A transition state view on reactive scattering: initial state-selected reaction probabilities for the H + CH4 → H2 + CH3 reaction studied in full dimensionality

Initial state-selected reaction probabilities for the H+CH(4)→H(2)+CH(3) reaction are computed for vanishing total angular momentum by full-dimensional calculations employing the multiconfigurational time-dependent Hartree approach. An ensemble of wave packets completely describing reactivity for total energies up to 0.58 eV is constructed in the transition state region by diagonalization of the thermal flux operator. These wave packets are then propagated into the reactant asymptotic region to obtain the initial state-selected reaction probabilities. Reaction probabilities for reactants in all rotational states of the vibrational 1A(1), 1F(2), and 1E levels of methane are presented. Vibrational excitation is found to decrease reactivity when reaction probabilities at equivalent total energies are compared but to increase reaction probabilities when the comparison is done at the basis of equivalent collision energies. Only a fraction of the initial vibrational energy can be utilized to promote the reaction. The effect of rotational excitation on the reactivity differs depending on the initial vibrational state of methane. For the 1A(1) and 1F(2) vibrational states of methane, rotational excitation decreases the reaction probability even when comparing reaction probabilities at equivalent collision energies. In contrast, rotational energy is even more efficient than translational energy in increasing the reaction probability when the reaction starts from the 1E vibrational state of methane. All findings can be explained employing a transition state based interpretation of the reaction process.     

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.     

Dynamically weighted multiconfiguration self-consistent field: multistate calculations for F+H2O-->HF+OH reaction paths

A novel method of dynamically adjusted weighting factors in state-averaged multiconfiguration self-consistent-field calculations (SA-MCSCF) is described that is applicable to systems of arbitrary dimensionality. The proposed dynamically weighted approach automatically weights the relevant electronic states in each region of the potential energy surface, smoothly adjusting between these regions with an energy dependent functional. This method is tested on the F(2P)+H2O-->HF+OH(2Pi) reaction, which otherwise proves challenging to describe with traditional SA-MCSCF methods due to (i) different asymptotic degeneracies of reactant (threefold) and product (twofold) channels, and (ii) presence of low-lying charge transfer configurations near the transition state region. The smoothly varying wave functions obtained by dynamically weighted multiconfigurational self-consistent field represent excellent reference states for high-level multireference configuration interaction calculations and offer an ideal starting point for construction of multiple state potential energy surfaces.     

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.     

A quantum theory of chemical processes and reaction rates based on diabatic electronic functions coupled in an external field

The method discussed in this work provides a theoretical framework where simple chemical reactions resemble any other standard quantum process, i.e., a transition in quantum state mediated by the electromagnetic field. In our approach, quantum states are represented as a superposition of electronic diabatic basis functions, whose amplitudes can be modulated by the field and by the external control of nuclear configurations. Using a one-dimensional three-state model system, we show how chemical structure and dynamics can be represented in terms of these control parameters, and propose an algorithm to compute the reaction probabilities. Our analysis of effective energy barriers generalizes previous ideas on structural similarity between reactant, and product, and transition states using the geometry of conventional reaction paths. In the present context, exceptions to empirical rules such as the Hammond postulate appear as effects induced by the environment that supplies the external field acting on the quantum system.     

Franck-Condon theory of reactive scattering

A Franck-Condon theory of reactive scattering is introduced which generalizes previous works in a number of respects. We consider the collinear AB + C → A + BC reaction where A, B, and C may be polyatomic species and show how the multi-dimensional continuum-continuum Franck-Condon integral can exactly be reduced to a two-dimensional one involving the nonorthogonal reaction coordinates on the reactant and product diabatic surfaces. These integrals are then written in a rapidly convergent series of products of one-dimensional bound-continuum integrals of a form closely related to those studied in recent theories of photodissociation where accurate analytical and numerical methods are available for treating them. The theory is applied to the case of the D + Hl isotope exchange for a model surface to enable a comparison of exact quantum calculations with those of the Franck-Condon theory for the identical surface in both cases. The calculations are all performed at energies where the reaction is classically forbidden. The relative Dl vibrational distributions (as a function of initial Hl state) are accurately reproduced in a fashion that is fairly insensitive to the choice of the reactant and product diabatic surfaces, but the absolute probabilities are shown to be sensitively dependent on this choice.     

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 study of the N+N(2) exchange reaction: state-to-state reaction probabilities, initial state selected probabilities, Feshbach resonances, and product distributions

We report a detailed three-dimensional time-dependent quantum dynamics study of the state-to-state N+N(2) exchange scattering in the 2.1-3.2 eV range using a recently developed ab initio potential energy surface (PES). The reactive flux arrives at the dividing surface in the asymptotic product region in a series of six packets, instead of a single packet. Further study shows that these features arise from the "Lake Eyring" region of the PES, a region with a shallow well between two transition states. Trappings due to Feshbach resonances are found to be the major cause of the time delay. A detailed analysis of the Feshbach resonance features is carried out using an L(2) calculation of the metastable states in the "Lake Eyring" region. Strong resonance features are found in the state-to-state and initial state selected reaction probabilities. The metastable states with bending motions and/or bending coupled with stretching motions are found to be the predominant source of the resonance structure. Initial state selected reaction probabilities further indicate that the lifetimes of the metastable states with bending motions in the "Lake Eyring" region are longer than those of states with stretching motions and thus dominate the reactive resonances. Resonance structures are also visible in some of the integral cross sections and should provide a means for future experimental observation of the resonance behavior. A study of the final rotational distributions shows that, for the energy range studied here, the final products are distributed toward high-rotational states. Final vibrational distributions at the temperatures 2000 and 10,000 K are also reported.     

Quantum and quasiclassical study of the collinear reaction O(3P) + H2 → OH + H using a LEPS and fitted AB initio potential energy surface

Accurate quantum calculations of reaction probabilities P^T_ν′←ν have been carried out for the collinear reaction O(³P) + H₂ (ν = 0,1) → OH(ν′) + H using a LEPS and fitted ab initio potential energy surface. The energy dependence of the P^T_{ν′ ← ν} is similar for both surfaces. Collinear quasiclassical trajectory calculations have also been carried out, for comparison, on the LEPS surface for ν = 0, 1 and 2.     

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.     

Association rate constants for reactions between resonance-stabilized radicals: C3H3 + C3H3, C3H3 + C3H5, and C3H5 + C3H5

Reactions between resonance-stabilized radicals play an important role in combustion chemistry. The theoretical prediction of rate coefficients and product distributions for such reactions is complicated by the fact that the initial complex-formation steps and some dissociation steps are barrierless. In this paper direct variable reaction coordinate transition state theory (VRC-TST) is used to predict accurately the association rate constants for the self and cross reactions of propargyl and allyl radicals. For each reaction, a set of multifaceted dividing surfaces is used to account for the multiple possible addition channels. Because of their resonant nature the geometric relaxation of the radicals is important. Here, the effect of this relaxation is explicitly calculated with the UB3LYP/cc-pvdz method for each mutual orientation encountered in the configurational integrals over the transition state dividing surfaces. The final energies are obtained from CASPT2/cc-pvdz calculations with all pi-orbitals in the active space. Evaluations along the minimum energy path suggest that basis set corrections are negligible. The VRC-TST approach was also used to calculate the association rate constant and the corresponding number of states for the C(6)H(5) + H --> C(6)H(6) exit channel of the C(3)H(3) + C(3)H(3) reaction, which is also barrierless. For this reaction, the interaction energies were evaluated with the CASPT2(2e,2o)/cc-pvdz method and a 1-D correction is included on the basis of CAS+1+2+QC/aug-cc-pvtz calculations for the CH(3) + H reference system. For the C(3)H(3) + C(3)H(3) reaction, the VRC-TST results for the energy and angular momentum resolved numbers of states in the entrance channels and in the C(6)H(5) + H exit channel are incorporated in a master equation simulation to determine the temperature and pressure dependence of the phenomenological rate coefficients. The rate constants for the C(3)H(3) + C(3)H(3) and C(3)H(5) + C(3)H(5) self-reactions compare favorably with the available experimental data. To our knowledge there are no experimental rate data for the C(3)H(3) + C(3)H(5) reaction.     

Full-dimensional quantum dynamics study of the H + H2O and H + HOD exchange reactions

The initial state-selected time-dependent wave packet approach is employed to study the H' + H(2)O → H'OH + H and H' + HOD → H'OD + H, HOH' + D exchange reactions with both OH bonds in the H(2)O reactant and OH(D) bond in the HOD reactant treated as reactive bonds. The total reaction probabilities for different partial waves, as well as the integral cross sections, which are the exact CC (coupled-channel) results, are first obtained in this study for the H(2)O(HOD) reactant initially in the ground rovibrational state. Because of the shallow C(3v) minimum along the reaction path, the reaction probabilities for the three reactions present several resonance peaks, with one dominant resonance peak just above the threshold. The cross sections for the H' + HOD → HOH' + D reaction are substantially smaller than those for the H' + H(2)O → H'OH + H and H' + HOD → H'OD + H reactions, indicating that the H'/H exchange reactions are much more favored. In the CC calculations, the resonance peaks in the reaction probabilities diminish quickly with the increase in total angular momenta J, resulting in the existence of a clear step-like feature just above the threshold in the cross sections for the title reactions, which manifests the signature of shape resonances in these reactions. In the CS calculations, the resonance peaks on reaction probabilities persist in many partial waves, and thus the resonance structures can no longer survive the partial-wave summation and are washed out completely in the CS cross sections for the title reactions.     

Quantum dynamical study of the O(1D)+HCl reaction employing three electronic state potential energy surfaces

Quantum dynamical calculations are reported for the title reaction, for both product arrangement channels and using potential energy surfaces corresponding to the three electronic states, 1 1A', 2 1A', and 1 1A", which correlate with both reactants and products. The calculations have been performed for J=0 using the time-dependent real wavepacket approach by Gray and Balint-Kurti [J. Chem. Phys. 108, 950 (1998)]. Reaction probabilities for both product arrangement channels on all three potential energy surfaces are presented for total energies between 0.1 and 1.1 eV. Product vibrational state distributions at two total energies, 0.522 and 0.722 eV, are also presented for both channels and all three electronic states. Product rotational quantum state distributions are presented for both product arrangement channels and all three electronic states for the first six product vibrational states.     

Ab initio potential energy surfaces of the ion-molecule reaction: C2H2 + O+

High level ab initio calculations using complete active space self-consistent field and multi reference single and double excitation configuration interaction methods with cc-pVDZ (correlation consistent polarized valence double zeta) and cc-pVTZ (triple zeta) basis sets have been performed to elucidate the reaction mechanism of the ion-molecule reaction, C2H2(1Sigmag+) + O+(4S), for which collision experiment has been performed by Chiu et al. [J. Chem. Phys. 109, 5300 (1998)]. The minor low-energy process leading to the weak spin-forbidden product C2H2+ (2Piu) + O(1D) has been studied previously and will not be discussed here. The major pathways to form charge-transfer (CT) products, C2H2+ (2Piu) + O(3P) (CT1) and C2H2+ (4A2) + O(3P) (CT2), and the covalently bound intermediates are investigated. The approach of the oxygen atom cation to acetylene goes over an energy barrier TS1 of 29 kcal/mol (relative to the reactant) and adiabatically leads the CT2 product or a weakly bound intermediate Int1 between CT2 products. This transition state TS1 is caused by the avoided crossing between the reactant and CT2 electronic states. As the C-O distance becomes shorter beyond the above intermediate, the C1 reaction pathway is energetically more favorable than the Cs pathway and goes over the second transition state TS2 of a relative energy of 39 kcal/mol. Although this TS connects diabatically to the covalent intermediate Int2, there are many states that interact adiabatically with this diabatic state and these lead to the other charge-transfer product CT1 via either of several nonadiabatic transitions. These findings are consistent with the experiment, in which charge transfer and chemical reaction products are detected above 35 and 39 kcal/mol collision energies, respectively.     

Exact quantum scattering study of the H + HS reaction on a new ab initio potential energy surface H2S (3A")

We present an exact quantum dynamical study and quasi-classical trajectory (QCT) calculations for the exchange and abstraction processes for the H + HS reaction. These calculations were based on a newly constructed high-quality potential energy surface for the lowest triplet state of H(2)S ((3)A"). The ab initio single-point energies were computed using complete active space self-consistent field and multi-reference configuration interaction method with a basis set of aug-cc-pV5Z. The time-dependent wave packet (TDWP) method was used to calculate the total reaction probabilities and integral cross sections over the collision energy (E(col)) range of 0.0-2.0 eV for the reactant HS initially at the ground state and the first vibrationally excited state. It was found that the initial vibrational excitation of HS enhances both abstraction and exchange processes. In addition, a good agreement is found between QCT and TDWP reaction probabilities at the total momentum J = 0 as a function of collision energy for the H + HS (v = 0, j = 0) reaction.     

A quantum equation of motion for chemical reaction systems on an adiabatic double-well potential surface in solution based on the framework of mixed quantum-classical molecular dynamics

We present a quantum equation of motion for chemical reaction systems on an adiabatic double-well potential surface in solution in the framework of mixed quantum-classical molecular dynamics, where the reactant and product states are explicitly defined by dividing the double-well potential into the reactant and product wells. The equation can describe quantum reaction processes such as tunneling and thermal excitation and relaxation assisted by the solvent. Fluctuations of the zero-point energy level, the height of the barrier, and the curvature of the well are all included in the equation. Here, the equation was combined with the surface hopping technique in order to describe the motion of the classical solvent. Applying the present method to model systems, we show two numerical examples in order to demonstrate the potential power of the present method. The first example is a proton transfer by tunneling where the high-energy product state was stabilized very rapidly by solvation. The second example shows a thermal activation mechanism, i.e., the initial vibrational excitation in the reactant well followed by the reacting transition above the barrier and the final vibrational relaxation in the product well.     

基态氧(3^O2)氧化硅烯的密度泛函计算研究

采用密度泛函[B3LYP(full)/6-311+G^*]方法研究了基态氧(3^O2)氧化硅烯(Si2H4)的机理。计算了三重态初始中间体(IM(T1)到单重态中间体IM2(S0)反应交叉势能面,报道了各反应中间体、产物和过渡态的构型和能量,用频率分析方法对各过渡态进行了验证,进一步用IRC方法对主要的基元反应进行了考察,确定了历经生成1,2-二氧环氧硅烷中间体的氧化过程的主要反应通道。     

The importance of tunneling in the first hydrogenation step in ammonia synthesis over a Ru(0001) surface

The hydrogenation of nitrogen (N(ads)+H(ads)-->NH(ads)) on metal surfaces is an important step in ammonia catalysis. We investigate the reaction dynamics of this hydrogenation step by time independent scattering theory and variational transition state theory (VTST) including tunneling corrections. The potential energy surface is derived by hybrid density functional theory on a model cluster composed of 12 ruthenium atoms resembling a Ru(0001) surface. The scattering calculations are performed on a reduced dimensionality potential energy hypersurface, where two dimensions are treated explicitly and all others are included implicitly by the zero-point correction. The VTST calculations include quantum effects along the reaction coordinate by applying the small curvature tunneling scheme. Even at room temperature (where ruthenium already shows catalytic activity) we find rate enhancement by tunneling by a factor of approximately 70. Inspection of the reaction probabilities shows that the major contribution to reactivity comes from the vibrational ground state of the reactants into vibrationally excited product states. The reaction rates are higher than determined in previous studies, and are compatible with experimental overall rates for ammonia synthesis.     

Full dimensional time-dependent quantum dynamics study of the H + NH3 --> H2 + NH2 reaction

A rigorous full dimensional time-dependent wave packet method has been developed for the reactive scattering between an atom and a tetra-atomic molecule. The method has been applied to the hydrogen abstraction reaction H+NH(3)-->H(2)+NH(2). Initial state-selected total reaction probabilities are investigated for the reactions from the ground vibrational state and from four excited vibrational states of ammonia. The total reaction probabilities from two lowest "tunneling doublets" due to the inversion barrier for the umbrella bending motion of NH(3) and from two pairs of doubly degenerate vibrational states of NH(3) are also inspected. Integral cross sections and rate constants are calculated for the reaction from the ground state with the centrifugal-sudden approximation. The calculated results are compared with those from the previous seven dimensional calculations [M. Yang and J. C. Corchado, J. Chem. Phys. 126, 214312 (2007)]. This work shows that the full dimensional rate constants are a factor of 3 larger than the corresponding seven dimensional calculated values at T=200 K and are overall smaller than those obtained from the variational transition state theory in the whole temperature region. The work also reveals that nonreactive NH bonds of NH(3) cannot be treated as spectators due to the fact that three NH bonds are coupled with each other during the reaction process.