Constraints at the transition state of the D + H2 reaction: quantum bottlenecks vs. stereodynamics

This article presents a quasiclassical trajectory method for the calculation of cumulative reaction probabilities by sampling of the helicity quantum number of the reagents (k). The method is applied to the D + H(2) reaction at various total angular momentum (J) values, and the helicity-resolved quasiclassical cumulative reaction probabilities are compared to their quantum mechanical counterparts. The agreement between the two sets of results is fairly good. In particular, k-dependent, J-independent reaction thresholds found with quantum methods are reproduced by the quasiclassical calculations. The shift of these thresholds with increasing k, which has been previously attributed to the quantum bottleneck states taking part in the reaction, is revisited and discussed also in terms of the reaction stereodynamics.     

Quantum dynamics study of H+NH3-->H2+NH2 reaction

We report in this paper a quantum dynamics study for the reaction H+NH3-->NH2+H2 on the potential energy surface of Corchado and Espinosa-Garcia [J. Chem. Phys. 106, 4013 (1997)]. The quantum dynamics calculation employs the semirigid vibrating rotor target model [J. Z. H. Zhang, J. Chem. Phys. 111, 3929 (1999)] and time-dependent wave packet method to propagate the wave function. Initial state-specific reaction probabilities are obtained, and an energy correction scheme is employed to account for zero point energy changes for the neglected degrees of freedom in the dynamics treatment. Tunneling effect is observed in the energy dependency of reaction probability, similar to those found in H+CH4 reaction. The influence of rovibrational excitation on reaction probability and stereodynamical effect are investigated. Reaction rate constants from the initial ground state are calculated and are compared to those from the transition state theory and experimental measurement.     

Explanation of the unusual temperature dependence of the atmospherically important OH + H(2)S --> H(2)O + HS reaction and prediction of the rate constant at combustion temperatures

Rate constants for the OH + H2S --> H2O + HS reaction, which is important for both atmospheric chemistry and combustion, are calculated by direct dynamics with the M06-2X density functional using the MG3S basis set. Energetics are compared to high-level MCG3/3//MC-QCISD/3 wave function theory and to results obtained by other density functionals. We employ canonical variational transition-state theory with multidimensional tunneling contributions and scaled generalized normal-mode frequencies evaluated in redundant curvilinear coordinates with anharmonicity included in the torsion. The transition state has a quantum mechanically distinguishable, nonsuperimposable mirror image that corresponds to a separate classical reaction path; the effect of the multiple paths is examined through use of a symmetry number and by torsional methods. Calculations with the reference-potential Pitzer-Gwinn treatment of the torsional mode agree with experiment, within experimental scatter, and predict a striking temperature dependence of the activation energy, increasing from -0.1 kcal/mol at 200 K to 0.2, 1.0, 3.4, and 9.8 kcal/mol at 300, 500, 1000, and 2400 K. The unusual temperature dependence arises from a dynamical bottleneck at an energy below reactants, following an addition complex on the reaction path with a classical binding energy of 4.4 kcal/mol. As a way to check the mechanism, kinetic isotope effects of the OH + D2S and OD + D2S reactions have been predicted.     

Reaction rates for O + HD → OH + D and O + HD → OD + H

We have calculated reaction rates for the reactions O + HD → OH + D and O + DH → OD + H using improved canonical variational transition state theory and least-action ground-state transmission coefficients with an ab initio potential energy surface. The kinetic isotope effects are in good agreement with experiment. The optimized tunneling paths and properties of the variational transition states and the rate enhancement for vibrationally excited reactants are also presented and compared with those for the isotopically unsubstituted reaction O + H₂ → OH + H. The thermal reactions at low and room temperature are predicted to occur by tunneling at extended configurations, i.e., to initiate early on the reaction path and to avoid the saddle point regions. Tunneling also dominates the low and room temperature reactions for excited vibrational states, but in these cases the results are not as sensitive to the nature of the tunneling path. Overbarrier mechanisms dominate for both thermal and excited-vibrational state reactions for T > 600 K. For the excited-state reaction (with initial vibrational quantum number n > 0) a transition state switch occurs for T > 1000 K for the O + HD(n = 1) → OD + H case and for T > 1500 K for the O + DH(n = 1) → OD + H reaction, and this may be a general phenomenon for excited-state reactions at higher temperature. In the present case the switch occurs from an early variational transition state where the vibrationally adiabatic approximation is expected to be valid to a tighter variational transition state where nonadiabatic effects are probably important and should be included.     

Rate Coefficients of Roaming Reaction H+MgH Using Ring Polymer Molecular Dynamics

The ring-polymer molecular dynamics (RPMD) was used to calculate the thermal rate coefficients of the multi-channel roaming reaction H+MgH→Mg+H₂. Two reaction channels, tight and roaming, are explicitly considered. This is a pioneering attempt of exerting RPMD method to multi-channel reactions. With the help of a newly developed optimization-interpolation protocol for preparing the initial structures and adaptive protocol for choosing the force constants, we have successfully obtained the thermal rate coefficients. The results are consistent with those from other theoretical methods, such as variational transition state theory and quantum dynamics. Especially, RPMD results exhibit negative temperature dependence, which is similar to the results from variational transition state theory but different from the ones from ground state quantum dynamics calculations.     

Quantum dynamics of H + LiH reaction and its isotopic variants

Time-dependent quantum wave packet dynamics study is carried out to investigate the initial state selected channel specific reactivity of H + LiH collisional system on a new and more accurate ab initio potential energy surface developed by Wernli et al. [J. Phys. Chem. A 113, 1121 (2009)]. The H + LiH reaction proceeds through LiH depletion and H-exchange paths. While the former path is highly exoergic (by ～2.258 eV), the latter path is thermoneutral. State selected and energy resolved integral reaction cross sections and thermal rate constants are reported and compared with the literature data. The reactivity of the LiH depletion channel is found to be greater than the H-exchange channel. Rotational excitation of the reagent LiH molecule causes a decrease of reactivity of both the channels. On the other hand, the vibrational excitation of the reagent LiH decreases the reactivity of the LiH depletion channel and increases the reactivity of the H-exchange channel. The effect of isotopic substitution (H by D) on the reaction dynamics is also examined.     

Semiclassical nonadiabatic dynamics based on quantum trajectories for the O(3P,1D) + H2 system

The O(3P,1D) + H2 --> OH + H reaction is studied using trajectory dynamics within the approximate quantum potential approach. Calculations of the wave-packet reaction probabilities are performed for four coupled electronic states for total angular momentum J = 0 using a mixed coordinate/polar representation of the wave function. Semiclassical dynamics is based on a single set of trajectories evolving on an effective potential-energy surface and in the presence of the approximate quantum potential. Population functions associated with each trajectory are computed for each electronic state. The effective surface is a linear combination of the electronic states with the contributions of individual components defined by their time-dependent average populations. The wave-packet reaction probabilities are in good agreement with the quantum-mechanical results. Intersystem crossing is found to have negligible effect on reaction probabilities summed over final electronic states.     

Ab initio rate constants from hyperspherical quantum scattering: application to H+C2H6 and H+CH3OH

The dynamics and kinetics of the abstraction reactions of H atoms with ethane and methanol have been studied using a quantum mechanical procedure. Bonds being broken and formed are treated with explicit hyperspherical quantum dynamics. The ab initio potential energy surfaces for these reactions have been developed from a minimal number of grid points (average of 48 points) and are given by analytical functionals. All the degrees of freedom except the breaking and forming bonds are optimized using the second order perturbation theory method with a correlation consistent polarized valence triple zeta basis set. Single point energies are calculated on the optimized geometries with the coupled cluster theory and the same basis set. The reaction of H with C2H6 is endothermic by 1.5 kcal/mol and has a vibrationally adiabatic barrier of 12 kcal/mol. The reaction of H with CH3OH presents two reactive channels: the methoxy and the hydroxymethyl channels. The former is endothermic by 0.24 kcal/mol and has a vibrationally adiabatic barrier of 13.29 kcal/mol, the latter reaction is exothermic by 7.87 kcal/mol and has a vibrationally adiabatic barrier of 8.56 kcal/mol. We report state-to-state and state-selected cross sections together with state-to-state rate constants for the title reactions. Thermal rate constants for these reactions exhibit large quantum tunneling effects when compared to conventional transition state theory results. For H+CH3OH, it is found that the CH2OH product is the dominant channel, and that the CH3O channel contributes just 2% at 500 K. For both reactions, rate constants are in good agreement with some measurements.     

Imaging studies of the photodissociation of H2S+ cations. I. Illustrations of the role of nuclear spin

Ion imaging methods have been used to study the dynamics of H(2)(D(2)) molecular elimination from H(2)S(+)(D(2)S(+)) cations following photoexcitation to the A(2)A(1) state in the wavelength range 300相似文献   

State-to-state reaction probabilities within the quantum transition state framework

Rigorous quantum dynamics calculations of reaction rates and initial state-selected reaction probabilities of polyatomic reactions can be efficiently performed within the quantum transition state concept employing flux correlation functions and wave packet propagation utilizing the multi-configurational time-dependent Hartree approach. Here, analytical formulas and a numerical scheme extending this approach to the calculation of state-to-state reaction probabilities are presented. The formulas derived facilitate the use of three different dividing surfaces: two dividing surfaces located in the product and reactant asymptotic region facilitate full state resolution while a third dividing surface placed in the transition state region can be used to define an additional flux operator. The eigenstates of the corresponding thermal flux operator then correspond to vibrational states of the activated complex. Transforming these states to reactant and product coordinates and propagating them into the respective asymptotic region, the full scattering matrix can be obtained. To illustrate the new approach, test calculations study the D + H(2)(ν, j) → HD(ν', j') + H reaction for J = 0.     

Computational study of the ion-molecule reactions involving fluxional cations: CH4+ + H2--> CH5+ + H and isotope effect

Potential energy surfaces for the reactions of CH4+ with H2, HD, and D2 have been calculated using high-level ab initio methods, including coupled cluster theory, complete active space self-consistent field, and multireference configuration interaction. The energies are extrapolated to the complete basis set limit using the basis sets aug-cc-pVXZ (X = D, T, Q, 5, 6). The CH4+ + H2 reaction produces CH5+ and H exclusively. Three types of reaction mechanisms have been found, namely, complex-forming abstraction, scrambling, and S(N)2 displacement. The abstraction occurs via a very minor barrier and it is dominant. The other two mechanisms are negligible because of the significant barriers involved. Quantum phase space theory and variational transition state theory are used to calculate the rate coefficients as a function of temperatures in the range of 5-1000 K. The theoretical rate coefficients are compared with the available experimental data and the discrepancy is discussed. The significance of isotope effect, tunneling effect, and nuclear spin effect is investigated. The title reaction is predicted to be slightly exothermic with DeltaHr = -12.7 +/- 5.2 kJ/mol at 0 K.     

Seven-dimensional quantum dynamics study of the H+NH3-->H2+NH2 reaction

Initial state-selected time-dependent wave packet dynamics calculations have been performed for the H+NH3-->H2+NH2 reaction using a seven-dimensional model and an analytical potential energy surface based on the one developed by Corchado and Espinosa-Garcia [J. Chem. Phys. 106, 4013 (1997)]. The model assumes that the two spectator NH bonds are fixed at their equilibrium values. The total reaction probabilities are calculated for the initial ground and seven excited states of NH3 with total angular momentum J=0. The converged cross sections for the reaction are also reported for these initial states. Thermal rate constants are calculated for the temperature range 200-2000 K and compared with transition state theory results and the available experimental data. The study shows that (a) the total reaction probabilities are overall very small, (b) the symmetric and asymmetric NH stretch excitations enhance the reaction significantly and almost all of the excited energy deposited was used to reduce the reaction threshold, (c) the excitation of the umbrella and bending motion have a smaller contribution to the enhancement of reactivity, (d) the main contribution to the thermal rate constants is thought to come from the ground state at low temperatures and from the stretch excited states at high temperatures, and (e) the calculated thermal rate constants are three to ten times smaller than the experimental data and transition state theory results.     

Stochastic path-integral method for chemical reaction dynamics: Application to the full 3D H3 system

A stochastic path-integral (SPI) technique for chemical reaction dynamics is explored. It is shown that this technique enables the direct computation of the transition amplitude with a finite space-time range, by generating a set of classical paths subject to simultaneous stochastic differential equations. The numerical values of the Boltzmann matrix elements for a harmonic potential are in good agreement with the analytical ones. Within the quantum transition state theory, the flux-flux autocorrelation function is also evaluated at 630 K for the H + H₂ exchange reaction and is found to give a satisfactory agreement with the previous studies. To appraise the influence of the dimensionality, both one-dimensional Eckart potential and a full three-dimensional (3D) Liu-Siegbahn-Truhlar-Horowitz (LSTH) potential calculations have been performed. The calculated values of the Boltzmann matrix elements for the colinear and the full 3D cases are found to deviate slightly from each other in the lower temperature range. The 3D thermal rate constant is in very good agreement with the previous one. © 1996 John Wiley & Sons, Inc.     

Seven dimensional quantum dynamics study of the H2+NH2-->H+NH3 reaction

Initial state-selected time-dependent wave packet dynamics calculations have been performed for the H2+NH2-->H+NH3 reaction using a seven dimensional model on an analytical potential energy surface based on the one developed by Corchado and Espinosa-Garcia [J. Chem. Phys. 106, 4013 (1997)]. The model assumes that the two spectator NH bonds are fixed at their equilibrium values and nonreactive NH2 group keeps C2v symmetry and the rotation-vibration coupling in NH2 is neglected. The total reaction probabilities are calculated when the two reactants are initially at their ground states, when the NH2 bending mode is excited, and when H2 is on its first vibrational excited state, with total angular momentum J=0. The converged cross sections for the reaction are also reported for these initial states. Thermal rate constants and equilibrium constants are calculated for the temperature range of 200-2000 K and compared with transition state theory results and the available experimental data. The study shows that (a) the reaction is dominated by ground-state reactivity and the main contribution to the thermal rate constants is thought to come from this state, (b) the excitation energy of H2 was used to enhance reactivity while the excitation of the NH2 bending mode hampers the reaction, (c) the calculated thermal rate constants are very close to the experimental data and transition state theory results at high and middle temperature, while they are ten times higher than that of transition state theory at low temperature (T=200 K), and (d) the equilibrium constants results indicate that the approximations applied may have different roles in the forward and reverse reactions.     

A coupled states calculation of accurate quantum rate constants for H + H2

In this article we present the results of converged quantum reactivescattering calculations of thermal rate constants for H + H₂ using the Liu-Siegbahn-Truhlar-Horowitz (LSTH) potential energy surface. These calculations are based on the coupled states (CS) approximation wherein rotational states having different body fixed angular momentum projection quantum numbers are decoupled. By comparision with accurate coupled channel results on the Porter-Karplus No. 2 (PK2) potential surface, we estimate that the maximumerror in thermal rate constants arising from both this approximation and from other numerical approximations in the calculation is less than 25%. We also show that the sum over projection quantum numbers Ω associated with the CS calculation may be approximated quite accurately in terms of the Ω = 0 rate constants by assuming that the |Ω| > 0 rate constants differ from Ω = 0 by a shift in activation energy, which reflects the vibrationally adiabatic bending energy associated with each Ω. Comparison of the LSTH rate constants with experiment indicates average errors of 16% and 24% relative to the two modern measurementsof the rate constants for H + H₂. These errors are reduced to 18% and 9% if the CS rate constants are multiplied by exp(0.0065 eV/kT). The expected error (based on recent quantum structure calculations) associated with the 0.425 eV barrier of theLSTH potential surface is 0.0065 eV. Overall, the agreement of either the LSTH or modified LSTH rate constants with experiment is within the 32% maximum disagreement between the two experimental measurements at all butthe lowest temperature that has been studied. Comparison of our CS rate constants with the results from simpler theories is considered using both the LSTH and PK2 potential surfaces. The best overall agreement is with transition state theories that use accurate dynamical methods to calculate tunnelling factors. These include reduced dimensionality quantum dynamics methods and variational transition state theory using either the Marcus-Coltrin or least action ground-state tunnelling paths. Comparison with the results of quasiclassical trajectory calculations indicates substantial errors at low temperatures.     

Exact quantum mechanical reaction probabilities for the collinear H + H2 reaction on a porter-karplus potential energy surface

Exact quantum mechanical calculation of the reaction probability for the collinear H + H₂ reaction on a Porter-Karplus potential energy surface are carried out by the finite-difference boundary value method at 6 energes in the threshold region and compared to close coupling, distorted wave, classical S matrix, transition state theory, and vibrational adiabatic calculations.     

变分过渡态理论对H＋H2及其同位素选态反应的研究

将选态速度常数的计算推广到任意指定反应物、过渡态的振动激发态.用此法计算了H+H_2(v)及其同位素经不同振动激发过渡态时的速度常数,发现弯曲振动模激发所得结果与实验值更符合,并且在给定能量下,过渡态的弯曲振动模激发比其对称伸缩模激发更有利于反应进行.     

Quantum and classical studies of the O(3P) + H2(v = 0-3,j = 0) --> OH + H reaction using benchmark potential surfaces

We present results of time-dependent quantum mechanics (TDQM) and quasiclassical trajectory (QCT) studies of the excitation function for O(3P) + H2(v = 0-3,j = 0) --> OH + H from threshold to 30 kcal/mol collision energy using benchmark potential energy surfaces [Rogers et al., J. Phys. Chem. A 104, 2308 (2000)]. For H2(v = 0) there is excellent agreement between quantum and classical results. The TDQM results show that the reactive threshold drops from 10 kcal/mol for v = 0 to 6 for v = 1, 5 for v = 2 and 4 for v = 3, suggesting a much slower increase in rate constant with vibrational excitation above v = 1 than below. For H2(v > 0), the classical results are larger than the quantum results by a factor approximately 2 near threshold, but the agreement monotonically improves until they are within approximately 10% near 30 kcal/mol collision energy. We believe these differences arise from stronger vibrational adiabaticity in the quantum dynamics, an effect examined before for this system at lower energies. We have also computed QCT OH(v',j') state-resolved cross sections and angular distributions. The QCT state-resolved OH(v') cross sections peak at the same vibrational quantum number as the H2 reagent. The OH rotational distributions are also quite hot and tend to cluster around high rotational quantum numbers. However, the dynamics seem to dictate a cutoff in the energy going into OH rotation indicating an angular momentum constraint. The state-resolved OH distributions were fit to probability functions based on conventional information theory extended to include an energy gap law for product vibrations.     

Strange Kinetics of the C(2)H(6) + CN Reaction Explained

In this paper, we employ state of the art quantum chemical and transition state theory methods in making a priori kinetic predictions for the abstraction reaction of CN with ethane. This reaction, which has been studied experimentally over an exceptionally broad range of temperature (25-1140 K), exhibits an unusually strong minimum in the rate constant near 200 K. The present theoretical predictions, which are based on a careful consideration of the two distinct transition state regimes, quantitatively reproduce the measured rate constant over the full range of temperature, with no adjustable parameters. At low temperatures, the rate-determining step for such radical-molecule reactions involves the formation of a weakly bound van der Waals complex. At higher temperatures, the passage over a subthreshold saddle point on the potential energy surface, related to the formation and dissolution of chemical bonds, becomes the rate-determining step. The calculations illustrate the changing importance of the two transition states with increasing temperature and also clearly demonstrate the need for including accurate treatments of both transition states. The present two transition state model is an extension of that employed in our previous work on the C2H4 + OH reaction [J. Phys. Chem. A 2005, 109, 6031]. It incorporates direct ab initio evaluations of the potential in classical phase space integral based calculations of the fully coupled anharmonic transition state partition functions for both transition states. Comparisons with more standard rigid-rotor harmonic oscillator representations for the "inner" transition state illustrate the importance of variational, anharmonic, and nonrigid effects. The effects of tunneling through the "inner" saddle point and of dynamical correlations between the two transition states are also discussed. A study of the kinetic isotope effect provides a further test for the present two transition state model.