Citation: LU Tian, CHEN Fei-Wu. Meaning and Functional Form of the Electron Localization Function[J]. Acta Physico-Chimica Sinica, ;2011, 27(12): 2786-2792. doi: 10.3866/PKU.WHXB20112786 shu

Meaning and Functional Form of the Electron Localization Function

LU Tian ,
CHEN Fei-Wu

1.
School of Chemical and Biological Engineering, University of Science and Technology Beijing, Beijing 100083, P. R. China

Received Date: 2 August 2011
Available Online: 10 October 2011
Fund Project: 国家自然科学基金(20773011)资助项目 (20773011)

The electron localization function (ELF) is an important tool to study electronic structure. In this article, the concept of electron localization is introduced and the overlap between the physical meaning and functional form of the ELF is discussed in detail from two points of view: electron pair density and kinetic energy density. Additionally, we extend the ELF to a generalized spin-polarized form. From case studies we found that the reference term plays an important role in the ELF. A comparison between the two spinpolarized forms of ELF shows that the form used in the CheckDen and TopMoD programs is unreasonable as they obviously underestimate the degree of localization in the single-electron region. Finally, we point out some mistakes in the literature because of a misunderstanding of the ELF.
- Electron localization function,
- Kinetic energy density,
- Fermi hole,
- Spin-polarization,
- Quantum chemistry
1. [1]
  (1) Becke, A. D.; Edgecombe, K. E. J. Chem. Phys. 1990, 92, 5397.
2. [2]
  (2) Savin, A.; Becke, A. D.; Flad, J.; Nesper, R.; Preuss, H.; von Schnering, H. G. Angew. Chem. Int. Edit. Engl. 1991, 30, 409.
3. [3]
  (3) Grin, Y.;Wagner, F. R.; Armbrüster, M.; Kohout, M.; Leithe- Jasper, A.; Schwarz, U.;Wedig, U.; Georg von Schnering, H. J. Solid State Chem. 2006, 179, 1707.
4. [4]
  (4) Savin, A.; Jepsen, O.; Flad, J.; Andersen, O. K.; Preuss, H.; von Schnering, H. G. Angew. Chem. Int. Edit. Engl. 1992, 31, 187.
5. [5]
  (5) mes, J. R. B.; Illas, F.; Silvi, B. Chem. Phys. Lett. 2004, 388, 132.
6. [6]
  (6) Kohout, M.;Wagner, F. R.; Grin, Y. Theor. Chem. Acc. 2002, 108, 150.
7. [7]
  (7) Rousseau, R.; Marx, D. Chem. -Eur. J. 2000, 6, 2982.
8. [8]
  (8) Räsänen, E.; Castro, A.; Gross, E. K. U. Phys. Rev. B 2008, 77, 115108.
9. [9]
  (9) Kohout, M.; Savin, A. Int. J. Quantum Chem. 1996, 60, 875.
10. [10]
  (10) Poater, J.; Duran, M.; Solà, M.; Silvi, B. Chem. Rev. 2005, 105, 3911.
11. [11]
  (11) Santos, J. C.; Andres, J.; Aizman, A.; Fuentealba, P. J. Chem. Theory Comput. 2004, 1, 83.
12. [12]
  (12) Shaik, S.; Danovich, D.; Silvi, B.; Lauvergnat, D. L.; Hiberty, P. C. Chem. -Eur. J. 2005, 11, 6358.
13. [13]
  (13) Grabowski, S. J. Chem. Rev. 2011, 111, 2597.
14. [14]
  (14) Llusar, R.; Beltrán, A.; Andrés, J.; Fuster, F.; Silvi, B. J. Phys. Chem. A 2001, 105, 9460.
15. [15]
  (15) Molina Molina, J.; Dobado, J. A. Theor. Chem. Acc. 2001, 105, 328.
16. [16]
  (16) Berski, S.; Andrés, J.; Silvi, B.; Domin , L. R. J. Phys. Chem. A 2003, 107, 6014.
17. [17]
  (17) Polo, V.; Andres, J.; Berski, S.; Domin , L. R.; Silvi, B. J. Phys. Chem. A 2008, 112, 7128.
18. [18]
  (18) Krokidis, X.; Noury, S.; Silvi, B. J. Phys. Chem. A 1997, 101, 7277.
19. [19]
  (19) Chamorro, E. J. Chem. Phys. 2001, 114, 23.
20. [20]
  (20) Burnus, T.; Marques, M. A. L.; Gross, E. K. U. Phys. Rev. A 2005, 71, 010501.
21. [21]
  (21) Bader, F.W. Atoms in Molecules: A Quantum Theory; Oxford University Press: New York, 1994; pp 332-343.
22. [22]
  (22) Silvi, B.; Savin, A. Nature 1994, 371, 683.
23. [23]
  (23) The Quantum Theory of Atoms in Molecules-From Solid State to DNA and Drug Design; Matta, C. F., Boyd, R. J. Eds.; WILEY-VCH Verlag GmbH & Co. KGaA:Weinheim, 2007.
24. [24]
  (24) Bader, R. F.W.; Stephens, M. E. J. Am. Chem. Soc. 1975, 97, 7391.
25. [25]
  (25) Koch,W.; Holthausen, M. C. A Chemist's Guide to Density Functional Theory, 2nd ed.;Wiley-VCH Verlag GmbH: Germany, 2001.
26. [26]
  (26) McWeeny, R. Methods of Molecular Quantum Mechanics, 2nd ed.; Academic Press: San Die , 1992.
27. [27]
  (27) Fradera, X.; Austen, M. A.; Bader, R. F.W. J. Phys. Chem. A 1998, 103, 304.
28. [28]
  (28) Sagar, R. P.; Ku, A. C. T.; Smith, J. V. H.; Simas, A. M. J. Chem. Phys. 1988, 88, 4367.
29. [29]
  (29) Shi, Z.; Boyd, R. J. J. Chem. Phys. 1988, 88, 4375.
30. [30]
  (30) Becke, A. D. Int. J. Quantum Chem. 1985, 27, 585.
31. [31]
  (31) Weizsäcker, v. C. F. v. Z. Phys. 1935, 96, 431.
32. [32]
  (32) Tal, Y.; Bader, R. F.W. Int. J. Quantum Chem. 1978, 14, 153.
33. [33]
  (33) Lignères, V. L.; Carter, E. A. An Introduction to Orbital-Free Density Functional Theory. In Handbook of Materials Modeling; Yip, S. Ed.; Springer: Netherlands, 2005; pp 137-148.
34. [34]
  (34) Oliver, G. L.; Perdew, J. P. Phys. Rev. A 1979, 20, 397.
35. [35]
  (35) Bader, R. F.W.; Johnson, S.; Tang, T. H.; Popelier, P. L. A. J. Phys. Chem. 1996, 100, 15398.
36. [36]
  (36) Frisch, M. J.; Trucks, G.W.; Schlegel, H. B.; et al . Gaussian 03, Revison E.01; Gaussian Inc.:Wallingford, CT, 2004.
37. [37]
  (37) Becke, A. D. J. Chem. Phys. 1993, 98, 1372.
38. [38]
  (38) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys. 1980, 72, 650.
39. [39]
  (39) Hariharan, P. C.; Pople, J. A. Theor. Chem. Acc. 1973, 28, 213.
40. [40]
  (40) Lu, T. Multiwfn, 2.0, 2011. http://Multiwfn.codeplex.com.
41. [41]
  (41) Pacios, L. F.; Fernandez, A. J. Mol. Graph. Model. 2009, 28, 102.
42. [42]
  (42) Noury, S.; Krokidis, X.; Fuster, F.; Silvi, B. Comput. Chem. 1999, 23, 597.
43. [43]
  (43) Burdett, J. K.; McCormick, T. A. J. Phys. Chem. A 1998, 102, 6366.
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