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
-
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.
-
-
-
[1]
(1) Becke, A. D.; Edgecombe, K. E. J. Chem. Phys. 1990, 92, 5397.
-
[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) 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) 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) mes, J. R. B.; Illas, F.; Silvi, B. Chem. Phys. Lett. 2004, 388, 132.
-
[6]
(6) Kohout, M.;Wagner, F. R.; Grin, Y. Theor. Chem. Acc. 2002, 108, 150.
-
[7]
(7) Rousseau, R.; Marx, D. Chem. -Eur. J. 2000, 6, 2982.
-
[8]
(8) Räsänen, E.; Castro, A.; Gross, E. K. U. Phys. Rev. B 2008, 77, 115108.
-
[9]
(9) Kohout, M.; Savin, A. Int. J. Quantum Chem. 1996, 60, 875.
-
[10]
(10) Poater, J.; Duran, M.; Solà, M.; Silvi, B. Chem. Rev. 2005, 105, 3911.
-
[11]
(11) Santos, J. C.; Andres, J.; Aizman, A.; Fuentealba, P. J. Chem. Theory Comput. 2004, 1, 83.
-
[12]
(12) Shaik, S.; Danovich, D.; Silvi, B.; Lauvergnat, D. L.; Hiberty, P. C. Chem. -Eur. J. 2005, 11, 6358.
- [13]
-
[14]
(14) Llusar, R.; Beltrán, A.; Andrés, J.; Fuster, F.; Silvi, B. J. Phys. Chem. A 2001, 105, 9460.
-
[15]
(15) Molina Molina, J.; Dobado, J. A. Theor. Chem. Acc. 2001, 105, 328.
-
[16]
(16) Berski, S.; Andrés, J.; Silvi, B.; Domin , L. R. J. Phys. Chem. A 2003, 107, 6014.
-
[17]
(17) Polo, V.; Andres, J.; Berski, S.; Domin , L. R.; Silvi, B. J. Phys. Chem. A 2008, 112, 7128.
-
[18]
(18) Krokidis, X.; Noury, S.; Silvi, B. J. Phys. Chem. A 1997, 101, 7277.
- [19]
-
[20]
(20) Burnus, T.; Marques, M. A. L.; Gross, E. K. U. Phys. Rev. A 2005, 71, 010501.
-
[21]
(21) Bader, F.W. Atoms in Molecules: A Quantum Theory; Oxford University Press: New York, 1994; pp 332-343.
- [22]
-
[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) Bader, R. F.W.; Stephens, M. E. J. Am. Chem. Soc. 1975, 97, 7391.
-
[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) McWeeny, R. Methods of Molecular Quantum Mechanics, 2nd ed.; Academic Press: San Die , 1992.
-
[27]
(27) Fradera, X.; Austen, M. A.; Bader, R. F.W. J. Phys. Chem. A 1998, 103, 304.
-
[28]
(28) Sagar, R. P.; Ku, A. C. T.; Smith, J. V. H.; Simas, A. M. J. Chem. Phys. 1988, 88, 4367.
- [29]
- [30]
- [31]
-
[32]
(32) Tal, Y.; Bader, R. F.W. Int. J. Quantum Chem. 1978, 14, 153.
-
[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) Oliver, G. L.; Perdew, J. P. Phys. Rev. A 1979, 20, 397.
-
[35]
(35) Bader, R. F.W.; Johnson, S.; Tang, T. H.; Popelier, P. L. A. J. Phys. Chem. 1996, 100, 15398.
-
[36]
(36) Frisch, M. J.; Trucks, G.W.; Schlegel, H. B.; et al . Gaussian 03, Revison E.01; Gaussian Inc.:Wallingford, CT, 2004.
- [37]
-
[38]
(38) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys. 1980, 72, 650.
-
[39]
(39) Hariharan, P. C.; Pople, J. A. Theor. Chem. Acc. 1973, 28, 213.
-
[40]
(40) Lu, T. Multiwfn, 2.0, 2011. http://Multiwfn.codeplex.com.
-
[41]
(41) Pacios, L. F.; Fernandez, A. J. Mol. Graph. Model. 2009, 28, 102.
-
[42]
(42) Noury, S.; Krokidis, X.; Fuster, F.; Silvi, B. Comput. Chem. 1999, 23, 597.
-
[43]
(43) Burdett, J. K.; McCormick, T. A. J. Phys. Chem. A 1998, 102, 6366.
-
[1]
-
-
-
[1]
Jia Zhou . Constructing Potential Energy Surface of Water Molecule by Quantum Chemistry and Machine Learning: Introduction to a Comprehensive Computational Chemistry Experiment. University Chemistry, 2024, 39(3): 351-358. doi: 10.3866/PKU.DXHX202309060
-
[2]
Dongju Zhang , Rongxiu Zhu . Construction of Ideological and Political Education in Quantum Chemistry Course: Several Teaching Cases to Reveal the Universal Connection of Things. University Chemistry, 2024, 39(7): 272-277. doi: 10.3866/PKU.DXHX202311032
-
[3]
Yanan Jiang , Yuchen Ma . Brief Discussion on the Electronic Exchange Interaction in Quantum Chemistry Computations. University Chemistry, 2025, 40(3): 10-15. doi: 10.12461/PKU.DXHX202402058
-
[4]
Yaqin Zheng , Lian Zhuo , Meng Li , Chunying Rong . Enhancing Understanding of the Electronic Effect of Substituents on Benzene Rings Using Quantum Chemistry Calculations. University Chemistry, 2025, 40(3): 193-198. doi: 10.12461/PKU.DXHX202406119
-
[5]
Jiabo Huang , Quanxin Li , Zhongyan Cao , Li Dang , Shaofei Ni . Elucidating the Mechanism of Beckmann Rearrangement Reaction Using Quantum Chemical Calculations. University Chemistry, 2025, 40(3): 153-159. doi: 10.12461/PKU.DXHX202405172
-
[6]
Huiying Xu , Minghui Liang , Zhi Zhou , Hui Gao , Wei Yi . Application of Quantum Chemistry Computation and Visual Analysis in Teaching of Weak Interactions. University Chemistry, 2025, 40(3): 199-205. doi: 10.12461/PKU.DXHX202407011
-
[7]
Xueli Mu , Lingli Han , Tao Liu . Quantum Chemical Calculation Study on the E2 Elimination Reaction of Halohydrocarbon: Designing a Computational Chemistry Experiment. University Chemistry, 2025, 40(3): 68-75. doi: 10.12461/PKU.DXHX202404057
-
[8]
Wenkai Chen , Yunjia Shen , Xiangmeng Kong , Yanli Zeng . Quantum Chemistry Calculation of Key Physical Quantity in Circularly Polarized Luminescence: Introducing an Exploratory Computational Chemistry Experiment. University Chemistry, 2025, 40(3): 83-91. doi: 10.12461/PKU.DXHX202405018
-
[9]
Guoxian Zhu , Jing Chen , Rongkai Pan . Enhancing the Teaching Quality of Atomic Structure: Insights and Strategies. University Chemistry, 2024, 39(3): 376-383. doi: 10.3866/PKU.DXHX202305027
-
[10]
Cuicui Yang , Bo Shang , Xiaohua Chen , Weiquan Tian . Understanding the Wave-Particle Duality and Quantization of Confined Particles Starting from Classic Mechanics. University Chemistry, 2025, 40(3): 408-414. doi: 10.12461/PKU.DXHX202407066
-
[11]
Meifeng Zhu , Jin Cheng , Kai Huang , Cheng Lian , Shouhong Xu , Honglai Liu . Classical Density Functional Theory for Understanding Electrochemical Interface. University Chemistry, 2025, 40(3): 148-152. doi: 10.12461/PKU.DXHX202405166
-
[12]
Xin Zhou , Zhi Zhang , Yun Yang , Shuijin Yang . A Study on the Enhancement of Photocatalytic Performance in C/Bi/Bi2MoO6 Composites by Ferroelectric Polarization: A Recommended Comprehensive Chemical Experiment. University Chemistry, 2024, 39(4): 296-304. doi: 10.3866/PKU.DXHX202310008
-
[13]
Lu XU , Chengyu ZHANG , Wenjuan JI , Haiying YANG , Yunlong FU . Zinc metal-organic framework with high-density free carboxyl oxygen functionalized pore walls for targeted electrochemical sensing of paracetamol. Chinese Journal of Inorganic Chemistry, 2024, 40(5): 907-918. doi: 10.11862/CJIC.20230431
-
[14]
Yanhui XUE , Shaofei CHAO , Man XU , Qiong WU , Fufa WU , Sufyan Javed Muhammad . Construction of high energy density hexagonal hole MXene aqueous supercapacitor by vacancy defect control strategy. Chinese Journal of Inorganic Chemistry, 2024, 40(9): 1640-1652. doi: 10.11862/CJIC.20240183
-
[15]
Qiqi Li , Su Zhang , Yuting Jiang , Linna Zhu , Nannan Guo , Jing Zhang , Yutong Li , Tong Wei , Zhuangjun Fan . 前驱体机械压实制备高密度活性炭及其致密电容储能性能. Acta Physico-Chimica Sinica, 2025, 41(3): 2406009-. doi: 10.3866/PKU.WHXB202406009
-
[16]
Peifeng Su , Xin Lu . Development of Undergraduate Quantum Mechanics Module in Chemistry Department under the “Double First Class” Initiative. University Chemistry, 2024, 39(8): 99-103. doi: 10.3866/PKU.DXHX202401087
-
[17]
Jingwen Wang , Minghao Wu , Xing Zuo , Yaofeng Yuan , Yahao Wang , Xiaoshun Zhou , Jianfeng Yan . Advances in the Application of Electrochemical Regulation in Investigating the Electron Transport Properties of Single-Molecule Junctions. University Chemistry, 2025, 40(3): 291-301. doi: 10.12461/PKU.DXHX202406023
-
[18]
Ruming Yuan , Pingping Wu , Laiying Zhang , Xiaoming Xu , Gang Fu . Patriotic Devotion, Upholding Integrity and Innovation, Wholeheartedly Nurturing the New: The Ideological and Political Design of the Experiment on Determining the Thermodynamic Functions of Chemical Reactions by Electromotive Force Method. University Chemistry, 2024, 39(4): 125-132. doi: 10.3866/PKU.DXHX202311057
-
[19]
Hao XU , Ruopeng LI , Peixia YANG , Anmin LIU , Jie BAI . Regulation mechanism of halogen axial coordination atoms on the oxygen reduction activity of Fe-N4 site: A density functional theory study. Chinese Journal of Inorganic Chemistry, 2025, 41(4): 695-701. doi: 10.11862/CJIC.20240302
-
[20]
Jinfu Ma , Hui Lu , Jiandong Wu , Zhongli Zou . Teaching Design of Electrochemical Principles Course Based on “Cognitive Laws”: Kinetics of Electron Transfer Steps. University Chemistry, 2024, 39(3): 174-177. doi: 10.3866/PKU.DXHX202309052
-
[1]
Metrics
- PDF Downloads(2142)
- Abstract views(4578)
- HTML views(116)