Advertisement

The subtlety of resolving orbital angular momenta in calculating Hubbard U parameters in the density functional tight-binding theory and its delicacy is illustrated by the calculated magnetic properties of carbon clusters

  • T. W. Yen
  • S. K. Lai
Regular Article
  • 38 Downloads

Abstract

We study magnetic properties of carbon clusters Cn by combining the spin-polarized parametrized density functional tight-binding (SDFTB) theory with an unbiased modified basin hopping (MBH) optimization algorithm. With an intent to develop a physically self-consistent technique, we deliberately treat valence electronic charges, spin charges and ionic charges on equal footing. Within the density functional tight-binding (DFTB) theory, we examine the effect of using the orbital angular-momentum unresolved and resolved schemes in calculating the on-site Coulombic energy which, we judge, will have subtle but significant influence on the Cn’s magnetism, their topologies and the change with size n their conformational structures. As a concrete means to substantiate our conjecture, we apply the SDFTB/MBH method to Cns and determine their stable magnetic structures within the angular-momentum resolved scheme. Our calculations show that the lowest energy Cn changes from a linear-chain shape for n = 3–9, turns over to a singlet monocyclic ring for n = 10–18, becomes a polycyclic ring for n = 19–25 and finally assumes a cage-like geometry at n = 26. Except for n = 4, 6 and 8, all other Cns are found unmagnetized. Accordingly, the newly discovered n that marks the first occurrence of a bi- to tridimensional transition occurs at n = 26, and this size is in contrast to n = 24 which was predicted by similar calculations using the unresolved scheme. Our calculations reveal furthermore two different features. The first one is that the predicted optimized geometries for all of the Cns, except for C24, are structurally the same as the size n = 3–23 of Cn calculated by the DFTB/MBH employing the unresolved orbital angular-momentum scheme. As a result, the present calculations which employ the resolved angular-momentum scheme thus showed that the latter affects only the larger size Cn starting at C24; this finding redefines therefore the turnover transition point of Cn from a bidimensional planar at n = 25 to a tridimensional cage-like at n = 26. The second feature is that the SDFTB/MBH method yields only triplet C4, C6 and C8, whereas in our previous work employing DFTB/MBH, not only C4 and C6, all of C13, C15, C17, C19, C22 and C23 were predicted to carry a magnetic moment of 2 μB. These differences in the magnetism obtained are attributed to the combined use of both the SDFTB/MBH procedure and the orbital angular-momentum resolved scheme.

Keywords

Magnetic carbon cluster Spin-polarized DFTB theory Structural optimization Topological transition 

Notes

Acknowledgements

This work is financially supported by the Ministry of Science and Technology (MOST103-2112-M-008-015-MY3) and (MOST106-2112-M-008-015), Taiwan. S.K.L. is grateful to the National Center for High-performance Computing for computer time and facilities.

References

  1. 1.
    Coey M, Sanvito S (2004) Phys World 17:33CrossRefGoogle Scholar
  2. 2.
    Raghavachari K, Binkley J (1987) J Chem Phys 87:2191CrossRefGoogle Scholar
  3. 3.
    Pan L, Rao BK, Gupta AK, Das GP, Ayyub P (2003) J Chem Phys 119:7705CrossRefGoogle Scholar
  4. 4.
    Li ZY, Sheng W, Ning ZY, Zhang ZH, Yang ZQ, Guo H (2009) Phys Rev B 80:115429CrossRefGoogle Scholar
  5. 5.
    Afshar M, Babaei M, Kordbacheh AH (2014) J Theor Appl Phys 8:103CrossRefGoogle Scholar
  6. 6.
    Dupree R, Ford C (1973) Phys Rev B 8:1780CrossRefGoogle Scholar
  7. 7.
    Pereiro M, Baldomir D, Arias J (2007) Phys Rev A 75:063204CrossRefGoogle Scholar
  8. 8.
    Dunlap BI (1990) Phys Rev A 41:5691CrossRefGoogle Scholar
  9. 9.
    Yen TW, Lai SK (2016) J Magn Magn Mater 397:295CrossRefGoogle Scholar
  10. 10.
    Zeiri Y (1995) Phys Rev E 51:R2769CrossRefGoogle Scholar
  11. 11.
    Niesse JA, Mayne HR (1996) J Chem Phys 105:4700CrossRefGoogle Scholar
  12. 12.
    Li Z, Scheraga HA (1987) PNAS 84:6611CrossRefGoogle Scholar
  13. 13.
    Wales DJ, Doye JP (1997) J Phys Chem A 101:5111CrossRefGoogle Scholar
  14. 14.
    Botana J, Pereiro M, Baldomir D, Arias JE, Warda K, Wojtczak L (2008) J Appl Phys 103:7B716CrossRefGoogle Scholar
  15. 15.
    Assadollahzadeha B, Schwerdtfegera P (2009) J Chem Phys 131:064306CrossRefGoogle Scholar
  16. 16.
    Köhler C, Seifert G, Frauenheim Th (2005) Chem Phys 309:23CrossRefGoogle Scholar
  17. 17.
    Yen TW, Lai SK (2015) J Chem Phys 142:084313CrossRefGoogle Scholar
  18. 18.
    Frauenheim Th, Seifert G, Elstner M, Hajnal Z, Jungnickel G, Porezag D, Suhai S, Scholz R (2000) Phys Status Solidi (b) 217:41CrossRefGoogle Scholar
  19. 19.
    Frauenheim Th, Seifert G, Elstner M, Niehaus Th, Köhler C, Amkreutz M, Sternberg M, Hajnal Z, Di Carlo A, Suhai S (2002) J Phys Condens Matter 14:3015CrossRefGoogle Scholar
  20. 20.
    Mulliken RS (1955) J Chem Phys 23:1833CrossRefGoogle Scholar
  21. 21.
    Aradi B, Hourahine B, Frauenheim Th (2007) J Phys Chem A 111:5678CrossRefGoogle Scholar
  22. 22.
  23. 23.
    Bodrog Z, Aradi B (2012) Phys Status Solidi B 249:259CrossRefGoogle Scholar
  24. 24.
    Gaus M, Jin H, Demapan D, Christensen AS, Goyal P, Elstner M, Cui Q (2015) J Chem Theor Comput 11:4205CrossRefGoogle Scholar
  25. 25.
    Lai SK, Setiyawati I, Yen TW, Tang YH (2017) Theor Chem Acc 136:20CrossRefGoogle Scholar
  26. 26.
    Johansson MP, Sundholm D, Vaara J (2004) Angew Chem Int Ed 43:2678CrossRefGoogle Scholar
  27. 27.
    Gu X, Ji M, Wei SH, Gong XG (2004) Phys Rev B 70:205401CrossRefGoogle Scholar
  28. 28.
    Ji M, Gu X, Li X, Gong XG, Li J, Wang LS (2005) Angew Chem Int Ed 44:7719Google Scholar
  29. 29.
    Feyereisen M, Gutowski M, Simons J (1989) J Chem Phys 96:2926CrossRefGoogle Scholar
  30. 30.
    Liang C, Schaefer HF III (1990) J Chem Phys 93:8844CrossRefGoogle Scholar
  31. 31.
    Watts JD, Barlett RJ (1992) Chem Phys Lett 190:19CrossRefGoogle Scholar
  32. 32.
    Jensen F, Toftlund H (1993) Chem Phys Lett 201:89CrossRefGoogle Scholar
  33. 33.
    Raghavachari K, Zhang B, Pople JA, Johnson BG, Gill PMW (1994) Chem Phys Lett 220:385CrossRefGoogle Scholar
  34. 34.
    Kent PRC, Towler MD, Needa RJ, Rajagopal G (2000) Phys Rev B 62:15394CrossRefGoogle Scholar
  35. 35.
    An W, Shao N, Bulusu S, Zeng XC (2008) J Chem Phys 128:084301CrossRefGoogle Scholar
  36. 36.
    Wang Z, Zhang J, Cao Z (2010) J Mol Struct THEOCHEM 949:88CrossRefGoogle Scholar
  37. 37.
    An J, Gan LH, Zhao JQ, Li R (2010) J Chem Phys 132:154304CrossRefGoogle Scholar
  38. 38.
    Jin Y, Perera A, Lotrich VF, Bartlett RJ (2015) Chem Phys Lett 629:76CrossRefGoogle Scholar
  39. 39.
    Manna D, Martin JML (2016) J Phys Chem A 120:153CrossRefGoogle Scholar
  40. 40.
    Karton A, Thimmakondu VS (2018) Chem Phys Lett 706:19CrossRefGoogle Scholar
  41. 41.
    Parasuk V, Almlöf J (1992) Theor Chim Acta 83:227CrossRefGoogle Scholar
  42. 42.
    Hutter J, Luthi HP, Diederich F (1994) J Am Chem Soc 116:750CrossRefGoogle Scholar
  43. 43.
    Martin JML, Taylor PR (1996) J Phys Chem 100:6047CrossRefGoogle Scholar
  44. 44.
    Grossman JC, Mitas L, Raghavachari K (1995) Phys Rev Lett 75:3870CrossRefGoogle Scholar
  45. 45.
    Li P (2012) J At Mol Sci 3:308Google Scholar
  46. 46.
    Shlyakhter Y, Sokolova S, Lüchow A, Andersona JB (1999) J Chem Phys 110:10725CrossRefGoogle Scholar
  47. 47.
    Liang C, Schaefer HF III (1990) Chem Phys Lett 169:150CrossRefGoogle Scholar
  48. 48.
    JrTH Dunning (1989) J Chem Phys 90:1007CrossRefGoogle Scholar
  49. 49.
    Yen TW, Lim TL, Yoon TL, Lai SK (2017) Comput Phys Commun 220:143CrossRefGoogle Scholar
  50. 50.
    Adamowicz L, Kurtz K (1989) Chem Phys Lett 162:342CrossRefGoogle Scholar
  51. 51.
    Parasuk V, Almlöf J (1989) J Chem Phys 91:1137CrossRefGoogle Scholar
  52. 52.
    Kurtz J, Adamowicz L (1991) Astrophys J 370:784CrossRefGoogle Scholar
  53. 53.
    Martin JML, El-Yazal J, Francois JF (1996) Chem Phys Lett 252:9CrossRefGoogle Scholar
  54. 54.
    Heath JR, Saykally RJ (1991) J Chem Phys 94:3271CrossRefGoogle Scholar
  55. 55.
    Hwang HJ, van Orden A, Tanaka K, Kuo EW, Heath JR, Saykally RJ (1993) Mol Phys 79:769CrossRefGoogle Scholar
  56. 56.
    Shen LN, Graham WRM (1989) J Chem Phys 91:5115CrossRefGoogle Scholar
  57. 57.
    van Zee RJ, Ferrante RF, Zeringue KJ, Weltner JW (1987) J Chem Phys 86:5212CrossRefGoogle Scholar
  58. 58.
    van Zee RJ, Ferrante RF, Zeringue KJ, Weltner JW, Ewing DW (1988) J Chem Phys 88:3465CrossRefGoogle Scholar
  59. 59.
    Han MJ, Kim G, Lee JII, Yu J (2009) J Chem Phys 130:184107CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Complex Liquids Laboratory, Department of PhysicsNational Central UniversityChungliTaiwan

Personalised recommendations