Citation: CÁRDENAS Carlos, MUÑOZ Macarena, CONTRERAS Julia, AYERS Paul W., GÓMEZ Tatiana, FUENTEALBA Patricio. Understanding Chemical Reactivity in Extended Systems: Exploring Models of Chemical Softness in Carbon Nanotubes
[J]. Acta Physico-Chimica Sinica, ;2018, 34(6): 631-638. doi: 10.3866/PKU.WHXB201710201 shu

Understanding Chemical Reactivity in Extended Systems: Exploring Models of Chemical Softness in Carbon Nanotubes

1.
Departamento de Fısica, Facultad de Ciencias, Universidad de Chile, Casilla, 653 Santiago, Chile
2.
Centro para el Desarrollo de la Nanociencias y Nanotecnologia, CEDENNA, Avenida Ecuador 3493, Santiago, Chile
3.
Núcleo de Matemáticas, Física y Estadística, Facultad de Ciencias, Universidad Mayor, Manuel Montt 367, Providencia, Santiago, Chile
4.
Sorbonne Universités, UPMC and CNRS, Laboratoire de Chimie Théorique (LCT), 75005 Paris, France
5.
Department of Chemistry & Chemical Biology; McMaster University; Hamilton, L8S 4M1 Ontario, Canada
6.
Institute of Applied Chemical Sciences, Theoretical and Computational Chemistry Center, Universidad Autónoma de Chile, El Llano Subercaceaux 2801, San Miguel, Santiago, Chile

Corresponding author: CÁRDENAS Carlos, cardena@macul.ciencias.uchile.cl FUENTEALBA Patricio,
Received Date: 30 August 2017
Revised Date: 12 October 2017
Accepted Date: 17 October 2017
Available Online: 20 June 2017
Fund Project: This work has been supported by FONDECYT grants 1140313 and 11150164. CC and PF acknowledge support by Financiamiento Basal para Centros Científicos y Tecnológicos de Excelencia-FB0807, and project RC-130006 CILIS, granted by the Fondo de Innovación para la Competitividad del Ministerio de Economía, Fomento y Turismo de Chile. MM acknowledge supports by CONICYT through grant 21130691. PWA acknowledges support from NSERC, Compute Canada, and the Canada Research Chairs

Chemical reactivity towards electron transfer is captured by the Fukui function. However, this is not well defined when the system or its ions have degenerate or pseudo-degenerate ground states. In such a case, the first-order chemical response is not independent of the perturbation and the correct response has to be computed using the mathematical formalism of perturbation theory for degenerate states. Spatial pseudo-degeneracy is ubiquitous in nanostructures with high symmetry and totally extended systems. Given the size of these systems, using degenerate-state perturbation theory is impractical because it requires the calculation of many excited states. Here we present an alternative to compute the chemical response of extended systems using models of local softness in terms of the local density of states. The local softness is approximately equal to the density of states at the Fermi level. However, such approximation leaves out the contribution of inner states. In order to include and weight the contribution of the states around the Fermi level, a model inspired by the long-range behavior of the local softness is presented. Single wall capped carbon nanotubes (SWCCNT) illustrate the limitation of the frontier orbital theory in extended systems. Thus, we have used a C₃₆₀ SWCCNT to test the proposed model and how it compares with available models based on the local density of states. Interestingly, a simple Hückel approximation captures the main features of chemical response of these systems. Our results suggest that density-of-states models of the softness along simple tight binding Hamiltonians could be used to explore the chemical reactivity of more complex system, such a surfaces and nanoparticles.
- Local softness,
- Fukui function,
- Reactivity,
- Carbon nanotubes,
- Density of states
1. [1]
  Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules; Oxford UP: New York, NY, USA, 1989.
2. [2]
  Geerlings, P.; De Proft, F.; Langenaeker, W. Chem. Rev. 2003, 103, 1793. doi: 10.1021/cr990029p doi: 10.1021/cr990029p
3. [3]
  Chermette, H. J. Comput. Chem. 1999, 20, 129. doi: 10.1002/(SICI)1096-987X(19990115)20:1 doi: 10.1002/(SICI)1096-987X(19990115)20:1
4. [4]
  Liu, S. B. Acta Phys. -Chim. Sin. 2009, 25, 590. doi: 10.3866/PKU.WHXB20090332 doi: 10.3866/PKU.WHXB20090332
5. [5]
  Gazquez, J. L. J. Mex. Chem. Soc. 2008, 52, 3.
6. [6]
  Ayers, P. W.; Anderson, J. S. M.; Bartolotti, L. J. Int. J. Quantum Chem. 2005, 101, 520. doi: 10.1002/qua.20307 doi: 10.1002/qua.20307
7. [7]
  Chattaraj, P. K.; Sarkar, U.; Roy, D. R. Chem. Rev. 2006, 106, 2065. doi: 10.1021/cr040109f doi: 10.1021/cr040109f
8. [8]
  Johnson, P. A.; Bartolotti, L. J.; Ayers, P. W.; Fievez, T.; Geerlings, P. Modern Charge-Density Analysis; Springer: The Netherlands, 2012; p. 715.
9. [9]
  Parr, R. G.; Yang, W. T. J. Am. Chem. Soc. 1984, 106, 4049. doi: 10.1021/ja00326a036 doi: 10.1021/ja00326a036
10. [10]
  Yang, W. T.; Parr, R. G.; Pucci, R. J. Chem. Phys. 1984, 81, 2862. doi: 10.1063/1.447964 doi: 10.1063/1.447964
11. [11]
  Yang, W. T.; Parr, R. G. Proc. Natl. Acad. Sci. USA 1985, 82, 6723. doi: 10.1073/pnas.82.20.6723 doi: 10.1073/pnas.82.20.6723
12. [12]
  Fukui, K. Science 1982, 218, 747. doi: 10.1126/science.218.4574.747 doi: 10.1126/science.218.4574.747
13. [13]
  Ayers, P. W.; Levy, M. Theo. Chem. Acc. 2000, 103, 353. doi: 10.1007/s002149900093 doi: 10.1007/s002149900093
14. [14]
  Fuentealba, P.; Cardenas, C.; Pino-Rios, R.; Tiznado, W. Applications of Topological Methods in Molecular Chemistry; Springer International Publishing: Switzerland, 2016; p. 227.
15. [15]
  Ayers, P. W.; Yang, W. T.; Bartolotti, L. J. Chemical Reactivity Theory: A Density Functional View; Chattaraj, P. K., Ed.; CRC Press: Boca Raton, FL, USA, 2009; p. 255.
16. [16]
  Perdew, J. P.; Parr, R. G.; Levy, M.; Balduz, J. L., Jr. Phys. Rev. Lett. 1982, 49, 1691. doi: 10.1103/PhysRevLett.49.1691 doi: 10.1103/PhysRevLett.49.1691
17. [17]
  Chan, G. K. L. J. Chem. Phys. 1999, 110, 4710. doi: 10.1063/1.478357 doi: 10.1063/1.478357
18. [18]
  Yang, W. T.; Zhang, Y. K.; Ayers, P. W. Phys. Rev. Lett. 2000, 84, 5172. doi: 10.1103/PhysRevLett.84.5172 doi: 10.1103/PhysRevLett.84.5172
19. [19]
  Cohen, M. H.; Wasserman, A. Isr. J. Chem. 2003, 43, 219. doi: 10.1560/3R9J-FHB5-51UV-C4BJ doi: 10.1560/3R9J-FHB5-51UV-C4BJ
20. [20]
  Ayers, P. W. J. Math. Chem. 2008, 43, 285. doi: 10.1007/s10910-006-9195-5 doi: 10.1007/s10910-006-9195-5
21. [21]
  Cohen, A. J.; Mori-Sanchez, P.; Yang, W. T. Science 2008, 321, 792. doi: 10.1126/science.1158722 doi: 10.1126/science.1158722
22. [22]
  Parr, R. G.; Donnelly, R. A.; Levy, M.; Palke, W. E. J. Chem. Phys. 1978, 68, 3801. doi: 10.1063/1.436185 doi: 10.1063/1.436185
23. [23]
  Nalewajski, R. F.; Kozlowski, P. M. Acta Phys. Polon. 1986, A70, 457.
24. [24]
  Cárdenas, C.; Heidar-Zadeh, F.; Ayers, P. W. Phys. Chem. Chem. Phys. 2016, 18, 25721. doi: 10.1039/C6CP04533B doi: 10.1039/C6CP04533B
25. [25]
  Sablon, N.; De Proft, F.; Ayers, P. W.; Geerlings, P. J. Chem. Phys. 2007, 126, 224108. doi: 224108/Artn 224108 doi: 10.1063/1.2736698
26. [26]
  Fievez, T.; Sablon, N.; De Proft, F.; Ayers, P. W.; Geerlings, P. J. Chem. Theory Comput. 2008, 4, 1065. doi: 10.1021/ct800027e doi: 10.1021/ct800027e
27. [27]
  Fuentealba, P.; Chamorro, E.; Cárdenas, C. Int. J. Quantum Chem. 2007, 107, 37. doi: 10.1002/qua.21021 doi: 10.1002/qua.21021
28. [28]
  Bartolotti, L. J.; Ayers, P. W. J. Phys. Chem. A 2005, 109, 1146. doi: 10.1021/jp0462207 doi: 10.1021/jp0462207
29. [29]
  Echegaray, E.; Rabi, S.; Cardenas, C.; Zadeh, F. H.; Rabi, N.; Lee, S.; Anderson, J. S.; Toro-Labbe, A.; Ayers, P. W. J. Mol. Model. 2014, 20, 1. doi: 10.1007/s00894-014-2162-3 doi: 10.1007/s00894-014-2162-3
30. [30]
  Cardenas, C.; Ayers, P. W.; Cedillo, A. J. Chem. Phys. 2011, 134, 174103. doi: 10.1063/1.3585610 doi: 10.1063/1.3585610
31. [31]
  Bultinck, P.; Cardenas, C.; Fuentealba, P.; Johnson, P. A.; Ayers, P. W. J. Chem. Theory Comput. 2013, 10, 202. doi: 10.1021/ct400874d doi: 10.1021/ct400874d
32. [32]
  Bultinck, P.; Cardenas, C.; Fuentealba, P.; Johnson, P. A.; Ayers, P. W. J. Chem. Theory Comput. 2013, 9, 4779. doi: 10.1021/ct4005454 doi: 10.1021/ct4005454
33. [33]
  Bultinck, P.; Jayatilaka, D.; Cardenas, C. Comput. Theor. Chem. 2015, 1053, 106. doi: 10.1016/j.comptc.2014.06.017 doi: 10.1016/j.comptc.2014.06.017
34. [34]
  Avouris, P. Accounts Chem. Res. 2002, 35, 1026. doi: 10.1021/ar010152e doi: 10.1021/ar010152e
35. [35]
  Fowler, P. W.; Manopoulos, D. E. An Atlas of Fullerene; Oxford Press University: Oxford, UK, 1995.
36. [36]
  Banerjee, S.; Hemraj-Benny, T.; Wong, S. S. Adv. Mater. 2005, 17, 17. doi: 10.1002/adma.200401340 doi: 10.1002/adma.200401340
37. [37]
  Fowler, P. W. Contemp. Phys. 1996, 37, 235. doi: 10.1080/00107519608217530 doi: 10.1080/00107519608217530
38. [38]
  Prodan, E.; Kohn, W. Proc. Natl. Acad. Sci. USA 2005, 102, 11635. doi: 10.1073/pnas.0505436102 doi: 10.1073/pnas.0505436102
39. [39]
  Prodan, E. Phys. Rev. B 2006, 73, 085108. doi: 10.1103/PhysRevB.73.085108 doi: 10.1103/PhysRevB.73.085108
40. [40]
  Cardenas, C.; Rabi, N.; Ayers, P. W.; Morell, C.; Jaramillo, P.; Fuentealba, P. J. Phys. Chem. A 2009, 113, 8660. doi: 10.1021/jp902792n doi: 10.1021/jp902792n
41. [41]
  Flores-Moreno, R. J. Chem. Theory Comput. 2009, 6, 48. doi: 10.1021/ct9002527 doi: 10.1021/ct9002527
42. [42]
  Martínez, J. Chem. Phys. Lett. 2009, 478, 310. doi: 10.1016/j.cplett.2009.07.086 doi: 10.1016/j.cplett.2009.07.086
43. [43]
  Pino-Rios, R.; Ya ez, O.; Inostroza, D.; Ruiz, L.; Cardenas, C.; Fuentealba, P.; Tiznado, W. J. Comput. Chem. 2017, 38, 481. doi: 10.1002/jcc.24699 doi: 10.1002/jcc.24699
44. [44]
  Berkowitz, M.; Parr, R. G. J. Chem. Phys. 1988, 88, 2554. doi: 10.1063/1.454034 doi: 10.1063/1.454034
45. [45]
  Cohen, M. H.; Ganduglia-Pirovano, M. V. J. Chem. Phys. 1994, 101, 8988. doi: 10.1063/1.468026 doi: 10.1063/1.468026
46. [46]
  Cohen, M. H.; Ganduglia-Pirovano, M. V.; Kudrnovsky, J. J. Chem. Phys. 1995, 103, 3543. doi: 10.1063/1.470238 doi: 10.1063/1.470238
47. [47]
  Cohen, M. H.; Ganduglia-Pirovano, M. V.; Kudrnovsky, J. Phys. Rev. Lett. 1994, 72, 3222. doi: 10.1103/PhysRevLett.72.3222 doi: 10.1103/PhysRevLett.72.3222
48. [48]
  Cohen, M. H. Top. Curr. Chem. Density Functional Theory Ⅳ; Springer-Verlag, Berlin, Germany, 1996; Vol. 183, p. 143.
49. [49]
  Santos, J. C.; Contreras, R.; Chamorro, E.; Fuentealba, P. J. Chem. Phys. 2002, 116, 4311. doi: 10.1063/1.1449944 doi: 10.1063/1.1449944
50. [50]
  Alzate-Morales, J. H.; Tiznado, W.; Santos, J. C.; Cardenas, C.; Contreras, R. J. Phys. Chem. B 2007, 111, 3293. doi: 10.1021/jp064549h doi: 10.1021/jp064549h
51. [51]
  Santos, J. C.; Chamorro, E.; Contreras, R.; Fuentealba, P. Chem. Phys. Lett. 2004, 383, 612. doi: 10.1016/j.cplett.2003.11.083 doi: 10.1016/j.cplett.2003.11.083
52. [52]
  Brommer, K. D.; Galván, M.; Dal Pino, A.; Joannopoulos, J. D. Surf. Sci. 1994, 314, 57. doi: 10.1016/0039-6028(94)90212-7 doi: 10.1016/0039-6028(94)90212-7
53. [53]
  Nguyen, L. T.; De Proft, F.; Amat, M. C.; Van Lier, G.; Fowler, P. W.; Geerlings, P. J. Phys. Chem. A 2003, 107, 6837. doi: 10.1021/jp034388 doi: 10.1021/jp034388
54. [54]
  Cardenas, C.; De Proft, F.; Chamorro, E.; Fuentealba, P.; Geerlings, P. J. Chem. Phys. 2008, 128, 034708. doi: 10.1063/1.2819239 doi: 10.1063/1.2819239
55. [55]
  Morrell, M. M.; Parr, R. G.; Levy, M. J. Chem. Phys. 1975, 62, 549. doi: 10.1063/1.430509 doi: 10.1063/1.430509
56. [56]
  Katriel, J.; Davidson, E. R. Proc. Natl. Acad. Sci. USA 1980, 77, 4403. doi: 10.1073/pnas.77.8.4403 doi: 10.1073/pnas.77.8.4403
57. [57]
  Hoffmann-Ostenhof, M.; Hoffmann-Ostenhof, T. Phys. Rev. A 1977, 16, 1782. doi: 10.1103/PhysRevA.16.1782 doi: 10.1103/PhysRevA.16.1782
58. [58]
  Ahlrichs, R.; Hoffmann-Ostenhof, M.; Hoffmann-Ostenhof, T.; Morgan, J. D., Ⅲ. Phys. Rev. A 1981, 23, 2106. doi: 10.1103/PhysRevA.23.2106 doi: 10.1103/PhysRevA.23.2106
59. [59]
  Levy, M.; Perdew, J. P.; Sahni, V. Phys. Rev. A 1984, 30, 2745. doi: 10.1103/PhysRevA.30.2745 doi: 10.1103/PhysRevA.30.2745
60. [60]
  Handy, N. C.; Marron, M. T.; Silverstone, H. J. Phys. Rev. 1969, 180, 45. doi: 10.1103/PhysRev.180.45 doi: 10.1103/PhysRev.180.45
61. [61]
  Yang, W. T.; Mortier, W. J. J. Am. Chem. Soc. 1986, 108, 5708. doi: 10.1021/ja00279a008 doi: 10.1021/ja00279a008
62. [62]
  Mulliken, R. S. J. Chem. Phys. 1955, 23, 1833. doi: 10.1063/1.1740588 doi: 10.1063/1.1740588
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