Real wave packet and flux analysis studies of the H + F2 → HF + F reaction

The H + F₂ → HF + F reaction on ground state potential energy surface is investigated using the quantum mechanical real wave packet and Flux analysis method based on centrifugal sudden approximation. The initial state selected reaction probabilities for total angular momentum J = 0 have been calculated by both methods while the probabilities for J > 0 have been calculated by Flux analysis method. The initial state selected reaction probabilities, integral cross sections and rate coefficients have been calculated for a broad range of collision energy. The results show a large rotational enhancement of the reaction probability. Some resonances were seen in the state‐to‐state reaction probabilities while state‐to‐all reaction probabilities and the reaction cross section do not manifest any oscillations and the initial state selected reaction rate constants are sensitive to the temperature. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Quantum scattering calculation for reaction Br + H2 on two potential energy surfaces

Three‐dimensional time‐dependent quantum wave packet calculations have been carried out for Br + H₂ on a new global ab initio and a semi‐empirical extended London–Eyring–Polanyi–Sato potential energy surface. It is shown that on the ab initio surface, the threshold energy is much lower, and the reaction probabilities, cross sections, and rate constants are much larger. The effects of the initial rovibrational excitation have also been studied. Comparison of rate constants with experimental measurement implies that the ab initio surface is more suitable for quantum dynamic calculation. The possible reasons and mechanism for the dynamical difference on the two PES are analyzed and discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

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.     

Tests of semiclassical treatments of vibrational-translational energy transfer collinear collisions of helium with hydrogen molecules

Three kinds of semiclassical theory are tested against quantum mechanical results for vibrational transition probabilities and average vibrational energy transfers in collinear collisions of atoms with harmonic and Morse vibrators for the He-H₂ mass combination. The interaction potential is assumed to be a repulsive exponential function with an exponential parameter which is realistic for He-H₂ collisions. The energy range studied is total energies of 2–8 in units of ?ω_e. The uniform semiclassical approximations of classical S matrix theory are tested only for classically allowed transitions, i.e., for transition probabilities greater than about 0.2. They are accurate quantitatively for both harmonic and Morse vibrators. The integral expressions of classical S matrix theory are found to be quantitatively accurate for classically allowed and weakly classically forbidden transitions, i.e., for transition probabilities greater than about 0.01–0.05, and to be unreliable for strongly classically forbidden transitions. Quasiclassical trajectory methods yield qualitatively accurate results only for classically allowed transitions but the phase-averaged energy transfer in quasiclassical collisions may be accurate even when classically forbidden transition probabilities are important for the calculation of the average energy transfer. Forced quantum oscillator methods using a classical path whose initial velocity is the average of the initial and final velocities corresponding to the transition of interest are accurate for transition probabilities as small as 4 × 10^?8 for harmonic vibrators but do not seem to accurately account for the effect of anharmonicity.     

Calculations of vibrational energy transfer using semi-classicals matrix theory

We utilize an extension of Miller's semi-classical S matrix theory to calculate resonant and non-resonant vibrational energy transfer probabilities. The collisions under study are collinear D₂D₂ interactions at energies below and above the classical dynamic transition threshold and collinear H₂D₂ interactions above the dynamic threshold. Below threshold we employ an initial angle representation. We find that the computed probabilities are in substantial agreement with exact quantum mechanical computations and represent a major improvement over quasi-classical results. At energies above threshold we apply the first order and the classical semi-classical versions of the theory. The results indicate fair agreement with quantum mechanical calculations, but no significant improvement over quasi-classical results.     

Surface temperature effect on the scattering of D2(v = 0, j = 0)-Cu(111) system

We perform four-dimensional (4D?2D) as well as six-dimensional (6D) quantum dynamics on a parametrically time- and temperature-dependent effective Hamiltonian for D(2)(v, j)-Cu(111) system, where such effective potential has been derived through a mean-field approach between molecular degrees of freedom and surface modes with Bose-Einstein probability factor for their initial state distribution. We present the convergence of the theoretically calculated sticking probabilities employing 4D?2D quantum dynamics with increasing number of surface atoms as well as layers for rigid surface and the surface at a particular temperature, where the temperature-dependent sticking probabilities appear exclusively dictated by those surface modes directed along the Z-axis. The sticking and state-to-state transition probabilities obtained from 6D quantum dynamics are shown as a function of initial kinetic energy of the diatom at different surface temperature. Theoretically calculated sticking probabilities display the similar trend with the experimentally measured one.     

Time-dependent Quantum Wave Packet Study of F+HCl and F+DCl Reactions

The F+HCl and F+DCl reactions are studied by the time-dependent quantum wave packet method, using the most recent potential energy surface reported by Deskevich et al.. Total reaction probabilities for a number of initial ro-vibrational states of HCl and DCl diatomic moiety are presented in the case of total angular momentum J=0. It is found that for both reactions the initial rotational excitation of the diatomic moiety enhances greatly the reaction probabilities but this e?ect is more signiˉcant for F+HCl system. This is mainly due to larger rotational constant of the HCl reagent. The initial vibrational excitation of the diatomic moiety has little e?ect on the reactivity for both systems except shifting down the collision energy threshold. The results indicate that the reaction coordinates for these two systems are e?ectively along rotational freedom degree. More quantum phenomena, such as tunneling and resonance, are observed in F+HCl reaction than F+DCl reaction, and for the initial states studied, the reactivity of the later is lower. Di?erent skewing angles of these two systems account for these isotopic di?erences.     

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.     

Calculation of multiple initial state selected reaction probabilities from Chebyshev flux-flux correlation functions: influence of reactant internal excitations on H + H2O → OH + H2

A Chebyshev-based flux-flux correlation function approach is introduced for calculating multiple initial state selected reaction probabilities for bimolecular reactions. Based on the quantum transition-state theory, this approach propagates, with the exact Chebyshev propagator, transition-state wave packets towards the reactant asymptote. It is accurate and efficient if many initial state selected reaction probabilities are needed. This approach is applied to the title reaction to elucidate the influence of the H(2)O ro-vibrational states on its reactivity. Results from several potential energy surfaces are compared.     

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.     

Quasi-classical trajectory calculations on the H + O2 reaction

Quasi-classical trajectory calculations have been performed on the H + O₂ system. Significant reaction probabilities are obtained when the initial energy is in rotation or vibration, or a combination of the two, but not when the initial energy is in translation. The opacity function shows a bimodal dependence on the impact parameter, with a small peak at 0.9 Å < b < 1.5 Å and a very prominent peak at 2.5 Å < b < 3.3 Å. The product scattering angles and product energy distributions also depend on b and to a limited extent on the initial energy distribution. The observations can be largely interpreted in terms of the nature of the motion on the potential energy surface, while the effects of rotational energy on the reaction follow qualitatively from statistical phase-space theory.     

Quantum dynamics of the dissociation of H2 on Cu(100): dependence of the site-reactivity on initial rovibrational state

We perform six-dimensional (6D) quantum wavepacket calculations for H2 dissociatively adsorbing on Cu(100) from a variety of rovibrational initial states. The calculations are performed on a new potential energy surface (PES), the construction of which is also detailed. Reaction probabilities are in good agreement with experimental findings. Using a new flux analysis method, we calculate the reaction probability density as a function of surface site and collision energy, for a variety of initial states. This approach is used to study the effects of rotation and vibration on reaction at specific surface sites. The results are explained in terms of characteristics of the PES and intrinsically dynamic effects. An important observation is that, even at low collision energies, reaction does not necessarily proceed predominantly in the region of the minimum potential barrier, but can occur almost exclusively at a site with a higher barrier. This suggests that experimental control of initial conditions could be used to selectively induce reaction at particular surface sites. Our predictions for site-reactivity could be tested using contemporary experimental methods: The calculations predict that, for reacting molecules, there will be a dependence of the quadrupole alignment of j on the incident vibrational state, v. This is a direct result of PES topography in the vicinity of the preferred reaction sites of v = 0 and v = 1 molecules. Invoking detailed balance, evidence for this difference in preferred reaction site of v = 0 and 1 molecules could be obtained through associative desorption experiments.     

Violation of microscopic reversibility and the use of reverse quais-classical trajectories for calculating reaction cross sections

In order to calculate the transition probabilities (or cross sections) for reactive collisions, such as A + BC(ν, j)→ AB(ν′, j) + C, using the quasi-classical trajectory method, one quantizes the internal energy of the reagents and in addition adopts some algorithm for calculating the internal quantum numbers of the products. A serious consequence of this procedure is that the quasi-classical results do not obey microscopic reversibility. It is shown that for the collinear F + H₂(ν = 0) → FH(ν = 2, 3)+ H reaction (and its D₂ counterpart), the quasi-classical trajectory probabilities for the reverse reaction not only differ substantially from the forward ones but in general are in much better agreement with accurate quantum calculations. A similar situation was found for the collinear H + H₂(0) → H₂(1) + H reaction. We suggest that in doing quasi-classical calculations, the reverse of the process of interest should also be considered. Comparison of forward and reverse quasi-classical collinear calculations with accurate collinear quantum results could give an indication of whether forward or reverse calculations should be used for the three-dimensional case.     

Quantum dynamics study of the Langmuir–Hinshelwood H + H recombination mechanism and H2 formation on a graphene model surface

We examine in this paper the associative desorption of two hydrogen atoms on a slab model that mimics a C(0 0 0 1) surface. Initially the two separated H atoms are physisorbed onto the graphene surface, then diffuse and recombine and H₂ gets desorbed into the gas phase. We use density functional theory (DFT) on a supercell model and apply periodic boundaries to build a potential energy surface (PES). The reaction is barrier less and exhibits a small H₂ vdW well on the global potential energy surface. We employ a two-dimensional quantum dynamics method exploiting the hyperspherical coordinates and report reaction probabilities for this mechanism. The calculations are performed for collision energies ranging from 1 to 15 meV relevant to the interstellar medium (ISM). The entrance channel dominates the reaction and the vibrational excitation of the desorbed H₂ is important and peaked at v′ = 8.     

Quantum scattering calculation of the O(1D)+HBr reaction

Three-dimensional time-dependent quantum wave packet calculation for the O((1)D)+HBr reaction has been carried out using an accurate ab initio global potential energy surface [K. A. Peterson, J. Chem. Phys. 113, 4598 (2000)]. The calculations show that the initial state-selected reaction probabilities are dominated by resonance structures, and the lifetime of the resonance is generally in the subpicosecond time scale. The energy dependence of the reaction cross section is computed, which manifests still resonance structures, and is a decreasing function of the translational energy. The thermal rate constants are also computed, which are nearly independent on the temperature. The calculation results are discussed and compared to similar reaction with deep well.     

Quantum dynamics calculation of reaction probability for H + Cl2 → HCl + Cl

We present in this paper a time-dependent quantum wave packet calculation of the initial state selected reaction probability for H + Cl₂ based on the GHNS potential energy surface with total angular momentumJ = 0. The effects of the translational, vibrational and rotational excitation of Cl₂ on the reaction probability have been investigated. In a broad region of the translational energy, the rotational excitation enhances the reaction probability while the vibrational excitation depresses the reaction probability. The theoretical results agree well with the fact that it is an early down-hill reaction.     

Vibrational matrix elements of the quadrupole moment functions of H2, N2 and CO

The quadrupole moment functions (molecular quadrupole moment versus internuclear distance) have been determined by quantum mechanical calculations for H₂ (by Kolos and Wolniewicz), N₂ (by Wahl and Nesbet), and CO (by Nesbet). These functions are used with numerical vibrational wave functions to compute matrix elements which are useful for calculations of scattering cross sections, energy transfer rates and excitation probabilities, and infrared intensities of forbidden bands.     

Quantum dynamics calculation of reaction probability for H + Cl2 → HCl + Cl

We present in this paper a time-dependent quantum wave packet calculation of the initial state selected reaction probability for H + Cl₂ based on the GHNS potential energy surface with total angular momentumJ = 0. The effects of the translational, vibrational and rotational excitation of Cl₂ on the reaction probability have been investigated. In a broad region of the translational energy, the rotational excitation enhances the reaction probability while the vibrational excitation depresses the reaction probability. The theoretical results agree well with the fact that it is an early down-hill reaction.     

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.