects the SII→SII minimum energy pathway, so a slight perturbation sends the molecule to a SII site instead of the W site. As a consequence, the prefactor for the W→W jump is found to be almost one order of magnitude smaller than the prefactor for the W→ SII jump, although the activation energies are similar.

Thermochemistry and Thermal Decomposition of the Chlorinated Disilanes (Si2HnCl6-n, n = 0−6) Studied by ab Initio Molecular Orbital Methods

The thermochemistry and thermal unimolecular decomposition reactions of the chlorinated disilanes have been characterized using ab initio molecular orbital techniques. Silylene, chlorosilylene, dichlorosilylene, and hydrogen elimination reactions and their reverse insertions were considered. Reactant, product, and transition-state geometries and vibrational frequencies were calculated at the MP2/6-31G(d,p) level. Energetics were obtained at the MP2/6-31+G(2df,p), MP4/6-31+G(2df,p), G2(MP2), and/or G2 levels of theory, depending on the number of chlorine atoms in the molecule. In addition to the expected insertion reactions, direct reaction paths for SiHCl + SiHnCl4-n h SiH2 + SiHn-1Cl5-n and SiHCl + SiHnCl4-n h SiCl2 + SiHn+1Cl3-n were observed, with energetic barriers lying a few kcal/mol above the insertion reactions. To our knowledge, these concerted, two-atom exchange reactions have not previously been observed or predicted. They appear to represent a new type of elementary reaction for these compounds. Heats of formation for the chlorinated disilane reactants and chlorinated silylsilylene products of hydrogen elimination were calculated using isodesmic reactions. Energy barriers and conventional transition state theory rate constants for all of the reactions are presented. These can provide a basis for the construction of a detailed mechanism for the multistep thermal decomposition of the chlorinated silanes, which plays an important role in the chemical vapor deposition of epitaxial silicon from the chlorinated silanes.