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).
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 characterize the employed potentials by their centrifugal barriers E0(J). The derived specific rigidity factors frigid(E,J) are consistent with previously calculated thermal rigidity factors frigid(T). The present approach properly accounts for angular momentum conservation and, at the same time, facilitates the calculation of specific rate constants k(E,J) and falloff curves for unimolecular bond fission and the reverse radical recombination reactions.
The addition of atoms to linear molecules forming linear or nonlinear adducts is treated using standardized valence potentials. The dynamics is analyzed with a combination of classical trajectory (CT) and statistical adiabatic channel (SACM) calculations. For classical adiabatic conditions, the two approaches coincide. The transition from adiabatic to nonadiabatic dynamics is investigated using CT calculations. The low-temperature adiabatic quantum range is studied by SACM. Thermal capture rate constants are represented in analytical form. Thermal rigidity factors are expressed in terms of molecular parameters such as the frequencies of transitional bending modes, the bond dissociation energy, the rotational constant of the linear fragment, and the ratio of the looseness and Morse parameters α/β of the potential-energy surface. The final rate expressions are of simple form suitable for direct practical applications.
The energy dependence of the capture cross section and the temperature dependence of the capture rate constants for inverse power attractive potentials VϰϪR Ϫn is considered in the regime where the quantum character of the relative motion of colliding partners is important. For practically interesting cases nϭ4 and nϭ6, a simple formula for the cross section is suggested which interpolates between the classical and the quantum Bethe limits. We have shown that the classical approximation for the capture cross section performs well far below the simple estimations of the onset the quantum regime. This seemingly ''classical'' feature of the cross section and the rate constant is due to the large quantum effects of the waves in transmission through and reflection above the centrifugal potential barriers.
The potential energy surface of the HO+O⇔HO2⇔H+O2 reaction system is characterized by ab initio calculations. The complex-forming bimolecular reaction is then treated by statistical rate theory, using statistical adiabatic channel and classical trajectory calculations for the HO+O⇔HO2 and HO2⇔H+O2 association/dissociation processes. Specific rate constants k(E,J) of both reactions as well as thermal rate constants are calculated over wide ranges of conditions. Open shell quantum effects are important up to room temperature. The good agreement with experimental results suggests that the ab initio potential is of sufficient accuracy. There is no evidence for non-statistical effects or for a significant contribution from electronically excited states. The comparison with rate data for the H+O2→HO+O reaction, because of the remaining uncertainty in the heat of formation of HO, is somewhat inconclusive. Apart from this problem, the calculated rate constants appear reliable between 0 and 5000 K.
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