Quantum-mechanical calculations on termolecular association reactions XY+Z+M→XYZ+M: Application to ozone formation

Lifetimes and decay mechanisms of isotopically substituted ozone above the dissociation threshold: matching quantum and classical dynamics

Energies and lifetimes of vibrational resonances were computed for 18O-enriched isotopologue 50O3 = {16O16O18O and 16O18O16O} of the ozone molecule using hyperspherical coordinates and the method of complex absorbing potential. Various types of scattering resonances were identified, including roaming OO-O rotational states, the series corresponding to continuation of bound vibrational resonances of highly excited bending or symmetric stretching vibrational modes. Such a series become metastable above the dissociation limit. The coupling between the vibrationally excited O2 fragment and rotational roaming gives rise to Feshbach type resonances in ozone. Different paths for the formation and decay of symmetric 16O18O16O and asymmetric species 16O16O18O were also identified. The symmetry properties of the total rovibronic wave functions of the 18O-enriched isotopologues are discussed in the context of allowed dissociation channels.

Ab initio study of the O3-N2 complex: Potential energy surface and rovibrational states

The formation and destruction of O₃ within the Chapman cycle occurs as a result of inelastic collisions with a third body. Since N₂ is the most abundant atmospheric molecule, it can be considered as the most typical candidate when modeling energy-transfer dynamics. We report a new ab initio potential energy surface (PES) of the O₃-N₂ van der Waals complex. The interaction energies were calculated using the explicitly correlated single- and double-excitation coupled cluster method with a perturbative treatment of triple excitations [CCSD(T)-F12a] with the augmented correlation-consistent triple-zeta aug-cc-pVTZ basis set. The five-dimensional PES was analytically represented by an expansion in spherical harmonics up to eighth order inclusive. Along with the global minimum of the complex (D_e = 348.88 cm^-1), with N₂ being perpendicular to the O₃ plane, six stable configurations were found with a smaller binding energy. This PES was employed to calculate the bound states of the O₃-N₂ complex with both ortho- and para-N₂ for total angular momentum J = 0 and 1, as well as dipole transition probabilities. The nature of the bound states of the O₃-oN₂ and O₃-pN₂ species is discussed based on their rovibrational wave functions.

Direct time delay computation applied to the O + O2 exchange reaction at low energy: Lifetime spectrum of O3 * species

We report full quantum dynamical calculations for lifetimes of scattering resonances, among which are true metastable states, of the intermediate heavy ozone complex ⁵⁰O₃ ^* of the ¹⁸O + ¹⁶O¹⁶O reaction, for any value of the total angular momentum quantum number J. We show that computations for nonzero values of J are mandatory in order to properly analyze resonances and time delays, with a view to establish a somewhat comprehensive eigenlife spectrum of the complex O₃ ^*. Calculations have been performed in a given low to moderate energy range, including the interval between zero-point energies (ZPEs) of reagents and product species. Quasi-bound states tend to be more numerous, and eigenlifetimes themselves are seen to increase with J, reaching unusually large values for J = 30. A very dense forest of O₃ ^* species is pictured already for J greater than 20, especially at the highest energies considered, leading to a quasi-continuum of metastable states. On the contrary, they appear as rather sparse and isolated at J = 0 and lower energies, including the domain between ¹⁸O¹⁶O and ¹⁶O¹⁶O ZPEs, embedded among many overlapping resonances that turn out to be not long-lived enough to be associated with genuine metastable states.

Four Isotope-Labeled Recombination Pathways of Ozone Formation

A theoretical approach is developed for the description of all possible recombination pathways in the ozone forming reaction, without neglecting any process a priori, and without decoupling the individual pathways one from another. These pathways become physically distinct when a rare isotope of oxygen is introduced, such as ¹⁸O, which represents a sensitive probe of the ozone forming reaction. Each isotopologue of O₃ contains two types of physically distinct entrance channels and two types of physically distinct product wells, creating four recombination pathways. Calculations are done for singly and doubly substituted isotopologues of ozone, eight rate coefficients total. Two pathways for the formation of asymmetric ozone isotopomer exhibit rather different rate coefficients, indicating large isotope effect driven by ΔZPE-difference. Rate coefficient for the formation of symmetric isotopomer of ozone (third pathway) is found to be in between of those two, while the rate of insertion pathway is smaller by two orders of magnitude. These trends are in good agreement with experiments, for both singly and doubly substituted ozone. The total formation rates for asymmetric isotopomers are found to be somewhat larger than those for symmetric isotopomers, but not as much as in the experiment. Overall, the distribution of lifetimes is found to be very similar for the metastable states in symmetric and asymmetric ozone isotopomers.

Influence of the Coriolis effect on the properties of scattering resonances in symmetric and asymmetric isotopomers of ozone

Scattering resonances above dissociation threshold are computed for four isotopically substituted ozone species: 16O18O16O, 16O16O18O, 18O16O18O and 16O18O18O, using a variational method with accurate treatment of the rotation-vibration coupling terms (Coriolis effect) for all values of the total angular momentum J from 0 to 4. To make these calculations numerically affordable, a new approach was developed which employs one vibrational basis set optimized for a typical rotational excitation (J,Λ), to run coupled rotation-vibration calculations at several desired values of J. In order to quantify the effect of Coriolis coupling, new data are contrasted with those computed using the symmetric-top rotor approximation, where the rotation-vibration coupling terms are neglected. It is found that, overall, the major properties of scattering resonances (such as their lifetimes, the number of these states, and their cumulative partition function Q) are all influenced by the Coriolis effect and this influence grows as the angular momentum J is raised. However, it is found that the four isotopically substituted ozone molecules are affected roughly equally by the Coriolis coupling. When the ratio η of partition functions for asymmetric over symmetric ozone molecules is computed, the Coriolis effect largely cancels, and this cancelation seems to occur for all values of J. Therefore, it does not seem grounded to attribute any appreciable mass-independent symmetry-driven isotopic fractionation to the Coriolis coupling effect.

Development of a potential energy surface for the O3–Ar system: rovibrational states of the complex

Collisional stabilization is an important step in the process of atmospheric formation of ozone.

Several Levels of Theory for Description of Isotope Effects in Ozone: Symmetry Effect and Mass Effect

The essential components of theory for the description of isotope effects in recombination reaction that forms ozone are presented, including the introduction of three reaction pathways for symmetric and asymmetric isotopomers, a brief review of relevant experimental data for singly- and doubly substituted isotopologues, the definitions of ζ-effect and η-effect, and the introduction of isotopic enrichment δ. Two levels of theory are developed to elucidate the role of molecular symmetry, atomic masses, vibrational zero-point energies, and rotational excitations in the recombination process. The issue of symmetry is not trivial, since the important factors, such as 1/2 and 2, appear in seven different places in the formalism. It is demonstrated that if all these effects are taken into account properly, then no anomalous isotope effects emerge. At the next level of theory, a model is considered in which one scattering resonance (sitting right at the top of centrifugal barrier) is introduced per ro-vibrational channel. It is found that this approach is equivalent to statistical treatment with partition functions at the transition state. Accurate calculations using hyper-spherical coordinates show that no isotope effects come from difference in the number of states. In contrast, differences in vibrational and rotational energies lead to significant isotope effects. However, those effects appear to be local, found for the rather extreme values of rotational quantum numbers. They largely cancel when rate coefficients are computed for the thermal distribution of rotational excitations. Although large isotope effects (observed in experiments) are not reproduced here, this level of theory can be used as a foundation for more detailed computational treatment, with accurate information about resonance energies and lifetimes computed and included.

Several levels of theory for description of isotope effects in ozone: Effect of resonance lifetimes and channel couplings

In this paper, two levels of theory are developed to determine the role of scattering resonances in the process of ozone formation. At the lower theory level, we compute resonance lifetimes in the simplest possible way, by neglecting all couplings between the diabatic vibrational channels in the problem. This permits to determine the effect of "shape" resonances, trapped behind the centrifugal barrier and populated by quantum tunneling. At the next level of theory, we include couplings between the vibrational channels, which permits to determine the role of Feshbach resonances and interaction of different reaction pathways on the global PES of ozone. Pure shape resonances are found to contribute little to the overall recombination process since they occur rather infrequently in the spectrum, in the vicinity of the top of the centrifugal barrier only. Moreover, the associated isotope effects are found to disagree with experimental data. By contrast, Feshbach-type resonances are found to make dominant contribution to the process. They occur in a broader range of spectrum, and their density of states is much higher. The properties of Feshbach resonances are studied in detail. They explain the isotopic ζ -effect, giving theoretical prediction in good agreement with experiments for both singly and doubly substituted ozone molecules. Importantly, Feshbach resonances also contribute to the isotopic η -effect, moving theoretical predictions in the right direction. Some differences with experimental data remain, which indicates that there may be another additional source of the η -effect.

Spiers Memorial Lecture : Introductory lecture: quantum dynamics of chemical reactions

This Spiers Memorial Lecture discusses quantum effects that can be calculated and observed in the chemical reactions of small molecules.

On stabilization of scattering resonances in recombination reaction that forms ozone

Calculations of energy transfer in the recombination reaction that forms ozone are carried out within the framework of the mixed quantum/classical theory and using the dimensionally reduced 2D-model of ozone molecule, with bending motion neglected. Recombination rate coefficients are obtained at room temperature for symmetric and asymmetric isotopomers of singly and doubly substituted isotopologues. The processes of resonance formation, spontaneous decay, collisional dissociation, and stabilization by bath gas (Ar) are all characterized and taken into account within the steady-state approximation for kinetics. The focus is on stabilization step, where the mysterious isotopic η-effect was thought to originate from. Our results indicate no difference in cross sections for stabilization of scatteringresonances in symmetric and asymmetric isotopomers. As practical results, the general and simple analytic models for stabilization and dissociation cross sections are presented, which can be applied to resonances in any ozone molecule, symmetric or asymmetric, singly or doubly substituted. Present calculations show some isotope effect that looks similar to the experimentally observed η-effect, and the origin of this phenomenon is in the rates of formation/decay of scatteringresonances, determined by their widths, that are somewhat larger in asymmetric isotopomers than in their symmetric analogues. However, the approximate two-dimensional model used here is insufficient for consistent and reliable description of all features of the isotopic effect in ozone. Calculations using an accurate 3D model are still needed.

A full-dimensional model of ozone forming reaction: the absolute value of the recombination rate coefficient, its pressure and temperature dependencies

Rigorous calculations of scattering resonances in ozone are carried out for a broad range of rotational excitations with a detailed analysis of their properties and contribution into recombination process.

Theory of mass-independent fractionation of isotopes, phase space accessibility, and a role of isotopic symmetry

Key experimental and theoretical features of mass-independent fractionation (MIF) of isotopes, also known as the η-effect, are summarized, including its difference from the exit channel zero-point energy difference effect. The latter exactly cancels in the MIF. One key experimental result is that the MIF for O3 formation is a low-pressure phenomenon and, moreover, that it decreases with increasing pressure of third bodies at pressures far below the "Lindemann fall-off" pressures for three-body recombination of O and O2. A possible origin of the MIF is discussed in terms of a role for isotopologue symmetry in intramolecular energy sharing. An explanation is suggested for the large difference in the fall-off pressure for recombination and the pressure for a large decrease in MIF, in terms of a difference between deactivating collisions and what we term here "symmetry-changing collisions". It is noted that the theory of the MIF involves four recombination rate constants and an equilibrium constant, for each trace isotope, seven rate constants in all and two equilibrium constants. A conceptual shortcut is noted. Experimental and computational information that may provide added insight into the MIF mechanism and tests is described.

On molecular origin of mass-independent fractionation of oxygen isotopes in the ozone forming recombination reaction

Theoretical treatment of ozone forming reaction is developed within the framework of mixed quantum/classical dynamics. Formation and stabilization steps of the energy transfer mechanism are both studied, which allows simultaneous capture of the delta zero-point energy effect and η-effect and identification of the molecular level origin of mass-independent isotope fractionation. The central role belongs to scattering resonances; dependence of their lifetimes on rotational excitation, asymmetry; and connection of their vibrational wave functions to two different reaction channels. Calculations, performed within the dimensionally reduced model of ozone, are in semiquantitative agreement with experiment.

Mixed quantum-classical theory for the collisional energy transfer and the rovibrational energy flow: application to ozone stabilization

A mixed quantum-classical approach to the description of collisional energy transfer is proposed in which the vibrational motion of an energized molecule is treated quantum mechanically using wave packets, while the collisional motion of the molecule and quencher and the rotational motion of the molecule are treated using classical trajectories. This accounts rigorously for quantization of vibrational states, zero-point energy, scattering resonances, and permutation symmetry of identical atoms, while advantage is taken of the classical scattering regime. Energy is exchanged between vibrational, rotational, and translational degrees of freedom while the total energy is conserved. Application of this method to stabilization of the van der Waals states in ozone is presented. Examples of mixed quantum-classical trajectories are discussed, including an interesting example of supercollision. When combined with an efficient grid mapping procedure and the reduced dimensionality approximation, the method becomes very affordable computationally.

Matching-pursuit/split-operator-Fourier-transform simulations of excited-state nonadiabatic quantum dynamics in pyrazine

A simple approach for numerically exact simulations of nonadiabatic quantum dynamics in multidimensional systems is introduced and applied to the description of the photoabsorption spectroscopy of pyrazine. The propagation scheme generalizes the recently developed matching-pursuit/split-operator-Fourier-transform (MP/SOFT) method [Y. Wu and V. S. Batista, J. Chem. Phys. 121, 1676 (2004)] to simulations of nonadiabatic quantum dynamics. The time-evolution operator is applied, as defined by the Trotter expansion to second order accuracy, in dynamically adaptive coherent-state expansions. These representations are obtained by combining the matching-pursuit algorithm with a gradient-based optimization method. The accuracy and efficiency of the resulting computational approach are demonstrated in calculations of time-dependent survival amplitudes and photoabsorption cross sections, using a model Hamiltonian that allows for direct comparisons with benchmark calculations. Simulations in full-dimensional potential energy surfaces involve the propagation of a 24-dimensional wave packet to describe the S(1)S(2) interconversion of pyrazine after S(0)-->S(2) photoexcitation. The reported results show that the generalized MP/SOFT method is a practical and accurate approach to model nonadiabatic reaction dynamics in polyatomic systems.

Semiclassical wave packet study of ozone forming reaction

We have applied the semiclassical wave packet method (SWP) to calculate energies and lifetimes of the metastable states (scattering resonances) in a simplified model of the ozone forming reaction. All values of the total angular momentum up to J=50 were analyzed. The results are compared with numerically exact quantum mechanical wave packet propagation and with results of the time-independent WKB method. The wave functions for the metastable states in the region over the well are reproduced very accurately by the SWP; in the classically forbidden region and outside of the centrifugal barrier, the SWP wave functions are qualitatively correct. Prony's method was used to extract energies and lifetimes from the autocorrelation functions. Energies of the metastable states obtained using the SWP method are accurate to within 0.1 and 2 cm(-1) for under-the-barrier and over-the-barrier states, respectively. The SWP lifetimes in the range of 0.5<tau(n)<100 ps are accurate to within 10%. A three-level model was used to investigate accuracies of different approximations for the reaction rate constant. It was shown that the majority of the metastable states in this system are either long lived (narrow resonances) which can be treated as stable, or short lived (broad resonances) which can be treated without the knowledge of their lifetimes. Only a few metastable states fall into the intermediate range where both energies and lifetimes are needed to model the kinetics. The recombination rate constant calculated with the SWP method at room temperature and pressure is in good agreement with available experimental data.

Matching-pursuit split-operator Fourier-transform simulations of excited-state intramolecular proton transfer in 2-(2′-hydroxyphenyl)-oxazole

The excited-state intramolecular proton-transfer dynamics associated with the keto-enolic tautomerization reaction in 2-(2(')-hydroxyphenyl)-oxazole is simulated according to a numerically exact quantum-dynamics propagation method and a full-dimensional excited-state potential energy surface, based on an ab initio reaction surface Hamiltonian. The reported simulations involve the propagation of 35-dimensional wave packets according to the recently developed matching-pursuit/split-operator-Fourier-transform (MP/SOFT) method by Wu and Batista. The underlying propagation scheme recursively applies the time-evolution operator as defined by the Trotter expansion to second order accuracy in dynamically adaptive coherent-state expansions. Computations of time-dependent survival amplitudes, photoabsorption cross sections, and time-dependent reactant(product) populations are compared to the corresponding calculations based on semiclassical approaches, including the Herman-Kluk semiclassical initial value representation method. The reported results demonstrate the capabilities of the MP/SOFT method as a valuble computational tool to study ultrafast reaction dynamics in polyatomic systems as well as to validate semiclassical simulations of complex (nonintegrable) quantum dynamics in multidimensional model systems.

Quantum-mechanical calculations on pressure and temperature dependence of three-body recombination reactions: application to ozone formation rates

A quantum-mechanical model is designed for the calculation of termolecular association reaction rate coefficients in the low-pressure fall-off regime. The dynamics is set up within the energy transfer mechanism and the kinetic scheme is the steady-state approximation. We applied this model to the formation of ozone O + O2 + M --> O3 + M for M = Ar, making use of semiquantitative potential energy surfaces. The stabilization process is treated by means of the vibrational close-coupling infinite order sudden scattering theory. Major approximations include the neglect of the O3 vibrational bending mode and rovibrational couplings. We calculated individual isotope-specific rate constants and rate constant ratios over the temperature range 10-1000 K and the pressure fall-off region 10(-7)-10(2) bar. The present results show a qualitative and semiquantitative agreement with available experiments, particularly in the temperature region of atmospheric interest.

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.

Recombination of ozone via the chaperon mechanism

The recombination of ozone via the chaperon mechanism, i.e., ArO+O2 --> Ar+O3 and ArO2+O --> Ar+O3, is studied by means of classical trajectories and a pairwise additive Ar-O3 potential energy surface. The recombination rate coefficient has a strong temperature dependence, which approximately can be described by T(-n) with n approximately 3. It is negligible for temperatures above 700 K or so, but it becomes important for low temperatures. The calculations unambiguously affirm the conclusions of Hippler et al. [J. Chem. Phys. 93, 6560 (1990)] and Luther et al. [Phys. Chem. Chem. Phys. 7, 2764 (2005)] that the chaperon mechanism makes a sizable contribution to the recombination of O3 at room temperature and below. The dependence of the chaperon recombination rate coefficient on the isotopomer, studied for two different isotope combinations, is only in rough qualitative agreement with the experimental data. The oxygen atom isotope exchange reaction involving ArO and ArO2 van der Waals complexes is also investigated; the weak binding of O or O2 to Ar has only a small effect.

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.

A Quantum Dynamical Treatment of Symmetry-Induced Kinetic Isotope Effects in the Formation of He2+

Kinetic isotope effects for He(2)(+) formation are calculated quantum dynamically using high-quality Born-Oppenheimer (BO) potentials for two electronic states of He(2)(+) and an accurate treatment of all nonadiabatic BO corrections. The two potentials are coupled only when the helium isotopes are different, and the calculations reveal that this coupling is sufficient to allow the two sets of distinguishable reactants, (4)He(+) + (3)He or (3)He(+) + (4)He, to yield He(2)(+) with comparable efficiency over a wide temperature range. Consequently, the potential coupling provides a significant formation rate enhancement for the low isotopic symmetry reactants, as compared to the symmetrical cases (e.g., (4)He(+) + (4)He or (3)He(+) + (3)He). The computed symmetry-induced kinetic isotope effects (SIKIEs) are in substantial agreement with the available experimental results and represent the first theoretical demonstration of this unusual kinetic phenomenon. Possible application of SIKIE to ozone formation and other chemical systems is discussed.

Incorporation of nonadiabatic transition into wave-packet dynamics

Nonadiabatic wave-packet dynamics is factorized into purely adiabatic propagation and instantaneous localized nonadiabatic transition. A general formula is derived for the quantum-mechanical local nonadiabatic operator which is implemented within the framework of the R-matrix method. The operator can be used for incorporating the nonadiabatic transition in semiclassical wave-packet dynamics.

Temperature dependent energy transfer in Ar–O3 collisions

The energy transfer between argon atoms and ozone complexes O3*, excited in the region of the dissociation threshold, is calculated for fixed temperatures (100 K< or =T < or =2500 K) using classical trajectories. The internal energy of ozone is resolved in terms of vibrational and rotational energies. For all temperatures, energy flows from O3* to Ar. The vibrational energy transfer, relative to k(B)T, is very small below 500 K, but gradually increases towards high temperatures. The relative rotational energy transfer, on the other hand, monotonously decreases with T; around 1100 K it falls below the relative vibrational energy transfer. Thermally averaged cross sections for vibrational and rotational energy transfers are also calculated. The implications for the stabilization of ozone complexes in the energy transfer model are discussed.

The role of the radical-complex mechanism in the ozone recombination/dissociation reaction

The data bases for low-pressure rate coefficients of the dissociation of O3 and the reverse recombination of O with O2 in the bath gases M=He, Ar, N2, CO2 and SF6 are carefully analyzed. At very high temperatures, the rate constants have to correspond solely to the energy transfer (ET) mechanism. On condition that this holds for Ar and N2 near 800 K, average energies transferred per collision of -DeltaE/hc=18 and 25 cm-1 are derived, respectively. Assuming an only weak temperature dependence of DeltaE as known in similar systems, rate coefficients for the ET-mechanism are extrapolated to lower temperatures and compared with the experiments. The difference between measured and extrapolated rate coefficients is attributed to the radical complex (RC) mechanism. The derived rate coefficients for the RC-mechanism are rationalized in terms of equilibrium constants for equilibria of van der Waals complexes of O (or O2) with the bath gases and with rate coefficients for oxygen abstraction from these complexes. The latter are of similar magnitude as rate coefficients for oxygen isotope exchange which provides support for the present interpretation of the reaction in terms of a superposition of RC- and ET-mechanisms. We obtained rate coefficients for the ET-mechanism of k/[Ar]=2.3x10(-34) (T/300)(-1.5) and k/[N2]=3.5x10(-34) (T/300)(-1.5) cm6 molecule-2 s-1 and rate coefficients for the RC-mechanism of k/[Ar]=1.7x10(-34) (T/300)(-3.2) and k/[N2]=2.5x10(-34) (T/300)(-3.3) cm6 molecule-2 s-1. The data bases for M=He, CO2 and SF6 are less complete and only approximate separations of RC- and ET-mechanism were possible. The consequences of the present analysis for an analysis of isotope effects in ozone recombination are emphasized.

Matching-pursuit∕split-operator Fourier-transform simulations of nonadiabatic quantum dynamics

A rigorous and practical approach for simulations of nonadiabatic quantum dynamics is introduced. The algorithm involves a natural extension of the matching-pursuitsplit-operator Fourier-transform (MPSOFT) method [Y. Wu and V. S. Batista, J. Chem. Phys. 121, 1676 (2004)] recently developed for simulations of adiabatic quantum dynamics in multidimensional systems. The MPSOFT propagation scheme, extended to nonadiabatic dynamics, recursively applies the time-evolution operator as defined by the standard perturbation expansion to first-, or second-order, accuracy. The expansion is implemented in dynamically adaptive coherent-state representations, generated by an approach that combines the matching-pursuit algorithm with a gradient-based optimization method. The accuracy and efficiency of the resulting propagation method are demonstrated as applied to the canonical model systems introduced by Tully for testing simulations of dual curve-crossing nonadiabatic dynamics.

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.

Matching-pursuit/split-operator-Fourier-transform computations of thermal correlation functions

A rigorous and practical methodology for evaluating thermal-equilibrium density matrices, finite-temperature time-dependent expectation values, and time-correlation functions is described. The method involves an extension of the matching-pursuit/split-operator-Fourier-transform method to the solution of the Bloch equation via imaginary-time propagation of the density matrix and the evaluation of Heisenberg time-evolution operators through real-time propagation in dynamically adaptive coherent-state representations.

Quantum tunneling dynamics in multidimensional systems: A matching-pursuit description

Rigorous simulations of quantum tunneling dynamics in model systems with up to 20 coupled degrees of freedom are reported. The simulations implement an extension of the recently developed matching-pursuit/split-operator Fourier-transform method to complex-valued coherent-state representations. The resulting method recursively applies the time-evolution operator, as defined by the Trotter expansion to second order accuracy, in dynamically adaptive coherent-state representations generated by an approach that combines the matching-pursuit algorithm with a gradient-based optimization method.

Some symmetry-induced isotope effects in the kinetics of recombination reactions

Symmetry-induced isotope effects in recombination and collision-induced dissociation reactions are discussed. Progress on understanding the anomalous isotope effects in ozone is reviewed. Then, calculations are performed for the simpler reaction xNe+yNe+H<-->xNeyNe+H, where x and y label either identical or different isotopes. The atomic masses in the model are chosen so that symmetry is the only difference between the systems. Starting from a single potential energy surface, the properties of the bound, quasibound, and continuum states of the neon dimer are calculated. Then, the vibration rotation infinite order sudden approximation is used to calculate cross sections for all possible inelastic and dissociative processes. A rate constant matrix that exactly satisfies detailed balance is constructed. It allows recombination to occur both via direct three-body collisions and via tunneling into the quasibound states of the energy transfer mechanism. The eigenvalue rate coefficients are determined. Significant isotope effects are clearly found, and their behavior depends on the pressure, temperature, and mechanism of the reaction. Both spin statistics and symmetry breaking produce isotope effects. Under most conditions the breaking of symmetry enhances the rates, but a wide spectrum of effects is observed; they range from isotope effects with a normal mass dependence to huge, mass-independent isotope effects to cancellation and even to reversal of the isotope effects. This is the first calculation of symmetry-induced isotope effects in recombination rates from first principles. The relevance of the present effects to ozone recombination is discussed.

Intra- and intermolecular energy transfer in highly excited ozone complexes

The energy transfer of highly excited ozone molecules is investigated by means of classical trajectories. Both intramolecular energy redistribution and the intermolecular energy transfer in collisions with argon atoms are considered. The sign and magnitude of the intramolecular energy flow between the vibrational and the rotational degrees of freedom crucially depend on the projection K(a) of the total angular momentum of ozone on the body-fixed a axis. The intermolecular energy transfer in single collisions between O(3) and Ar is dominated by transfer of the rotational energy. In accordance with previous theoretical predictions, the direct vibrational de-excitation is exceedingly small. Vibration-rotation relaxation in multiple Ar+O(3) collisions is also studied. It is found that the relaxation proceeds in two clearly distinguishable steps: (1) During the time between collisions, the vibrational degrees of freedom are "cooled" by transfer of energy to rotation; even at low pressure equilibration of the internal energy is slow compared to the time between collisions. (2) In collisions, mainly the rotational modes are "cool" by energy transfer to argon.