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Relativistic effects on the energetic stability of \(\hbox {Pb}_5\) clusters

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Abstract

In this work, we study isomers of small lead clusters with five atoms, \(\hbox {Pb}_5\), at different levels of approximation namely Scalar-Relativistic (SR), Scalar-Relativistic plus Spin–Orbit coupling interaction (SR + SO) and four-component Dirac–Hartree–Fock (4c-DHF), in order to analyze the effects of relativity in these heavy molecular systems. The exploration of potential energy surface (PES) with a genetic algorithm produces four possible equilibrium structures, and we find that when Relativity is included at a major level in calculations, the global minimum energy structure changes from S4 isomer with \(\hbox {D}_{3\mathrm{h}}\) symmetry at SR level to S1 isomer with \(\hbox {C}_2\) symmetry at 4c-DHF level; this change is related to modifications in the electronic structure and geometric parameters. We explain this significant result using two methodologies in order to analyze the electronic structure and strength of chemical bonds, like energy decomposition analysis (EDA) and Quantum Theory Atoms In Molecules (QTAIM). On the one hand, in the framework of EDA, results at SR + SO level show significant differences on the steric and orbital interactions compared with SR ones, with which the S1 isomer is more stable than S4; this means that SO effects stabilize the interactions on S1 isomer more than S4. The HOMO–LUMO gap also shows a drastic reduction due to the SO effects on S4 isomer, while for the other systems remains unchanged. This result can be associated with the lower stability of S4 isomer with respect to the others when Relativity is included at a major level. On the other hand, in the framework of QTAIM, calculations with SR + SO scheme show the formation of two new critical points compared with SR for S1 isomer, which is reflected in a greater stability of this system.

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References

  1. Khanna SN, Jena P (1995) Phys Rev B 51:13705–13716

    CAS  Google Scholar 

  2. Claridge SA, Castleman AW, Khanna SN, Murray CB, Sen A, Weiss PS (2009) ACS Nano 3:244–255

    CAS  PubMed  Google Scholar 

  3. Brutschy B, Bisling P, Rühl E, Baumgärtel HZ (1987) Phys D Atom Mol Cl 5:217–231

    CAS  Google Scholar 

  4. Ohshimo K, Komukai T, Takahashi T, Norimasa N, Wu JWJ, Moriyama R, Koyasu K, Misaizu F (2014) Mass Spectrom 3:S0043

    Google Scholar 

  5. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Science 220:671–680

    CAS  PubMed  Google Scholar 

  6. Jones RO (1991) Angew Chem Int Ed Engl 30:630–640

    Google Scholar 

  7. Alexandrova AN, Boldyrev AI (2005) J Chem Theory Comput 1:566–580

    CAS  PubMed  Google Scholar 

  8. Kanters RPF, Donald KJ (2014) J Chem Theory Comput 10:5729–5737

    CAS  PubMed  Google Scholar 

  9. Stekolnikov AA, Furthmüller J, Bechstedt F (2002) Phys Rev B 65:115318–115327

    Google Scholar 

  10. Sahin H, Cahangirov S, Topsakal M, Bekaroglu E, Akturk E, Senger RT, Ciraci S (2009) Phys Rev B 80:155453–155464

    Google Scholar 

  11. Matusalem F, Marques M, Teles LK, Bechsted F (2015) Phys Rev B 92:045436

    Google Scholar 

  12. Andreoni W (1993) Nanostruct Mater 3:293–300

    CAS  Google Scholar 

  13. Martins JL, Reuse FA, Khanna SN (2001) J Clust Sci 12:513–525

    CAS  Google Scholar 

  14. Popov VN (2004) Mater Sci Eng R 43:61–102

    Google Scholar 

  15. Trojanowicz M (2006) Trac-Trend Anal Chem 25:480–489

    CAS  Google Scholar 

  16. Li X, Yang JJ (2014) Mater Chem C 2:7071–7076

    CAS  Google Scholar 

  17. Wirths S, Buca D, Mantl S (2016) Prog Cryst Growth Charact Mater 62:1–39

    CAS  Google Scholar 

  18. Wang B, Molina LM, Lopez MJ, Rubio A, Alonso JA, Stott MJ (1998) Ann Phys 510:107–119

    Google Scholar 

  19. Negishi Y, Kawamata H, Nakajima A, Kaya K (2000) J Electron Spectrosc Relat Phenom 106:117–125

    CAS  Google Scholar 

  20. Wang B, Zhao J, Chen X, Shi D, Wang G (2005) Phys Rev A 71:033201

    Google Scholar 

  21. Rajesh C, Majumder C (2007) J Chem Phys 126:244704

    PubMed  Google Scholar 

  22. Shkrob IA, Marin TW (2014) J Phys Chem Lett 5:1066–1071

    CAS  PubMed  Google Scholar 

  23. Yusoff ARM, Nazeeruddin MK (2016) J Phys Chem Lett 7:851–866

    CAS  PubMed  Google Scholar 

  24. Yang J-Y, Hu M (2017) J Phys Chem Lett 8:3720–3725

    CAS  PubMed  Google Scholar 

  25. Farley RW, Ziemann P, Castleman AWZ (1989) Phys D Atom Mol Cl 14:353–360

    CAS  Google Scholar 

  26. Balasubramanian K, Majumdar D (2001) J Chem Phys 115:8795–8809

    CAS  Google Scholar 

  27. Mühlbach J, Sattler K, Pfau P, Recknagel E (1982) Phys Lett A 87:415–417

    Google Scholar 

  28. LaiHing K, Wheeler RG, Wilson WL, Duncan MA (1987) J Chem Phys 87:3401–3409

    CAS  Google Scholar 

  29. Rabanal-León WA, Tiznado W, Osorio E, Ferraro F (2018) RSC Adv 8:145–152

    Google Scholar 

  30. Rajesh C, Majumder C, Rajan MGR, Kulshreshtha SK (2005) Phys Rev B 72:235411

    Google Scholar 

  31. Li X-P, Lu W-C, Zang Q-J, Chen G-J, Wang CZ, Ho KM (2009) J Phys Chem A 113:6217–6221

    CAS  PubMed  Google Scholar 

  32. van Lenthe E, Baerends EJ, Snijders JG (1993) J Chem Phys 99:4597–4610

    Google Scholar 

  33. Fass S, van Lenthe E, Hennum AC (2000) J Chem Phys 113:4052–4059

    Google Scholar 

  34. Zeng T, Fedorov DG, Schmidt MW, Klobukowski M (2011) J Chem Phys 134:214107

    PubMed  Google Scholar 

  35. Höfener S, Ahlrichs R, Knecht S, Visscher L (2012) Chem Phys Chem 13:3952–3957

    PubMed  Google Scholar 

  36. Bader RFW (1990) Atoms in molecules: a quantum theory. Oxford University Press, Oxford

    Google Scholar 

  37. Anderson JSM, Rodríguez JI, Ayers PW, Trujillo-González DE, Götz AW, Autschbach J, Castillo-Alvarado FL, Yamashita K (2019) Chem Eur J 25:2538

    CAS  PubMed  Google Scholar 

  38. Kitaura K, Morokuma K (1976) Int J Quantum Chem 10:325–340

    CAS  Google Scholar 

  39. Morokuma K (1971) J Chem Phys 55:1236–1244

    CAS  Google Scholar 

  40. Ziegler T, Rauk A (1977) Theor Chim Acta 46:1–10

    CAS  Google Scholar 

  41. Ziegler T, Rauk A (1979) Inorg Chem 18:1755–1759

    CAS  Google Scholar 

  42. Baerends EJ, Branchadell V, Sodupe M (1997) Chem Phys Lett 265:481–489

    CAS  Google Scholar 

  43. Bickelhaupt FM, Baerends EJ (2000) Reviews in computational chemistry, vol 15. Wiley, New York, pp 1–86

    Google Scholar 

  44. Anderson JSM, Ayers PW (2011) J Phys Chem A 115:13001–13006

    CAS  PubMed  Google Scholar 

  45. Cioslowski J, Karwowski J (2001) In: Carbó-Dorca R, Gironés X, Mezey PG (eds) Fundamentals of molecular similarity. Springer, Boston, pp 101–112

    Google Scholar 

  46. Dirac PAM (1928) Proc R Soc Lond A 117:610–624

    Google Scholar 

  47. Abramov YA (1997) Acta Cryst 53:264–272

    Google Scholar 

  48. Espinosa E, Molins E, Lecomte C (1998) Chem Phys Lett 285:170–173

    CAS  Google Scholar 

  49. Espinosa E, Alkorta I, Rozas I, Elguero J, Molins E (2001) Chem Phys Lett 336:457–461

    CAS  Google Scholar 

  50. Espinosa E, Alkorta I, Elguero J, Molins E (2002) J Chem Phys 117:5529–5542

    CAS  Google Scholar 

  51. Deaven DM, Ho K-M (1995) Phys Rev Lett 75:288

    CAS  PubMed  Google Scholar 

  52. Gregurick SK, Alexander MH, Hartke B (1996) J Chem Phys 104:2684–2691

    CAS  Google Scholar 

  53. Ernzerhof M, Scuseria GE (1999) J Chem Phys 110:5029–5036

    CAS  Google Scholar 

  54. Adamo C, Barone V (1999) J Chem Phys 110:6158–6170

    CAS  Google Scholar 

  55. Faas S, Snijders JG, van Lenthe JH, van Lenthe E, Baerends EJ (1995) Chem Phys Lett 246:632–640

    CAS  Google Scholar 

  56. Vosko SH, Wilk L, Nusair M (1980) Can J Phys 58:1200–1211

    CAS  Google Scholar 

  57. Perdew JP, Chevary JA, Vosko SH, Jackson KA, Pederson MR, Singh DJ, Fiolhais C (1962) Phys Rev B 46:6671–6687

    Google Scholar 

  58. Perdew JP, Burke K, Ernzerhof M (1996) Phys Rev Lett 77:3865–3868

    CAS  PubMed  Google Scholar 

  59. Te Velde G, Bickelhaupt FM, Baerends EJ, Fonseca Guerra C, van Gisbergen SJA, Snijders JG, Ziegler T (2001) J Comput Chem 22:931–967

    Google Scholar 

  60. Dyall KG (1998) Theor Chem Acc 99:366–371

    CAS  Google Scholar 

  61. DIRAC, a Relativistic ab initio Electronic Structure Program, Release DIRAC16 (2016) written by Jensen HJA, Bast R, Saue T, Visscher L, with contributions from Bakken V, Dyall KG, Dubillard S, Ekström U, Eliav E, Enevoldsen T, Faßhauer E, Fleig T, Fossgaard O, Gomes ASP, Helgaker T, Henriksson J, Iliaš M, Jacob Ch, Knecht S, Komorovský S, Kullie O, Lærdahl JK, Larsen CV, Lee YS, Nataraj HS, Nayak MK, Norman P, Olejniczak G, Olsen J, Park YC, Pedersen JK, Pernpointner M, di Remigio R, Ruud K, Sałek P, Schimmelpfennig B, Shee A, Sikkema J, Thorvaldsen AJ, Thyssen J, van Stralen J, Villaume S, Visser O, Winther T, Yamamoto S. http://www.diracprogram.org

  62. Bučinský L, Kucková L, Malček M, Kožíšek J, Biskupič S, Jayatilaka D, Büchel GE, Arion VB (2014) Chem Phys 438:37–47

    Google Scholar 

  63. Pearson RG (1993) Acc Chem Res 26:250–255

    CAS  Google Scholar 

  64. Gázquez JL (2008) J Mex Chem Soc 52:3–10

    Google Scholar 

  65. Anderson JSM, Rodríguez JI, Ayers PW, Götz AW (2017) J Comput Chem 38:81–86

    CAS  PubMed  Google Scholar 

Download references

Acknowledgements

AFM is fellow of the Argentinian National Research Council, CONICET, and ADZE has a fellowship from CONICET. We gratefully acknowledge partial support from the Argentinian National Research Council for Science and Technology (CONICET, Grant PIP 112-201301-361) and the Argentinian Agency for Promotion of Science (FONCYT, Grant PICT2016 - 2936).

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Authors and Affiliations

  1. Departamento de Ciencias Básicas, Universidad Católica Luis Amigó, Transversal 51A #67B 90, Medellín, Colombia

    Franklin Ferraro

  2. Physics Department, Natural and Exact Science Faculty, Northeastern University of Argentina, Corrientes, Argentina

    Andy D. Zapata-Escobar

  3. Institute of Modelling and Innovative Technology (IMIT), Corrientes, Argentina

    Andy D. Zapata-Escobar & Alejandro F. Maldonado

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  1. Franklin Ferraro
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Correspondence to Franklin Ferraro.

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Ferraro, F., Zapata-Escobar, A.D. & Maldonado, A.F. Relativistic effects on the energetic stability of \(\hbox {Pb}_5\) clusters. Theor Chem Acc 139, 111 (2020). https://doi.org/10.1007/s00214-020-02622-y

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