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.     

Computation of correlation functions and wave function projections in the context of quantum trajectory dynamics

The de Broglie-Bohm formulation of the Schrodinger equation implies conservation of the wave function probability density associated with each quantum trajectory in closed systems. This conservation property greatly simplifies numerical implementations of the quantum trajectory dynamics and increases its accuracy. The reconstruction of a wave function, however, becomes expensive or inaccurate as it requires fitting or interpolation procedures. In this paper we present a method of computing wave packet correlation functions and wave function projections, which typically contain all the desired information about dynamics, without the full knowledge of the wave function by making quadratic expansions of the wave function phase and amplitude near each trajectory similar to expansions used in semiclassical methods. Computation of the quantities of interest in this procedure is linear with respect to the number of trajectories. The introduced approximations are consistent with approximate quantum potential dynamics method. The projection technique is applied to model chemical systems and to the H+H(2) exchange reaction in three dimensions.     

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.     

Kinetics and dynamics of the NH3 + H → NH2 + H2 reaction using transition state methods, quasi-classical trajectories, and quantum-mechanical scattering

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.     

A full dimensional, nine-degree-of-freedom, time-dependent quantum dynamics study for the H2+C2H reaction

A full dimensional, nine-degree-of-freedom (9DOF), time-dependent quantum dynamics wave packet approach is presented for the study of the H2+C2H-->H+C2H2 reaction system. This is the first full dimensional quantum dynamics study for a diatom-triatom reaction system. The effects of the initial vibrational and rotational excitations of the reactants on the reactivity of this reaction are investigated. This study shows that vibrational excitations of H2 enhance the reactivity; whereas, the vibrational excitations of C2H only have a small effect on the reaction probability. In addition, the bending excitations of C2H, compared to the ground state reaction probability, hinder the reactivity. Comparison of the ground state reaction probabilities of the 9DOF and 8DOF shows the reaction probability from the full dimensional calculation is larger, with more prominent resonance features.     

State-to-state reactive scattering in six dimensions using reactant-product decoupling: OH + H2 → H2O + H (J = 0)

We extend to full dimensionality a recently developed wave packet method [M. T. Cvitas? and S. C. Althorpe, J. Phys. Chem. A 113, 4557 (2009)] for computing the state-to-state quantum dynamics of AB + CD → ABC + D reactions and also increase the computational efficiency of the method. This is done by introducing a new set of product coordinates, by applying the Crank-Nicholson approximation to the angular kinetic energy part of the split-operator propagator and by using a symmetry-adapted basis-to-grid transformation to evaluate integrals over the potential energy surface. The newly extended method is tested on the benchmark OH + H(2) → H(2)O + H reaction, where it allows us to obtain accurately converged state-to-state reaction probabilities (on the Wu-Schatz-Fang-Lendvay-Harding potential energy surface) with modest computational effort. These methodological advances will make possible efficient calculations of state-to-state differential cross sections on this system in the near future.     

A quantum wave packet dynamics study of the N(2D) + H2 reaction

We report a dynamics study of the reaction N((2)D) + H(2) (v=0, j=0-5) --> NH + H using the time-dependent quantum wave packet method and a recently reported single-sheeted double many-body expansion potential energy surface for NH(2)(1(2)A' ') which has been modeled from accurate ab initio multireference configuration-interaction calculations. The calculated probabilities for (v=0, j=0-5) are shown to display resonance structures, a feature also visible to some extent in the calculated total cross sections for (v=0, j=0). A comparison between the calculated centrifugal-sudden and coupled-channel reaction probabilities validate the former approximation for the title system. Rate constants calculated using a uniform J-shifting scheme and averaged over a Boltzmann distribution of rotational states are shown to be in good agreement with the available experimental values. Comparisons with other theoretical results are also made.     

Multidimensional reactive scattering with quantum trajectories: dynamics with Morse vibrational modes

The reactive scattering of a wave packet is studied by the quantum trajectory method for a model system with up to 25 Morse vibrational modes. The equations of motion are formulated in curvilinear reaction path coordinates with the restriction to a planar reaction path. Spatial derivatives are evaluated by the least squares method using contracted basis sets. Dynamical results, including trajectory evolution and time-dependent reaction probabilities, are presented and analyzed. For the case of one Morse vibrational mode, the results are in good agreement with those derived through direct numerical integration of the time-dependent Schrodinger equation.     

Accurate time dependent wave packet calculations for the N + OH reaction

We present accurate quantum calculations of state-to-state cross sections for the N + OH → NO + H reaction performed on the ground (3)A' global adiabatic potential energy surface of Guadagnini et al. [J. Chem. Phys. 102, 774 (1995)]. The OH reagent is initially considered in the rovibrational state ν = 0, j = 0 and wave packet calculations have been performed for selected total angular momentum, J = 0, 10, 20, 30, 40,...,120. Converged integral state-to-state cross sections are obtained up to a collision energy of 0.5 eV, considering a maximum number of eight helicity components, Ω = 0,...,7. Reaction probabilities for J = 0 obtained as a function of collision energy, using the wave packet method, are compared with the recently published time-independent quantum mechanical one. Total reaction cross sections, state-specific rate constants, opacity functions, and product state-resolved integral cross-sections have been obtained by means of the wave packet method for several collision energies and compared with recent quasi-classical trajectory results obtained with the same potential energy surface. The rate constant for OH(ν = 0, j = 0) is in good agreement with the previous theoretical values, but in disagreement with the experimental data, except at 300 K.     

Using redundant coordinates to represent potential energy surfaces with lower-dimensional functions

We propose a method for fitting potential energy surfaces with a sum of component functions of lower dimensionality. This form facilitates quantum dynamics calculations. We show that it is possible to reduce the dimensionality of the component functions by introducing new and redundant coordinates obtained with linear transformations. The transformations are obtained from a neural network. Different coordinates are used for different component functions and the new coordinates are determined as the potential is fitted. The quality of the fits and the generality of the method are illustrated by fitting reference potential surfaces of hydrogen peroxide and of the reaction OH+H(2)-->H(2)O+H.     

Quantum dynamics study on multichannel dissociation and isomerization reactions of formaldehyde

We study quantum dynamics of the multichannel reactions of H(2)CO including the molecular and radical dissociation channels as well as the isomerization ones, H(2)CO-->trans-HCOH and trans-HCOH-->cis-HCOH. For this purpose, the previously developed potential energy function [T. Yonehara and S. Kato, J. Chem. Phys. 117, 11131 (2002)] is refined to give accurate transition state energies and to describe the radical dissociation channel. The cumulative reaction probabilities for the molecular dissociation and two isomerization channels are calculated by using the full Watson Hamiltonian. We also carry out wave packet dynamics calculations starting from the transition state region for the molecular dissociation. A contracted basis set for the angular coordinates is constructed to reduce the size of dynamics calculations. The intramolecular vibrational relaxation dynamics is found to be fast and almost complete within 300 fs. Using the energy filtered wave functions, the time propagation of HCOH population is obtained in the energy range from 81 to 94 kcal/mol. The branching ratio of the radical product is estimated by calculating the time dependent reactive fluxes to the molecular and radical dissociation products.     

Time dependent quantum dynamics study of the Ne + H2+(v=0-4)-->NeH+ + H proton transfer reaction

The Ne + H2+-->NeH+ + H proton transfer reaction was studied using the time dependent real wave packet quantum dynamics method at the helicity decoupling level, considering the H2+ molecular ion in the (v=0-4, j=0) vibrorotational states and a wide collision energy interval. The calculated reaction probabilities and reaction cross sections were in a rather good agreement with reanalyzed previous exact quantum dynamics results, where a much smaller collision energy interval was considered. Also, a quite good agreement with experimental data was found. These results suggested the adequacy of the approach used here to describe this and related systems.     

H+H2(v=0,1)→H2(v′)+H反应截面的电子非绝热三维量子散射近似计算

本文把电子非绝热一维量子散射反应几率和三维量子散射反应截面的近似公式结合起来, 对于反应物分子(H_2)不同的量子振动态(v=0, 1) 分别计算了H+H_2(v=0)→H_2(v′=0, 1)+H和H+H_2(v=1)→H_2(v′=0, 1)+H的平均反应截面σ_0和σ_1, 并同文献上用电子绝热理论计算的结果作了比较, 表明对这类中性原予-分子反应碰撞的过程, 特别是当反应物分子处于振动激发态时, 电子非绝热效应是存在的。     

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.     

On the dynamics of the H+ +D2(v=0,j=0)-->HD+D + reaction: a comparison between theory and experiment

The H+ +D2(v=0,j=0)-->HD+D + reaction has been theoretically investigated by means of a time independent exact quantum mechanical approach, a quantum wave packet calculation within an adiabatic centrifugal sudden approximation, a statistical quantum model, and a quasiclassical trajectory calculation. Besides reaction probabilities as a function of collision energy at different values of the total angular momentum, J, special emphasis has been made at two specific collision energies, 0.1 and 0.524 eV. The occurrence of distinctive dynamical behavior at these two energies is analyzed in some detail. An extensive comparison with previous experimental measurements on the Rydberg H atom with D2 molecules has been carried out at the higher collision energy. In particular, the present theoretical results have been employed to perform simulations of the experimental kinetic energy spectra.     

Time-dependent wave packet quantum and quasi-classical trajectory study of He + H₂⁺, D₂⁺ → HeH⁺ + H, HeD⁺ + D reaction on an accurate FCI potential energy surface

The quantum scattering dynamics and quasi-classical trajectory (QCT) calculations have been carried out for the title reaction on an accurate potential energy surface (PES) computed using the full configuration interaction (FCI). On the basis of the PES, the integral cross-sections of He + H?? (v = 0-3, j = 1) → HeH? + H reaction have been calculated, and the results are generally agreed with the experimental cross-sections obtained by Tang et al. [J. Chem. Phys. 2005, 122, 164301] after taking into account the experimental uncertainties, which proves the reliability of implementing dynamics calculations on the FCI PES. The reaction probability of He + D?? (v = 0-2, j = 0) → HeD? + D reactions for total angular momentum J = 0 and the integral cross-section (ICS) have been calculated. The significant quantum effect has been explored by the comparison between the QCT reaction probabilities (or ICS) and the quantum mechanical (QM) reaction probabilities (or ICS), which may be attributed to the deep well in the PES of this light atoms system. Furthermore, the role of Coriolis coupling (CC) effects has also been found not important by the comparison between the CC calculation and the centrifugal sudden (CS) approximation calculation, except that the CC total cross-sections for the v = 1 and 2 states show the collision energy-dependent behaviors in the low-energy area, which are different from those based on the CS calculation.     

Theories of reactive scattering

This paper is an overview of the theory of reactive scattering, with emphasis on fully quantum mechanical theories that have been developed to describe simple chemical reactions, especially atom-diatom reactions. We also describe related quasiclassical trajectory applications, and in all of this review the emphasis is on methods and applications concerned with state-resolved reaction dynamics. The review first provides an overview of the development of the theory, including a discussion of computational methods based on coupled channel calculations, variational methods, and wave packet methods. Choices of coordinates, including the use of hyperspherical coordinates are discussed, as are basis set and discrete variational representations. The review also summarizes a number of applications that have been performed, especially the two most comprehensively studied systems, H+H2 and F+H2, along with brief discussions of a large number of other systems, including other hydrogen atom transfer reactions, insertion reactions, electronically nonadiabatic reactions, and reactions involving four or more atoms. For each reaction we describe the method used and important new physical insight extracted from the results.     

Time-dependent reactive scattering for the system H- + D2 <--> HD + D- and comparison with H- + H2 <--> H2 + H-

This work presents results of quantum mechanical calculations of reaction probabilities for the ion-neutral molecule collisions H- + D2 <--> HD + D-. Time-dependent wave packet propagations for total angular momentum J not equal to 0, including the full Coriolis coupling, are performed. The calculated state-to-state reaction probabilities using product Jacobi coordinates are compared with energy-resolved reaction probabilities calculated with the flux-operator using reactant Jacobi coordinates and with time-independent calculations. Differences between nearly converged integral cross sections and those using the J-shifting method and centrifugal sudden approximation and comparison with experimental results will be presented.