V. G. Ushakov

Classical trajectory and statistical adiabatic channel study of the dynamics of capture and unimolecular bond fission. IV. Valence interactions between atoms and linear rotors

The combination of two linear rotors forming linear or nonlinear adducts is treated using standardized valence potentials. Classical trajectory (CT) and statistical adiabatic channel (SACM) calculations are used for the calculation of thermal capture rate constants. At very low temperatures, only SACM applies. At intermediate temperatures SACM and CT approach each other; however, Landau–Zener-type multiple crossings of adiabatic channel potentials introduce local nonadiabaticity which has to be accounted for. The high-temperature transition from globally adiabatic to nonadiabatic (sudden) dynamics is studied by CT. Thermal rigidity factors, accounting for the influence of the anisotropy of the potential on the capture rate constant, are expressed in simple analytical form which facilitates practical applications. The present work complements similar studies on the addition of atoms to linear molecules in standardized valence potentials (part IV of this series).

Classical trajectory and statistical adiabatic channel study of the dynamics of capture and unimolecular bond fission. VI. Properties of transitional modes and specific rate constants k(E,J)

Transitional modes in simple unimolecular bond fission and in the reverse recombination reactions are characterized quantitatively by statistical adiabatic channel (SACM) and classical trajectory (CT) calculations. Energy E- and angular momentum J-specific numbers of open channels (or activated complex states) W(E,J) and capture probabilities w(E,J) are determined for a series of potentials such as ion—dipole, dipole–dipole, and various model valence potentials. SACM and CT treatments are shown to coincide under classical conditions. Adiabatic as well as nonadiabatic dynamics are considered. The dominant importance of angular momentum couplings is elaborated. A sequence of successive approximations, from phase space theory neglecting centrifugal barriers E0(J), via phase space theory accounting for centrifugal barriers E0(J), toward the final result, expressing the effects of the anisotropy of the potentials by specific rigidity factors frigid(E,J), is described. This approach emphasizes the importance to...

Activation of Methane by FeO+: Determining Reaction Pathways through Temperature-Dependent Kinetics and Statistical Modeling

The temperature dependences of the rate constants and product branching ratios for the reactions of FeO(+) with CH4 and CD4 have been measured from 123 to 700 K. The 300 K rate constants are 9.5 × 10(-11) and 5.1 × 10(-11) cm(3) s(-1) for the CH4 and CD4 reactions, respectively. At low temperatures, the Fe(+) + CH3OH/CD3OD product channel dominates, while at higher temperatures, FeOH(+)/FeOD(+) + CH3/CD3 becomes the majority channel. The data were found to connect well with previous experiments at higher translational energies. The kinetics were simulated using a statistical adiabatic channel model (vibrations are adiabatic during approach of the reactants), which reproduced the experimental data of both reactions well over the extended temperature and energy ranges. Stationary point energies along the reaction pathway determined by ab initio calculations seemed to be only approximate and were allowed to vary in the statistical model. The model shows a crossing from the ground-state sextet surface to the excited quartet surface with large efficiency, indicating that both states are involved. The reaction bottleneck for the reaction is found to be the quartet barrier, for CH4 modeled as -22 kJ mol(-1) relative to the sextet reactants. Contrary to previous rationalizations, neither less favorable spin-crossing at increased energies nor the opening of additional reaction channels is needed to explain the temperature dependence of the product branching fractions. It is found that a proper treatment of state-specific rotations is crucial. The modeled energy for the FeOH(+) + CH3 channel (-1 kJ mol(-1)) agrees with the experimental thermochemical value, while the modeled energy of the Fe(+) + CH3OH channel (-10 kJ mol(-1)) corresponds to the quartet iron product, provided that spin-switching near the products is inefficient. Alternative possibilities for spin switching during the reaction are considered. The modeling provides unique insight into the reaction mechanisms as well as energetic benchmarks for the reaction surface.

Further Insight into the Reaction FeO+ + H2 → Fe+ + H2O: Temperature Dependent Kinetics, Isotope Effects, and Statistical Modeling

The reactions of FeO(+) with H2, D2, and HD were studied in detail from 170 to 670 K by employing a variable temperature selected ion flow tube apparatus. High level electronic structure calculations were performed and compared to previous theoretical treatments. Statistical modeling of the temperature and isotope dependent rate constants was found to reproduce all data, suggesting the reaction could be well explained by efficient crossing from the sextet to quartet surface, with a rigid near thermoneutral barrier accounting for both the inefficiency and strong negative temperature dependence of the reactions over the measured range of thermal energies. The modeling equally well reproduced earlier guided ion beam results up to translational temperatures of about 4000 K.

Adiabatic and postadiabatic channel description of atom–diatom long‐range half‐collision dynamics: Interchannel radial coupling for P1 and P2 anisotropy

It is shown that the adiabatic channel states of an atom–diatom system with a low‐rank interaction anisotropy (proportional to cos γ and cos2 γ) exhibit a nonlocalized nonadiabatic coupling which persists into the strong coupling region. This feature of adiabatic channel states restricts application of the statistical adiabatic channel model (SACM) for processes of complex decomposition and complex formation to low energies. The change of the representation from adiabatic into the postadiabatic (dynamic) one transforms the coupling to a localized form and makes it possible to find conditions for description of the half‐collision dynamics in terms of uncoupled dynamic states. This result can be regarded as the extension of the statistical adiabatic channel model beyond its formal limits of applicability provided the adiabatic channel potentials are replaced by the postadiabatic (dynamic) potentials. The obtained results are exemplified by calculation of the capture cross section in the approximation of unc...

Rotational effects in broadening factors of fall-off curves of unimolecular dissociation reactions

Strong collision fall-off curves of unimolecular dissociation and the reverse recombination reactions are calculated by using the statistical adiabatic channel/classical trajectory model (SACM/CT). This formalism properly accounts for angular momentum coupling of transitional modes with overall rotation. Calculations are made for linear molecules dissociating into linear fragments and atoms with randomly chosen properties of the transitional modes and for isotropic as well as anisotropic potentials. Analytical representations of center broadening factors as a function of molecular parameters are given. A comparison between fall-off curves from rigid activated complex RRKM theory, from the present loose activated complex SACM/CT model, and from CT calculations on an ab initio potential is made for the HO2-->H + O2 system. It is shown that, besides rotational effects, energy-dependent anharmonicities of the density of states also influence the shape of the fall-off curves in this system.

Spin-inversion and spin-selection in the reactions FeO+ + H2 and Fe+ + N2O

The reactions of FeO(+) with H2 and of Fe(+) with N2O were studied with respect to the production and reactivity of electronically excited (4)Fe(+) cations. The reaction of electronic ground state (6)FeO(+) with H2 was found to predominantly produce electronically excited (4)Fe(+) as opposed to electronic ground state (6)Fe(+) corresponding to a spin-allowed reaction. (4)Fe(+) was observed to react with N2O with a rate constant of 2.3 (+0.3/-0.8) × 10(-11) cm(3) molecule(-1) s(-1), smaller than the ground state (6)Fe(+) rate constant of 3.2 (±0.5) × 10(-11) cm(3) molecule(-1) s(-1) (at room temperature). While the overall reaction of (6)FeO(+) with H2 within the Two-State-Reactivity concept is governed by efficient sextet-quartet spin-inversion in the initial reaction complex, the observation of predominant (4)Fe(+) production in the reaction is attributed to a much less efficient quartet-sextet back-inversion in the final reaction complex. Average spin-inversion probabilities are estimated by statistical modeling of spin-inversion processes and related to the properties of spin-orbit coupling along the reaction coordinate. The reaction of FeO(+) with H2 served as a source for (4)Fe(+), subsequently reacting with N2O. The measured rate constant has allowed for a more detailed understanding of the ground state (6)Fe(+) reaction with N2O, leading to a significantly improved statistical modeling of the previously measured temperature dependence of the reaction. In particular, evidence for the participation of electronically excited states of the reaction complex was found. Deexcitation of (4)Fe(+) by He was found to be slow, with a rate constant <3 × 10(-14) cm(3) molecule(-1) s(-1).

Statistical modeling of the reactions Fe+ + N2O → FeO+ + N2 and FeO+ + CO → Fe+ + CO2

The rates of the reactions Fe(+) + N2O → FeO(+) + N2 and FeO(+) + CO → Fe(+) + CO2 are modeled by statistical rate theory accounting for energy- and angular momentum-specific rate constants for formation of the primary and secondary cationic adducts and their backward and forward reactions. The reactions are both suggested to proceed on sextet and quartet potential energy surfaces with efficient, but probably not complete, equilibration by spin-inversion of the populations of the sextet and quartet adducts. The influence of spin-inversion on the overall reaction rate is investigated. The differences of the two reaction rates mostly are due to different numbers of entrance states (atom + linear rotor or linear rotor + linear rotor, respectively). The reaction Fe(+) + N2O was studied either with (6)Fe(+) or with (4)Fe(+) reactants. Differences in the rate constants of (6)Fe(+) and (4)Fe(+) reacting with N2O are attributed to different contributions from electronically excited potential energy surfaces, such as they originate from the open-electronic shell reactants.

Intensity anomalies in the rotational and ro-vibrational spectra of diatomic molecules

We study the anomalies in the distributions of intensities of transitions in the purely rotational bands and the rotational branches of the vibrational bands within the unperturbed ground electronic states in spectra of diatomic molecules. While normally these distributions follow smooth patterns, sudden drops in intensity values are often observed. We analyze the origin of these anomalies in HF, DF, and CO and find that they are predominantly associated with specific forms of the dipole-moment functions (DMFs). The rotational transitions at which these anomalies occur and their severity are very sensitive to these forms, which makes them a promising tool for refining the empirical DMFs.

On some methods for improving time of reachability sets computation for the dynamic system control problem

The paper presents two different approaches to reduce the time of computer calculation of reachability sets. First of these two approaches use different data structures for storing the reachability sets in the computer memory for calculation in single-threaded mode. Second approach is based on using parallel algorithms with reference to the data structures from the first approach. Within the framework of this paper parallel algorithm of approximate reachability set calculation on computer with SMP-architecture is proposed. The results of numerical modelling are presented in the form of tables which demonstrate high efficiency of parallel computing technology and also show how computing time depends on the used data structure.