Time-Dependent Wave Packet Study of the O + O2 (v = 0, j = 0) Exchange Reaction

Time-dependent quantum mechanical wave packet dynamics

Starting from a model study of the collinear (H, H₂) exchange reaction in 1959, the time-dependent quantum mechanical wave packet (TDQMWP) method has come a long way in dealing with systems as large as Cl + CH₄. The fast Fourier transform method for evaluating the second order spatial derivative of the wave function and split-operator method or Chebyshev polynomial expansion for determining the time evolution of the wave function for the system have made the approach highly accurate from a practical point of view. The TDQMWP methodology has been able to predict state-to-state differential and integral reaction cross sections accurately, in agreement with available experimental results for three dimensional (H, H₂) collisions, and identify reactive scattering resonances too. It has become a practical computational tool in predicting the observables for many A + BC exchange reactions in three dimensions and a number of larger systems. It is equally amenable to determining the bound and quasi-bound states for a variety of molecular systems. Just as it is able to deal with dissociative processes (without involving basis set expansion), it is able to deal with multi-mode nonadiabatic dynamics in multiple electronic states with equal ease. We present an overview of the method and its strength and limitations, citing examples largely from our own research groups.

The Role of Ozone Vibrational Resonances in the Isotope Exchange Reaction 16O16O + 18O → 18O16O + 16O: The Time-Dependent Picture

We consider the time-dependent dynamics of the isotope exchange reaction in collisions between an oxygen molecule and an oxygen atom: ¹⁶O¹⁶O + ¹⁸O → ¹⁶O¹⁸O + ¹⁶O. A theoretical approach using the multiconfiguration time-dependent Hartree method was employed to model the time evolution of the reaction. Two potential surfaces available in the literature were used in the calculations, and the results obtained with the two surfaces are compared with each other as well as with results of a previous theoretical time-independent approach. A good agreement for the reaction probabilities with the previous theoretical results is found. Comparing the results obtained using two potential energy surfaces allows us to understand the role of the reef/shoulder-like feature in the minimum energy path of the reaction in the isotope exchange process. Also, it was found that the distribution of final products of the reaction is highly anisotropic, which agrees with experimental observations and, at the same time, suggests that the family of approximated statistical approaches, assuming a randomized distribution over final exit channels, is not applicable to this case.

Wave packet and statistical quantum calculations for the He + NeH⁺ → HeH⁺ + Ne reaction on the ground electronic state

A real wave packet based time-dependent method and a statistical quantum method have been used to study the He + NeH(+) (v, j) reaction with the reactant in various ro-vibrational states, on a recently calculated ab initio ground state potential energy surface. Both the wave packet and statistical quantum calculations were carried out within the centrifugal sudden approximation as well as using the exact Hamiltonian. Quantum reaction probabilities exhibit dense oscillatory pattern for smaller total angular momentum values, which is a signature of resonances in a complex forming mechanism for the title reaction. Significant differences, found between exact and approximate quantum reaction cross sections, highlight the importance of inclusion of Coriolis coupling in the calculations. Statistical results are in fairly good agreement with the exact quantum results, for ground ro-vibrational states of the reactant. Vibrational excitation greatly enhances the reaction cross sections, whereas rotational excitation has relatively small effect on the reaction. The nature of the reaction cross section curves is dependent on the initial vibrational state of the reactant and is typical of a late barrier type potential energy profile.

Huge Quantum Symmetry Effect in the O + O2 Exchange Reaction

We report extensive, full quantum-mechanical calculations for the (16)O + (16)O(16)O → (16)O(16)O + (16)O collisions, for both inelastic and atom exchange processes, using a time-independent method based on hyperspherical coordinates. The rates obtained in the present study are much larger than the previously reported ones for this system. The discrepancy is attributed to a huge symmetry effect that was missing in the studies so far. This effect differs from the well-known isotope effect. Importance of this quantum effect is further confirmed by comparison with results for the (16)O + (18)O(18)O → (16)O(18)O + (18)O, exchange reaction.

Quantum dynamical study of the He + NeH+ reaction on a new analytical potential energy surface

An analytical potential energy surface (PES) for the ground state of the [HeHNe](+) system has been constructed from a set of 19,605 ab initio data points, obtained from coupled cluster singles and doubles with perturbative triples correction calculations and the aug-cc-pVQZ basis set. The PES is based on the many-body expansion form proposed by Aguado and Paniagua (J. Chem. Phys. 1992, 96, 1265), and it has a root-mean-square error of 0.03 kcal/mol. The minimum energy pathways (MEPs) for different Ne-H-He angles are calculated, and it is found that the MEP for 180° (linear) goes through the deepest potential energy well. Preliminary quantum dynamical studies are performed for the He + NeH(+) (v = 0-2, j = 0-3) → HeH(+) + Ne reaction in the 0.0-0.5 eV collision energy range. Quantum calculations are carried out using a time-dependent wave packet method within the centrifugal sudden approximation. Reaction probabilities exhibit strong oscillatory behavior arising because of the metastable [HeHNe](+). Vibrational excitation has been found to enhance the reaction cross sections.

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.

Theoretical investigation of exchange and recombination reactions in O(P3)+NO(Π2) collisions

We present a detailed dynamical study of the kinetics of O(3P)+NO(2Pi) collisions including O atom exchange reactions and the recombination of NO2. The classical trajectory calculations are performed on the lowest 2A' and 2A" potential energy surfaces, which were calculated by ab initio methods. The calculated room temperature exchange reaction rate coefficient, kex, is in very good agreement with the measured one. The high-pressure recombination rate coefficient, which is given by the formation rate coefficient and to a good approximation equals 2kex, overestimates the experimental data by merely 20%. The pressure dependence of the recombination rate, kr, is described within the strong-collision model by assigning a stabilization probability to each individual trajectory. The measured falloff curve is well reproduced over five orders of magnitude by a single parameter, i.e., the strong-collision stabilization frequency. The calculations also yield the correct temperature dependence, kr proportional, T-1.5, of the low-pressure recombination rate coefficient. The dependence of the rate coefficients on the oxygen isotopes are investigated by incorporating the difference of the zero-point energies between the reactant and product NO radicals, DeltaZPE, into the potential energy surface. Similar isotope effects as for ozone are predicted for both the exchange reaction and the recombination. Finally, we estimate that the chaperon mechanism is not important for the recombination of NO2, which is in accord with the overall T-1.4 dependence of the measured recombination rate even in the low temperature range.

DYNAMICAL STUDIES OF THE OZONE ISOTOPE EFFECT: A Status Report

▪ Abstract  Dynamical studies of the recombination of O and O2 to form ozone are reviewed. The focus is the intriguing isotope dependence of the recombination rate coefficient as observed by Mauersberger and coworkers in the last decade. The key quantity for understanding of this dependence appears to be the difference of zero-point energies of the two fragmentation channels to which excited ozone can dissociate, i.e., X + YZ ← XYZ* → XY + Z, where X, Y, and Z stand for the three isotopes of oxygen. Besides the isotope dependence, the variation of the recombination rate coefficient with pressure and temperature is also addressed. Despite the numerous approaches of recent years, the recombination of ozone is far from being satisfactorily explained; there are still several essential questions to be solved by detailed theoretical analysis. We mainly discuss—and critically assess—the results of our own investigations of the ozone kinetics. The work of other research groups is also evaluated.

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.

Ab Initio Molecular Dynamics Simulations of an Excited State of X-(H2O)3 (X = Cl, I) Complex

Upon excitation of Cl(-)(H(2)O)(3) and I(-)(H(2)O)(3) clusters, the electron transfers from the anionic precursor to the solvent, and then the excess electron is stabilized by polar solvent molecules. This process has been investigated using ab initio molecular dynamics (AIMD) simulations of excited states of Cl(-)(H(2)O)(3) and I(-)(H(2)O)(3) clusters. The AIMD simulation results of Cl(-)(H(2)O)(3) and I(-)(H(2)O)(3) are compared, and they are found to be similar. Because the role of the halogen atom in the photoexcitation mechanism is controversial, we also carried out AIMD simulations for the ground-state bare excess electron -- water trimer [e(-)(H(2)O)(3)] at 300 K, the results of which are similar to those for the excited state of X(-)(H(2)O)(3) with zero kinetic energy at the initial excitation. This indicates that the rearrangement of the complex is closely related to that of e(-)(H(2)O)(3), whereas the role of the halide anion is not as important.

The effect of zero-point energy differences on the isotope dependence of the formation of ozone: A classical trajectory study

The effect of zero-point energy differences (DeltaZPE) between the possible fragmentation channels of highly excited O(3) complexes on the isotope dependence of the formation of ozone is investigated by means of classical trajectory calculations and a strong-collision model. DeltaZPE is incorporated in the calculations in a phenomenological way by adjusting the potential energy surface in the product channels so that the correct exothermicities and endothermicities are matched. The model contains two parameters, the frequency of stabilizing collisions omega and an energy dependent parameter Delta(damp), which favors the lower energies in the Maxwell-Boltzmann distribution. The stabilization frequency is used to adjust the pressure dependence of the absolute formation rate while Delta(damp) is utilized to control its isotope dependence. The calculations for several isotope combinations of oxygen atoms show a clear dependence of relative formation rates on DeltaZPE. The results are similar to those of Gao and Marcus [J. Chem. Phys. 116, 137 (2002)] obtained within a statistical model. In particular, like in the statistical approach an ad hoc parameter eta approximately 1.14, which effectively reduces the formation rates of the symmetric ABA ozone molecules, has to be introduced in order to obtain good agreement with the measured relative rates of Janssen et al. [Phys. Chem. Chem. Phys. 3, 4718 (2001)]. The temperature dependence of the recombination rate is also addressed.

The transition-state region of the O(3P)+O2(3Σg−) potential energy surface

New electronic structure calculations for the transition-state region of the lowest ozone potential energy surface are reported. A two-dimensional potential energy surface in the asymptotic channel is calculated with the O(2) bond distance being fixed. The calculations are performed at the multireference average quadratic coupled cluster level of theory using full-valence complete active space self-consistent field wave functions and the augmented correlation consistent polarized V6Z atomic basis set. The general shape of the potential energy surface as predicted in earlier studies, that is, a narrow transition state below the O+O(2) asymptote, is confirmed by the present calculations. The transition state is 181 cm(-1) below the asymptote and 72 cm(-1) above the van der Waals-like minimum. The changes in the O+O(2)-->O(3) (*) capture cross section and rate constant when the new potential energy surface is employed are investigated by means of classical trajectory calculations.

Quantum wave-packet dynamics of H+HLi scattering: Reaction cross section and thermal rate constant

The channel specific and initial state-selected reaction cross section and temperature-dependent rate constant for the title system is calculated with the aid of a time-dependent wave-packet approach and using the ab initio potential energy surface of Dunne et al. [Chem. Phys. Lett. 336, 1 (2001)]. All partial-wave contributions up to the total angular momentum J=74 are explicitly calculated within the coupled states (CS) approximation. Companion calculations are also carried out employing the standard as well as the uniform J-shifting (JS) approximation. The overall variation of reaction cross sections corresponds well to the behavior of a barrierless reaction. The hydrogen exchange channel yielding HLi+H products is seen to be more favored over the HLi depletion channel yielding Li+H(2) products at low and moderate collision energies. Sharp resonance features are observed in the cross-section results for the HLi depletion channel at low energies. Resonance features in the reaction cross sections average out with various partial-wave contributions, when compared to the same observed in the individual reaction probability curve. Except near the onset of the reaction, the vibrational and rotational excitation of the reagent HLi, in general, does not dramatically influence the reactivity of either channel. The thermal rate constants calculated up to 4000 K show nearly Arrhenius type behavior. The rate constant decreases with vibrational excitation of the reagent HLi, indicating that the cold HLi molecules are efficiently depleted in the reactive encounter with H at relatively low temperatures. The results obtained from the JS approximation are found to agree well qualitatively with the CS results.