Lifetimes and wave functions of ozone metastable vibrational states near the dissociation limit in a full-symmetry approach

Abstract

Energies and lifetimes (widths) of vibrational states above the lowest dissociation limit of 16 O 3 were determined using a previously-developed efficient approach, which combines hyperspherical coordinates and a complex absorbing potential. The calculations are based on a recently-computed potential energy surface of ozone determined with a spectroscopic accuracy [J. Chem. Phys. 139, 134307 (2013)]. The effect of permutational symmetry on rovibrational dynamics and the density of resonance states in O 3 is discussed in detail. Correspondence between quantum numbers appropriate for short-and long-range parts of wave functions of the rovibrational continuum is established. It is shown, by symmetry arguments, that the allowed purely vibrational (J = 0) levels of 16 O 3 and 18 O 3 , both made of bosons with zero nuclear spin, cannot dissociate on the ground state potential energy surface. Energies and wave functions of bound states of the ozone isotopologue 16 O 3 with rotational angular momentum J = 0 and 1 up to the dissociation threshold were also computed. For bound levels, good agreement with experimental energies is found:The RMS deviation between observed and calculated vibrational energies is 1 cm −1 . Rotational constants were determined and used for a simple identification of vibrational modes of calculated levels.

Several levels of theory for description of isotope effects in ozone: Effect of resonance lifetimes and channel couplings

“…1(b) correlate asymptotically with even rotational states of homo-nuclear O 2 that are forbidden by symmetry. 13,26 Only pathway B is affected by this modification. There is no simple way of taking this effect into account in the electronically adiabatic single-surface calculations 23,46 because the electronic state symmetry of the PES changes from being symmetric over the covalent well to being antisymmetric in the dissociation asymptote.…”

“…The potential energy surface of the adiabatic ground electronic state is sufficient for this problem, but a switch of the electronic state character from being symmetric X 1 A 1 in the covalent well region, where ozone is formed, to being anti-symmetric in the O 2 ( 3 Σ − g ) + O( 3 P) asymptote (the geometric phase effect) should be incorporated into the treatment of vibrational states, for example, using the non-Born-Oppenheimer gauge theory. 22,23 In practice, it is impossible to carry out all these calculations since the PES of ozone is deep and the oxygen nuclei are all heavy, which results in more than three hundred vibrational [24][25][26] and many rotational states in the ozone molecule itself, but also requires an unaffordable number of partial waves for the quantum description of scattering of a heavy quencher M, such as Ar or N 2 . For this reason, many authors employed approximations, by simplifying either the treatment of the ozone molecule itself (e.g., by dimensional reductions or neglecting its rotation), 27,28 or the description of the O 3 * + M collision process (e.g., by sudden approximation or strong collision assumption), 29,30 or by mixing the classical and quantum mechanics.…”

Several Levels of Theory for Description of Isotope Effects in Ozone: Symmetry Effect and Mass Effect

“…Namely, in the heteronuclear diatomic molecule 16 O 18 O of the pathway A all rotational states are allowed, while in the homonuclear 16 O 16 O (or 18 O 18 O) of the pathway B only odd rotational states are allowed (it is well-known that rotational levels j = 0, 2, 4, etc.are forbidden). (16,30,38) So, the partition function of reagents for pathway A is larger, roughly by a factor of 2, compared to the partition function of reagents in pathway B. Note that the formation of symmetric ozone molecules, such as 16 On the basis of this discussion, and from the structure of eqs 6-7, it makes sense to introduce the following three recombination rate coefficients:…”

“…What we propose to do here is to analyze the ε i (ρ) dependencies first, since they carry a lot of useful information. Although in the past similar adiabatic curves for ozone have been computed and presented by several authors, (16,18,38) they have never been systematically analyzed, to the best of our knowledge. Our experience shows that the dominant contribution to the recombination process comes, typically, from one resonance found at energy close to the barrier top.…”

A general variational approach for computing rovibrational resonances of polyatomic molecules. Application to the weakly bound H2He+ and H2⋅CO systems

“…7 Both the CAP and the CCS methods have been applied during the past two decades to study molecular resonance states. 7,[40][41][42][43][44][45][46] Up to now, mostly triatomic molecules have been subjected to detailed resonance computations; nevertheless, resonances of the four-atomic HOCO system have also been investigated, using simplified models. [47][48][49] Hernández and Clary 47 identified resonance states of HOCO using the stabilization method in a two-dimensional (2D) model, while later Bowman and co-workers computed HOCO resonance states with the help of the CAP technique, first within a 2D 48 and then a 3D model of the system.…”