Transcript Document

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
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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
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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
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Error evaluation and computational time
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A trajectory tj(0) is integrated with a time step TSo, 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 TSo, then a forward
integration with tj(1) is performed with TS1<TSo; if the
test fails, a new tj(2) is integrated with TS2<TS1 and
compared with tj(1), and so on (tj checking)
Only one step of tj(0) is integrated with a time step TSo,
then a forward integration is performed as a check within
a given tolerance on final positions and velocities with
TS1=TSo/n, and so on (step checking)
Some Details
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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
 (v,v',Trot )   (v, j,v')g j exp(Ev, j / kTrot )/Qrot
j
Qrot (v)   g j exp(Ev, j / kTrot )
j
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Dissociation cross sections for nitrogen
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Rotationally averaged cross sections from v=40, Trot=
50,1000,3000K
Dissociation cross sections for nitrogen
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Trot = 3000K, v=40,50,60,65
Nitrogen dissociation rate coefficients
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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
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From v to v-1,v-5,v-15,v-25,v-35
Comparison with Lagana’ and Garcia results
(1996)
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T = 1000K
Lines without points are reactive rates
Oxygen dissociation rates
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T = 300K, 1000K, 3000K
Oxygen vibrational de-excitation rates at T=1000K
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De-excitation from vv-1 as a function of initial v (red)
Oxygen vibrational de-excitation rates at T=1000K
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De-excitation from vv-5 as a function of initial v (green)
Oxygen vibrational de-excitation rates at T=1000K
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De-excitation from vv-15 as a function of initial v (blue)
Oxygen vibrational de-excitation rates at T=1000K
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De-excitation from vv-25 as a function of initial v
(magenta)
Oxygen vibrational de-excitation rates at T=1000K
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De-excitation from vv-35 as a function of initial v (light
blue)
Oxygen vibrational de-excitation rates at T=1000K
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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
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Dissociation cross sections for v=30, Trot = 50, 1000,
3000, 10000
Oxygen rotationally averaged cross sections
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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
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Approximation for excited electronic states
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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
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Oxygen electronic states having a minimum
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Conclusions
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Detailed cross sections database are nowadays fundamental for
kinetic studies
In compiling large and detailed sets of cross sections for atommolecule 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