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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

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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.

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Notes

  1. We should perhaps point out that the nonclassical fullerene obtained by An et al. [35] could be due to their use of the DFT/BH strategy. Our conjecture is confirmed by repeating a calculation with our extended MBH method (technical details are described in Ref. [49]) without the cut-and-splice genetic-like operator which then results in the optimization to effectively the same as that of An et al.’s DFT/BH. The optimized C24 geometry was found to be a classical fullerene cage-like with two six-membered rings sharing the sides of six five-membered rings.

  2. In assessing our calculated results against Ref. [53], the C7 and C9 there are to be compared.

  3. Linear-chain geometries do appear in the present work for C10 and C11 but at M = 3 and 5, respectively; these energies are relatively higher than the mono-ring structures as detailed in Table 1 (see also Fig. 1b, c).

References

  1. Coey M, Sanvito S (2004) Phys World 17:33

    Article  CAS  Google Scholar 

  2. Raghavachari K, Binkley J (1987) J Chem Phys 87:2191

    Article  CAS  Google Scholar 

  3. Pan L, Rao BK, Gupta AK, Das GP, Ayyub P (2003) J Chem Phys 119:7705

    Article  CAS  Google Scholar 

  4. Li ZY, Sheng W, Ning ZY, Zhang ZH, Yang ZQ, Guo H (2009) Phys Rev B 80:115429

    Article  Google Scholar 

  5. Afshar M, Babaei M, Kordbacheh AH (2014) J Theor Appl Phys 8:103

    Article  Google Scholar 

  6. Dupree R, Ford C (1973) Phys Rev B 8:1780

    Article  CAS  Google Scholar 

  7. Pereiro M, Baldomir D, Arias J (2007) Phys Rev A 75:063204

    Article  Google Scholar 

  8. Dunlap BI (1990) Phys Rev A 41:5691

    Article  CAS  Google Scholar 

  9. Yen TW, Lai SK (2016) J Magn Magn Mater 397:295

    Article  CAS  Google Scholar 

  10. Zeiri Y (1995) Phys Rev E 51:R2769

    Article  CAS  Google Scholar 

  11. Niesse JA, Mayne HR (1996) J Chem Phys 105:4700

    Article  CAS  Google Scholar 

  12. Li Z, Scheraga HA (1987) PNAS 84:6611

    Article  CAS  Google Scholar 

  13. Wales DJ, Doye JP (1997) J Phys Chem A 101:5111

    Article  CAS  Google Scholar 

  14. Botana J, Pereiro M, Baldomir D, Arias JE, Warda K, Wojtczak L (2008) J Appl Phys 103:7B716

    Article  Google Scholar 

  15. Assadollahzadeha B, Schwerdtfegera P (2009) J Chem Phys 131:064306

    Article  Google Scholar 

  16. Köhler C, Seifert G, Frauenheim Th (2005) Chem Phys 309:23

    Article  Google Scholar 

  17. Yen TW, Lai SK (2015) J Chem Phys 142:084313

    Article  CAS  Google Scholar 

  18. Frauenheim Th, Seifert G, Elstner M, Hajnal Z, Jungnickel G, Porezag D, Suhai S, Scholz R (2000) Phys Status Solidi (b) 217:41

    Article  CAS  Google Scholar 

  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 14:3015

    Article  CAS  Google Scholar 

  20. Mulliken RS (1955) J Chem Phys 23:1833

    Article  CAS  Google Scholar 

  21. Aradi B, Hourahine B, Frauenheim Th (2007) J Phys Chem A 111:5678

    Article  CAS  Google Scholar 

  22. Web site: https://www.dftb.org/parameters/download/mio/mio-1-1-cc/; https://www.dftb.org/fileadmin/DFTB/public/misc/slakoformat.pdf. Accessed 20 Apr 2017

  23. Bodrog Z, Aradi B (2012) Phys Status Solidi B 249:259

    Article  CAS  Google Scholar 

  24. Gaus M, Jin H, Demapan D, Christensen AS, Goyal P, Elstner M, Cui Q (2015) J Chem Theor Comput 11:4205

    Article  CAS  Google Scholar 

  25. Lai SK, Setiyawati I, Yen TW, Tang YH (2017) Theor Chem Acc 136:20

    Article  Google Scholar 

  26. Johansson MP, Sundholm D, Vaara J (2004) Angew Chem Int Ed 43:2678

    Article  CAS  Google Scholar 

  27. Gu X, Ji M, Wei SH, Gong XG (2004) Phys Rev B 70:205401

    Article  Google Scholar 

  28. Ji M, Gu X, Li X, Gong XG, Li J, Wang LS (2005) Angew Chem Int Ed 44:7719

    Google Scholar 

  29. Feyereisen M, Gutowski M, Simons J (1989) J Chem Phys 96:2926

    Article  Google Scholar 

  30. Liang C, Schaefer HF III (1990) J Chem Phys 93:8844

    Article  CAS  Google Scholar 

  31. Watts JD, Barlett RJ (1992) Chem Phys Lett 190:19

    Article  CAS  Google Scholar 

  32. Jensen F, Toftlund H (1993) Chem Phys Lett 201:89

    Article  CAS  Google Scholar 

  33. Raghavachari K, Zhang B, Pople JA, Johnson BG, Gill PMW (1994) Chem Phys Lett 220:385

    Article  CAS  Google Scholar 

  34. Kent PRC, Towler MD, Needa RJ, Rajagopal G (2000) Phys Rev B 62:15394

    Article  CAS  Google Scholar 

  35. An W, Shao N, Bulusu S, Zeng XC (2008) J Chem Phys 128:084301

    Article  Google Scholar 

  36. Wang Z, Zhang J, Cao Z (2010) J Mol Struct THEOCHEM 949:88

    Article  CAS  Google Scholar 

  37. An J, Gan LH, Zhao JQ, Li R (2010) J Chem Phys 132:154304

    Article  Google Scholar 

  38. Jin Y, Perera A, Lotrich VF, Bartlett RJ (2015) Chem Phys Lett 629:76

    Article  CAS  Google Scholar 

  39. Manna D, Martin JML (2016) J Phys Chem A 120:153

    Article  CAS  Google Scholar 

  40. Karton A, Thimmakondu VS (2018) Chem Phys Lett 706:19

    Article  CAS  Google Scholar 

  41. Parasuk V, Almlöf J (1992) Theor Chim Acta 83:227

    Article  CAS  Google Scholar 

  42. Hutter J, Luthi HP, Diederich F (1994) J Am Chem Soc 116:750

    Article  CAS  Google Scholar 

  43. Martin JML, Taylor PR (1996) J Phys Chem 100:6047

    Article  CAS  Google Scholar 

  44. Grossman JC, Mitas L, Raghavachari K (1995) Phys Rev Lett 75:3870

    Article  CAS  Google Scholar 

  45. Li P (2012) J At Mol Sci 3:308

    Google Scholar 

  46. Shlyakhter Y, Sokolova S, Lüchow A, Andersona JB (1999) J Chem Phys 110:10725

    Article  CAS  Google Scholar 

  47. Liang C, Schaefer HF III (1990) Chem Phys Lett 169:150

    Article  CAS  Google Scholar 

  48. JrTH Dunning (1989) J Chem Phys 90:1007

    Article  Google Scholar 

  49. Yen TW, Lim TL, Yoon TL, Lai SK (2017) Comput Phys Commun 220:143

    Article  CAS  Google Scholar 

  50. Adamowicz L, Kurtz K (1989) Chem Phys Lett 162:342

    Article  CAS  Google Scholar 

  51. Parasuk V, Almlöf J (1989) J Chem Phys 91:1137

    Article  CAS  Google Scholar 

  52. Kurtz J, Adamowicz L (1991) Astrophys J 370:784

    Article  CAS  Google Scholar 

  53. Martin JML, El-Yazal J, Francois JF (1996) Chem Phys Lett 252:9

    Article  CAS  Google Scholar 

  54. Heath JR, Saykally RJ (1991) J Chem Phys 94:3271

    Article  CAS  Google Scholar 

  55. Hwang HJ, van Orden A, Tanaka K, Kuo EW, Heath JR, Saykally RJ (1993) Mol Phys 79:769

    Article  CAS  Google Scholar 

  56. Shen LN, Graham WRM (1989) J Chem Phys 91:5115

    Article  CAS  Google Scholar 

  57. van Zee RJ, Ferrante RF, Zeringue KJ, Weltner JW (1987) J Chem Phys 86:5212

    Article  Google Scholar 

  58. van Zee RJ, Ferrante RF, Zeringue KJ, Weltner JW, Ewing DW (1988) J Chem Phys 88:3465

    Article  Google Scholar 

  59. Han MJ, Kim G, Lee JII, Yu J (2009) J Chem Phys 130:184107

    Article  Google Scholar 

Download references

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.

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  1. Complex Liquids Laboratory, Department of Physics, National Central University, Chungli, 320, Taiwan

    T. W. Yen & S. K. Lai

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Yen, T.W., Lai, S.K. 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. Theor Chem Acc 137, 134 (2018). https://doi.org/10.1007/s00214-018-2334-9

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