Skip to main content
Log in

Charge and energy sharing in the fragmentation of astrophysically relevant carbon clusters

  • Regular Article
  • Published:
Theoretical Chemistry Accounts Aims and scope Submit manuscript

Abstract

The breakup of a molecule following a fast collision with an atom in gas phase can be understood as resulting from two steps. In the first step, the atom transfers energy to the molecule, which is thus electronically and vibrationally excited. In the second step, the molecule decays leading to different fragments, while the initial charge, energy, and angular momentum are conserved. Here, we demonstrate that, by maximizing the entropy of the system under these conservation laws, it is possible to reproduce the fragmentation yields resulting from collision experiments. In particular, our model is applied to investigate fragmentation of excited neutral and singly charged carbon clusters and mono-hydrogenated carbon clusters. These species are commonly exposed to energetic ionizing radiation in the interstellar medium, so understanding the key aspects of their fragmentation, in particular the way energy and charge are shared in the process, can be relevant to get a deeper insight on the evolution of carbonaceous species in the universe.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Agúndez M, Wakelam V (2013) Chemistry of dark clouds: Databases, networks, and models. Chem Rev 113(12):8710. https://doi.org/10.1021/cr4001176 PMID: 24099569

    Article  CAS  PubMed  Google Scholar 

  2. Brünken S, Kluge L, Stoffels A, Asvany O, Schlemmer S (2014) Laboratory Rotational Spectrum of \(l-{\rm C}_3H^+\) and Confirmation of its Astronomical Detection. Astrophys J Lett 783(1):L4 http://stacks.iop.org/2041-8205/783/i=1/a=L4

  3. Maciel WJ (2013) Astrophysics of the interstellar medium. Springer, Berlin. https://doi.org/10.1007/978-1-4614-3767-3

    Book  Google Scholar 

  4. Yamada KMT, Winnewisser G (eds.), Interstellar Molecules (Springer, 2011). https://doi.org/10.1007/978-3-642-16268-8

  5. Wakelam V, Herbst E, Loison JC, Smith IWM, Chandrasekaran V, Pavone B, Adams NG, Bacchus-Montabonel MC, Bergeat A, Béroff K, Bierbaum VM, Chabot M, Dalgarno A, van Dishoeck EF, Faure A, Geppert WD, Gerlich D, Galli D, Hébrard E, Hersant F, Hickson KM, Honvault P, Klippenstein SJ, Picard SL, Nyman G, Pernot P, Schlemmer S, Selsis F, Sims IR, Talbi D, Tennyson J, Troe J, Wester R, Wiesenfeld L (2012) A kinetic database for astrochemistry (kida). Astrophys. J. Suppl. S. 199(1):21 http://stacks.iop.org/0067-0049/199/i=1/a=21

  6. Ullrich J, Shevelko V (eds.), Many-Particle Quantum Dynamics in Atomic and Molecular Fragmentation (Springer, Berlin, Heidelberg, 2003). https://doi.org/10.1007/978-3-662-08492-2

  7. Whelan CT (ed.), Fragmentation Processes: Topics in Atomic and Molecular Physics (Cambridge University Press, 2012). https://doi.org/10.1017/CBO9781139017572

  8. Collins MA, Bettens RPA (2015) Energy-based molecular fragmentation methods. Chem Rev 115:5607. https://doi.org/10.1021/cr500455b

    Article  CAS  PubMed  Google Scholar 

  9. Martinet G, Díaz-Tendero S, Chabot M, Wohrer K, Negra SD, Mezdari F, Hamrita H, Désesquelles P, Padellec AL, Gardés D, Lavergne L, Lalu G, Grave X, Clavelin JF, Hervieux PA, Alcamí M, Martín F (2004) Fragmentation of highly excited small neutral carbon clusters. Phys. Rev. Lett. 93:063401. 10.1103/PhysRevLett.93.063401. http://link.aps.org/doi/10.1103/PhysRevLett.93.063401

  10. Tuna T, Chabot M, Pino T, Désesquelles P, LePadellec A, Martinet G, Barat M, Lucas B, Mezdari F, Montagnon L, Van-Oanh NT, Lavergne L, Lachaize A, Carpentier Y, Béroff K (2008) Fragmentation branching ratios of highly excited hydrocarbon molecules C\(_n\)H and their cations \({\rm C}_n{\rm H}^+\) (n\(\le \)4). J. Chem. Phys. 128(12):124312. 10.1063/1.2884862. http://dx.doi.org/10.1063/1.2884862

  11. Chabot M, éroff KB, Gratier P, Jallat A, Wakelam V (2013) Reactions Forming \({\rm C}_{n=2, 10}^{(0,+)}\), \({\rm C}_{n=2,4}{\rm H}^{(0, +)}\), and \({\rm C}_3{\rm H}_2^{(0, +)}\) in the Gas Phase: Semiempirical Branching Ratios, Astrophys. J. 771(2), 90. http://stacks.iop.org/0004-637X/771/i=2/a=90

  12. Chabot M, Fossé R, Wohrer K, Gardès D, Maynard G, Rabilloud F, Spiegelman F (2001) Multi-ionization cross-sections of small ionic carbon clusters by particle impact as a tool to investigate their shapes. Eur Phys J D 14(1):5. https://doi.org/10.1007/s100530170226

    Article  CAS  Google Scholar 

  13. Reinhard P, Suraud E (2008) Introduction to cluster dynamics. Wiley, New York. https://doi.org/10.1002/9783527602520

    Book  Google Scholar 

  14. Vincendon M, Suraud E, Reinhard P (2017) Dissipation and energy balance in electronic dynamics of na clusters. Eur Phys J D 71:179. https://doi.org/10.1140/epjd/e2017-80067-0

    Article  CAS  Google Scholar 

  15. Wang ZP, Dinh PM, Reinhard PG, Suraud E (2014) Ultrafast nonadiabatic dynamics of a water dimer in femtosecond laser pulses. Laser Phys 24(10):106004. https://doi.org/10.1088/1054-660x/24/10/106004

    Article  Google Scholar 

  16. Hansen K (2018) Statistical Physics of Nanoparticles in the Gas Phase, Springer Series on Atomic, Optical, and Plasma Physics, vol. 73 (Springer, Cham). https://doi.org/10.1007/978-3-319-90062-9

  17. Hansen K, Näher U (1999) Evaporation and cluster abundance spectra. Phys Rev A 60(2):1240. https://doi.org/10.1103/PhysRevA.60.1240

    Article  CAS  Google Scholar 

  18. Calvo F, Galindez J, Gadéa FX (2003) Internal conversion in the photofragmentation of \({\rm Ar}_n^+\) clusters (\(n = 38\)). Phys Chem Chem Phys 5(2):321. https://doi.org/10.1039/B210796C

    Article  CAS  Google Scholar 

  19. Calvo F, Berthias F, Feketeová L, Abdoul-Carime H, Farizon B, Farizon M (2017) Collision-induced evaporation of water clusters and contribution of momentum transfer. Eur Phys J D 71(5):110. https://doi.org/10.1140/epjd/e2017-80062-5

    Article  CAS  Google Scholar 

  20. Abdoul-Carime H, Berthias F, Feketeová L, Marciante M, Calvo F, Forquet V, Chermette H, Farizon B, Farizon M, Märk TD (2015) Velocity of a Molecule Evaporated from a Water Nanodroplet: Maxwell-Boltzmann Statistics versus Non-Ergodic Events. Angew Chem Int Ed 54(49):14685. https://doi.org/10.1002/anie.201505890

    Article  CAS  Google Scholar 

  21. Berthias F, Buridon V, Abdoul-Carime H, Farizon B, Farizon M, Dinh PM, Reinhard PG, Suraud E, Märk TD (2014) Collision-induced dissociation of protonated water clusters. Phys Rev A 89:062705. https://doi.org/10.1103/PhysRevA.89.062705

    Article  CAS  Google Scholar 

  22. Hervieux PA, Gross DHE (1995) Evaporation of hot mesoscopic atomic metal clusters. Z Phys D - Atoms, Molecules Clusters 33:295–299. https://doi.org/10.1007/BF01437510

    Article  CAS  Google Scholar 

  23. Gross DHE, Hervieux PA (1995) Statistical fragmentation of hot atomic metal clusters. Z Phys D - Atoms, Molecules Clusters 35:27–42. https://doi.org/10.1007/BF01439980

    Article  CAS  Google Scholar 

  24. Hervieux PA, Zarour B, Hanssen J, Politis MF, Martín F (2001) Fragmentation in collisions of Na\(_9^+\) clusters with Cs atoms. J Phys B: Atom Mol Opt Phys 34(16):3331. https://doi.org/10.1088/0953-4075/34/16/310

    Article  CAS  Google Scholar 

  25. Bréchignac C, Cahuzac P, Concina B, Leygnier J, Ruiz LF, Zarour B, Hervieux PA, Hanssen J, Politis MF, Martín F (2002) Charge transfer and dissociation in collisions of metal clusters with atoms. Phys Rev Lett 89:183402. https://doi.org/10.1103/PhysRevLett.89.183402

    Article  CAS  PubMed  Google Scholar 

  26. Calvo F, Spiegelman F (2004) On the premelting features in sodium clusters. J Chem Phys 120(20):9684. https://doi.org/10.1063/1.1714792

    Article  CAS  PubMed  Google Scholar 

  27. Díaz-Tendero S, Ruiz LF, Zarour B, Calvo F, Spiegelman F, Hervieux P-A, Martín F, Hanssen J, Politis MF (2007) Fragmentation induced by charge exchange in collisions of charged alkaline clusters with alkali atoms. Eur Phys J D 44(3):525. https://doi.org/10.1140/epjd/e2007-00216-4

    Article  CAS  Google Scholar 

  28. Martinet G, Chabot M, Wohrer K, Della Negra S, Gardés D, Scarpaci JA, Désesquelles P, Lima V, Díaz-Tendero S, Alcamí M, Hervieux P-A, Politis MF, Hanssen J, Martín F (2003) Fragmentation of neutral C\(_n\) clusters (\(n<9\)): experimental and theoretical investigations. Eur Phys J D 24(1–3):149. https://doi.org/10.1140/epjd/e2003-00102-1

    Article  CAS  Google Scholar 

  29. Díaz-Tendero S, Hervieux PA, Alcamí M, Martín F (2005) Statistical fragmentation of small neutral carbon clusters. Phys Rev A 71:033202. https://doi.org/10.1103/PhysRevA.71.033202

    Article  CAS  Google Scholar 

  30. Díaz-Tendero S, Sánchez G, Hervieux PA, Alcamí M, Martín F (2006) Ionization potentials, dissociation energies and statistical fragmentation of neutral and positively charged small carbon clusters. Braz J Phys 36:529

    Article  Google Scholar 

  31. Daz-Tendero S, Snchez G, Alcam M, Martn F, Hervieux PA, Chabot M, Martinet G, Dsesquelles P, Mezdari F, Wohrer-Broff K, Negra SD, Hamrita H, LePadellec A, Montagnon L (2006) Fragmentation of small neutral carbon clusters. Int J Mass Spectrom 252(2):126. https://doi.org/10.1016/j.ijms.2005.12.055 Special Issue on Cluster Cooling

    Article  CAS  Google Scholar 

  32. Calvo F, Parneix P (2006) Statistical dissociation of small carbon clusters: A phase space theory investigation. Comput Mater Sci 35(3):198. https://doi.org/10.1016/j.commatsci.2004.07.007

    Article  CAS  Google Scholar 

  33. Montagnon L, Spiegelman F (2007) Self-consistent field tight-binding model for neutral and (multi-) charged carbon clusters. J Chem Phys 127(8):084111. https://doi.org/10.1063/1.2759210

    Article  CAS  PubMed  Google Scholar 

  34. Désesquelles P, Van-Oanh NT, Thomas S, Domin D (2020) Statistical molecular fragmentation: which parameters influence the branching ratios? Phys Chem Chem Phys 22(6):3160. https://doi.org/10.1039/C9CP05095G

    Article  PubMed  Google Scholar 

  35. Aguirre NF, Díaz-Tendero S, Hervieux PA, Alcamí M, Martín F (2017) \(M3C\): a computational approach to describe statistical fragmentation of excited molecules and clusters. J Chem Theory Comput 13(3):992. https://doi.org/10.1021/acs.jctc.6b00984 PMID: 28005371

    Article  CAS  PubMed  Google Scholar 

  36. Aguirre NF, Díaz-Tendero S, IdBarkach T, Chabot M, Béroff K, Alcamí M, Martín F (2019) Fully versus constrained statistical fragmentation of carbon clusters and their heteronuclear derivatives. J Chem Phys 150(14):144301. https://doi.org/10.1063/1.5083864

    Article  CAS  PubMed  Google Scholar 

  37. Chabot M, Mezdari F, Béroff K, Martinet G, Hervieux PA (2010) Scaling law for the partitioning of energy in fragmenting multicharged carbon clusters. Phys Rev Lett 104:043401. https://doi.org/10.1103/PhysRevLett.104.043401

    Article  CAS  PubMed  Google Scholar 

  38. Díaz-Tendero S, Martín F (2002) Structure, dissociation energies, and harmonic frequencies of small doubly charged carbon clusters C\(_n^{2+}\) (\(n = 3--9\)). J Phys Chem A 106(45):10782. https://doi.org/10.1021/jp0257956

    Article  CAS  Google Scholar 

  39. Sánchez JP, Aguirre NF, Díaz-Tendero S, Martín F, Alcamí M (2016) Structure, ionization, and fragmentation of neutral and positively charged hydrogenated carbon clusters: C\(_n\)H\(_m^q+\) (\(n = 1--5\), \(m = 1--4\), \(q = 0--3\)). J Phys Chem A 120(4):588. https://doi.org/10.1021/acs.jpca.5b10143 PMID: 26683517

    Article  CAS  PubMed  Google Scholar 

  40. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery JA Jr, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam JM, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas Ö, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2010) Gaussian 09 Revision B.01

  41. Chen L, Martin S, Bernard J, Brédy R (2007) Direct measurement of internal energy of fragmented \({\rm c}_{60}\). Phys Rev Lett 98:193401. https://doi.org/10.1103/PhysRevLett.98.193401

    Article  CAS  PubMed  Google Scholar 

  42. Maclot S, Delaunay R, Piekarski DG, Domaracka A, Huber BA, Adoui L, Martín F, Alcamí M, Avaldi L, Bolognesi P, Díaz-Tendero S, Rousseau P (2016) Determination of energy-transfer distributions in ionizing ion-molecule collisions. Phys Rev Lett 117:073201. https://doi.org/10.1103/PhysRevLett.117.073201

    Article  CAS  PubMed  Google Scholar 

  43. Labaigt G, Jorge A, Illescas C, Béroff K, Dubois A, Pons B, Chabot M (2015) Electron capture and ionization processes in high-velocity C\(_n^+\), CAr and C\(_n^+\), CHe collisions. J Phys B: Atom, Mol Opt Phys 48(7):075201. https://doi.org/10.1088/0953-4075/48/7/075201

    Article  CAS  Google Scholar 

  44. Grimme S (2013) Towards first principles calculation of electron impact mass spectra of molecules. Angew Chem Int Ed 52(24):6306. https://doi.org/10.1002/anie.201300158

    Article  CAS  Google Scholar 

  45. Bauer CA, Grimme S (2014) Elucidation of electron ionization induced fragmentations of adenine by semiempirical and density functional molecular dynamics. J Phys Chem A 118(49):11479. https://doi.org/10.1021/jp5096618

    Article  CAS  PubMed  Google Scholar 

  46. Bauer CA, Grimme S (2016) How to compute electron ionization mass spectra from first principles. J Phys Chem A 120(21):3755. https://doi.org/10.1021/acs.jpca.6b02907

    Article  CAS  PubMed  Google Scholar 

  47. Ásgeirsson V, Bauer CA, Grimme S (2017) Quantum chemical calculation of electron ionization mass spectra for general organic and inorganic molecules. Chem Sci 8(7):4879. https://doi.org/10.1039/C7SC00601B

    Article  PubMed  PubMed Central  Google Scholar 

  48. de Hoffmann E, Stroobant V (2007) Mass spectrometry: principles and applications, 3rd edn. Wiley, New York

    Google Scholar 

  49. Gross JH (2017) Fragmentation of organic ions and interpretation of EI mass spectra. Springer International Publishing, Cham, pp 325–437

    Google Scholar 

  50. Nicolas C, Shu J, Peterka DS, Hochlaf M, Poisson L, Leone SR, Ahmed M (2006) Vacuum ultraviolet photoionization of C\(_3\). J Am Chem Soc 128(1):220. https://doi.org/10.1021/ja055430 PMID: 16390150

    Article  CAS  PubMed  Google Scholar 

  51. Jallat A (2015) Fragmentation de molécules carbonées d’intérêt astrophysique auprès des accélérateurs. Ph.D. thesis, Université Paris-11

  52. Misakian M, Zorn JC (1972) Dissociative excitation of molecular hydrogen by electron impact. Phys Rev A 6(6):2180. https://doi.org/10.1103/PhysRevA.6.2180

    Article  CAS  Google Scholar 

  53. Brouillard F et al (1986) Atomic processes in electron-ion and ion-ion collisions. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-5224-2

    Book  Google Scholar 

  54. Belki D (2012) Fast ion-atom and ion-molecule collisions. World Scientific, Singapore. https://doi.org/10.1142/8485

    Book  Google Scholar 

  55. Calvo F, Díaz-Tendero S, Lebeault MA (2009) Translational, rotational and vibrational energy partitioning in the sequential loss of carbon dimers from fullerenes. Phys Chem Chem Phys 11:6345. https://doi.org/10.1039/B901557D

    Article  CAS  PubMed  Google Scholar 

  56. Rentenier A, Ruiz LF, Díaz-Tendero S, Zarour B, Moretto-Capelle P, Bordenave-Montesquieu D, Bordenave-Montesquieu A, Hervieux PA, Alcamí M, Politis MF, Hanssen J, Martín F (2008) Absolute charge transfer and fragmentation cross sections in \({\rm He}^{2+}- {\rm C}_{60}\) collisions. Phys Rev Lett 100:183401. https://doi.org/10.1103/PhysRevLett.100.183401

    Article  CAS  PubMed  Google Scholar 

  57. Díaz-Tendero S, Alcamí M, Martín F (2003) Theoretical study of ionization potentials and dissociation energies of C\(_n^{q+}\) fullerenes (\(n=50-60\), \(q=0\), 1 and 2). J Chem Phys 119(11):5545. https://doi.org/10.1063/1.1597634

    Article  CAS  Google Scholar 

  58. Tomita S, Andersen JU, Gottrup C, Hvelplund P, Pedersen UV (2001) Dissociation energy for \({\rm C}_{2}\) loss from Fullerene Cations in a Storage Ring. Phys Rev Lett 87:073401. https://doi.org/10.1103/PhysRevLett.87.073401

    Article  CAS  PubMed  Google Scholar 

  59. Wörgötter R, Dünser B, Scheier P, Märk TD, Foltin M, Klots CE, Laskin J, Lifshitz C (1996) Self-consistent determination of fullerene binding energies BE (\({\rm C}_n^+-{\rm C}_2\)), \(n=58,\ldots,44\). J Chem Phys 104(4):1225. https://doi.org/10.1063/1.471708

    Article  Google Scholar 

  60. Campbell E (2003) Fullerene Collision Reactions. Developments in Fullerene Science (Springer). https://books.google.es/books?id=2ekBUHXNcRwC

  61. Maclot S, Piekarski DG, Domaracka A, Méry A, Vizcaino V, Adoui L, Martín F, Alcamí M, Huber BA, Rousseau P, Díaz-Tendero S (2013) Dynamics of glycine dications in the gas phase:ultrafast intramolecular hydrogen migration versus coulomb repulsion. J Phys Chem Lett 4(22):3903. https://doi.org/10.1021/jz4020234

    Article  CAS  Google Scholar 

  62. Jochim B, Lueking A, Doshier L, Carey S, Wells E, Parke E, Leonard M, Carnes KD, Ben-Itzhak I (2009) Rapid formation of \({\rm H}_3^+\) from ammonia and methane following 4 MeV proton impact. J. Phys. B At. Mol. Opt.Phys 42(9):091002 http://stacks.iop.org/0953-4075/42/i=9/a=091002

  63. De S, Roy A, Rajput J, Ghosh P, Safvan C (2008) Dissociation of methanol by ion-impact: breakup dynamics, bond rearrangement and kinetic energy release. Int J Mass Spectrom 276(1):43. https://doi.org/10.1016/j.ijms.2008.06.021

    Article  CAS  Google Scholar 

  64. De S, Rajput J, Roy A, Ghosh PN, Safvan CP (2008) Ion-induced dissociation dynamics of acetylene. Phys Rev A 77:022708. https://doi.org/10.1103/PhysRevA.77.022708

    Article  CAS  Google Scholar 

  65. De S, Rajput J, Roy A, Ghosh PN, Safvan CP (2006) Formation of \({\rm H}_{3}{}^{+}\) due to intramolecular bond rearrangement in doubly charged methanol. Phys Rev Lett 97:213201. https://doi.org/10.1103/PhysRevLett.97.213201

    Article  CAS  PubMed  Google Scholar 

  66. Wohrer K, Chabot M, Fossé R, Gards D, Hervieux P, Calvayrac F, Reinhard P, Suraud E (1998) Swift cluster–atom collisions: a progress report. Nucl Instrum Methods Phys Res B 146(1):29. https://doi.org/10.1016/S0168-583X(98)00421-2

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We acknowledge the generous allocation of computer time at the Centro de Computación Científica at the Universidad Autónoma de Madrid (CCC-UAM). The research was conducted in the framework of the COST action CA18212 Molecular Dynamics in the GAS phase (MD-GAS). This work was partially supported by the MICINN—Spanish Ministry of Science and Innovation—projects FIS2016-77889-R, CTQ2016-76061-P, and PID2019-110091GB-I00.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Néstor F. Aguirre or Sergio Díaz-Tendero.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Published as part of the special collection of articles “Festschrift in honor of Fernand Spiegelmann”.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aguirre, N.F., Díaz-Tendero, S., Hervieux, PA. et al. Charge and energy sharing in the fragmentation of astrophysically relevant carbon clusters. Theor Chem Acc 140, 22 (2021). https://doi.org/10.1007/s00214-020-02702-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00214-020-02702-z

Keywords

Navigation