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

Liu, Shubin; 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 sup>; Rong, Chunying; Wu, Zhi Yuan; Lu, Tian; 北京科音自然科学研究中心, 北京 sup>

doi:10.3866/pku.whxb201509183

Cited by 61 publications

(47 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Other quantities introduced as new reactivity descriptors in ITA include Rényi entropy R n , Tsallis entropy T n , and Onicescu information energy E n . The Rényi entropy of order n is:

R_{n} = \frac{1}{1 - n} \ln ([], \int ρ^{n} ((), r) d boldr)

with the condition that n ≥ 0 and n ≠ 1.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Information‐theoretic approach in density functional theory and its recent applications to chemical problems

Rong

Wang

Zhao

et al. 2019

WIREs Comput Mol Sci

106

116

View full text Add to dashboard Cite

Using simple functionals of the electron density to appreciate and quantify molecular structure and chemical reactivity properties is a recent endeavor in density functional theory (DFT) toward the development of a new chemical reactivity theory. According to the first Hohenberg–Kohn theorem in DFT, the electron density alone should be able to determine any property in the ground state. Exchange and correlation energies are such properties, so are molecular structure and chemical reactivity, and hence they all should accurately be determined by electron density functionals. Quantities such as Shannon entropy, Fisher information, Ghosh–Berkowitz–Parr entropy, information gain, Onicescu information energy, etc., from the information‐theoretic approach are simple electron density functionals, whose analytical forms are exactly known. In this article, we demonstrate their usefulness and validity to quantify regioselectivity, stereoselectivity, and other structure and reactivity properties. We will outline the current understanding of its theoretical framework at first, and then highlight recent applications to chemical problems including isomeric and conformational stability, electrophilicity and nucleophilicity, strong covalent and weak noncovalent interactions, acidity and basicity, aromaticity and antiaromaticity, and numerous other properties. The effort of employing electron density functionals to quantify chemical concepts should open up a new door for us to ultimately develop a chemical reactivity theory using the DFT language. This article is characterized under: Structure and Mechanism > Reaction Mechanisms and Catalysis Electronic Structure Theory > Density Functional Theory Structure and Mechanism > Molecular Structures Molecular and Statistical Mechanics > Molecular Interactions

show abstract

“…Other quantities introduced as new reactivity descriptors in ITA include Rényi entropy R n , Tsallis entropy T n , and Onicescu information energy E n . The Rényi entropy of order n is:

R_{n} = \frac{1}{1 - n} \ln ([], \int ρ^{n} ((), r) d boldr)

with the condition that n ≥ 0 and n ≠ 1.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Information‐theoretic approach in density functional theory and its recent applications to chemical problems

Rong

Wang

Zhao

et al. 2019

WIREs Comput Mol Sci

106

116

View full text Add to dashboard Cite

show abstract

“…Very recently, three‐additional information‐theoretic quantities, Rényi entropy, Tsallis entropy, and Onicescu information energy, were introduced as new reactivity descriptors in DFRT . The Rényi entropy of order n , where n ≥ 0 and n ≠ 1, is defined as

R_{n} = \frac{1}{1 - n} \ln true[true \int ρ (r)^{n} d r true] .

…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Molecular acidity: An accurate description with information‐theoretic approach in density functional reactivity theory

et al. 2017

View full text Add to dashboard Cite

Molecular acidity is one of the important physiochemical properties of a molecular system, yet its accurate calculation and prediction are still an unresolved problem in the literature. In this work, we propose to make use of the quantities from the information-theoretic (IT) approach in density functional reactivity theory and provide an accurate description of molecular acidity from a completely new perspective. To illustrate our point, five different categories of acidic series, singly and doubly substituted benzoic acids, singly substituted benzenesulfinic acids, benzeneseleninic acids, phenols, and alkyl carboxylic acids, have been thoroughly examined. We show that using IT quantities such as Shannon entropy, Fisher information, Ghosh-Berkowitz-Parr entropy, information gain, Onicescu information energy, and relative Rényi entropy, one is able to simultaneously predict experimental pKa values of these different categories of compounds. Because of the universality of the quantities employed in this work, which are all density dependent, our approach should be general and be applicable to other systems as well. © 2017 Wiley Periodicals, Inc.

show abstract

“…Formulas for conversion between IT quantities using the two different densities are [27,29,32,[55][56][57]59,72]…”

Section: Information-theoretic Quantities In the Position Spacementioning

confidence: 99%

Shannon, Rényi, Tsallis Entropies and Onicescu Information Energy for Low-Lying Singly Excited States of Helium

2019

Atoms

View full text Add to dashboard Cite

Knowledge of the electronic structures of atomic and molecular systems deepens our understanding of the desired system. In particular, several information-theoretic quantities, such as Shannon entropy, have been applied to quantify the extent of electron delocalization for the ground state of various systems. To explore excited states, we calculated Shannon entropy and two of its one-parameter generalizations, Rényi entropy of order α and Tsallis entropy of order α , and Onicescu Information Energy of order α for four low-lying singly excited states (1s2s 1 S e , 1s2s 3 S e , 1s3s 1 S e , and 1s3s 3 S e states) of helium. This paper compares the behavior of these three quantities of order 0.5 to 9 for the ground and four excited states. We found that, generally, a higher excited state had a larger Rényi entropy, larger Tsallis entropy, and smaller Onicescu information energy. However, this trend was not definite and the singlet–triplet reversal occurred for Rényi entropy, Tsallis entropy and Onicescu information energy at a certain range of order α .

show abstract

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

Cited by 61 publications

References 21 publications

Information‐theoretic approach in density functional theory and its recent applications to chemical problems

Information‐theoretic approach in density functional theory and its recent applications to chemical problems

Molecular acidity: An accurate description with information‐theoretic approach in density functional reactivity theory

Shannon, Rényi, Tsallis Entropies and Onicescu Information Energy for Low-Lying Singly Excited States of Helium

Contact Info

Product

Resources

About