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WIREs Comput Mol Sci
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Information‐theoretic approach in density functional theory and its recent applications to chemical problems

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Abstract 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
Twenty‐one electrophilic molecules studied
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Strong linear correlations between the Hirshfeld charge and aromatic electrophilic substitution barrier heights for mono‐substituted benzene derivatives with para and meta directing groups. (Reprinted with permission from Reference . Copyright 2015 American Chemical Society)
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Strong linear correlations between the aromaticity index ASE and the ITA quantity SGBP for different substituted fulvene derivatives. (Reprinted with permission from Reference . Copyright 2017 PCCP Owner Societies)
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Comparisons of experimental pKa data of all five series of compounds with the fitted pKa data using five ITA quantities from (a) the acidic atom and (b) the leaving proton. (Reprinted with permission from Reference . Copyright 2017 John Wiley & Sons)
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Strong linear correlations obtained between frontier orbital properties and ITA quantities for systems in Scheme . (Reprinted with permission from Reference . Copyright 2017 Springer Nature)
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Repeating units (1) trans‐ethylene, (2) benzene, (3) naphthalene, (4) di‐thiophene, and (5) phenanthrene chains. (Reprinted with permission from Reference . Copyright 2017 Springer Nature)
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Cooperativity profiles of the six cluster models studied in Scheme . (Reprinted with permission from Reference . Copyright 2019 American Chemical Society)
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The optimized structure for six cluster models with n = 20 as illustrative examples. (Reprinted with permission from Reference . Copyright 2019 American Chemical Society)
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ELF and SCI isosurface shapes as descriptors of strong covalent interactions with (a, b) double, (c, d) triple, and (e, f) quadruple covalent bonds (Reprinted with permission from Reference . Copyright 2018 American Chemical Society)
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Relationships between difference in rotation barriers and its energetic components for all six molecules. (Reprinted with permission from Reference . Copyright 2013 American Chemical Society)
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Strong linear correlation between differences in the total energy and Shannon entropy for all conformers from the four fullerene systems. (Reprinted with permission from Reference . Copyright 2018 American Chemical Society)
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The strong linear correlation between the steric charge and barrier height for SN2 reactions. (Reprinted with permission from Reference . Copyright 2018 PCCP Owner Societies)
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Steric force as a reliable descriptor of stereoselectivity as illustrated by PhMeHC–CHO and ClMeHC–CHO molecules. (Reprinted with permission from Reference . Copyright 2017 PCCP Owner Societies)
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Comparing the experimental nucleophilicity scale with theoretical results of (a) information gain and (b) Hirshfeld charge for systems in Scheme . (Reprinted with permission from Reference . Copyright 2015 American Chemical Society)
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Comparing experimental electrophilicity scale with theoretical results of (a) information gain and (b) Hirshfeld charge for systems in Scheme . (Reprinted with permission from Reference . Copyright 2015 American Chemical Society)
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Twenty‐two nucleophilic molecules studied
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Molecular and Statistical Mechanics > Molecular Interactions
Structure and Mechanism > Molecular Structures
Electronic Structure Theory > Density Functional Theory
Structure and Mechanism > Reaction Mechanisms and Catalysis

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