Skip to main content
SpringerLink
Log in

Size evolution of characteristic acoustic oscillations of fullerenes and its connection to continuum elasticity theory

  • Regular Article – Clusters and Nanostructures
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

We performed a theoretical investigation, based on density functional theory, on the vibrational properties of fullerenes and its dependence with size (\(20\rightarrow 720\) atoms). Characteristic acoustic oscillations like the breathing (BM) and quadrupolar (QM) modes were located using the calculated vibrational density of states. In particular, it was obtained that the acoustic gap (lowest frequency value) corresponds to the QM five-fold degenerate frequency, as expected in cage-like quasi-spherical nanostructures. The main finding indicates a linear dependence for the vibrational periods of the BM and QM with the fullerenes size. The results obtained for the BM are consistent with a continuum elastic theory approach to describe the acoustic oscillations of a cage-like structure. Moreover, this behavior is also similar to that one found in metal nanoparticles with size in the range of 0.5–4 nm, indicating that the covalent nature of the bonding in fullerenes does not induce anomalous effects in their acoustic oscillations.

Graphic Abstract)

.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Data Availability

This manuscript has associated data in a data repository. [Authors‘ comment:The TURBOMOLE code outputs containing optimized structures and their frequencies generated for our study have been deposited in the NOMAD repository (https://doi.org/ 10.17172/NOMAD/2021.06.12-1) (Reference [29])].

References

  1. J.G. Aguilar, A. Mañanes, M.J. López, M.P. Iñiguez, J.A. Alonso, Int. J. Quantum Chem. 56, 589 (1995). https://doi.org/10.1002/qua.560560515

    Article  Google Scholar 

  2. J.G. Aguilar, A. Mañanes, F. Duque, M.J. López, M.P. Iñiguez, J.A. Alonso, Int. J. Quantum Chem. 61, 613 (1997). https://doi.org/10.1002/(SICI)1097-461X(1997)61:4<613::AID-QUA2>3.0.CO;2-Z

    Article  Google Scholar 

  3. H.E. Sauceda, D. Mongin, P. Maioli, A. Crut, M. Pellarin, N. Del Fatti, F. Vallée, I.L. Garzón, J. Phys. Chem. C 116, 25147 (2012). https://doi.org/10.1021/jp309499t

    Article  Google Scholar 

  4. P. Maioli, T. Stoll, H.E. Sauceda, I. Valencia, A. Demessence, F. Bertorelle, A. Crut, F. Vallée, I.L. Garzón, G. Cerullo, N. Del Fatti, Nano Lett. 18, 6842 (2018). https://doi.org/10.1021/acs.nanolett.8b02717

    Article  ADS  Google Scholar 

  5. S. Carnalla, A. Posada, I.L. Garzón, Nanostructured Mater. 3, 385 (1993). https://doi.org/10.1016/0965-9773(93)90103-I

    Article  Google Scholar 

  6. A. Posada-Amarillas, I.L. Garzón, Phys. Rev. B 54, 10362 (1996). https://doi.org/10.1103/PhysRevB.54.10362

    Article  ADS  Google Scholar 

  7. H.E. Sauceda, F. Salazar, L.A. Pérez, I.L. Garzón, J. Phys. Chem. C 117, 25160 (2013). https://doi.org/10.1021/jp408976f

    Article  Google Scholar 

  8. H.E. Sauceda, I.L. Garzón, J. Phys. Chem. C 119, 10876 (2015). https://doi.org/10.1021/jp510666v

    Article  Google Scholar 

  9. J.N. Pedroza-Montero, I.L. Garzón, H.E. Sauceda, Commun. Chem. 4, 103 (2021). https://doi.org/10.1038/s42004-021-00540-z

    Article  Google Scholar 

  10. S. Adhikari, R. Chowdhury, Phys. Lett. A 375, 2166 (2011). https://doi.org/10.1016/j.physleta.2011.04.019

    Article  ADS  Google Scholar 

  11. H.-J. Eisler, S. Gilb, F.H. Hennrich, M.M. Kappes, J. Phys. Chem. A 104, 1762 (2000). https://doi.org/10.1021/jp9932665

    Article  Google Scholar 

  12. H.-J. Eisler, F.H. Hennrich, S. Gilb, M.M. Kappes, J. Phys. Chem. A 104, 1769 (2000). https://doi.org/10.1021/jp9932618

    Article  Google Scholar 

  13. H. Nejat Pishkenari, Comp. Mater. Sci 122, 38 (2016). https://doi.org/10.1016/j.commatsci.2016.05.011

    Article  Google Scholar 

  14. L.D. Landau, L.P. Pitaevskii, A.M. Kosevich, E. Lifshitz, Theory of Elasticity, Course of Theoretical Physics (Pergamon, Oxford, 1959). https://doi.org/10.1016/C2009-0-25521-8

    Book  Google Scholar 

  15. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). https://doi.org/10.1103/PhysRevLett.77.3865

    Article  ADS  Google Scholar 

  16. P. Fuentealba, H. Preuss, H. Stoll, L.V. Szentpály, Chem. Phys. Lett. 89, 418 (1982). https://doi.org/10.1016/0009-2614(82)80012-2

    Article  ADS  Google Scholar 

  17. V.V. Gobre, A. Tkatchenko, Nat. Commun. 4, 2341 (2013). https://doi.org/10.1038/ncomms3341

    Article  ADS  Google Scholar 

  18. TURBOMOLE V7.0 2015, a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989–2007, TURBOMOLE GmbH, since 2007; Available from http://www.turbomole.com

  19. W. Haynes, CRC Handbook of Chemistry and Physics, 93rd Edition, 100 Key Points Taylor & Francis, (2012) https://books.google.com.mx/books?id=-BzP7Rkl7WkC

  20. S.J. Blanksby, G.B. Ellison, Acc. Chem. Res. 36, 255 (2003). https://doi.org/10.1021/ar020230d

    Article  Google Scholar 

  21. K.K. Irikura, J. Phys. Chem. Ref. Data 36, 389 (2007). https://doi.org/10.1063/1.2436891

    Article  ADS  Google Scholar 

  22. R. Meilunas, R.P.H. Chang, S. Liu, M. Jensen, M.M. Kappes, J. Appl. Phys. 70, 5128 (1991). https://doi.org/10.1063/1.348986

    Article  ADS  Google Scholar 

  23. A.M. Vassallo, L.S.K. Pang, P.A. Cole-Clarke, M.A. Wilson, J. Am. Chem. Soc. 113, 7820 (1991). https://doi.org/10.1021/ja00020a086

    Article  Google Scholar 

  24. C.H. Choi, M. Kertesz, L. Mihaly, J. Phys. Chem. A 104, 102 (2000). https://doi.org/10.1021/jp991420h

    Article  Google Scholar 

  25. V. Schettino, M. Pagliai, L. Ciabini, G. Cardini, J. Phys. Chem. A 105, 11192 (2001). https://doi.org/10.1021/jp012874t

    Article  Google Scholar 

  26. T.A. Beu, J. Onoe, Phys. Rev. B 74, 195426 (2006). https://doi.org/10.1103/PhysRevB.74.195426

    Article  ADS  Google Scholar 

  27. N. Combe, L. Saviot, Phys. Rev. B 80, 035411 (2009). https://doi.org/10.1103/PhysRevB.80.035411

    Article  ADS  Google Scholar 

  28. B. Lan, D.Y. Sun, Phys. Rev. B 103, 134108 (2021). https://doi.org/10.1103/PhysRevB.103.134108

    Article  ADS  Google Scholar 

  29. J. N. Pedroza-Montero, I. L. Garzón, and H. E. Sauceda, https://doi.org/10.17172/NOMAD/2021.06.12-1 (2021b), https://doi.org/10.17172/NOMAD/2021.06.12-1

  30. G.A. Narvaez, J. Kim, J.W. Wilkins, Phys. Rev. B 72, 155411 (2005). https://doi.org/10.1103/PhysRevB.72.155411

    Article  ADS  Google Scholar 

  31. E. Ghavanloo, S.A. Fazelzadeh, Eur. J. Mech.—A/Solids 41, 37 (2013). https://doi.org/10.1016/j.euromechsol.2013.02.003

    Article  ADS  MathSciNet  Google Scholar 

  32. X. Cong, Q.-Q. Li, X. Zhang, M.-L. Lin, J.-B. Wu, X.-L. Liu, P. Venezuela, P.-H. Tan, Carbon 149, 19 (2019). https://doi.org/10.1016/j.carbon.2019.04.006

    Article  Google Scholar 

  33. J. Sólyom, Fundamentals of the Physics of Solids: Volume I: Structure and Dynamics Springer (2008) https://doi.org/10.1007/978-3-540-72600-5

  34. T. Oroguchi, M. Nakasako, Sci. Rep. 7, 15859 (2017). https://doi.org/10.1038/s41598-017-16203-w

    Article  ADS  Google Scholar 

  35. P.K. Weiner, P.A. Kollman, J. Comput. Chem. 2, 287 (1981). https://doi.org/10.1002/jcc.540020311

    Article  Google Scholar 

  36. A.K. Rappe, C.J. Casewit, K.S. Colwell, W.A. Goddard, W.M. Skiff, J. Am. Chem. Soc. 114, 10024 (1992). https://doi.org/10.1021/ja00051a040

    Article  Google Scholar 

  37. K. T. Schütt, P.-J. Kindermans, H. E. Sauceda, S. Chmiela, A. Tkatchenko, and K.-R. Müller, In Advances in Neural Information Processing Systems 30 Curran Associates, Inc., (2017) pp. 991–1001 http://papers.nips.cc/paper/6700-schnet-a-continuous-filter-convolutional-neural-network-for-modeling-quantum-interactions.pdf

  38. K.T. Schütt, H.E. Sauceda, P.-J. Kindermans, A. Tkatchenko, K.-R. Müller, J. Chem. Phys. 148, 241722 (2018). https://doi.org/10.1063/1.5019779

    Article  ADS  Google Scholar 

  39. O.T. Unke, S. Chmiela, M. Gastegger, K.T. Schütt, H.E. Sauceda, K.-R. Müller, Nat. Commun. 12, 7273 (2021). https://doi.org/10.1038/s41467-021-27504-0

    Article  ADS  Google Scholar 

Download references

Acknowledgements

I.L.G. thanks support from DGTIC-UNAM under Project LANCADUNAM- DGTIC-049, DGAPA-UNAM under Project IN106021 and CONACYT-Mexico under Project 285821. H.E.S. thanks the support from DGTIC-UNAM under Project LANCAD-UNAM-DGTIC-419. H.E.S. carried out part of this project at the Machine Learning Group, Technische Universität Berlin, Berlin, Germany.

Author information

Authors and Affiliations

  1. Programa de Doctorado en Nanociencias y Nanotecnologías, CINVESTAV, Av. Instituto Politécnico Nacional, 2508, México, México

    Jesús N. Pedroza-Montero

  2. Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-346, 01000, México, D.F., México

    Ignacio L. Garzón

  3. Departamento de Materia Condensada, Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-346, 01000, México, D.F., México

    Huziel E. Sauceda

Authors
  1. Jesús N. Pedroza-Montero
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ignacio L. Garzón
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Huziel E. Sauceda
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

H.E.S. and I.L.G. conceptualized the project and designed the research; J.N.P.M. and H.E.S. performed the calculations; All the authors analysed and interpreted the data and contributed to the writing of the manuscript.

Corresponding author

Correspondence to Huziel E. Sauceda.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pedroza-Montero, J.N., Garzón, I.L. & Sauceda, H.E. Size evolution of characteristic acoustic oscillations of fullerenes and its connection to continuum elasticity theory. Eur. Phys. J. D 76, 123 (2022). https://doi.org/10.1140/epjd/s10053-022-00449-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/s10053-022-00449-9

Search

Navigation