Rényi Entropies of Multidimensional Oscillator and Hydrogenic Systems with Applications to Highly Excited Rydberg States.

The various facets of the internal disorder of quantum systems can be described by means of the Rényi entropies of their single-particle probability density according to modern density functional theory and quantum information techniques. In this work, we first show the lower and upper bounds for the Rényi entropies of general and central-potential quantum systems, as well as the associated entropic uncertainty relations. Then, the Rényi entropies of multidimensional oscillator and hydrogenic-like systems are reviewed and explicitly determined for all bound stationary position and momentum states from first principles (i.

High Dimensional Atomic States of Hydrogenic Type: Heisenberg-like and Entropic Uncertainty Measures.

High dimensional atomic states play a relevant role in a broad range of quantum fields, ranging from atomic and molecular physics to quantum technologies. The -dimensional hydrogenic system (i.e.

Spherical-Symmetry and Spin Effects on the Uncertainty Measures of Multidimensional Quantum Systems with Central Potentials.

The spreading of the stationary states of the multidimensional single-particle systems with a central potential is quantified by means of Heisenberg-like measures (radial and logarithmic expectation values) and entropy-like quantities (Fisher, Shannon, Rényi) of position and momentum probability densities. Since the potential is assumed to be analytically unknown, these dispersion and information-theoretical measures are given by means of inequality-type relations which are explicitly shown to depend on dimensionality and state's angular hyperquantum numbers. The spherical-symmetry and spin effects on these spreading properties are obtained by use of various integral inequalities (Daubechies-Thakkar, Lieb-Thirring, Redheffer-Weyl, .

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.

Quantum Entanglement and Chemical Reactivity.

The water molecule and a hydrogenic abstraction reaction are used to explore in detail some quantum entanglement features of chemical interest. We illustrate that the energetic and quantum-information approaches are necessary for a full understanding of both the geometry of the quantum probability density of molecular systems and the evolution of a chemical reaction. The energy and entanglement hypersurfaces and contour maps of these two models show different phenomena.

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.

The Fisher-Shannon information plane, an electron correlation tool.

A new correlation measure, the product of the Shannon entropy power and the Fisher information of the electron density, is introduced by analyzing the Fisher-Shannon information plane of some two-electron systems (He-like ions, Hooke's atoms). The uncertainty and scaling properties of this information product are pointed out. In addition, the Fisher and Shannon measures of a finite many-electron system are shown to be bounded by the corresponding single-electron measures and the number of electrons of the system.

Shannon entropy as an indicator of atomic avoided crossings in strong parallel magnetic and electric fields.

Avoided crossings are the most distinctive atomic spectroscopic features in the presence of magnetic and electric fields. We point out the role of Shannon's information entropy as an indicator or predictor of these phenomena by studying the dynamics of some excited states of hydrogen in the presence of parallel magnetic and electric fields. Moreover, in addition to the well-known energy level repulsion, it is found that Shannon's entropy manifests the informational exchange of the involved states as the magnetic field strength is varied across the narrow region where an avoided crossing occurs.