A wave packet based statistical approach to complex-forming reactions

Full-dimensional coupled-channel statistical approach to atom-triatom systems and applications to H/D + O3 reaction

The statistical quantum model (SQM), which assumes that the reactivity is controlled by entrance/exit channel quantum capture probabilities, is well suited for chemical reactions with a long-lived intermediate complex. In this work, a time-independent coupled-channel implementation of the SQM approach is developed for atom-triatom systems in full dimensionality. As SQM treats the capture dynamics quantum mechanically, it is capable of handling quantum effects such as tunneling. A detailed study of the H/D + O3 capture dynamics was performed by applying the newly developed SQM method on an accurate global potential energy surface. Agreement with previous ring polymer molecular dynamics (RPMD) results on the same potential energy surface is excellent except for very low temperatures. The SQM results are also in reasonably good agreement with available experimental rate coefficients. The strong H/D kinetic isotope effect underscores the dominant role of quantum tunneling under an entrance channel barrier at low temperatures.

Recent advances in quantum theory on ro-vibrationally inelastic scattering

Molecular collisions are of fundamental importance in understanding intermolecular interaction and dynamics. Its importance is accentuated in cold and ultra-cold collisions because of the dominant quantum mechanical nature of the scattering. We review recent advances in the time-independent approach to quantum mechanical characterization of non-reactive scattering in tetratomic systems, which is ideally suited for large collisional de Broglie wavelengths characteristic in cold and ultracold conditions. We discuss quantum scattering algorithms between two diatoms and between a triatom and an atom and their implementation, as well as various approximate schemes. They not only enable the characterization of collision dynamics in realistic systems but also serve as benchmarks for developing more approximate methods.

Quantum interference in the mechanism of H + LiH+ → H2 + Li+ reaction dynamics

In this work, the detailed reaction mechanism of the astrochemically relevant exoergic and barrierless H + LiH⁺ → H₂ + Li⁺ reaction is investigated by both time-dependent wave packet and quasi-classical trajectory (QCT) methods on the ab initio electronic ground state potential energy surface reported by Martinazzo et al. [Martinazzo et al., J. Chem. Phys., 2003, 119, 11241]. The interference terms due to the coherence between the partial waves are quantified. When plotted along the scattering angle they reveal interference of constructive or destructive nature. Significant interference was found in the differential cross-section (DCS) which is a symbolic of the non-statistical nature of the reaction. This is further complemented by calculating the lifetime of the collision complex by the QCT method. It is found that the reaction follows a direct stripping mechanism at higher collision energies and yields forward scattered products from collisions involving high total angular momentum. At low collision energies, the reaction follows a mixed direct/indirect mechanism but with a dominant indirect contribution. The product state-resolved DCSs reveal that two opposite mechanisms co-exist, both at low and high collision energies. The microscopic scattering mechanism of the reaction is found to be unaffected by the ro-vibrational excitation of the reagent diatom.

Time-independent quantum theory on vibrational inelastic scattering between atoms and open-shell diatomic molecules: Applications to NO + Ar and NO + H scattering

A full-dimensional rigorous quantum mechanical treatment of non-reactive inelastic scattering of an open-shell diatom [e.g., NO(²Π)] with a structureless and spinless atom is presented within the time-independent close-coupling framework. The inclusion of the diatomic vibrational degree of freedom allows the investigation of transitions between different vibrational manifolds, in addition to those between different rotational, spin-orbit, and Λ-doublet states. This method is applied to the scattering of vibrationally excited NO(²Π) with Ar and H (with its spin ignored). The former has negligible vibrational inelasticity, thanks to the weak interaction between the two collisional partners. This conclusion justifies the commonly used two-dimensional approximation in treating NO scattering with rare gas atoms. The latter, on the other hand, is shown to undergo significant vibrational relaxation, even in the ultra-cold regime, owing to a chemically bonded (HNO) complex on the lowest-lying singlet potential energy surfaces.

Dynamics study on the non-adiabatic Na(3p) + HD → NaH/NaD + D/H reaction: insertion-abstraction mechanism

Time-dependent wave packet calculations are carried out for two reaction channels of the non-adiabatic Na(3p) + HD → NaH/NaD + D/H reaction. The potential well on the excited state potential energy surface makes the reaction preferable to proceed through the insertion reaction path. The dominance of the NaD + H reaction channel and product rotational state distributions are found to be in agreement with the characteristics of typical adiabatic insertion reactions. However, significant forward scattering peaks in the differential cross sections (DCS) are found to be inconsistent with the forward-backward symmetric scattering characteristic of typical adiabatic insertion reactions, which indicate that the Na(3p) + HD reaction is dominated by a direct reaction mechanism. The comparison between adiabatic and non-adiabatic calculated DCSs reveals that the non-adiabatic couplings in the reaction could reduce the lifetime of the intermediate complex. Finally, the insertion-abstraction mechanism is put forward for the non-adiabatic Na(3p) + HD reaction.

Quantum Dynamics Study of the C(1D) + HD Reaction on the ã1A' and b̃1A″ Potential Energy Surfaces

We present an in-depth theoretical study of the C(¹D) + HD (v = 0, j = 0) → CD (CH) (v', j') + H (D) reaction using a time-dependent wave packet method with full Coriolis coupling on the Zhang-Ma-Bian potential energy surfaces (PESs) recently constructed by our group. The integral cross sections (ICS), differential cross sections, CD/CH branching ratios, and product state distributions are calculated over a wide range of collision energies. We find that the vibrational branching ratio defined as ICS(v'=1)/ICS(v'=0) obtained from the b̃¹A″ PES is much smaller than that from the ã¹A' PES for both product channels, which may be attributed to the dynamical effects of the conical intersection regulated (CI-R) intermediate on the b̃¹A″ PES. The collision energy dependence of CD/CH branching ratios displays oscillatory structures, which may be caused by the resonance states supported by the wells on the PESs. The high-temperature rate coefficients are also obtained and compared with previous results. The role of the excited-state PESs is also discussed.

An Empirical Dynamical Barrier for Statistical Theory of Low-Energy Reactive S(1D) + HD(j = 0), H2(j = 0) Collisions

A simple model potential is proposed to describe the dynamical barrier in the mean interaction potential at small distances between the reactants in S(¹D) + HD(¹Σ, v = 0, j = 0) reaction. The statistical theory of collision complex formation and complex decay is applied to calculate the total reaction cross sections and the cross sections for SH and SD productions in the range of low collision energies E_c = (0.4-60) meV. The results are compared with measured cross sections and results of hyperspherical close coupling calculations. As a check of consistency the same comparisons are presented for the case of S(¹D) + H₂(¹Σ, v = 0, j = 0) reaction.

State-to-state quantum dynamics of the N(4S) + CH(X2Π) → CN(X2Σ+,A2Π) + H(2S) reactions

The reactions between N((4)S) and CH(X(2)Π) lead to H((2)S) plus CN in its two lowest electronic states (X(2)Σ(+) and A(2)Π), which are responsible for the interstellar CN formation. Accurate quantum dynamics of these reactions are investigated on new global potential energy surfaces of the two lowest-lying triplet states of HCN (1(3)A' and 1(3)A") fitted to more than 37,000 points at the internally contracted multi-reference configuration interaction level with the Davidson correction. The pathways for these highly exothermic and barrierless reactions feature both the HCN and HNC wells. Long-lived resonances supported by these wells manifest in reaction probabilities as numerous oscillations, particularly for low J partial waves. The 1(3)A" state is found to be more reactive than the 1(3)A' state, due apparently to its more attractive nature in the entrance channel. The CN products in both electronic states are highly excited in both vibrational and rotational degrees of freedom. The near forward-backward symmetric differential cross sections are consistent with a complex-forming mechanism.

Quantum Dynamics of the HO + CO → H + CO2 Reaction on an Accurate Potential Energy Surface

Full-dimensional quantum dynamics of the HO + CO → H + CO2 reaction is investigated on a recent global potential energy surface based on a large number of ab initio points. The J = 0 reaction probability is small and essentially a monotonically increasing function with energy, superimposed by overlapping resonances. The reactivity is considerably enhanced by OH vibrational excitation while relatively insensitive to CO vibrational excitation. The rate constant estimated by the J-shifting approximation indicates a much better agreement with experiment than that obtained on a previous potential energy surface.

The O((1)D) + H2 (X (1)Σ+, v, j) → OH(X (2)Π, v', j') + H((2)S) reaction at low collision energy: when a simple statistical description of the dynamics works

In this communication, we highlight that statistical approaches for chemical reactions describe reasonably well the low energy dynamics of the title process. Consequently, such methods prove to be valuable to compute rate constants from low to room temperatures. Results are compared with experiment and recent precise quantum wave packet calculations [J. Phys. Chem. A, 2009, 113, 5285].

State-to-state quantum dynamics of O + O2 isotope exchange reactions reveals nonstatistical behavior at atmospheric conditions

The O + O(2) exchange reaction is a prerequisite for the formation of ozone in Earth's atmosphere. We report here state-to-state differential and integral cross sections for several O + O(2) isotope-exchange reactions obtained by dynamically exact quantum scattering calculations at collision energies relevant to atmospheric conditions. These reactions are shown to be highly nonstatistical, evidenced by dominant forward scattering and deviation of the integral cross section from the statistical limit. Mechanistic analyses revealed that the nonstatistical channel is facilitated by short-lived osculating resonances. The theoretical results provided an in-depth interpretation of a recent molecular beam experiment of the exchange reaction and shed light on the initial step of ozone recombination.

Mean potential phase space theory of chemical reactions

A nonconventional application of phase space theory to the insertion reactions A+H(2), with A=C((1)D) and S((1)D), is presented. Instead of approximating the potential energies of interaction between separated fragments by their isotropic long-range contributions, as in the original theory, the latter are replaced by the accurate potential energies averaged with respect to Jacobi angles. The integral and differential cross sections obtained from this mean potential phase space theory (MPPST) turn out to be in very satisfying agreement with the benchmark predictions of the time-independent and time-dependent statistical quantum methods. The formal and numerical simplicity of MPPST with respect to any approach combining statistical assumptions and dynamical calculations makes it a promising tool for studying indirect polyatomic reactions.

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.

Differential and Integral Cross Sections of the N(2D) + H2 → NH + H Reaction from Exact Quantum and Quasi-Classical Trajectory Calculations

Exact quantum mechanical state-to-state differential and integral cross sections and their energy dependence have been calculated on an accurate NH2 potential energy surface (PES), using a newly proposed Chebyshev wave packet method. The NH product is found to have a monotonically decaying vibrational distribution and an inverted rotational distribution. The product angular distributions peak in both forward and backward directions, but with a backward bias. This backward bias is more pronounced than that observed previously on a less accurate PES. Both the differential and integral cross sections oscillate mildly with collision energy, indicating the dominance of short-lived resonances. The quantum mechanical results are compared with those obtained from quasi-classical trajectories. The agreement is generally reasonable and the discrepancies can be attributed to the neglect of quantum effects such as tunneling. Detailed analysis of the trajectories revealed that the backward bias in the differential cross section stems overwhelmingly from the fast insertion component of the reaction, augmented with some flux from the abstraction channel, particularly at high collision energies.

Dynamics of insertion reactions of H2 molecules with excited atoms

Recent progress in the study of insertion reactions of hydrogen molecules with excited atoms is reviewed in this article. In particular, the dynamics of the reaction of O(1D), N(2D), C(1D), and S(1D) with H2 and its isotopomers, which have received a great deal of attention over the past decade, are examined in detail. All of these systems have in common the existence of several potential energy surfaces (PES) correlating with the reagents' states, and consequently, they can give rise to reaction following different adiabatic and nonadiabatic pathways. The main contribution, however, arises from their ground singlet PESs which feature the existence of deep wells with small or null barriers for insertion. Accordingly, these reactions proceed mainly via formation of relatively long-lived collision complexes and display an overall nearly statistical behavior. In spite of their similarities, the various reactions have peculiar characteristics caused by important differences of their respective PESs. The contribution of excited PES to the global reactivity, which has also become an important issue and a challenge both for theory and experiment, is also examined. The different theoretical approaches are discussed in the text, along with the experimental results obtained by a variety of techniques. The recent exact quantum treatments of these reactive systems together with the development of a rigorous statistical model have contributed to a very accurate description which in many cases matches very well the detailed measurements. The quasi-classical trajectory (QCT) method has also provided a fairly accurate description of the reaction dynamics for these systems. In particular, the analysis in terms of collision times has yielded interesting clues about the reaction mechanisms.

A new ab initio potential-energy surface of HO2(X2A") and quantum studies of HO2 vibrational spectrum and rate constants for the H + O2 <--> O + OH reactions

A new global potential-energy surface for the ground electronic state of HO(2)(X(2)A(")) has been developed by three-dimensional cubic spline interpolation of more than 15 000 ab initio points, which were calculated at the multireference configuration-interaction level with Davidson correction using the augmented correlation-consistent polarized valence quadruple zeta basis set. Low-lying vibrational states were obtained in this new potential using the Lanczos method and assigned. The calculated vibrational frequencies are in much better agreement with the available experimental band origins than those obtained from a previous potential. In addition, rate constants for the H+O(2) <--> O + OH reactions were obtained using a wave-packet-based statistical model. Reasonably good agreement with experimental data was obtained. These results demonstrate the accuracy of the potential.

Time dependent wave packet and statistical calculations on the H + O(2) reaction

The H + O(2)--> OH + O reaction has been theoretically investigated by means of an exact time dependent wave packet method and two statistical approaches: a recently developed statistical quantum model and phase-space theory. The exhaustive analysis of reaction probabilities at a zero total angular momentum would, in principle, reveal the existence of a complex-forming mechanism at low collision energies (E(c) = 1.15 eV), whereas deviations from a statistical behaviour at higher energies may be interpreted as the onset of a direct abstraction pathway which favours the production of highly excited rotational states of the OH fragment in its ground vibrational state. The good description by statistical means of previously measured product rotational distributions and excitation functions seems to support such an interpretation. However the statistical predictions clearly overestimate both existing and present exact quantum mechanical reaction probabilities and total cross sections, thereby precluding to conclude definitely the statistical nature of the collision. The exact time dependent method yields values of the integral cross sections in agreement with results by Goldfield and Meijer, and below the experimental findings.

Coupled-states statistical investigation of vibrational and rotational relaxation of OH(2pi) by collisions with atomic hydrogen

We report state-to-state cross sections and thermal rate constants for vibrational and rotational relaxation of OH(2pi) by collision with H atoms. The cross sections are calculated by the coupled-states (CS) statistical method including the full open-shell character of the OH + H system. Four potential energy surfaces (PESs) ((1,3)A' and (1,3)A'') describe the interaction of OH(X2pi) with H atoms. Of these, three are repulsive, and one (1A') correlates with the deep H2O well. Consequently, rotationally and ro-vibrationally inelastic scattering of OH in collisions with H can occur by scattering on the repulsive PESs, in a manner similar to the inelastic scattering of OH by noble gas atoms, or by collisions which enter the H2O well and then reemerge. At 300 K, we predict large (approximately 1 x 10(-10) cm3 molecule(-1) s(-1)) vibrational relaxation rates out of both v = 2 and v = 1, comparable to earlier experimental observations. This anomalously fast relaxation results from capture into the H2O complex. There exists a significant propensity toward formation of OH in the pi(A') lambda-doublet level. We also report state-resolved cross sections and rate constants for rotational excitation within the OH v = 0 manifold. Collisional excitation from the F1 to the F2 spin-orbit manifold leads to an inverted lambda-doublet population.

Theoretical Study of the Complex-Forming CH + H2 → CH2 + H Reaction

The complex-forming CH + H2 --> CH2 + H reaction is studied employing a recently developed global potential energy function. The reaction probability in the total angular momentum J = 0 limit is estimated with a four-atom quantum wave packet method and compared with classical trajectory and statistical theory results. The formation of complexes from different reactant internal states is also determined with wave packet calculations. While there is no barrier to reaction along the minimum energy path, we find that there are angular constraints to complex formation. Trajectory-based estimates of the low-pressure rate constants are made and compared with experimental results. We find that zero-point energy violation in the trajectories is a particularly severe problem for this reaction.

Exact quantum dynamics of N(D2)+H2→NH+H reaction: Cross-sections, rate constants, and dependence on reactant rotation

Using an exact Chebyshev wave packet method, initial state-specified (upsilon(i)=0, j(i)=0,2) integral cross-sections and rate constants are obtained for the title reaction on the latest ab initio potential energy surface. Reaction probabilities up to J=29 are dependent on the reactant rotation and show mild oscillations superimposed on a broad background. Due to a barrier in the entrance channel, the cross sections increase with energy with clear thresholds and the rate constants vary with temperature in the Arrhenius form. The calculated canonical rate constant is in good agreement with the experimental measurements. Our results also indicate that the quasiclassical trajectory method underestimates the rate due to the neglect of tunneling, while the quantum statistical approach overestimates because of the short lifetime of the reaction intermediate.

Influence of rotation and isotope effects on the dynamics of the N(D2)+H2 reactive system and of its deuterated variants

Integral cross sections and thermal rate constants have been calculated for the N((2)D)+H(2) reaction and its isotopic variants N((2)D)+D(2) and the two-channel N((2)D)+HD by means of quasiclassical trajectory and statistical quantum-mechanical model methods on the latest ab initio potential-energy surface [T.-S. Ho et al., J. Chem. Phys. 119, 3063 (2003)]. The effect of rotational excitation of the diatom on the dynamics of these reactions has been investigated and interesting discrepancies between the classical and statistical model calculations have been found. Whereas a net effect of reagent rotation on reactivity is always observed in the classical calculations, only a very slight effect is observed in the case of the asymmetric N((2)D)+HD reaction for the statistical quantum-mechanical method. The thermal rate constants calculated on this Potential-Energy Surface using quasiclassical trajectory and statistical model methods are in good agreement with the experimental determinations, although the latter are somewhat larger. A reevaluation of the collinear barrier of the potential surface used in the present study seems timely. Further theoretical and experimental studies are needed for a full understanding of the dynamics of the title reaction.

Quantum Statistical Study of O + O2 Isotopic Exchange Reactions: Cross Sections and Rate Constants

Using a wave packet based statistical model, we compute cross sections and thermal rate constants for various isotopic variants of the O + O2 exchange reaction on a recently modified ab initio potential energy surface. The calculation predicts a highly excited rotational distribution and relatively cold vibrational distribution for the diatomic product. A small but important threshold effect was identified for the (16)O + 18O2 reaction, which is suggested to contribute to the experimentally observed negative temperature dependence of the rate ratio, k(18O + 16O2)/k(16O + 18O2). Despite reasonable agreement with quasiclassical trajectory results, however, the calculated thermal rate constants are smaller than experimental measurements by a factor from 2 to 5. The experimentally observed negative temperature dependence of the rate constants is not reproduced. Possible reasons for the theory-experiment discrepancies are discussed.