Approximate quantum calculation of the dynamics of gas-phase reactions of a light-atom transfer in the tunnelling energy region (original) (raw)
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Journal of Physical Organic Chemistry, 2010
Arrhenius curves of selected hydrogen transfer reactions in organic molecules and enzymes are reviewed with the focus on systems exhibiting temperature‐independent kinetic isotope effects. The latter can be rationalized in terms of a ‘pre‐tunneling state’ which is formed from the reactants by heavy atom motions and which represents a suitable molecular configuration for tunneling to occur. Within the Bell–Limbach tunneling model, formation of the pre‐tunneling state dominates the Arrhenius curves of the H and the D transfer even at higher temperatures if a large energy Em is required to reach the pre‐tunneling state. Tunneling from higher vibrational levels and the over‐barrier reaction via the transition state which lead to temperature‐dependent kinetic isotope effects dominate the Arrhenius curves only if Em is small compared to the energy of the transition state. Using published data on several hydrogen transfer systems, the type of motions leading to the pre‐tunneling state is e...
Large Tunnelling Corrections in Chemical Reaction Rates
Advances in Chemical Physics, 2007
In terms of certain lengths near the saddlepoint of an activated complex relative to the de Broglie wave length of the atom being transferred, the reaction coordinate of bimolecular atom-transfer reactions is profitably classified as: (1) essentially classical, (2) essentially separable or (3) non-separable. In terms of the location of the saddlepoint and energy-distance curvatures through the saddlepoint, simple general rate expressions for case 1 and case 2 are given, including a small degree of tunnelling, utilizing the recent general method (ref. 6) of evaluating the configuration integral of any molecule. Hydrogen atom transfer reactions below several hundred degrees centigrade are in the region of non-separable reaction coordinates. For these cases more information about the potential energy surface is needed than the saddlepoint geometry and curvatures. Sample calculations using the Sato-potential energy surface for Ha, as evaluated by Weston, illustrate an approximate method for treating non-separable reactions, including large degrees of non-separable tunnelling. The hydrogendeuterium isotope effect in reactions of methyl radicals with hydrocarbons is worked out in detail, and this method of handling large degrees of tunnelling appears to agree with the experimental data over a wide temperature range (aithough there is large experimental error).
The Journal of Chemical Physics, 2000
We report results of quantum wave packet calculations of the O( 1 D)ϩHCl(vϭ0,j)→ClOϩH, OHϩCl, reactions for zero and nonzero total angular momentum, J, ͑using the centrifugal sudden approximation͒, and using a new fit to extensive ab initio calculations of a global potential ͓K. A. Peterson, S. Skokov, and J. M. Bowman, J. Chem. Phys. 111, 2445 ͑1999͔͒. Initial state-selected and cumulative reaction probabilities to form each set of products for Jϭ0 are calculated by a direct summation of the initial state-selected reaction probabilities. We propose and test a simple energy-shifting approximation that relates the initial state-selected reaction probability for arbitrary j to the one for jϭ0. Extensions of standard J-and K-shifting methods are suggested and applied to both reaction channels. In doing this extension the adiabatic rotation approximation is used to determine the rotational barriers in the entrance and exit channels. The energy dependence of the reaction cross sections to form the two products is calculated for O( 1 D)ϩHCl(vϭ0,jϭ0) using Jand K-shifting and compared at two translational energies to results of quasiclassical trajectory calculations. The thermal rate constants for the two reaction channels are calculated from 200 to 400 K and compared to experiment.
Accurate time dependent wave packet calculations for the N + OH reaction
The Journal of Chemical Physics, 2011
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A formulation is presented for the application of tools from quantum chemistry and transition-state theory to phenomenologically cover cases where reaction rates deviate from Arrhenius law at low temperatures. A parameter d is introduced to describe the deviation for the systems from reaching the thermodynamic limit and is identified as the linearizing coefficient in the dependence of the inverse activation energy with inverse temperature. Its physical meaning is given and when deviation can be ascribed to quantum mechanical tunneling its value is calculated explicitly. Here, a new derivation is given of the previously established relationship of the parameter d with features of the barrier in the potential energy surface. The proposed variant of transition state theory permits comparison with experiments and tests against alternative formulations. Prescriptions are provided and implemented to three hydrogen transfer reactions: CH 4 1 OH ! CH
Interesting discussions with the members of the Quantum Reactive Scattering (QRS) group of interest is acknowledged. The work illustrated here has been financially supported by MIUR, ASI, CNR and COST Chemistry (Action D23). Specific mention needs to be made to Italian Space Agency (Project ASI PQE2000) and the Italian MIUR FIRB Grid.it project (RBNE01KNFP) on High performance Grid Platforms and Tools, and to the MIUR CNR Strategic Project L 499/97-2000 on High performance Distributed Enabling Platforms.
The Journal of Chemical Physics, 2011
On a recent analytical potential energy surface developed by two of the authors, an exhaustive kinetics study, using variational transition state theory with multidimensional tunneling effect, and dynamics study, using both quasi-classical trajectory and full-dimensional quantum scattering methods, was carried out to understand the reactivity of the NH 3 + H → NH 2 + H 2 gas-phase reaction. Initial state-selected time-dependent wave packet calculations using a full-dimensional model were performed, where the total reaction probabilities were calculated for the initial ground vibrational state and for four excited vibrational states of ammonia. Thermal rate constants were calculated for the temperature range 200-2000 K using the three methods and compared with available experimental data. We found that (a) the total reaction probabilities are very small, (b) the symmetric and asymmetric N-H stretch excitations enhance the reactivity, (c) the quantum-mechanical calculated thermal rate constants are about one order of magnitude smaller than the transition state theory results, which reproduce the experimental evidence, and (d) quasi-classical trajectory calculations, which were performed with the main goal of analyzing the influence of the zero-point energy problem on the final dynamics results, reproduce the quantum scattering calculations on the same surface.
Computer Physics Communications, 1987
We present a computer program for calculating rate constants of gas.phase chemical reactions involving one or two reactants with a total of three to ten atoms. The program accepts information about the potential energy surface in the form of either an analytic potential energy function or a sequence of geometries, energies, gradients and second (or higher) derivative matrices at points along the reaction path. In the former case the program itself calculates the reaction path and the sequence of derivative matrices. From this information the program calculates the rate constant for quantized internal degrees of freedom and classical reaction-path motion by variational transition state theory (VTST). The probabilities for tunneling and nonclassical reflection are estimated by semiclassical methods and incorporated by a transmission coefficient, which for thermal reactions is based on the ground state. There are several options for including the effects of anharmonicity in the independent-normal-mode approximation, and the reaction-path curvature may be included in the tunneling calculation by the small-curvature approximation. The article also presents test calculations illustrating the use of new reaction-path interpolation and extrapolation procedures which should be useful in conjunction with VTST calculations based on ab initio gradients and Hessian calculations.
Journal of Chemical Theory and Computation, 2005
We present a new algorithm for carrying out large-curvature tunneling calculations that account for extreme corner-cutting tunneling in hydrogen atom, proton, and hydride transfer reactions. The algorithm is based on two-dimensional interpolation in a physically motived set of variables that span the space of tunneling paths and tunneling energies. With this new algorithm, we are able to carry out density functional theory direct dynamics calculations of the rate constants, including multidimensional tunneling, for a set of hydrogen atom transfer reactions involving 9-15 atoms and up to 7 nonhydrogenic atoms. The reactions considered involve the abstraction of a hydrogen atom from hydrocarbons by a trifluoromethyl radical, and in particular, we consider the reactions of CF 3 with CH 4 , C 2 H 6 , and C 3 H 8 . We also calculate several kinetic isotope effects. The electronic structure is treated by the MPWB1K/6-31+G(d,p) method, which is validated by comparison to experimental results and to CBS-Q, MCG3, and G3SX(MP3) calculations for CF 3 + CH 4 . Harmonic vibrational frequencies along the reaction path are calculated in curvilinear coordinates with scaled frequencies, and anharmonicity is included in the lowest-frequency torsion.