Recombination Reactions as a Possible Mechanism of Mass-Independent Fractionation of Sulfur Isotopes in the Archean Atmosphere of Earth

A hierarchy of isotopically substituted recombination reactions is formulated for production of sulfur allotropes in the anoxic atmosphere of Archean Earth. The corresponding system of kinetics equations is solved analytically to obtain concise expressions for isotopic enrichments, with focus on mass-independent isotope effects due to symmetry, ignoring smaller mass-dependent effects. Proper inclusion of atom-exchange processes is shown to be important. This model predicts significant and equal depletions driven by reaction stoichiometry for all rare isotopes: 33S, 34S, and 36S. Interestingly, the ratio of capital Δ values obtained within this model for 33S and 36S is −1.16, very close to the mass-independent fractionation line of the Archean rock record. This model may finally offer a mechanistic explanation for the striking mass-independent fractionation of sulfur isotopes that took place in the Archean atmosphere of Earth

Recent Advances in Development and Applications of the Mixed Quantum/Classical Theory for Inelastic Scattering

A mixed quantum/classical approach to inelastic scattering (MQCT) is developed in which the relative motion of two collision partners is treated classically, and the rotational and vibrational motion of each molecule is treated quantum mechanically. The cases of molecule + atom and molecule + molecule are considered including diatomics, symmetric-top rotors, and asymmetric-top rotor molecules. Phase information is taken into consideration, permitting calculations of elastic and inelastic, total and differential cross sections for excitation and quenching. The method is numerically efficient and intrinsically parallel. The scaling law of MQCT is favorable, which enables calculations at high collision energies and for complicated molecules. Benchmark studies are carried out for several quite different molecular systems (N2 + Na, H2 + He, CO + He, CH3 + He, H2O + He, HCOOCH3 + He, and H2 + N2) in a broad range of collision energies, which demonstrates that MQCT is a viable approach to inelastic scattering. At higher collision energies it can confidently replace the computationally expensive full-quantum calculations. At low collision energies and for low-mass systems results of MQCT are less accurate but are still reasonable. A proposal is made for blending MQCT calculations at higher energies with full-quantum calculations at low energies

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

Inelastic Scattering of Identical Molecules within Framework of the Mixed Quantum/Classical Theory: Application to Rotational Excitations in H\u3csub\u3e2\u3c/sub\u3e + H\u3csub\u3e2\u3c/sub\u3e

Theoretical foundation is laid out for description of permutation symmetry in the inelastic scattering processes that involve collisions of two identical molecules, within the framework of the mixed quantum/classical theory (MQCT). In this approach, the rotational (and vibrational) states of two molecules are treated quantum-mechanically, whereas their translational motion (responsible for scattering) is treated classically. This theory is applied to H2 + H2 system, and the state-to-state transition cross sections are compared versus those obtained from the full-quantum calculations and experimental results from the literature. Good agreement is found in all cases. It is also found that results of MQCT, where the Coriolis coupling is included classically, are somewhat closer to exact full-quantum results than results of the other approximate quantum methods, where those coupling terms are neglected. These new developments allow applications of MQCT to a broad variety of molecular systems and processes

Global Permutationally Invariant Potential Energy Surface for Ozone Forming Reaction

We constructed new global potential energy surface for O + O2 → O3 reaction. It is based on high level electronic structure theory calculations and employs fitting by permutationally invariant polynomial functions. This method of surface construction takes full advantage of permutation symmetry of three O nuclei and allows reducing dramatically the number of ab initio data points needed for accurate surface representation. New potential energy surface offers dramatic improvement over older surface of ozone in terms of dissociation energy and behavior along the minimum energy path. It can be used to refine the existing theories of ozone formation

Improved Potential Energy Surface of Ozone Constructed Using the Fitting by Permutationally Invariant Polynomial Function

New global potential energy surface for the ground electronic state of ozone is constructed at the complete basis set level of the multireference configuration interaction theory. A method of fitting the data points by analytical permutationally invariant polynomial function is adopted. A small set of 500 points is preoptimized using the old surface of ozone. In this procedure the positions of points in the configuration space are chosen such that the RMS deviation of the fit is minimized. New ab initio calculations are carried out at these points and are used to build new surface. Additional points are added to the vicinity of the minimum energy path in order to improve accuracy of the fit, particularly in the region where the surface of ozone exhibits a shallow van der Waals well. New surface can be used to study formation of ozone at thermal energies and its spectroscopy near the dissociation threshold

MQCT. I. Inelastic Scattering of Two Asymmetric-Top Rotors with Application to H\u3csub\u3e2\u3c/sub\u3eO + H\u3csub\u3e2\u3c/sub\u3eO

A mixed quantum/classical theory (MQCT) for the inelastic collision of two asymmetric-top rotor molecules is developed. In this method, the quantum state-to-state transitions between the rotational states of molecules (internal) are treated quantum mechanically using the time-dependent Schrodinger equation, whereas their relative translational motion (responsible for scattering) is treated classically, using the average trajectory approach. Two versions of the formula for transition matrix elements are presented: a straightforward approach that uses numerical multidimensional quadrature over all the internal degrees of freedom and a more standard analytic approach that uses the expansion of the PES over the basis set of spherical harmonics. Adaptation to the case of identical molecules scattering is presented and is applied to the rotational excitation of two water molecules, H2O + H2O, using the PES from recent literature. Calculations of collisional excitation from the ground state of the system into a number of low-lying excited rotational states are carried out in a broad range of energies. Analysis of computed opacity functions shows a rather unusual scattering regime, dominated by a strong anisotropic long-range interaction (dipole–dipole). The coupled-states (CS) approximation is tested and found to agree semiquantitatively (within a factor of 2) with the fully coupled version of the method. Differential cross sections for the elastic scattering indicate a very narrow forward scattering peak

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)

Three Sources of Errors in The Ehrenfest Treatment of Inelastic Scattering and Possible Ways of Resolving Them

In order to identify the origin of possible errors in the mixed quantum/classical approach to inelastic scattering [A. Semenov and D. Babikov, J. Chem. Phys. 140, 044306 (2014) and A. Semenov, M.-L. Dubernet, and D. Babikov, J. Chem. Phys. 141, 114304 (2014)], a simplified model is considered that consists of one intermolecular degree of freedom and two intramolecular states, coupled by a simple potential. For this system, analytic derivations are carried out to determine (i) the exact quantum mechanical solutionof the inelastic scattering problem, (ii) a simplified version of it with all oscillatory terms neglected, and (iii) the Ehrenfest solution in which the translational motion is described by the mean-field trajectory while the internal molecular motion is treated by the time-dependent Schrodinger equation. It is shown that the appropriate choice of velocity for the mean-fieldtrajectory permits to enforce microscopic reversibility and gives results in excellent agreement with full-quantum results. The average velocity method of Billing is rigorously derived as a limiting case (of this more general approach), when reversibility is enforced locally, at the initial moment of time only. It is demonstrated that errors of state-to-state transition probabilities in the Ehrenfest approach occur at lower values of total energy E if the magnitudes of excitation energy ΔE, potential energy difference between the two states ΔV, and coupling of two states V12 are large. Possible ways of applying this concept to rotational transitions in real molecules are explored, using examples from CO + CO inelastic scattering

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