Efficient Method for Calculations of Ro-vibrational States in Triatomic Molecules Near Dissociation Threshold: Application to Ozone

A method for calculations of rotational-vibrational states of triatomic molecules up to dissociation threshold (and scattering resonances above it) is devised, that combines hyper-spherical coordinates, sequential diagonalization-truncation procedure, optimized grid DVR, and complex absorbing potential. Efficiency and accuracy of the method and new code are tested by computing the spectrum of ozone up to dissociation threshold, using two different potential energy surfaces. In both cases good agreement with results of previous studies is obtained for the lower energy states localized in the deep (∼10 000 cm−1) covalent well. Upper part of the bound state spectrum, within 600 cm−1 below dissociation threshold, is also computed and is analyzed in detail. It is found that long progressions of symmetric-stretching and bending states (up to 8 and 11 quanta, respectively) survive up to dissociation threshold and even above it, whereas excitations of the asymmetric-stretching overtones couple to the local vibration modes, making assignments difficult. Within 140 cm−1 below dissociation threshold, large-amplitude vibrational states of a floppy complex O⋯O2 are formed over the shallow van der Waals plateau. These are assigned using two local modes: the rocking-motion and the dissociative-motion progressions, up to 6 quanta in each, both with frequency ∼20 cm−1. Many of these plateau states are mixed with states of the covalent well. Interestingly, excitation of the rocking-motion helps keeping these states localized within the plateau region, by raising the effective barrier

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. The accurate potential energy surface of Dawes is adopted, and a new efficient method for calculations of ro–vibrational energies, wave functions and resonance lifetimes is employed (which uses hyper-spherical coordinates, the sequential diagonalization/truncation approach, grid optimization and complex absorbing potential). A detailed analysis is carried out to characterize distributions of resonance energies and lifetimes, their rotational/vibrational content and their positions with respect to the centrifugal barrier. Emphasis is on the contribution of these resonances to the recombination process that forms ozone. It is found that major contributions come from localized resonances at energies near the top of the barrier. Delocalized resonances at higher energies should also be taken into account, while very narrow resonances at low energies (trapped far behind the centrifugal barrier) should be treated as bound states. The absolute value of the recombination rate coefficient, its pressure and temperature dependencies are obtained using the energy-transfer model developed in the earlier work. Good agreement with experimental data is obtained if one follows the suggestion of Troe, who argued that the energy transfer mechanism of recombination is responsible only for 55% of the recombination rate (with the remaining 45% coming from the competing chaperon mechanism)

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

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

Frozen Rotor Approximation in the Mixed Quantum/Classical Theory for Collisional Energy Transfer: Application to Ozone Stabilization

A frozen-rotor approximation is formulated for the mixed quantum/classical theory of collisional energy transfer and ro-vibrational energy flow [M. Ivanov and D. Babikov, J. Chem. Phys.134, 144107 (Year: 2011)]. Numerical tests are conducted to assess its efficiency and accuracy, compared to the original version of the method, where rotation of the molecule in space is treated explicitly and adiabatically. New approach is considerably faster and helps blocking the artificial ro-vibrational transitions at the pre- and post-collisional stages of the process. Although molecular orientation in space is fixed, the energy exchange between rotational, vibrational, and translational digresses of freedom still occurs, allowing to compute ro-vibrational excitation and quenching. Behavior of the energy transfer function through eight orders of magnitude range of values and in a broad range of ΔE is reproduced well. In the range of moderate −500 ⩽ ΔE ⩽ +500 cm−1 the approximate method is rather accurate. The absolute values of stabilization cross sections for scattering resonances trapped behind the centrifugal threshold are a factor 2-to-3 smaller (compared to the explicit-rotation approach). This performance is acceptable and similar to the well-known sudden-rotation approximation in the time-independent inelastic scattering methods

Hydration of a B-DNA Fragment in the Method of Atom-atom Correlation Functions with the Reference Interaction Site Model Approximation

We propose an efficient numerical algorithm for solving integral equations of the theory of liquids in the Reference Interaction Site Model (RISM) approximation for infinitely dilute solution of macromolecules with a large number of atoms. The algorithm is based on applying the nonstationary iterative methods for solving systems of linear algebraic equations. We calculate the solvent-solute atom-atom correlation functions for a fragment of the B-DNA duplex d(GGGGG).d(CCCCC) in infinitely dilute aqueous solution. The obtained results are compared with available experimental data and results from computer simulations.Comment: 9 pages, RevTeX, 9 pages of ps figures, accepted for publications in JC

Theoretical Study of Ozone Forming Recombination Reaction and Anomalous Isotope Effect Associated with It

The ozone forming recombination reaction stands out among many chemical processes that take place in the atmosphere. This reaction is responsible for the reconstruction of ozone layer, which protects life on Earth from harmful ultra-violate radiation and is a source of so-called anomalous isotope effect in ozone. The reaction was intensively studied, but at a very basic level. There were only couple of papers where the recombination rate coefficient was computed and found to roughly agree with the experimental data. In this dissertation, the recombination process in ozone is approached using new and efficient method, which includes several modern techniques. The rovibrational scattering resonances of O3 are characterized by solving three-dimensional time-independent Schrödinger equation in symmetric-top approximation. The widths (or lifetimes) of scattering resonances are computed using complex absorbing potential. The high efficiency is achieved by using convenient vibrational coordinates, optimal grid for dissociative coordinate and construction of small Hamiltonian matrix in locally optimal basis. The symmetry of the problem is also utilized by implementing a symmetry-adapted basis for one of vibrational coordinates. Stabilization of scattering resonances is described approximately, using mixed quantum/classical theory, for which an efficient frozen rotor approximation is developed. The rate coefficient of ozone recombination, predicted here for unsubstituted ozone, 48O3, as well as its pressure and temperature dependencies, agrees very well with experimental data. The isotope effects, one related to zero-point energy and another to symmetry, are studied for a limited number of rotational excitations and for two isotopologues 50O3 and 52O3 (singly and doubly substituted with 18O). Both effects were found to be in the right direction and of right order of magnitude. The width of scattering resonances control these isotope effects. The approach is universal and can be applied to any other similar system, for example, S3

Interactive Tool for Visualization of Adiabatic Adjustment in APH Coordinates for Computational Studies of Vibrational Motion and Chemical Reactions

The adiabatically-adjusting principal-axes hyperspherical (APH) coordinates reviewed in this letter are one of the best coordinate sets developed for computational treatment of spectroscopy and dynamics of triatomic molecules. Unfortunately, it is not so easy to understand and interpret them, compared to other simpler coordinates, like valence coordinates or Jacobi coordinates. To address this issue, we developed a desktop application called APHDemo. This tool visualizes the process of adjustment of the APH coordinates to the shape of a triatomic molecule during molecular vibrations or chemical reaction, and helps to understand their physical meaning without going into complicated math

The Ratio of The Number of States in Asymmetric and Symmetric Ozone Molecules Deviates from The Statistical Value Of 2

Accurate calculations of vibrational states in singly and doubly substituted ozone molecules are carried out, up to dissociation threshold. Analysis of these spectra reveals noticeable deviations from the statistical factor of 2 for the ratio between the number of states in asymmetric and symmetric ozone molecules. It is found that, for the lower energy parts of spectra, the ratio is less than 2 in the singly substituted ozone molecules, but it is more than 2 in the doubly substituted ozone molecules. However, the upper parts of spectra, just below dissociation thresholds, exhibit a different behavior. In this energy range, the singly and doubly substituted ozone molecules behave similar, with the ratio of states in asymmetric and symmetric ozone molecules being more than 2 in both cases. This property may contribute to an explanation of the mysterious η-effect in the ozone forming reaction that favors the formation of the asymmetric ozone molecules