Transition State Theory Study Research Articles

The effect of surface relaxation on the N2 dissociation rate on stepped Ru: A transition state theory study

The interaction between N2 and the surface results in a considerable rearrangement of the structure of the surface near the steps. The present work investigates the effect of this interaction on the rate of dissociative adsorption within the framework of harmonic transition state theory. Employing different models where selected Ru degrees of freedom are included, we show that the dominant effect of surface relaxation is a shift of the classical barrier height. Therefore, the “relaxed/N2” model, which takes relaxation of the surface into account but neglects vibrations of the surface atoms explicitly, can be used for reliable rate constant calculations. Sticking coefficients calculated employing the relaxed/N2 model based on different density-functional theory (DFT) calculations are then compared with experiment. Comparison with the experiment suggests that for the best DFT calculations the barrier height (0.49eV) is about 0.15eV too high.

Variational Transition-State Theory Study of the Dimethyl Sulfoxide (DMSO) and OH Reaction

The mechanism for the atmospheric oxidation of DMSO has been studied. For the first time, all the possible channels in the DMSO + OH reaction are studied together theoretically, and their corresponding rate constants have been evaluated under the variational transition-state formalism. Three different channels have been characterized: an addition-elimination process to form MSIA (CH3SOOH) and CH3, a H-abstraction pathway to give CH3SOCH2 and H2O, and a nonkinetically relevant S(N)2-type reaction to form methanol and CH3SO. In agreement with previous experimental and theoretical works, the main product in the DMSO + OH reaction turns out to be the MSIA, with a branching ratio at 298.15 K around 97%. The effects of pressure in the global rate constant have also been analyzed.

Ab initio and transition state theory studies of the energetics of H atom resurfacing on Ni(1 1 1)

Ab initio methods based on density functional theory are used to compute the potential energy surface for the motion of H from the subsurface onto the Ni(1 1 1) surface. Transition state theory is used to calculate rate constants for this resurfacing. The influences of tunneling and lattice relaxation are computed and discussed, and comparisons are made with measured vibrational and thermal desorption spectra. Due to the metastable nature of the subsurface octahedral site, the resurfacing H has an excess energy of roughly 1 eV. The resulting hot and highly mobile atoms can engage in unique chemistry with surface-adsorbed species.

Quasiclassical Trajectory and Transition State Theory Studies of the N(4S) + H2 ↔ NH(X3Σ-) + H Reaction

Detailed forward and reverse quasiclassical trajectory and variational transition state theory studies of the title reaction are presented. The potential energy surface (PES) has been calculated at the MCQDPT2// FORS-MCSCF(7,6)/6-311++G * * level of theory using GAMESS. Selection of points and analytical interpolation of the surface was done using the GROW program of Collins, Thompson, Jordan, and Bettens. Broad ranges of translational energies, and ground and excited rovibrational energy levels (v,j) are chosen as initial conditions of the reactant molecules. All three reactions considered in this study (e.g., N + H 2 and NH + H abstraction and exchange) show angular distributions that are backward peaked. Both the forward ion and the exchange reactions show product vibrational distributions that are dominated by the ground state, whereas the reverse reaction prefers v' = 1 for trajectories initiated at low E T . The rate constants for the forward and reverse reactions were found to be in good accord with available experimental and theoretical data and can be expressed in the Arrhenius form as k(T) = 6.85 x 10 - 1 0 exp(-25.9(kcal/mol)/RT) and k(T) = 1.85 x 10 - 1 4 T 1 . 0 7 exp(-2.2(kcal/mol)/RT) cm 3 molecule - 1 s - 1 , respectively. For ICVT results, these rate constants can be similarly expressed as k(T) = 5.52 x 10 - 1 0 exp(-32.4(kcal/mol)/RT) and k(T) = 1.56 x 10 - 1 6 T 1 . 6 4 exp(-0.7(kcal/mol)/RT) cm 3 molecule - 1 s - 1 , respectively. The reasonable agreement with the available data substantiates the sufficiency of the computational methods employed in this study.

Ab initio, variational transition state theory and quasiclassical trajectory study on the lowest A′2 potential energy surface involved in the N(2D)+O2(X 3Σg−)→O(3P)+NO(X 2Π) atmospheric reaction

A CASSCF and CASPT2 ab initio study has been carried out for the lowest A′2 potential energy surface (2 2A′ PES) that correlates reactants and products of the N(2D)+O2→O(3P)+NO reaction. All the stationary points have been characterized and along with a grid of more than 600 ab initio points have been fitted to an analytical function. Afterwards, this analytical PES has been employed to study the kinetics [variational transition state theory (VTST) and quasiclassical trajectory (QCT) methods] and dynamics (QCT method) of the reaction. Concerning the rate constants, a good agreement with the experimental values corresponding to the global deactivation of N(2D) has been obtained. This suggests that this reaction is responsible of most of the reactivity of the N(2D)+O2 system. NO vibrational distributions have also been calculated. Although there is not a good agreement between the theoretical and experimental values, preliminary results show that they can become quite close by taking into account the contribution of the 1 2A″ PES.

Variational transition state theory and quasiclassical trajectory studies of the H2+OH→H+H2O reaction and some isotopic variants

Variational transition state theory (VTST) methods and quasiclassical trajectories (QCT) have been used to study the dynamics of the OH+H2 reaction, along with the isotopic counterparts OD+H2, OH+HD, OD+H2, OD+D2, and the reverse H+H2O→H2+OH reaction. Two new global analytical potential energy surfaces (PES) for H3O are employed, Wu, Schatz, Lendvay, Fang, Harding (WSLFH) and Ochoa, Clary (OC), both of which are based on high quality electronic structure calculations. Extensive comparisons with earlier results based on the Walch, Dunning, Schatz, Elgersma (WDSE) PES are also presented. The WSLFH PES surface, in combination with our best VTST estimate (ICVT/μOMT), yields rate constants for OH+H2 in quantitative agreement with experiment, while the OC PES yields somewhat less accurate results. The agreement with the OH+D2 experimental rate constants is less quantitative, but the WSLFH PES rate constant agrees with experiment to within a factor of 2 at all temperatures for which there are measurements. The OH+HD, OD+H2, and OD+D2 WSLFH PES rate constants calculated at the ICVT/μOMT level are in very good agreement with the less detailed experimental information that is available for these isotopes. The two surfaces give comparable predictions for the reverse H+H2O reaction at high temperatures, with deviations of less than 30%. This good agreement is maintained by the WSLFH PES at room temperature, while the OC PES predicts rate constants one order of magnitude larger than experiment. The QCT excitation functions for OH+H2, OH+D2, and OH+HD are well below experiment for both potentials, as was the case for earlier accurate quantum mechanical calculations that employed the WDSE PES. The WSLFH PES improves the agreement with the experimental vibrational state selected rate constants for the OH+H2 reaction compared to the WDSE PES. OC is also less accurate and presents antithreshold behavior for H2(v=1)+OH. H2 and OH rotational excitation have opposing effects: while rotation in H2 promotes reactivity, OH rotation impedes it. This impeding effect applies likewise to HD for high rotational excitation, explaining the selectivity toward HOH+D products in the OH+HD 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.

Role of the Surface Site in the Kinetics of H Atom Association with Diamond Surfaces

The reaction path Hamiltonian model and the MAPS/HDIAM analytic potential energy function were used in a canonical variational transition state theory (CVTST) study of H atom association with diamond surfaces. CVTST rate constants are compared for H atom association with a terrace site on the diamond {111} surface and two ledge sites on this surface. The CVTST association rate constant is largest for the terrace site and is 3.9 and 2.4 times larger than the rate constant for one of the ledge sites at 300 and 2000 K, respectively. Nonbonded interactions between the associating H atom and surface H atoms decrease the attractiveness and increase the repulsiveness of the radial and angular potentials, respectively, along the association reaction path. The CVTST rate constants are found to be in good agreement with classical trajectory rate constants, also calculated for the MAPS/HDIAM potential. This study shows how nonbonded interactions and steric effects may affect rate constants for diamond surfaces.

A theoretical analysis of the reaction of H with C 2H 5

The interaction of H with C2H5 is analyzed at the CAS+1+2 level using a correlation-consistent polarized valence double zeta basis set. These ab initio calculations show three barrierless pathways two leading to association and one for abstraction. The association channels are substantially more attractive than the abstraction one and thus dominate the kinetics. An analytic representation of the ab initio data is implemented in a variable reaction coordinate transition state theory study of the temperature dependence of the association kinetics. These theoretical estimates for the high pressure association rate constant are directly compared with related experimental measurements in an effort to resolve the discrepancy between recent and earlier results.

A combined quantum chemical and transition state theory study of the C2H+2+CH4 reaction dynamics

The stationary points of importance in the initial branching between complex formation and H transfer in the reaction of acetylene cation with methane are studied at the Gaussian-2 level of theory. Three separate C2H+2...CH4 ion-neutral complexes are found. One complex leads smoothly to the bridged form of C2H+3 plus CH3. A slightly exothermic saddlepoint also connects this ‘‘bridged’’ complex to a stable C3H+6 species. A ‘‘classical’’ complex leads to the more endothermic classical form of C2H+3. These classical and bridged ion-neutral complexes are nearly degenerate and are directly connected via a low energy saddlepoint which is substantially exothermic relative to reactants. The third, more weakly bound complex, is of a more electrostatic nature and appears to be of no importance in the subsequent branching between the C3H+6 and C2H+3+CH3 products. Transition state theory calculations employing the ab initio determined energetics and quadratic force fields provide estimated reactive cross sections which are in qualitative accord with recent experimental data. The quantitative discrepancies may be explained on the basis of the neglect of anharmonicites and/or errors in the estimated energetics. Consideration of the vibrational frequencies for the various stationary points provides a qualitative explanation for the observed variations in the reaction cross sections with initial vibrational excitations in the CC stretching and bending modes of C2H+2.

Canonical flexible transition state theory revisited

A simple formula for the canonical flexible transition state theory expression for the thermal reaction rate constant is derived that is exact in the limit of the reaction path being well approximated by the distance between the centers of mass of the reactants. This formula evaluates classically the contribution to the rate constant from transitional degrees of freedom (those that evolve from free rotations in the limit of infinite separation of the reactants). As a result of this treatment, the formula contains the product of two factors: one that exclusively depends on the collision kinematics and one that exclusively depends on the potential energy surface that controls the transitional degrees of freedom. This second factor smoothly varies, in the classical limit, from harmonic oscillator to hindered rotor to free rotor partition functions as the potential energy surface varies from quadratic to sinusoidal to a constant in its dependence on the relative orientation angles of the fragments. An application to the recombination of CH3+H essentially demonstrates exact agreement with a previous flexible transition state theory study in which all integrals are carried out numerically. The simple formulas presented in this paper allow the classical inclusion of large amplitude motion of arbitrary complexity in the determination of the canonical rate constant for reactions whose reaction path is dominated by the distance between the centers of mass of the reactants.

The quantum dynamics of hydrogen and deuterium on the Pd(111) surface: A path integral transition state theory study

The surface diffusion constant for hydrogen and deuterium on the palladium(111) surface is calculated using quantum mechanical transition state theory. The rate constants for diffusion into the subsurface layer are also calculated. Quantum effects are seen to be most important for the surface/subsurface transition and cause an inverse isotope effect in which the rate for deuterium is greater than the rate for hydrogen. The results of ground and excited state wave function calculations show localized hydrogenic states, despite large zero point energies, and that the preferred binding site can vary with isotope between surface and subsurface sites. In addition, estimates of the tunneling rate between the surface and subsurface are in qualitative agreement with the low temperature transition state results.

Experimental and transition-state theory studies of the gas-phase reactions of monochloroaluminum with nitrous oxide, carbon dioxide, and sulfur dioxide

The high-temperature fast-flow reactor technique has been used to make kinetic measurements. A weighted fit to the AlCl+N 2 O data gives k(700-990 K)=5.6×10 -11 exp(-7380 K/T) cm 3 molecule -1 s -1 . A weighted fit to the AlCl+CO 2 measurements leads to the expression k(900-1790 K)=4.4×10 -23 (T/K 3.0 exp(-3900 K/T) cm 3 molecule -1 s -1 . 2σ accuracy limits are about ±25%. An upper limit k(800-1100 K)<5×10 -14 cm 3 molecule -1 s -1 has been determined for the AlCl+SO 2 reaction

Multiple transition states in chemical reactions: Variational transition state theory studies of the HO2 and HeH+2 systems

The results of a microcanonical variational transition state theory study of the HO2 and HeH+2 systems are reported. The calculations were carried out using a modification of the Wardlaw–Marcus flexible transition state theory method in which the sum of states N(E,R) is calculated directly. For the HO2 system, the results obtained using the Melius–Blint potential surface are in excellent agreement with previously reported variational transition state theory calculations of Rai and Truhlar on this system. In particular, two transition states were found for the HO2→OH+O half-reaction. However, calculations using the Lemon–Hase surface produced only one transition state. From calculations carried out on surfaces constructed by combining the two original surfaces and calculations carried out using an orbiting transition state variational model (i.e., ignoring the angular part of the potential), it is shown conclusively that the two transition states found for the Melius–Blint surface arise from the peculiar shape of the minimum reaction path for this surface. Also, the orbiting transition state calculations suggest that phase space theory can describe this half-reaction on the Lemon–Hase surface over a large energy range provided that the potential along the minimum reaction path is used in the phase space theory calculations. Other calculations, in which the parameters of the Lemon–Hase surface were adjusted, were also carried out in order to determine the conditions necessary to support multiple transition states. The results of these calculations suggest that multiple transition states are more likely to occur when a strong bottleneck is present in the angular part of the potential, especially when the intermediate complex exists in a shallow well. These predictions were confirmed by the results obtained for the HeH+2 system using the McLaughlin–Thompson–Joseph–Sathyamurthy surface. Two transition states were found for the HeH+2→HeH++H half-reaction and calculations using the orbiting model showed that the origin of the multiple transition states is not the minimum reaction path as in the case of the Melius–Blint surface. Furthermore, the energy at which ‘‘transition state switching’’ occurs is in reasonable accord with the energy at which phase space theory calculations begin to diverge from the experimental data on the cross section for this system. Lifetime calculations for the pseudocomplex lying between the two transition states suggest that the observation of multiple transition states may be possible using femtosecond transition state spectroscopy. Finally, calculations on the HeH+2→He+H+2 half-reaction showed that one transition state exists for this half-reaction at low energy, while at higher energy there are no transition states.

Monte Carlo variational transition-state theory study of recombination and desorption of hydrogen on Si(111)

A variational transition-state theory study of the recombination/desorption rate of H2 from a Si(111) surface using a previously described Monte Carlo procedure [J. Chem. Phys. 83, 1389 (1985)] is reported. The potential-energy surface is expressed as the sum of a lattice potential, a lattice-adatom interaction term, and an adatom–adatom interaction. Keating’s formulation with the parameters suggested by Weber is used for the lattice potential. The adatom–lattice term is written as a pairwise sum of 60 Morse potentials each multiplied by a hyperbolic switching function that limits each absorption site to one bond. The adatom–adatom interaction is the product of an H2 Morse potential and a switching function that attenuates the H–H interaction as the Si–H bonds form. The parameters of the potential are adjusted to fit the results of hydrogen atom–silicon cluster calculations, the experimental and theoretical results for the H2 insertion barrier into Si and SiH2, and the measured H2(g) bond dissociation energy, fundamental frequency, and equilibrium bond distance. The minimum-energy path is obtained using a Monte Carlo random walk procedure with importance sampling. The potential surface predicts a 2.52 eV barrier for H2 recombination/desorption and a 0.182 eV barrier to the back reaction. Variational rate calculations are carried out by expressing the dividing surface as a linear combination of the recombination/desorption coordinates and minimizing the computed flux across the surface with respect to the expansion coefficients using a partial grid search. An Arrhenius plot of the minimized flux yields an activation energy and a frequency factor of 2.41 eV and 0.202 cm2 s, respectively. This activation energy is in good agreement with one reported experimental value and is 0.60 eV greater than that found in two other experiments. The frequency factor lies in the middle of the range of the reported experimental values.

Quasiclassical trajectory (and variational transition state theory) study of the rates and temperature-dependent activation energies of the reactions Mu+H2 (completely thermal) and H, D, and Mu+H2 (v=0, j=2)

We report forward and backward quasiclassical trajectory calculations of the rate constant for the reaction Mu+H2→MuH+H at 444–2400 K. The accuracy of the calculations is assessed by comparison to variational transition state theory, both with and without tunneling contributions, and to experiment. We find the backward trajectory calculations are more accurate, as would be expected since the dynamical bottleneck occurs towards the products in the Mu+H2 reaction. Both the reverse trajectory calculations and the variational transition state theory calculations including tunneling agree with the experimental rate constants within a factor of about 2, which is considered very good agreement. We also report trajectory calculations and variational transition state theory calculations for the temperature-dependent activation energy, which increases by about 4 kcal/mol over the temperature range studied. To aid in the interpretation of this temperature dependence and that found in previous studies for H+H2 and D+H2, we also report temperature-dependent activation energies for the three state-selected rate constants H(D,Mu)+H2(v=0, j=2) →H2(HD,HMu)+H.