电子定域化函数的含义与函数形式

引用本文: 卢天, 陈飞武. 电子定域化函数的含义与函数形式[J]. 物理化学学报, 2011, 27(12): 2786-2792. doi: 10.3866/PKU.WHXB20112786 shu

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

电子定域化函数的含义与函数形式

卢天 ,
陈飞武

基金项目:
国家自然科学基金(20773011)资助项目 (20773011)

摘要: 电子定域化函数(ELF)是研究电子结构的重要工具. 本文介绍了电子定域性的概念, 从电子对密度和动能密度两个角度详细讨论了ELF的物理意义与其函数形式的联系, 并将ELF推广到自旋极化形式. 通过实例分析, 指出了参考项在ELF 中起到了关键性作用. 对两种自旋极化形式的ELF 的比较发现: CheckDen 和TopMoD程序中使用的形式并不合理, 明显低估了单电子区域的定域性. 最后指出了一些文献由于对ELF函数的错误理解而在引用时出现的错误.

关键词:

English

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: 02 August 2011
Available Online: 25 November 2011
Fund Project:
国家自然科学基金(20773011)资助项目

Abstract: 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.

Key words:

1. [1]
  (1) Becke, A. D.; Edgecombe, K. E. J. Chem. Phys. 1990, 92, 5397. (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. (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. (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. (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. (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.(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. (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. (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. (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. (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.(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. (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. (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. (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.(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. (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. (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. (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. (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. (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.(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. (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.(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. (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.(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.(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.(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. (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. (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. (30) Becke, A. D. Int. J. Quantum Chem. 1985, 27, 585.
31. [31]
  (31) Weizsäcker, v. C. F. v. Z. Phys. 1935, 96, 431. (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. (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.(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. (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. (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.(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. (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. (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. (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.(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. (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. (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. (43) Burdett, J. K.; McCormick, T. A. J. Phys. Chem. A 1998, 102, 6366.

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电子定域化函数的含义与函数形式

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Meaning and Functional Form of the Electron Localization Function

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电子定域化函数的含义与函数形式

English

Meaning and Functional Form of the Electron Localization Function

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