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.     

Quantum wave-packet calculation of reaction probabilities, cross sections, and rate constants for Li + H2+ reaction

The Li + H2+(upsilon,j) --> LiH(upsilon',j') + H+ reactive scattering has been studied by using quantum real wave-packet method. The state-to-state and state-to-all reaction probabilities for the entitled collision have been calculated. The probabilities show a smooth variation for all initial rotational quantum states. The J-shifting approximation has been employed to estimate the integral cross sections and thermal rate constants have been calculated.     

Trajectory-based solution of the nonadiabatic quantum dynamics equations: an on-the-fly approach for molecular dynamics simulations

The non-relativistic quantum dynamics of nuclei and electrons is solved within the framework of quantum hydrodynamics using the adiabatic representation of the electronic states. An on-the-fly trajectory-based nonadiabatic molecular dynamics algorithm is derived, which is also able to capture nuclear quantum effects that are missing in the traditional trajectory surface hopping approach based on the independent trajectory approximation. The use of correlated trajectories produces quantum dynamics, which is in principle exact and computationally very efficient. The method is first tested on a series of model potentials and then applied to study the molecular collision of H with H(2) using on-the-fly TDDFT potential energy surfaces and nonadiabatic coupling vectors.     

Six-dimensional quasiclassical and quantum dynamics of H2 dissociation on the c(2 × 2)-Ti/Al(100) surface

Based on a slab model of H(2) dissociation on a c(2 × 2) structure with Ti atoms in the first and third layers of Al(100), a six-dimensional (6D) potential energy surface (PES) has been built. In this PES, a molecular adsorption well with a depth of 0.45 eV is present in front of a barrier of height 0.13 eV. Using this PES, H(2) dissociation probabilities are calculated by the classical trajectory (CT), the quasiclassical trajectory (QCT), and the time-dependent wave-packet (TDWP) method. The QCT study shows that trajectories can be trapped by the molecular adsorption well. Higher incident energy can lead to direct H(2) dissociation. Vibrational pre-excitation is the most efficient way to promote direct dissociation without trapping. We find that both rotational and vibrational excitation have efficacies close to 1.0 in the entire range of incident energies investigated, which supports the randomization in the initial conditions making the reaction rate solely dependent on the total (internal and translational) energy. The H(2) dissociation probabilities from quantum dynamics are in reasonable agreement with the QCT results in the energy range 50-200 meV, except for some fluctuations. However, the TDWP results considerably exceed the QCT results in the energy range 200-850 meV. The CT reaction probabilities are too low compared with the quantum dynamical results.     

Ab initio nonadiabatic quantum dynamics of cyclohexadiene/hexatriene ultrafast photoisomerization

Reaction mechanisms of the ultrafast photoisomerization between cyclohexadiene and hexatriene have been elucidated by the quantum dynamics on the ab initio potential energy surfaces calculated by multireference configuration interaction method. In addition to the quantum wave-packet dynamics along the two-dimensional reaction coordinates, the semiclassical analyses have also been carried out to correctly estimate the nonadiabatic transition probabilities around conical intersections in the full-dimensional space. The reaction time durations of radiationless decays in the wave-packet dynamics are found to be generally consistent with the femtosecond time-resolution experimental observations. The nonadiabatic transition probabilities among the ground (S0), first (S1), and second (S2) excited states have been estimated by using the semiclassical Zhu-Nakamura formula considering the full-dimensional wave-packet density distributions in the vicinity of conical intersections under the harmonic normal mode approximation. The cyclohexadiene (CHD) ring-opening process proceeds descending on the S1(1 1B) potential after the photoexcitation. The major part of the wave-packet decays from S1(1 1B) to S1(2 1A) by the first seam line crossing along the C2-symmetry-breaking directions. The experimentally observed ultrafast S1-S0 decay can be explained by the dynamics through the S1-S0 conical intersection along the direction toward the five-membered ring. The CHD: hexatriene (HT) branching ratio is estimated to be approximately 5:5, which is in accordance with the experiment in solution. This branching ratio is found to be mainly governed by the location of the five-membered ring S1-S0 conical intersection along the ground state potential ridge between CHD and HT.     

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.     

Dynamics of H2 dissociation on the 1/2 ML c(2 × 2)-Ti/Al(100) surface

The dissociation of H(2) on Ti-covered Al surfaces is relevant to the rehydrogenation and dehydrogenation of the NaAlH(4) hydrogen storage material. The energetically most stable structure for a 1/2 monolayer of Ti deposited on the Al(100) surface has the Ti atoms in the second layer with a c(2 × 2) structure, as has been confirmed by both low-energy electron diffraction and low-energy ion scattering experiments and density functional theory studies. In this work, we investigate the dynamics of H(2) dissociation on a slab model of this Ti/Al(100) surface. Two six-dimensional potential energy surfaces (PESs) have been built for this H(2) + Ti/Al(100) system, based on the density functional theory PW91 and RPBE exchange-correlation functionals. In the PW91 (RPBE) PES, the lowest H(2) dissociation barrier is found to be 0.65 (0.84) eV, with the minimum energy path occurring for H(2) dissociating above the bridge to top sites. Using both PESs, H(2) dissociation probabilities are calculated using the classical trajectory (CT), the quasi-classical trajectory (QCT), and the time-dependent wave-packet methods. We find that the QCT H(2) dissociation probabilities are in good agreement with the quantum dynamics results in the collision energy range studied up to 1.0 eV. We have also performed molecular beam simulations and present predictions for molecular beam experiments. Our molecular beam simulations show that H(2) dissociation on the 1/2 ML Ti/Al(100) surface is an activated process, and the reaction probability is found to be 6.9% for the PW91 functional and 1.8% for the RPBE at a nozzle temperature of 1700 K. Finally, we have also calculated H(2) dissociation rate constants by applying transition state theory and the QCT method, which could be relevant to modeling Ti-catalyzed rehydrogenation and dehydrogenation of NaAlH(4).     

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.     

A quantum reaction dynamics study of the translational, vibrational, and rotational motion effects on the HD + H3+ reaction

Time-dependent, quantum reaction dynamics wavepacket approach is employed to investigate the impacts of the translational, vibrational, and rotational motion on the HD+H(3)(+) → H(2)D(+) + H(2) reaction using the Xie-Braams-Bowman potential energy surface [Z. Xie, B. J. Braams, and J. M. Bowman, J. Chem. Phys. 122, 224307 (2005)]. We treat this five atom reaction with a seven-degree-of-freedom model by fixing one Jacobi and one torsion angle related to H(3) (+) at the lowest saddle point geometry of the potential energy surface. The initial state selected reaction probabilities show that the rotational excitations of H(+)-H(2) greatly enhance the reactivity with the reaction probabilities increased double at high rotational states compared to the ground state. However, the vibrational excitations of H(3) (+) hinder the reactivity. The ground state reaction probability shows no reaction threshold for this exoergic reaction, and as the translational energy increases, the reaction probability decreases. Furthermore, reactive resonances and zero point energy play very important roles on the reaction dynamics. The obtained integral cross section has the character of an exoergic reaction without a threshold: it decreases with the translational energy increasing. The calculated thermal rate constants using this seven-degree-of-freedom model are in agreement with a later experiment measurement.     

D+HCN反应的SVRT含时波包理论研究

基于Horst的势能面,用SVRT(SemirigidVibratingRotorTarget)方法对D+HCN反应进行了含时波包动力学研究,计算得到了不同初始振转态的总反应几率和积分反应截面,采用UniformJ-shifting方法得到该反应的热速率常数.计算结果与H+HCN反应进行了比和讨论.     

An ab initio quasi-diabatic potential energy matrix for OH(2Σ) + H2

A diabatic potential energy matrix for three electronic states of OH(3) has been constructed by interpolation of multi-reference configuration interaction electronic structure data. The reactive, exchange and non-reactive quenching dynamics are investigated using surface hopping classical trajectories. Classical trajectory simulations show good agreement with cross molecular beam data for the OH((2)Σ) + D(2) → HOD + D reaction.     

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。     

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.     

Accurate potential energy surface and quantum reaction rate calculations for the H+CH4-->H2+CH3 reaction

Calculations for the cumulative reaction probability N(E) (for J=0) and the thermal rate constant k(T) of the H+CH(4)-->H(2)+CH(3) reaction are presented. Accurate electronic structure calculations and a converged Shepard-interpolation approach are used to construct a potential energy surface which is specifically designed to allow the precise calculation of k(T) and N(E). Accurate quantum dynamics calculations employing flux correlation functions and multiconfigurational time-dependent Hartree wave packet propagation compute N(E) and k(T) based on this potential energy surface. The present work describes in detail the various convergence test performed to investigate the accuracy of the calculations at each step. These tests demonstrate the predictive power of the present calculations. In addition, approximate approaches for reaction rate calculations are discussed. A quite accurate approximation can be obtained from a potential energy surface which includes only interpolation points on the minimum energy path.     

Dissociative chemisorption of H2 on the Cu(110) surface: a quantum and quasiclassical dynamical study

Six-dimensional quantum dynamical and quasiclassical trajectory (QCT) calculations are reported for the reaction and vibrationally inelastic scattering of (v = 0,1,j = 0) H(2) scattering from Cu(110), and for the reaction and rovibrationally elastic and inelastic scattering of (v = 1,j = 1) H(2) scattering from Cu(110). The dynamics results were obtained using a potential energy surface obtained with density functional theory using the PW91 functional. The reaction probabilities computed with quantum dynamics for (v = 0,1,j = 0) were in excellent agreement with the QCT results obtained earlier for these states, thereby validating the QCT approach to sticking of hydrogen on Cu(110). The vibrational de-excitation probability P(v=1,j = 0 --> v = 0) computed with the QCT method is in remarkably good agreement with the quantum dynamical results for normal incidence energies E(n) between 0.2 and 0.6 eV. The QCT result for the vibrational excitation probability P(v = 0,j = 0 --> v = 1) is likewise accurate for E(n) between 0.8 and 1 eV, but the QCT method overestimates vibrational excitation for lower E(n). The QCT method gives probabilities for rovibrationally (in)elastic scattering, P(v = 1,j = 1 --> v('),j(')), which are in remarkably good agreement with quantum dynamical results. The rotationally averaged, initial vibrational state-selective reaction probability obtained with QCT agrees well with the initial vibrational state-selective reaction probability extracted from molecular beam experiments for v = 1, for the range of collision energies for which the v=1 contribution to the measured total sticking probability dominates. The quantum dynamical probabilities for rovibrationally elastic scattering of (v = 1,j = 1) H(2) from Cu(110) are in good agreement with experiment for E(n) between 0.08 and 0.25 eV.     

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.