Information and complexity measures in molecular reactivity studies

Abstract

The analysis of the information and complexity measures as tools for the investigation of the chemical reactivity has been done in the spin-position and the position spaces, for the density and shape representations. The concept of the transferability and additivity of atoms or functional groups were used as "checkpoints" in the analysis of obtained results. The shape function as an argument of various measures reveals less information than the spinor density. Use of the shape function can yield wrong conclusions when the information measures such as the Shannon entropy (SE, S), the Fisher information (FI, I), the Onicescu information (OI, D), and complexities based on them are used for the systems with different electron numbers. Results obtained in the spinor-density representation show the transferability and additivity (while lacking in the case of the shape representation). The group transferability is well illustrated in the example of the X-Y molecules and their benzene derivatives. Another example is the methyl group transferability presented on the alkane-alkene-alkyne set. Analysis of the results displayed on planes between the three information-theoretical (IT) based measures has shown that the S-I plane provides "richer" information about the pattern, organization, similarity of used molecules than the I-D and D-S planes. The linear relation of high accuracy is noted between the kinetic energy and the FI and the OI measures. Another interesting regression was found between the atomization total energy and the atomization entropy. Unfortunately, the lack of the group electronic energy transferability indicates that no general relations between the IT measures and the chemical reactivity indices are observed. The molecular set chosen for the study includes different types of molecules with various functional groups (19 groups). The used set is large enough (more than 700 molecules) and diverse to improve the previous understating of molecular complexities and to generalize obtained conclusions.

Shannon entropy and many‐electron correlations: Theoretical concepts, numerical results, and Collins conjecture

“…Other applications concern, for example, the use of Shannon entropy as indicator of avoided crossings in atomic spectroscopy for electronic systems in the presence of magnetic and electric fields [18] or the study of relevant chemical reactions like biomolecular nucleophilic substitutions reactions. [19][20][21][22] Moving forward, of particular interest for the discussion in this article is the recurrence of the idea of logarithm (and directly or indirectly of the Shannon entropy) to describe electronic correlations. The use of the logarithm of a distribution, and thus something strictly related to the Shannon entropy, as a statistical measure of the correlation strength was put forward, for example, by Gottlieb and Mauser.…”

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

“…Originated from Claude Shannon's 1948 paper entitled “The mathematical theory of communication,” and still entertaining widespread applications in mathematics, statistics, computer science, physics, neurobiology and many other disciplines, information theory studies the quantification and communication of information, for which a probability function is often associated. Because the electron density can in principle be regarded as such a continuous local distribution function, ever since its early days of density functional theory (DFT), there have been tremendous interests in the literature to apply information theory to the electronic structure theory of atoms and molecules . This effort is usually categorized as the information‐theoretic approach (ITA) in DFT.…”

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

“…Furthermore, Tsallis statistics is relevant to certain systems of ultracold atoms [124][125][126][127]. Moreover, these IT quantities are applied to investigate electron correlation [30,31,33,39,72,[128][129][130][131][132][133][134][135][136] and various molecular properties as well [28,36,45,48,49,[59][60][61]72,73]. Calculated with the highly correlated Hylleraas wave functions, the results in this work then serve as a useful and reliable reference for the various applications mentioned above.…”