物理化学学报 >> 2015, Vol. 31 >> Issue (11): 2057-2063.doi: 10.3866/PKU.WHXB201509183

理论与计算化学 上一篇    下一篇

密度泛函活性理论中的Rényi熵, Tsallis熵和Onicescu信息能

刘述斌1,2,*(),荣春英1,*(),吴泽民1,卢天3   

  1. 1 湖南师范大学化学化工学院,资源精细化与先进材料湖南省高校重点实验室,化学生物学及中药分析教育部重点实验室,长沙410081
    2 Research Computing Center, University of North Carolina, Chapel Hill, North Carolina 27599-3420, USA
    3 北京科音自然科学研究中心,北京100022
  • 收稿日期:2015-08-12 出版日期:2015-11-15 发布日期:2015-11-13
  • 通讯作者: 刘述斌,荣春英 E-mail:shubin@email.unc.edu;rongchunying@aliyun.com
  • 基金资助:
    国家自然科学基金(21503076);湖南省高校科技创新团队支持计划(湘教通[2012]318号)

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 Online:2015-11-15 Published:2015-11-13
  • Contact: Shu-Bin. LIU,Chun-Ying. RONG E-mail:shubin@email.unc.edu;rongchunying@aliyun.com
  • 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)

摘要:

根据密度泛函理论,分子的电子密度确定了该体系基态下的所有性质,其中包括结构和反应活性.如何运用电子密度泛函有效地预测分子反应活性仍然是一个有待解决的难题.密度泛函活性理论(DFRT)倾力打造这样一个理论和概念架构,使得运用电子密度以及相关变量准确地预测分子的反应特性成为可能.信息理论方法的香农熵和费舍尔信息就是这样的密度泛函,研究表明,它们均可作为反应活性的有效描述符.本文将在DFRT框架中介绍和引进三个密切相关的描述符, Rényi熵、Tsallis熵和Onicescu信息能.我们准确地计算了它们在一些中性原子和分子中的数值并讨论了它们随电子数量和电子总能量的变化规律.此外,以第二阶Onicescu信息能为例,在分子和分子中的原子两个层面上,系统地考察了其随乙烷二面角旋转的变化模式.这些新慨念的引入将为我们深入洞察和预测分子的结构和反应活性提供额外的描述工具.

关键词: Rényi熵, Tsallis熵, Onicescu信息能, 香农熵, 密度泛函活性理论

Abstract:

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

MSC2000: 

  • O641