Citation: LIU Shu-Bin, RONG Chun-Ying, WU Ze-Min, LU Tian. Rényi Entropy, Tsallis Entropy and Onicescu Information Energy in Density Functional Reactivity Theory[J]. Acta Physico-Chimica Sinica, ;2015, 31(11): 2057-2063. doi: 10.3866/PKU.WHXB201509183 shu

Rényi Entropy, Tsallis Entropy and Onicescu Information Energy in Density Functional Reactivity Theory

LIU Shu-Bin ^1,2,, ,
RONG Chun-Ying ^1,, ,
WU Ze-Min ¹ ,
LU Tian ³

1.
1 Key Laboratory of Sustainable Resources Processing and Advanced Materials of Hunan Province College, Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research (Ministry of Education of China), College of Chemistry and Chemical Engineering, Hunan Normal University, Changsha 410081, P. R. China;
2.
2 Research Computing Center, University of North Carolina, Chapel Hill, North Carolina 27599-3420, USA;
3.
3 Beijing Kein Research Center for Natural Sciences, Beijing 100022, P. R. China

Corresponding author: LIU Shu-Bin, RONG Chun-Ying,
Received Date: 12 August 2015
Available Online: 18 September 2015
Fund Project: 国家自然科学基金(21503076) (21503076)湖南省高校科技创新团队支持计划(湘教通[2012]318号)资助项目 (湘教通[2012]318号)

Density functional theory dictates that the electron density determines everything in a molecular system's ground state, including its structure and reactivity properties. However, little is known about how to use density functionals to predict molecular reactivity. Density functional reactivity theory is an effort to fill this gap: it is a theoretical and conceptual framework through which electron-related functionals can be used to accurately predict structure and reactivity. Such density functionals include quantities from the information-theoretic approach, such as Shannon entropy and Fisher information, which have shown great potential as reactivity descriptors. In this work, we introduce three closely related quantities: Rényi entropy, Tsallis entropy, and Onicescu information energy. We evaluated these quantities for a number of neutral atoms and molecules, revealing their scaling properties with respect to electronic energy and the total number of electrons. In addition, using the example of second-order Onicescu information energy, we examined how its patterns change with the angle of dihedral rotation of an ethane molecule at both the molecular level and atoms-in-molecules level. Using these quantities as additional reactivity descriptors, researchers can more accurately predict the structure and reactivity of molecular systems.
- Rényi entropy,
- Tsallis entropy,
- Onicescu information energy,
- Shannon entropy,
- Density functional reactivity theory
1. [1]
  (1) Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules; Clarendon Press: Oxford, England, 1989.
2. [2]
  (2) Geerlings, P.; DeProft, F.; Langenaeker, W. Chem. Rev. 2003, 103, 1793. doi: 10.1021/cr990029p
3. [3]
  (3) Chattaraj, P. K.; Sarkar, U.; Roy, D. R. Chem. Rev. 2006, 106, 2065. doi: 10.1021/cr040109f
4. [4]
  (4) Liu, S. B. Acta Phys. -Chim. Sin. 2009, 25, 590. [刘述斌. 物理化学学报, 2009, 25, 590.] doi: 10.3866/PKU.WHXB20090332
5. [5]
  (5) Shannon, C. E. Bell Syst. Tech. J. 1948, 27, 379. doi: 10.1002/bltj.1948.27.issue-3
6. [6]
  (6) Fisher, R. A. Proc. Cambridge Philos. Soc.1925, 22, 700. doi: 10.1017/S0305004100009580
7. [7]
  (7) Ghosh, S. K.; Berkowitz, M.; Parr, R. G. Proc. Natl. Acad. Sci. U. S. A. 1984, 81, 8028. doi: 10.1073/pnas.81.24.8028
8. [8]
  (8) Kullback, S.; Leibler, R. A. Ann. Math. Stat. 1951, 22, 79. doi: 10.1214/aoms/1177729694
9. [9]
  (9) Nalewajski, R. F.; Parr, R. G. Proc. Natl. Acad. Sci. U. S. A. 2000, 97, 8879. doi: 10.1073/pnas.97.16.8879
10. [10]
  (10) Nalewajski, R. F.; Parr, R. G. J. Phys. Chem. A 2001, 105, 7391. doi: 10.1021/jp004414q
11. [11]
  (11) Rong, C. Y.; Lu, T.; Liu, S. B. J. Chem. Phys. 2014, 140, 024109. doi: 10.1063/1.4860969
12. [12]
  (12) Liu, S. B.; Rong, C. Y.; Lu, T. J. Phys. Chem. A 2014, 118, 3698. doi: 10.1021/jp5032702
13. [13]
  (13) Rong, C. Y.; Lu, T.; Chattaraj, P. K.; Liu, S. B. Indian J. Chem., Sect. A 2014, 53, 970.
14. [14]
  (14) Liu, S. B. J. Chem. Phys. 2014, 141, 194109. doi: 10.1063/1.4901898
15. [15]
  (15) Zhou, X. Y.; Rong, C. Y.; Lu, T.; Liu, S. B. Acta Phys. -Chim. Sin. 2014, 30, 2055. [周夏禹, 荣春英, 卢天, 刘述斌. 物理化学学报, 2014, 30, 2055.] doi: 10.3866/PKU.WHXB201409193
16. [16]
  (16) Rong, C. Y.; Lu, T.; Ayers, P. W.; Chattaraj, P. K.; Liu, S. B. Phys. Chem. Chem. Phys. 2015, 17, 4977; Phys. Chem. Chem. Phys. 2015, 17, 11110.
17. [17]
  (17) Liu, S. B. J. Phys. Chem. A 2015, 119, 3107. doi: 10.1021/acs.jpca.5b00443
18. [18]
  (18) Wu, W. J.; Wu, Z. M., Rong, C. Y.; Lu, T.; Huang, Y.; Liu, S. B. J. Phys. Chem. A 2015, 119, 8216.
19. [19]
  (19) Ré nyi, A. Probability Theory; North-Holland: Amsterdam, 1970.
20. [20]
  (20) Tsallis, C. J. Stat. Phys. 1988, 52, 479. doi: 10.1007/BF01016429
21. [21]
  (21) Onicescu, O. C. R. Acad. Sci. Paris A 1966, 263, 25.
22. [22]
  (22) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Oxford University Press: Oxford, England, 1990.
23. [23]
  (23) Becke, A. D. J. Chem. Phys. 1988, 88, 2547. doi: 10.1063/1.454033
24. [24]
  (24) Hirshfeld, F. Theor. Chim. Acc. 1977, 44, 129. doi: 10.1007/BF00549096
25. [25]
  (25) Lu, T.; Chen, F. J. Comput. Chem. 2012, 33, 580. doi: 10.1002/jcc.v33.5
26. [26]
  (26) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; et al. Gaussian 09, Revision D.01; Gaussian Inc.:Wallingford, CT, 2009.
27. [27]
  (27) Zhao, Y.; Truhlar, D. G. Theor. Chem. Acc. 2008, 120, 215. doi: 10.1007/s00214-007-0310-x
28. [28]
  (28) Ditchfield, R.; Hehre, W. J.; Pople, J. J. Chem. Phys. 1971, 54, 724. doi: 10.1063/1.1674902
29. [29]
  (29) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007.
30. [30]
  (30) Liu, S. B. J. Phys. Chem. A 2013, 117, 962. doi: 10.1021/jp312521z
31. [31]
  (31) Liu, S. B.; Parr, R. G.; Nagy, A. Phys. Rev. A 1995, 52, 2645. doi: 10.1103/PhysRevA.52.2645
32. [32]
  (32) Liu, S. B. Int. J. Quantum Chem. 2006, 106, 1762.
33. [33]
  (33) Liu, S. B. J. Chem. Phys. 2007, 126, 191107. doi: 10.1063/1.2741244
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