The Separability Problem in Molecular Quantum Systems: Information-Theoretic Framework for Atoms in Molecules.

Even though molecules are fundamentally quantum entities, the concept of a molecule retains certain classical attributes concerning its constituents. This includes the empirical separability of a molecule into its three-dimensional, rigid structure in Euclidean space, a framework often obtained through experimental methods like X-Ray crystallography. In this work, we delve into the mathematical implications of partitioning a molecule into its constituent parts using the widely recognized Atoms-In-Molecules (AIM) schemes, aiming to establish their validity within the framework of Information Theory concepts.

3 Information-Theoretic Analysis of the Simplest Hydrogen Abstraction Reaction.

We investigate the course of an elementary chemical reaction from the perspective of information theory in 3 space through the hypersurface of several information-theoretic () functionals such as disequilibrium (), Shannon entropy (), Fisher information (), and the complexity measures of Fisher-Shannon () and López-Mancini-Calbet (). The probe for the study is the hydrogenic identity abstraction reaction. In order to perform the analysis, the reactivity pattern of the reaction is examined by use of the aforementioned functionals of the single-particle density, which is analyzed in position () and momentum () spaces.

Phenomenological description of the acidity of the citric acid and its deprotonated species: informational-theoretical study.

Context: In spite of the fact that molecular acidity is a fundamental physicochemical property of molecular systems, the vast majority of theoretical studies have focused attention on monoprotic acids and on the prediction of pKa's. Polyprotic acids, represent a challenge for electronic structure calculations since the multiple acidic sites result in a vast group of species with different conformations and reactivities. In this work, Information-theoretic (IT) concepts of localizability, order and uniformity are applied to the Citric Acid and its deprotonated species through the one-electron density functionals: Shannon entropy (S), Fisher information (I) and Disequilibrium (D), respectively.

Study of the Chemical Space of Selected Bacteriostatic Sulfonamides from an Information Theory Point of View.

The relative structural location of a selected group of 27 sulfonamide-like molecules in a chemical space defined by three information theory quantities (Shannon entropy, Fisher information, and disequilibrium) is discussed. This group is composed of 15 active bacteriostatic molecules, 11 theoretically designed ones, and para-aminobenzoic acid. This endeavor allows molecules that share common chemical properties through the molecular backbone, but with significant differences in the identity of the chemical substituents, which might result in bacteriostatic activity, to be structurally classified and characterized.

Predominant information quality scheme for the essential amino acids: an information-theoretical analysis.

In this work we undertake a pioneer information-theoretical analysis of 18 selected amino acids extracted from a natural protein, bacteriorhodopsin (1C3W). The conformational structures of each amino acid are analyzed by use of various quantum chemistry methodologies at high levels of theory: HF, M062X and CISD(Full). The Shannon entropy, Fisher information and disequilibrium are determined to grasp the spatial spreading features of delocalizability, order and uniformity of the optimized structures.

Insight into the informational-structure behavior of the Diels-Alder reaction of cyclopentadiene and maleic anhydride.

The course of the Diels-Alder reactions of cyclopentadiene and maleic anhydride were studied. Two reaction paths were modelled: endo- and exo-selective paths. All structures within the transient region were characterized and analyzed by means of geometrical descriptors, physicochemical parameters and information-theoretical measures in order to observe the linkage between chemical behavior and the carriage of information.

Fisher information and steric effect: study of the internal rotation barrier of ethane.

On the basis of a density-based quantification of the steric effect [Liu, S. B. J.

Analysis of complexity measures and information planes of selected molecules in position and momentum spaces.

The Fisher-Shannon and LMC shape complexities and the Shannon-disequilibrium, Fisher-Shannon and Fisher-disequilibrium information planes, which consist of two localization-delocalization factors, are computed in both position and momentum spaces for the one-particle densities of 90 selected molecules of various chemical types, at the CISD/6-311++G(3df,2p) level of theory. We found that while the two measures of complexity show general trends only, the localization-delocalization planes clearly exhibit chemically significant patterns. Several molecular properties (energy, ionization potential, total dipole moment, hardness, electrophilicity) are analyzed and used to interpret and understand the chemical nature of the composite information-theoretic measures above mentioned.

Fisher Information Study in Position and Momentum Spaces for Elementary Chemical Reactions.

The utility of the Fisher information measure is analyzed to detect the transition state, the stationary points of a chemical reaction, and the bond breaking/forming regions of elementary reactions such as the simplest hydrogen abstraction and the identity SN2 exchange ones. This is performed by following the intrinsic reaction path calculated at the MP2 and QCISD(T) levels of theory with a 6-311++G(3df, 2p) basis set. Selected descriptors of both position and momentum space densities are utilized to support the observations, such as the molecular electrostatic potential (MEP), the hardness, the dipole moment, along with geometrical parameters.

Phenomenological description of a three-center insertion reaction: an information-theoretic study.

Information-theoretic measures are employed to describe the course of a three-center chemical reaction in terms of detecting the transition state and the stationary points unfolding the bond-forming and bond-breaking regions which are not revealed in the energy profile. The information entropy profiles for the selected reactions are generated by following the intrinsic-reaction-coordinate (IRC) path calculated at the MP2 level of theory from which Shannon entropies in position and momentum spaces at the QCISD(T)/6-311++G(3df,2p) level are determined. Several complementary reactivity descriptors are also determined, such as the dipole moment, the molecular electrostatic potential (MEP) obtained through a multipole expansion (DMA), the atomic charges and electric potentials fitted to the MEP, the hardness and softness DFT descriptors, and several geometrical parameters which support the information-theoretic analysis.

Local correlation measures in atomic systems.

The phenomenon of electron correlation in atomic systems is examined and compared from the statistical, information theoretic, and energetic perspectives. Local correlation measures, based on the correlation coefficient, information entropies, and idempotency measure, are compared to the correlation energy density. Analysis of these local measures reveals that the chemically significant valence region is responsible for the behavior of their respective global measures in contrast to the correlation energy density which has large contributions to the correlation energy from both the core and valence regions.