In the contribution to conference theoretical calculations of state-by-state rate coefficients for electron-molecule and atom-molecule scattering, by using ab-initio methods, will be presented. In particular nitrogen- and oxygen-involving chemical reactions will be considered. These quantities are of primary importance to study the energy exchange and to implement kinetic models in thermal and chemical non-equilibrium high-temperature aerothermodynamics.

Atom-diatomic molecule collision processes are of particular importance in nonequilibrium numerical models in which rovibrational energy exchange and state-selected dissociation are taken into account by means of rate coefficients. If also translational nonequilibrium is considered, availability of large sets of cross sections is needed. To cope with this issue extended quasiclassical calculations have been performed to obtain translational energy dependent detailed data for hydrogen, nitrogen and oxygen, with particular attention devoted to computational optimization. Problems related to huge memory requirements of large cross section sets when used in numerical models can be effectively solved with an interpolation method proposed by the author, which seems to reach an optimal compromise between accuracy and amount of data storage required. Comparisons with literature are, when available, globally good. An important issue about the exclusion of rotational distribution in both vibrational energy exchange and dissociation rate coefficients is stressed. Rotational distribution can significantly change dynamical results, with obvious consequences in their applications to models, independently of its explicit or implicit consideration into models. Concerning collision induced dissociation/recombination dynamics, a strong rotational dependence is shown using two different mechanisms in the case of hydrogen.

The modeling of atmospheric gas, interacting with the space vehicles in re-entry conditions in planetary exploration missions, requires a large set of scattering data for all those elementary processes occurring in the system. A fundamental aspect of re-entry problems is represented by the strong non-equilibrium conditions met in the atmospheric plasma close to the surface of the thermal shield, where numerous interconnected relaxation processes determine the evolution of the gaseous system towards equilibrium conditions. A central role is played by the vibrational exchanges of energy, so that collisional processes involving vibrationally excited molecules assume a particular importance. In the present paper, theoretical calculations of complete sets of vibrationally state-resolved cross sections and rate coefficients are reviewed, focusing on the relevant classes of collisional processes: resonant and non-resonant electron-impact excitation of molecules, atom-diatom and molecule-molecule collisions as well as gas-surface interaction. In particular, collisional processes involving atomic and molecular species, relevant to Earth (N-2, O-2, NO), Mars (CO2, CO, N-2) and Jupiter (H-2, He) atmospheres are considered.

Some case studies are presented about the construction of databases of detailed dynamical data as a result of molecular dynamics calculations

Quantitative knowledge of elementary processes involved in plasmas are key to successfully perform accurate kinetic simulations. The issue is the huge amount of data to treat, both in the dynamical calculation and in the kinetic simulation. The aim of this paper is to study the dissociation in atom-molecule (AM) and molecule-molecule (MM) collisions involving nitrogen, obtained by molecular dynamics calculations considering vibrational states in the range 10-50 and collision energy up to 10 eV, in order to formulate suitable scaling laws resulting in less expensive computational procedures and easier to handle treatments in kinetic simulations. It is shown that, while a direct substitution of MM dissociation cross sections with AM ones might be acceptable only at very high collision energy, scaling laws application allows to obtain quite good results on almost the whole energy range of interest.

In this work we present a dynamical study of the H + HeH+ -> H+2+ He reaction in a collision energy range from 0.1 meV to 10 eV, suitable to be used in applicative models.

In the inner part of the dissociated boundary layer of hypersonic bodies, a vibrational freezing zone has been observed. This freezing region takes place even if, in the outer part of the boundary layer, translation and vibration temperatures are in equilibrium and even if the surface is catalytic. This phenomenon can be attributed to the diffusion towards the wall of the vibrational energy; consequently the dissociation rate constantsin this region can increase. Advanced physical models taking into account the vibration-chemistry interaction are required for the description of such flows. State-to-state and statistical global models are described in this paper and used in the computation of hypersonic boundary layers. All methods can predict the general features of the freezing phenomenon and present a qualitative agreement, as far as similar assumptions are used. Applications to boundary layers behind a reflected shock wave and along a hemispherical body are also presented.

A recent complete set of oxygen atom-molecule collision rate coefficients, calculated by means of a quasiclassical trajectory (QCT) method, has been used to evaluate the vibrational non-equilibrium in hypersonic boundary layer flows. The importance of multiquanta transitions has been demonstrated. Moreover a new 'direct dissociation-recombination' (DDR) model has been adopted and the corresponding results differ from the ones obtained with the Ladder-Climbing (LC) model, characterized by the extrapolation of bound-to-bound transitions to the continuum. The heat flux through the boundary layer and at the surface have been calculated too.

The chemistry of the early universe plays an important role in our understanding on the birth and evolution of galaxies and interstellar clusters. Molecular formation began at the end of the recombination era when the temperature was low enough that the newly formed atoms could survive for further evolution. After recombination, the matter density was still very low and three-body reactions were still very inefficient: however, it was there that the first molecular species were postulated to be formed through radiative association. In spite of the low fractional abundances which is expected for species like LiH, LiH+ and HeH+ these molecules have nevertheless been considered to be important in that domain, due to their large permanent dipole moment that make them possible candidates as coolant during the late stages of the gravitational collapse of the first cosmological objects. In fact, because of the high density of their rovibrational states, molecules can absorb thermal energy from the surrounding atomic gas via internal excitations and then release it through emission of photons, thereby efficiently cooling the clouds. In turn, these photons can increase the density of the cosmic background radiation inducing both spectral distortions and spatial anisotropies , representing a possible way to probe the features of the early universe chemistry. Moreover, at later stages, the molecular cooling mechanism is considered crucial for the formation of the first cosmological objects that are thought to be formed by collapse of the pristine molecular clouds. Among these objects, low-metallicity stars have formed, for which the only efficient cooling mechanism at low temperature can be provided by molecules like HD, HeH+, H3+, H2+, LiH+. Gas phase chemistry of their formation and destruction is therefore fundamental to have a good understanding of the early universe evolution. However, to evaluate the molecular abundance in the full redshift range from the Big-Bang to the formation of the first stars and galaxies, state-to-state rate coefficients in a large range of temperature (several order of magnitude) are required. Notwithstanding the simplicity of the reactive species, the broad range of the temperature required in the evolutionary cosmological models and the high complexity of chemical physical processes involving also non-adiabatic reactions, three-body recombination and collision induced dissociation processes, do not permit to obtain all the rate coefficients by 'exact'?quantum dynamical methods, so that benchmark quantum dynamical calculations are mandatory to properly assess dynamical approximations and/or models necessary to extend the numerical treatment to regimes where 'exact' quantum rates cannot be achieved.In the conference our recent effort [1-3] in this direction will be presented taking as example some prototypical key reaction of the early universe chemical network.References[1] F. Esposito and M. Capitelli; J. Phys.

We report cross-sections and rate coefficients for excited states colliding with electrons, heavy particles and walls useful for the description of H-2/He plasma kinetics under different conditions. In particular, the role of the rotational states in resonant vibrational excitations of the H-2 molecule by electron impact and the calculation of the related cross-sections are illustrated. The theoretical determination of the cross-section for the rovibrational energy exchange and dissociation of H-2 molecule, induced by He atom impact, by using the quasi-classical trajectory method is discussed. Recombination probabilities of H atoms on tungsten and graphite, relevant for the determination of the nascent vibrational distribution, are also presented. An example of a state-to-state plasma kinetic model for the description of shock waves operating in H-2 and He-H-2 mixtures is presented, emphasizing also the role of electronically-excited states in affecting the electron energy distribution function of free electrons. Finally, the thermodynamic properties and the electrical conductivity of non-ideal, high-density hydrogen plasma are finally discussed, in particular focusing on the pressure ionization phenomenon in high-pressure high-temperature plasmas.

The deconvolution of temperature dependent rate coefficients to energy dependent cross sections is accomplished by using a nonlinear optimization technique. The suggested method is successfully applied to atom-molecule and molecule-molecule dissociation processes in hydrogen.

Non-equilibrium effects in hydrogen plasmas have been investigated in different systems, ranging from RF plasmas to corona discharges. The existing measurements of vibrational and rotational temperatures, obtained by different spectroscopical techniques, are reported, rationalized by results calculated by kinetic models. Input data of these models are discussed with particular attention on the dependence of relevant cross sections on the vibrational quantum number. Moreover, the influence of the vibrational excitation of H(2) molecules on the translational distribution of atoms in ground and excited levels is shown. Finally, a collisional radiative model for atomic hydrogen levels, based on the coupling of the Boltzmann equation for electron energy distribution function (EEDF) and the excited state kinetics, is presented, emphasizing the limits of quasi-stationary approximation. In the last case, large deviations of the EEDF and atomic level distributions from the equilibrium are observed.

The space exploration is nowadays assisted by realistic modeling of re-entry conditions of space vehicles in planetary atmospheres, for the design of thermal protection systems. The detailed kinetic modeling relies on the accurate description of elementary process dynamics, including the role of the excitation of the internal degrees of freedom of chemical species. Efforts in the construction of a complete and consistent dynamical information are presented, focusing on hydrogen plasmas relevant to the Jupiter atmosphere. Examples of numerical experiments are given, emphasizing the relevance of the adopted state-to-state approach in reproducing the onset of non-equilibrium internal distributions governing the plasma system evolution. © Springer-Verlag 2011.

The space exploration is nowadays assisted by realisticmodeling of re-entry conditions of space vehicles inplanetary atmospheres, for design of thermal protection systems.The detailed kinetic modeling relies on the accuratedescription of elementary process dynamics, including therole of the excitation of the internal degrees of freedom ofchemical species. Efforts in the construction of a completeand consistent dynamical information are presented, focusingon hydrogen plasmas relevant to the Jupiter atmosphere.Examples of numerical experiments are given, emphasizingthe relevance of the adopted state-to-state approach inreproducing the onset of non-equilibrium internal distributionsgoverning the plasma-system evolution.

In the present chapter some prototype gas and gas-surface processes occurring within the hypersonic flow layersurrounding spacecrafts at planetary entry are discussed. The discussion is based on microscopic dynamical calculationsof the detailed cross sections and rate coefficients performed using classical mechanics treatments for atoms, moleculesand surfaces. Such treatment allows the evaluation of the efficiency of thermal processes (both at equilibrium and nonequilibrium distributions) based on state-to-state and state specific calculations properly averaged over the population ofthe initial states. The dependence of the efficiency of the considered processes on the initial partitioning of energy amongthe various degrees of freedom is discussed.

The NO formation in a hypersonic boundary layer is investigated by solving a numerical code that couples fluid dynamics and state-to-state vibrational kinetics. An N2/N/O2/O/NO mixture is considered to simulate the space vehicle Earth re-entry problem. Two new sets of state-to-state rate coefficients of the processes O + N2(v) <-> NO(w) + N and N + O2(v) <-> NO(w) + O are used, calculated in our research group by means of a molecular dynamics approach.Particular attention is payed to rescale the rates of different kinetic processes in order to have a unique vibrational scale for each molecular species (N2, O2, NO). This is not obvious because vibrational levels, obtained from asymptotics of three-body potential of different collisional systems, often do not match, particularly for high-lying vibrational states. The reactions involving NO affect the mass fractions, the molecular vibrational distributions and the heat flux in the boundary layer.

Non-adiabatic dynamics with quasiclassical trajectories:atrajectory surface sliding methodFabrizio Esposito1Instituto di Metodologie Inorganiche e dei Plasmi, Consiglio Nazionale delle Ricerche, (CNR- IMIP, via Amendola 122/D, 70126 Bari (Italy).e-mail: fabrizio.esposito@cnr.itA method for non-adiabatic dynamics using quasiclassical trajectories is proposed, based on the coherent propagation of eigenvectors of the diabatic potential matrix of the problem. The proposed method has the advantage of avoiding by construction the problem of frustrated hops. It treats the problem of multiple states with extreme simplicity. If the potential matrix is obtained by diatomics-in-molecule method with three body corrections added at the diabatic level, it can be directly used in the dynamics, without requiring any diabatization procedure. Various results for H++H2 system are presented in comparison with literature.AcknowledgementsThe support of European Space Agency (ESA ESTEC Contract 21790/08/NL/HE) and of 7FP Phys4Entry (Planetary Entry Integrated Models, n.242311) are acknowledged.

State-to-state non-equilibrium plasma kinetics is widely used to characterize cold molecular and reentry plasmas. The approach requires a high level of dynamical information, and demands a large effort in the creation of complete databases of state-resolved cross sections and rate coefficients. Recent results, emphasizing the dependence of elementary process probability on both the vibrational and rotational energy content of the H2 molecule, are presented for those channels governing the microscopic collisional dynamics in non-equilibrium plasmas, i.e. electron-impact induced resonant processes, vibrational deactivation and dissociation in atom-diatom collisions and atomic recombination at the surface. Results for H2 plasmas, i.e. negative ion sources for neutral beam injection in fusion reactors, RF parallel-plate reactors for microelectronics, atmospheric discharges and the shock wave formed in the hypersonic entry of vehicles in planetary atmosphere for aerothermodynamics, are discussed.

It is common in literature to read papers in which the need for quantum-mechanical treatment of molecular collisions is stressed, presenting it as a guarantee of accuracy. Often the same authors consider the quasiclassical trajectory method as only suited for qualitative results, or relegated to very high energy ranges. While the use of quantum mechanics in certain conditions is mandatory, its generalized application can bring to paradoxical situations, with expensive quantum mechanical calculations used for obtaining results clearly in the quasiclassical realm without great success, due to the approximations introduced in the quantum procedure for computational economy. Some examples will be shown and discussed, taken from personal experience of the author in the field and from literature, including light chemical species. The aim is to reconcile the use of both quantum-mechanical and quasiclassical calculations, with particular attention to the assessment of the suited ranges of applicability of the methodologies. Exploiting this complementarity can result in an optimal balance between accuracy and computational resources required.

We present the quantum mechanical (QM) and quasiclassical trajectory (QCT) dynamics of the title reac- tion on two uncoupled surfaces, using a wavepacket (WP) method and considering some N2(v, j) vibra- tional and rotational states. The reaction is investigated by calculating initial-state-resolved reaction probabilities, cross sections, and rate constants, which are explained in terms of energy profiles and col- lision mechanisms. These properties reflect the large endo-thermicity of the reaction and the features of the surfaces. Indeed, at low v values we obtain large thresholds and the lower surface is more reactive than the higher one, whereas at high v the thresholds decrease or disappear and the upper surface becomes more reactive. QM and QCT results are in satisfactory agreement, except some differences at low or high collision energy and temperature. QCT rate coefficients agree also with some published results. WP snapshots and movies of QCT time evolution show clearly abstraction and insertion mecha- nisms depending on the initial conditions. Insertion proceeds via a reaction complex and we observe a QM Feshbach resonance for a specific initial condition. On the overall, the dynamical observables are con- sistent with the collision mechanisms.

The quantum kinetic chemical reaction model proposed by Bird for the direct simu- lation Monte Carlo method is based on collision kinetics with no assumed Arrhenius- related parameters. It demonstrates an excellent agreement with the best estimates for thermal reaction rates coefficients and with two-temperature nonequilibrium rate coefficients for high-temperature air reactions. This paper investigates this model further, concentrating on the non-thermal reaction cross sections as a function of collision energy, and compares its predictions with those of the earlier total collision energy model, also by Bird, as well as with available quasi-classical trajectory cross section predictions (this paper also publishes for the first time a table of these com- puted reaction cross sections). A rarefied hypersonic flow over a cylinder is used to examine the sensitivity of the number of exchange reactions to the differences in the two models under a strongly nonequilibrium velocity distribution.

We report the results of detailed calculations of reactive, inelastic, and dissociative processes in collisions of atomic oxygen with molecular nitrogen in their respective electronic ground states. Cross sections are calculated as a function of collision energy in the range 0.001-10 eV, considering the whole rovibrational ladder. Some problems related to the vibrational energy levels of the asymptotes of 3A" and 3A' potential energy surfaces used in this work are solved by an appropriate scaling at the level of cross sections. The results are compared with data in the literature, obtaining excellent agreement with experimental thermal data for reactive processes on a very large temperature range, and reasonable agreement with indirect dissociative data. Significant discrepancies are observed with previous reactive state-to-state results calculated on less detailed potential energy surfaces. Inelastic results are compatible with extrapolation of experimental thermal rate coefficient for temperatures higher than 4500 K but completely fail to reproduce experimental data at room temperature. The issue is discussed, indicating the reasons and possible solutions to the problem, and a resonable rate coefficient is obtained combining experimental and theoretical results in the range 300-20000 K. Complete, accurate fits are provided for both reactive and dissociative state-to-state rate coefficients to use them in applicative numerical codes concerning air kinetics.

We investigate a kinetic model for H-H-2 mixtures in a regime where translational/rotational and vibrational-resonant energy exchanges are fast whereas vibrational energy variations are slow. In a relaxation regime, the effective volume viscosity is found to involve contributions from the rotational volume viscosity, the vibrational volume viscosity, the relaxation pressure, and the perturbed source term. In the thermodynamic equilibrium limit, the sum of these four terms converges toward the one-temperature two-mode volume viscosity. The theoretical results are applied to the calculation of the volume viscosities of molecular hydrogen in the trace limit on the basis of a complete set of state-selected cross sections for the H + H-2(v, j) system.

Collisions of atomic oxygen and nitrogen with nitrogen and oxygen molecules respectively have been sistematically studied with respect to initial and final vibration of the diatoms by the quasiclassical method, using the best potential energy surfaces available. Cross sections for dissociation, vibrational energy exchange and reaction have been calculated, in a translational energy range up to 10 eV. Comparisons with available thermal data are generally good. Special emphasis has been given to the inclusion of rotation in these calculations, for its importance in dissociation-recombination kinetics.

The radiative cooling of shocked gas with primordial chemical composition is an important process relevant to the formation of the first stars and structures, as well as taking place also in high-velocity cloud collisions and supernovae explosions. Among the different processes that need to be considered, the formation kinetics and cooling of molecular hydrogen are of prime interest, since they provide the only way to lower the gas temperature to values well below similar to 10(4) K. In previous works, the internal energy level structure of H-2 and its cation has been treated in the approximation of ro-vibrational ground state at low densities, or trying to describe the dynamics using some arbitrary v > 0 H-2 level that is considered representative of the excited vibrational manifold. In this study, we compute the vibrationally resolved kinetics for the time-dependent chemical and thermal evolution of the post-shock gas in a medium of primordial composition. The calculated non-equilibrium distributions are used to evaluate effects on the cooling function of the gas and on the cooling time. Finally, we discuss the dependence of the results to different initial values of the shock velocity and redshift.

He+H2(v,j) collisions have been computationally studied. The whole sets of cross sections for rovibrationalenergy exchange and dissociation have been calculated in the translational energy range 0.001-10 eV, including quasibound states. Comparisons with literature will be discussed.

A collisional-radiative model for the H2/He plasma, coupled to a Boltzmann solver for the free electron kinetics is used to investigate the non-equilibrium conditions created in the expansion of an high-temperature plasma flow through a converging-diverging nozzle, starting from the steady state composition at T 0 = 10 000 K and p 0 = 1 atm in the reservoir. It is shown that the plasma optical thickness plays a major role on the evolution of macroscopic quantities and internal distributions along the nozzle axis. Structured electron energy distribution functions, characterized by long plateaux and humps, are created due to superelastic collisions of cold electrons and electronically excited atomic hydrogen. The magnitudes of the plateaux are orders of magnitude higher in an optically thick plasma compared with a thin plasma, while the electron-electron collisions play a role in smoothing the peaks created by superelastic collisions between cold electrons and H (n > 2).