Study of the H+O2 reaction by means of quantum mechanical and statistical approaches: the dynamics on two different potential energy surfaces

The possible existence of a complex-forming pathway for the H+O(2) reaction has been investigated by means of both quantum mechanical and statistical techniques. Reaction probabilities, integral cross sections, and differential cross sections have been obtained with a statistical quantum method and the mean potential phase space theory. The statistical predictions are compared to exact results calculated by means of time dependent wave packet methods and a previously reported time independent exact quantum mechanical approach using the double many-body expansion (DMBE IV) potential energy surface (PES) [Pastrana et al., J. Phys. Chem. 94, 8073 (1990)] and the recently developed surface (denoted XXZLG) by Xu et al. [J. Chem. Phys. 122, 244305 (2005)]. The statistical approaches are found to reproduce only some of the exact total reaction probabilities for low total angular momenta obtained with the DMBE IV PES and some of the cross sections calculated at energy values close to the reaction threshold for the XXZLG surface. Serious discrepancies with the exact integral cross sections at higher energy put into question the possible statistical nature of the title reaction. However, at a collision energy of 1.6 eV, statistical rotationally resolved cross sections managed to reproduce the experimental cross sections for the H+O(2)(v=0,j=1)-->OH(v(')=1,j('))+O process reasonably well.     

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.     

Quantum dynamics study of Li + HF reaction

We report rigorous quantum dynamics studies of the Li + HF reaction using the time-dependent wavepacket approach. The dynamics study is carried out on a recent ab initio potential energy surface, and state-selected reaction probabilities and cross sections are calculated up to 0.4 eV of collision energy. Many long-lived resonances (as long as 10 ps) at low collision energies (below 0.1 eV) are uncovered from the dynamics calculation. These long-lived resonances play a dominant role in the title reaction at low collision energies (below 0.1 eV). At higher energies, the direct reaction process becomes very important. The reaction probabilities from even rotational states exhibit a different energy dependence than those from odd rotational states. Our calculated integral cross section exhibits a broad maximum near the collision energy of 0.26 eV with small oscillations superimposed on the broad envelope which is reminiscent of the underlying resonance structures in reaction probabilities. The energy dependence of the present CS cross section is qualitatively different from the simple J-shifting approximation, in which a monotonic increase of cross section with collision energy was obtained. Received: 8 January 1997 / Accepted: 14 January 1997     

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.     

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.     

State-to-state dynamics of H + O2 reaction, evidence for nonstatistical behavior

Converged differential and integral cross sections are reported for the H + O2 --> OH + O reaction on an improved potential energy surface of HO2(X2A') using a dynamically exact quantum wave packet method and Gaussian weighted quasi-classical trajectory method. The complex-forming mechanism is confirmed by strong forward and backward scattering peaks and by highly inverted OH rotational state distributions. Both the quantum and classical results provide strong evidence for nonstatistical behavior in this important reaction.     

Time dependent quantum dynamics study of the O++H2(v=0,j=0)-->OH++H ion-molecule reaction and isotopic variants (D2,HD)

The time dependent real wave packet method using the helicity decoupling approximation was used to calculate the cross section evolution with collision energy (excitation function) of the O++H2(v=0,j=0)-->OH++H reaction and its isotopic variants with D2 and HD, using the best available ab initio analytical potential energy surface. The comparison of the calculated excitation functions with exact quantum results and experimental data showed that the present quantum dynamics approach is a very useful tool for the study of the selected and related systems, in a quite wide collision energy interval (approximately 0.0-1.1 eV), involving a much lower computational cost than the quantum exact methods and without a significant loss of accuracy in the cross sections.     

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 time-dependent wave packet quantum scattering study of the reaction HD+ (v = 0 - 3;j0 = 1) + He --> HeH+(HeD+) + D(H)

Time-dependent wave packet quantum scattering (TWQS) calculations are presented for HD(+) (v = 0 - 3;j(0)=1) + He collisions in the center-of-mass collision energy (E(T)) range of 0.0-2.0 eV. The present TWQS approach accounts for Coriolis coupling and uses the ab initio potential energy surface of Palmieri et al. [Mol. Phys. 98, 1839 (2000)]. For a fixed total angular momentum J, the energy dependence of reaction probabilities exhibits quantum resonance structure. The resonances are more pronounced for low J values and for the HeH(+) + D channel than for the HeD(+) + H channel and are particularly prominent near threshold. The quantum effects are no longer discernable in the integral cross sections, which compare closely to quasiclassical trajectory calculations conducted on the same potential energy surface. The integral cross sections also compare well to recent state-selected experimental values over the same reactant and translational energy range. Classical impulsive dynamics and steric arguments can account for the significant isotope effect in favor of the deuteron transfer channel observed for HD(+)(v<3) and low translational energies. At higher reactant energies, angular momentum constraints favor the proton-transfer channel, and isotopic differences in the integral cross sections are no longer significant. The integral cross sections as well as the J dependence of partial cross sections exhibit a significant alignment effect in favor of collisions with the HD(+) rotational angular momentum vector perpendicular to the Jacobi R coordinate. This effect is most pronounced for the proton-transfer channel at low vibrational and translational energies.     

Quantum approaches for the insertion dynamics of the H+ + D2 and D+ + H2 reactive collisions

The H(+)+D(2) and D(+)+H(2) reactive collisions are studied using a recently proposed adiabatic potential energy surface of spectroscopic accuracy. The dynamics is studied using an exact wave packet method on the adiabatic surface at energies below the curve crossing occurring at approximately 1.5 eV above the threshold. It is found that the reaction is very well described by a statistical quantum method for a zero total angular momentum (J) as compared with the exact ones, while for higher J some discrepancies are found. For J >0 different centrifugal sudden approximations are proposed and compared with the exact and statistical quantum treatments. The usual centrifugal sudden approach fails by considering too high reaction barriers and too low reaction probabilities. A new statistically modified centrifugal sudden approach is considered which corrects these two failures to a rather good extent. It is also found that an adiabatic approximation for the helicities provides results in very good agreement with the statistical method, placing the reaction barrier properly. However, both statistical and adiabatic centrifugal treatments overestimate the reaction probabilities. The reaction cross sections thus obtained with the new approaches are in rather good agreement with the exact results. In spite of these deficiencies, the quantum statistical method is well adapted for describing the insertion dynamics, and it is then used to evaluate the differential cross sections.     

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.     

Accurate quantum wave packet calculations for the F + HCl → Cl + HF reaction on the ground 1(2)A' potential energy surface

We present converged exact quantum wave packet calculations of reaction probabilities, integral cross sections, and thermal rate coefficients for the title reaction. Calculations have been carried out on the ground 1(2)A' global adiabatic potential energy surface of Deskevich et al. [J. Chem. Phys. 124, 224303 (2006)]. Converged wave packet reaction probabilities at selected values of the total angular momentum up to a partial wave of J = 140 with the HCl reagent initially selected in the v = 0, j = 0-16 rovibrational states have been obtained for the collision energy range from threshold up to 0.8 eV. The present calculations confirm an important enhancement of reactivity with rotational excitation of the HCl molecule. First, accurate integral cross sections and rate constants have been calculated and compared with the available experimental data.     

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.     

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.     

Quasi-classical Trajectory Study of the Intramolecular Isotope Effect in the Reaction O（3p）＋H2/HD

Theoretical studies of the dynamics of the reactions O（3p）＋H2/HD（ν=0, j=0）→OH＋H have been performed with quasi-classical trajectory method （QCT） on an ab initio potential surface for the lowest triplet electronic state of H2O（aA＂）. The QCT-calculated integral cross sections are in good agreement with the earlier time-dependent quantum mechanics results. The state-resolved rotational distributions reveal that the product OH rotational distributions for O＋HD have a preference for populating highly internally excited states compared with the O＋H2 reaction. Distributions of differential cross sections show that directions of scattering are strongly dependent on the choice of quantum state. The polarization dependent generalized differential cross-sections and the distributions were calculated and a pronounced isotopic effect is revealed. The calculated results indicate that the product polarization is very sensitive to the mass factor.     

Bimolecular reactions of vibrationally excited molecules. Roaming atom mechanism at low kinetic energies

Quasiclassical trajectory calculations have been performed for the H + H'X(v) → X + HH' abstraction and H + H'X(v) → XH + H' (X = Cl, F) exchange reactions of the vibrationally excited diatomic reactant at a wide collision energy range extending to ultracold temperatures. Vibrational excitation of the reactant increases the abstraction cross sections significantly. If the vibrational excitation is larger than the height of the potential barrier for reaction, the reactive cross sections diverge at very low collision energies, similarly to capture reactions. The divergence is quenched by rotational excitation but returns if the reactant rotates fast. The thermal rate coefficients for vibrationally excited reactants are very large, approach or exceed the gas kinetic limit because of the capture-type divergence at low collision energies. The Arrhenius activation energies assume small negative values at and below room temperature, if the vibrational quantum number is larger than 1 for HCl and larger than 3 for HF. The exchange reaction also exhibits capture-type divergence, but the rate coefficients are larger. Comparisons are presented between classical and quantum mechanical results at low collision energies. At low collision energies the importance of the exchange reaction is enhanced by a roaming atom mechanism, namely, collisions leading to H atom exchange but bypassing the exchange barrier. Such collisions probably have a large role under ultracold conditions. The calculations indicate that for roaming to occur, long-range attractive interaction and small relative kinetic energy in the chemical reaction at the first encounter are necessary, which ensures that the partners can not leave the attractive well. Large orbital angular momentum of the primary products (equivalent to large rotational excitation in a unimolecular reaction) is favorable for roaming.     

State-to-state quantum dynamics of the H((2)S) + O2(ã(1)Δ(g)) → O((3)P)+OH(X(2)Π) reaction on the first excited state of HO2(Ã(2)A')

State-to-state differential and integral cross sections for the title reaction were calculated using an exact wave packet method on a recently developed ab initio potential energy surface of the first excited state HO(2)(?(2)A'). The calculation results indicate that the reaction is dominated by highly rotationally excited OH products scattered in both the forward and backward directions, consistent with the formation of a long-lived HO(2) reaction intermediate. However, a statistical model was found to overestimate the integral cross sections, due apparently to dynamical bottlenecks. In addition, a unique feature in the OH + O exit channel potential promotes rotational excitation of the departing OH product by exerting a torque force. The role of the title reaction in high temperature combustion is also discussed.