Atom-molecule energy transfer and dissociation processes for

nitrogen and oxygen

Fabrizio EspositoIMIP-CNR, Bari Section

(Institute of Inorganic Methodologies and Plasmas)

Ro-vibrational excitation-deexcitation and dissociation in heavy particle collisions

M+M2(v,j)M+M2(v’,j’)

M+M2(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

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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 TSo, then a back-integration tj

Some Details

In tj calculations, translational energy range is continuous from 10-3 to 3 eV

Discretization of energy axis is made with 500 bins Accuracy of tjs with the step checking (with x=10-10Å) is

of the order of one wrong tj in 105-106 Density of tjs is about 24000 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+N2; DMBE PES of

Varandas and Pais for O+O2

Rotationally averaged cross sections

€

Qrot (v) =j

∑ g j exp(−Ev, j / kTrot )

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σ (v,v',Trot ) = σ (v, j,v' )g j exp(−Ev, j / kTrot ) /Qrotj

∑

Dissociation cross sections for nitrogen

Rotationally averaged cross sections from v=40, Trot= 50,1000,3000K

Dissociation cross sections for nitrogen

Trot = 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 usObtained 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 vv-1 as a function of initial v (red)

Oxygen vibrational de-excitation rates at T=1000K

De-excitation from vv-5 as a function of initial v (green)

Oxygen vibrational de-excitation rates at T=1000K

De-excitation from vv-15 as a function of initial v (blue)

Oxygen vibrational de-excitation rates at T=1000K

De-excitation from vv-25 as a function of initial v (magenta)

Oxygen vibrational de-excitation rates at T=1000K

De-excitation from vv-35 as a function of initial v (light blue)

Oxygen vibrational de-excitation rates at T=1000K

Comparison of rate coefficients for T=1000K, vv-1 (yellow), vv-5 (black) with Lagana’ and Garcia results on the same PES

Oxygen rotationally averaged cross sections

Dissociation cross sections for v=30, Trot = 50, 1000, 3000, 10000

Oxygen rotationally averaged cross sections

Dissociation cross sections for Trot=1000K, v=20, 25, 30, 35, 40

Comparison of total dissociation rate for oxygen with some experimental fits

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Our rate is similar to that of Shatalov within ±13% over the whole interval 1000-10000K

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 O2 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

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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