Atom-molecule energy transfer and dissociation processes for nitrogen and oxygen Fabrizio Esposito IMIP-CNR, Bari Section (Institute of Inorganic Methodologies and Plasmas)

Ro-vibrational excitation-deexcitation and dissociation in heavy particle collisions M+M 2 (v,j)  M+M 2 (v’,j’) M+M 2 (v,j)  3M M = N (≈10000 states), O (≈6400 states) Quasiclassical method: a good compromise between global reliability of results and computational resources required

Method of Calculation: quasiclassical trajectories Pseudoquantization of reagents and products Classical evolution of the system All the possible outcomes of the collision process are taken into account (non-reactive, reactive, dissociation, quasibound states) Perfect for parallelization and distributed calculations “fast” and modular calculations

Quasibound states States classically trapped by the rotational barrier, but not from a quantum point of view

Error evaluation and computational time A trajectory tj(0) is integrated with a time step TS o, then a back-integration tj(1) is performed as a check with a given tolerance. Generally used as statistical testA tj(0) is integrated with a time step TS o, then a forward integration with tj(1) is performed with TS 1 <TS o ; if the test fails, a new tj(2) is integrated with TS 2 <TS 1 and compared with tj(1), and so on (tj checking) Only one step of tj(0) is integrated with a time step TS o, then a forward integration is performed as a check within a given tolerance on final positions and velocities with TS 1 =TS o /n, and so on (step checking)

Some Details In tj calculations, translational energy range is continuous from to 3 eV Discretization of energy axis is made with 500 bins Accuracy of tjs with the step checking (with  x= Å) is of the order of one wrong tj in Density of tjs is about tjs/(Å· eV) for nitrogen, 4000 for oxygen; stratified sampling is applied Over 1200 cpu hours of calculations have been spent for nitrogen, two years for oxygen up to now LEPS PES of Lagana’ et al. for N+N 2 ; DMBE PES of Varandas and Pais for O+O 2

Rotationally averaged cross sections

Dissociation cross sections for nitrogen Rotationally averaged cross sections from v=40, T rot = 50,1000,3000K

Dissociation cross sections for nitrogen T rot = 3000K, v=40,50,60,65

Nitrogen dissociation rate coefficients Rates are obtained at T=300,1000,3000K Lines are interpolations with polynomials of order 3-4

Comparison of total dissociation rate coefficient for nitrogen Lines: calculated by us Obtained experimentally by Roth and Thielen (1986, stars) and Appleton (1968 “x”)

Nitrogen vibrational deexcitation rate coefficients at T=1000K From v to v-1,v-5,v-15,v-25,v-35

Comparison with Lagana’ and Garcia results (1996) T = 1000K Lines without points are reactive rates

Oxygen dissociation rates T = 300K, 1000K, 3000K

Oxygen vibrational de-excitation rates at T=1000K De-excitation from v  v-1 as a function of initial v (red)

Oxygen vibrational de-excitation rates at T=1000K De-excitation from v  v-5 as a function of initial v (green)

Oxygen vibrational de-excitation rates at T=1000K De-excitation from v  v-15 as a function of initial v (blue)

Oxygen vibrational de-excitation rates at T=1000K De-excitation from v  v-25 as a function of initial v (magenta)

Oxygen vibrational de-excitation rates at T=1000K De-excitation from v  v-35 as a function of initial v (light blue)

Oxygen vibrational de-excitation rates at T=1000K Comparison of rate coefficients for T=1000K, v  v-1 (yellow), v  v-5 (black) with Lagana’ and Garcia results on the same PES

Oxygen rotationally averaged cross sections Dissociation cross sections for v=30, T rot = 50, 1000, 3000, 10000

Oxygen rotationally averaged cross sections Dissociation cross sections for T rot =1000K, v=20, 25, 30, 35, 40

Comparison of total dissociation rate for oxygen with some experimental fits Our rate is similar to that of Shatalov within ±13% over the whole interval K NF: no correction factor VF: variable factor

Approximation for excited electronic states We consider, following Nikitin, an equilibrium among vibrational levels belonging to different electronic states but with approximately the same energy. Nikitin hypotesis: this equilibrium is not significantly perturbed by molecular dissociation Dissociation can be calculated as originating concurrently from O 2 ground state and electronically excited states of oxygen, counting as many times the process as the sum of the degeneracies of excited states divided by that one of the ground state. Nikitin proposes for oxygen a global factor 16/3, considering the first six states having a minimum We propose a variable factor increasing with energy level

Nikitin approximation Oxygen electronic states having a minimum

Conclusions Detailed cross sections database are nowadays fundamental for kinetic studies In compiling large and detailed sets of cross sections for atom- molecule collision processes, the application of quasiclassical method is reliable and feasible; A good compromise between accuracy and computational time is found when step checking is applied Large sets of detailed dynamical data can be compiled using QCT calculations, substituting then gradually the classical results with semiclassical/quantum ones for more critical processes (tunneling, large energy spacing between initial/final states) The role of quasibound states in dissociation/recombination processes can now be considered in a detailed approximate way for oxygen and nitrogen in future kinetic studies