Frozen rotor approximation in the mixed quantum/classical theory for collisional energy transfer: Application to ozone stabilization

Abstract

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 (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 E is reproduced well. In the range of moderate −500 ≤ E ≤ +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.

Use of Isotope Effects To Understand the Present and Past of the Atmosphere and Climate and Track the Origin of Life

“…[39][40][41][42][43][44][45][46][47][48][49][50] In aq uantum-mechanicallybased approach, the energies and lifetimes of metastable states of ozone for total angular momentum J = 0w ere calculated using new potential energy surfaces. [39][40][41][42][43][44][45][46][47][48][49][50] In aq uantum-mechanicallybased approach, the energies and lifetimes of metastable states of ozone for total angular momentum J = 0w ere calculated using new potential energy surfaces.…”

“…Thed ifficulty in handling the simultaneous effect in the energy transfer process,zero-point energy effect, h-effect, requires state of art computational ability.T he core of the modeling is the dependence of lifetime upon rotational excitation, asymmetry,a nd connection of their vibrational wave functions to the different exit channels. [46,[48][49][50] Until the recent computation [48][49][50] the resonances were difficult to quantify and are of significance. [47] Them ost precise model to date has folded in symmetry,z ero-point energy,s cattering resonances.…”

“…Ad ifferent approach to modeling has been pursued by Babikov and colleagues. [39][40][41][42][43][44][45][46][47][48][49][50] In aq uantum-mechanicallybased approach, the energies and lifetimes of metastable states of ozone for total angular momentum J = 0w ere calculated using new potential energy surfaces. [40] It is in this specific energy transfer event of the transient ozone species stabilizes during collisions,n ot unlike the approach of Heidenreich and Thiemens [20] but more sophisticated in the modeling and potential energy surface.T he kinetics associated with the excited isotopic species and three exit channels were later included in the calculation as well as the differences in the molecular oxygen and in zero-point energies for the isotopologues.The lifetimes of the different excited states species are also included along with the effects arising from symmetries.The lifetimes were obtained from afull quantum mechanical scattering calculation following ac oupled-channel approach as well as the three-dimensional shapes of the surfaces.…”

Rotational quenching of H2O by He: Mixed quantum/classical theory and comparison with quantum results

“…dmitri.babikov@mu.edu and collaborators [12][13][14][15][16][17] and tested against the full-quantum calculations in a broad range of scattering energies. 18,19 Another option is to treat rotational motion of the molecule quantum mechanically, either keeping the vibrational motion frozen (which corresponds to the rigid rotor) or treating it also quantum mechanically, in which case all the internal molecular degrees of freedom are described coherently.…”

Efficient method for calculations of ro-vibrational states in triatomic molecules near dissociation threshold: Application to ozone

“…18 For example, for an ozone molecule in its equilibrium configuration the values of rotational constants are A 2 = 0.45 cm −1 , B 2 = 0.66 cm −1 , and C 2 = 3.56 cm −1 , which makes it very close to a prolate symmetric-top rotor. For this reason, the K-conserving approximation has been used in the past in several studies of ozone spectra and dynamics, 35,37 and was also adopted in our recent work. 11 Within this approximation, calculations of vibrational states are carried out independently for different values of K, such that K < J, for each J > 0.…”