Abstract
Accurate modeling of low-temperature plasmas requires molecular collision input data, including the detail over the whole ladder of vibrational states. Obtaining this kind of detailed data is a big challenge, both theoretically and experimentally. These data can be calculated with the aid of simple models (for inelastic processes essentially based on forced harmonic oscillator mechanism), or with molecular dynamics at various levels, namely quasiclassical (QCT), semiclassical (SC), approximate and exact quantum mechanical methods, with computational cost rapidly increasing with accuracy. However, while accurate methods can become unfeasible when applied to the wide total energy ranges typically required in plasma modeling, more approximate semiclassical methods rapidly become efficient and accurate for increasing total energy, as shown in the literature. The best strategy is to study the limits of application of less accurate methods, to use them as a seamless continuation of accurate calculations on the total energy axis. In this sense, it is the current development about inelastic processes treated by QCT and SC methods. The aspect of special interest is the indication of a criterion for easily extracting the reliable QCT contribution to the inelastic process, treating the missing contributions by other SC methods in a restricted range. This procedure allows to optimize the use of different methods to maintain both a high level of accuracy and a high computational efficiency. As a consequence of the study about inelastic processes, a better comprehension and possible treatment of the dissociation mechanisms are obtained, with an indication of reliability of QCT results about this kind of process.
Graphical abstract
Similar content being viewed by others
References
Aoiz FJ, Bañares Luis, Herrero VJ (1998) Recent results from quasiclassical trajectory computations of elementary chemical reactions. J Chem Soc Faraday Trans 94:2483–2500. https://doi.org/10.1039/a803469i
Balakrishnan N, Vieira M, Babb J, Dalgarno A, Forrey R, Lepp S (1999) Rate coefficients for ro-vibrational transitions in H2 due to collisions with He. Astrophys J 524:1122
Billing GD (1999) Time-dependent quantum dynamics in a Gauss-Hermite basis. J Chem Phys 110:5526–5537. https://doi.org/10.1063/1.478450
Blais NC, Truhlar DG (1978) Ab initio calculation of the vibrational energy transfer rate of H2 in Ar using Monte Carlo classical trajectories and the forced quantum oscillator model. J Chem Phys 69:846. https://doi.org/10.1063/1.436600
Bonnet L (2008) The method of Gaussian weighted trajectories. III. An adiabaticity correction proposal. J Chem Phys 128:044109. https://doi.org/10.1063/1.2827134
Bonnet L, Rayez J-C (2004) Gaussian weighting in the quasiclassical trajectory method. Chem Phys Lett 397:106–109. https://doi.org/10.1016/j.cplett.2004.08.068
Capitelli M (1986) Nonequilibrium vibrational kinetics. Springer, New York
Capitelli M, Ferreira CM, Gordiets B, Osipov AI (2000) Plasma kinetics in atmospheric gases. Springer, Berlin
Capitelli M, Cacciatore M, Celiberto R, De Pascale O, Diomede P, Esposito F, Gicquel A, Gorse C, Hassouni K, Laricchiuta A, Longo S, Pagano D, Rutigliano M (2006) Vibrational kinetics, electron dynamics and elementary processes in H2 and D2 plasmas for negative ion production: modelling aspects. Nucl Fusion 46:S260–S274. https://doi.org/10.1088/0029-5515/46/6/506
Capitelli M, Celiberto R, Colonna G, D’Ammando G, De Pascale O, Diomede P, Esposito F, Gorse C, Laricchiuta A, Longo S et al (2011) Plasma kinetics in molecular plasmas and modeling of reentry plasmas. Plasma Phys Control Fusion 53:124007
Capitelli M, Bruno D, Catalfamo C, Celiberto R, Colonna G, Coppola CM, D’Ammando G, De Pascale O, Diomede P, Esposito F, Gorse C, Laricchiuta A, Longo S, Taccogna F (2014) Elementary processes, thermodynamics and transport of H2 plasmas. Atomic and plasma-material interaction data for fusion. International Atomic Energy Agency, Vienna, pp 24–36
Capitelli M, Celiberto R, Colonna G, Esposito F, Gorse C, Hassouni K, Laricchiuta A, Longo S (2016a) Fundamental aspects of plasma chemical physics. Springer, New York
Capitelli M, Celiberto R, Colonna G, Esposito F, Gorse C, Hassouni K, Laricchiuta A, Longo S (2016b) Reactivity and relaxation of vibrationally/rotationally excited molecules with open shell atoms. Fundamental aspects of plasma chemical physics. Springer, New York, pp 31–56
Celiberto R, Armenise I, Cacciatore M, Capitelli M, Esposito F, Gamallo P, Janev RK, Laganà A, Laporta V, Laricchiuta A, Lombardi A, Rutigliano M, Sayós R, Tennyson J, Wadehra JM (2016) Atomic and molecular data for spacecraft re-entry plasmas. Plasma Sources Sci Technol 25:033004. https://doi.org/10.1088/0963-0252/25/3/033004
Celiberto R, Capitelli M, Colonna G, D’Ammando G, Esposito F, Janev R, Laporta V, Laricchiuta A, Pietanza L, Rutigliano M, Wadehra J (2017) Elementary processes and kinetic modeling for hydrogen and helium plasmas. Atoms 5:18. https://doi.org/10.3390/atoms5020018
Coppola CM, Mizzi G, Bruno D, Esposito F, Galli D, Palla F, Longo S (2016) State-to-state vibrational kinetics of H2 and H2 + in a post-shock cooling gas with primordial composition. Mon Not R Astron Soc 457:3732–3742. https://doi.org/10.1093/mnras/stw198
Dalgarno A (2005) Molecular processes in the early Universe. J Phys Conf Ser 4:10–16. https://doi.org/10.1088/1742-6596/4/1/002
Dalgarno A (2006) Introductory Lecture: the growth of molecular complexity in the Universe. Faraday Discuss 133:9. https://doi.org/10.1039/b605715b
De Fazio D (2014) The H + HeH+ → He + H2 + reaction from the ultra-cold regime to the three-body breakup: exact quantum mechanical integral cross sections and rate constants. Phys Chem Chem Phys 16:11662–11672. https://doi.org/10.1039/c4cp00502c
Dove JE, Mandy ME, Sathyamurthy N, Joseph T (1986) On the origin of the dynamical threshold for collision-induced dissociation processes. Chem Phys Lett 127:1–6. https://doi.org/10.1016/S0009-2614(86)80199-3
Esposito F, Armenise I (2017) Reactive, inelastic, and dissociation processes in collisions of atomic oxygen with molecular nitrogen. J Phys Chem A 121:6211–6219. https://doi.org/10.1021/acs.jpca.7b04442
Esposito F, Capitelli M (2009) Selective vibrational pumping of molecular hydrogen via gas phase atomic recombination. J Phys Chem A 113:15307–15314. https://doi.org/10.1021/jp9061829
Esposito F, Gorse C, Capitelli M (1999) Quasi-classical dynamics calculations and state-selected rate coefficients for H + H2(v, j)– > 3H processes: application to the global dissociation rate under thermal conditions. Chem Phys Lett 303:636–640
Esposito F, Coppola CM, De Fazio D (2015) Complementarity between quantum and classical mechanics in chemical modeling. The H + HeH+ → H2+ + He reaction: a rigorous test for reaction dynamics methods. J Phys Chem A 119:12615–12626. https://doi.org/10.1021/acs.jpca.5b09660
Esposito F, Macdonald R, Boyd ID, Neitzel K, Andrienko DA (2019) Heavy particle elementary processes in hypersonic flows. Hypersonic meteoroid entry physics. Springer, New York
Forrey RC (2013) Sturmian theory of three-body recombination: application to the formation of H2 in primordial gas. Phys Rev A 88:052709. https://doi.org/10.1103/physreva.88.052709
Fridman A (2008) Plasma chemistry. Cambridge University Press, Cambridge
Galli D, Palla F (2013) The Dawn of Chemistry. Ann Rev Astron Astrophys 51:163–206. https://doi.org/10.1146/annurev-astro-082812-141029
Garcia E, Saracibar A, Gómez-Carrasco S, Laganà A (2008) Modeling the global potential energy surface of the N + N2 reaction from ab initio data. Phys Chem Chem Phys 10:2552. https://doi.org/10.1039/b800593a
Giese CF, Gentry WR (1974) Classical trajectory treatment of inelastic scattering in collisions of H+ with H2, HD, and D2. Phys Rev A 10:2156
International Atomic Energy Agency V (Austria) (2001) Atomic and plasma-material interaction data for fusion, vol 9. IAEA, International Atomic Energy Agency (IAEA), Vienna
Kozák T, Bogaerts A (2014) Splitting of CO2 by vibrational excitation in non-equilibrium plasmas: a reaction kinetics model. Plasma Sources Sci Technol 23:045004. https://doi.org/10.1088/0963-0252/23/4/045004
Kumar S, Sathyamurthy N, Ramaswamy R (1995) Overcoming the zero-point dilemma in quasiclassical trajectories: (He, H2 +) as a test case. J Chem Phys 103:6021–6028. https://doi.org/10.1063/1.470430
Kustova EV, Nagnibeda EA, Armenise I (2014) Vibrational-chemical kinetics in mars entry problems. Open Plasma Phys J 7:76–87. https://doi.org/10.2174/1876534301407010076
Laganà A, Lombardi A, Pirani F, Gamallo P, Sayós R, Armenise I, Cacciatore M, Esposito F, Rutigliano M (2014) Molecular physics of elementary processes relevant to hypersonics: atom-molecule, molecule-molecule and atoms-surface processes. Open Plasma Phys J 7:48–59
Lebouvier A, Iwarere SA, d’Argenlieu P, Ramjugernath D, Fulcheri L (2013) Assessment of carbon dioxide dissociation as a new route for syngas production: a comparative review and potential of plasma-based technologies. Energy Fuels 27:2712–2722. https://doi.org/10.1021/ef301991d
Leforestier C (1986) Competition between dissociation and exchange processes in a collinear A + BC collision: comparison of quantum and classical results. Chem Phys Lett 125:373–377. https://doi.org/10.1016/0009-2614(86)85175-2
Lino da Silva M, Guerra V, Loureiro J (2009) A review of non-equilibrium dissociation rates and models for atmospheric entry studies. Plasma Sources Sci Technol 18:034023. https://doi.org/10.1088/0963-0252/18/3/034023
Lombardi A, Faginas-Lago N, Pacifici L, Grossi G (2015) Energy transfer upon collision of selectively excited CO2 molecules: state-to-state cross sections and probabilities for modeling of atmospheres and gaseous flows. J Chem Phys 143:034307. https://doi.org/10.1063/1.4926880
Macdonald RL, Jaffe RL, Schwenke DW, Panesi M (2018) Construction of a coarse-grain quasi-classical trajectory method. I. Theory and application to N2–N2 system. J Chem Phys 148:054309. https://doi.org/10.1063/1.5011331
Macheret SO, Adamovich IV (2000) Semiclassical modeling of state-specific dissociation rates in diatomic gases. J Chem Phys 113:7351
Miller WH (1970) The classical S-matrix: a more detailed study of classically forbidden transitions in inelastic collisions. Chem Phys Lett 7:431–435. https://doi.org/10.1016/0009-2614(70)80326-8
Morales JA, Diz AC, Deumens E, Öhrn Y (1995) Molecular vibrational state distributions in collisions. Chem Phys Lett 233:392–398. https://doi.org/10.1016/0009-2614(94)01472-8
Nagnibeda E, Kustova E (2009) Non-equilibrium reacting gas flows. Springer, Berlin
Palmieri P, Puzzarini C, Aquilanti V, Capecchi G, Cavalli S, De Fazio D, Aguilar A, Giménez X, Lucas J (2000) Ab initio dynamics of the He + H + 2 → HeH+ + H reaction: a new potential energy surface and quantum mechanical cross-sections. Mol Phys 98:1835–1849
Pietanza LD, Colonna G, D’Ammando G, Laricchiuta A, Capitelli M (2015) Vibrational excitation and dissociation mechanisms of CO2 under non-equilibrium discharge and post-discharge conditions. Plasma Sources Sci Technol 24:042002. https://doi.org/10.1088/0963-0252/24/4/042002
Pomerantz AE, Ausfelder F, Zare RN, Juanes-Marcos JC, Althorpe SC, Sáez Rábanos V, Aoiz FJ, Bañares L, Castillo JF (2004) Rovibrational product state distribution for inelastic H + D2 collisions. J Chem Phys 121:6587. https://doi.org/10.1063/1.1804940
Smith IW (1977) Reaction and relaxation of vibrationally excited molecules: a classical trajectory study of Br + HCl(v′) and Br + DCl(v′) collisions. Chem Phys 20:437–443
Tang XN, Xu H, Zhang T, Hou Y, Chang C, Ng CY, Chiu Y, Dressler RA, Levandier DJ (2005) A pulsed-field ionization photoelectron secondary ion coincidence study of the H2 +(X, υ+ = 0–15, N+ = 1) + He proton transfer reaction. J Chem Phys 122:164301. https://doi.org/10.1063/1.1883169
Treanor CE (1965) Vibrational energy transfer in high-energy collisions. J Chem Phys 43:532. https://doi.org/10.1063/1.1696777
Acknowledgements
The computational time was supplied by CINECA (Bologna) under ISCRA project N. HP10CGTAHE.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Esposito, F. Reactivity, relaxation and dissociation of vibrationally excited molecules in low-temperature plasma modeling. Rend. Fis. Acc. Lincei 30, 57–66 (2019). https://doi.org/10.1007/s12210-019-00778-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12210-019-00778-9