Acta Phys. -Chim. Sin. ›› 2015, Vol. 31 ›› Issue (11): 2057-2063.doi: 10.3866/PKU.WHXB201509183


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

Shu-Bin. LIU1,2,*(),Chun-Ying. RONG1,*(),Ze-Min. WU1,Tian. LU3   

  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 Research Computing Center, University of North Carolina, Chapel Hill, North Carolina 27599-3420, USA
    3 Beijing Kein Research Center for Natural Sciences, Beijing 100022, P. R. China
  • Received:2015-08-12 Published:2015-11-13
  • Contact: Shu-Bin. LIU,Chun-Ying. RONG;
  • Supported by:
    the National Natural Science Foundation of China(21503076);Aid Program for Science and TechnologyInnovative Research Team in Higher Educational Institutions of Hunan Province, China(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.

Key words: Rényi entropy, Tsallis entropy, Onicescu information energy, Shannon entropy, Density functional reactivity theory


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