J. Antolín

Atomic complexity measures in position and momentum spaces

Fisher-Shannon (FS) and Lopez-Ruiz, Mancini, and Calbet (LMC) complexity measures, detecting not only randomness but also structure, are computed by using near Hartree-Fock wave functions for neutral atoms with nuclear charge Z=1-103 in position, momentum, and product spaces. It is shown that FS and LMC complexities are qualitatively and numerically equivalent for these systems. New complexity candidates are defined, computed, and compared by using the following information-theoretic magnitudes: Shannon entropy, Fisher information, disequilibrium, and variance. Localization-delocalization planes are constructed for each complexity measure, where the subshell pattern of the periodic table is clearly shown. The complementary use of r and p spaces provides a compact and more complete understanding of the information content of these planes.

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. Chem. Phys.2007, 126, 244103], the origin of the internal rotation barrier between the eclipsed and staggered conformers of ethane is systematically investigated in this work from an information-theoretical point of view by using the Fisher information measure in conjugated spaces. Two kinds of computational approaches are considered in this work: adiabatic (with optimal structure) and vertical (with fixed geometry). The analyses are performed systematically by following, in each case, the conformeric path by changing the dihedral angle from 0 to 180° . This is calculated at the HF, MP2, B3LYP, and CCSD(T) levels of theory and with several basis sets. Selected descriptors of the densities are utilized to support the observations. Our results show that in the adiabatic case the eclipsed conformer possesses a larger steric repulsion than the staggered conformer, but in the vertical cases the staggered conformer retains a larger steric repulsion. Our results verify the plausibility for defining and computing the steric effect in the post-Hartree-Fock level of theory according to the scheme proposed by Liu.

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. Our results support the concept of a continuum of transient of Zewail and Polanyi for the transition state rather than a single state, which is also in agreement with reaction force analyses.

Fisher and Jensen-Shannon divergences: Quantitative comparisons among distributions. Application to position and momentum atomic densities.

The Fisher divergence (FD) and Jensen-Shannon divergence (JSD) are used in this work with the aim of providing quantitative measures of the discrepancies between two arbitrary D-dimensional distribution functions, the FD being of local character and the JSD of global one. In doing so, the concepts of Fisher information and Shannon entropy associated to a distribution are the essential quantities for building up these comparative functionals. This kind of relative measures are here applied to the study of the one-particle densities in both conjugated spaces (position and momentum) of neutral atoms, discussing the results as compared to those provided by other previous functional measures. It is clearly shown how these divergences provide relevant information on the atomic shell structure, up to a level which depends on the considered space and measure.

Atomic quantum similarity indices in position and momentum spaces

Quantum similarity for atoms is investigated using electron densities in position and momentum spaces. Contrary to the results in position space, the analysis in the momentum space shows how the momentum density carries fundamental information about periodicity and structure of the system and reveals the pattern of Mendeleevs table. A global analysis in the joint r-p space keeps this result.

Quantum entanglement and the dissociation process of diatomic molecules

In this work, we investigate quantum entanglement-related aspects of the dissociation process of some selected, representative homo- and heteronuclear diatomic molecules. This study is based upon high-quality ab initio calculations of the (correlated) molecular wavefunctions involved in the dissociation processes. The values of the electronic entanglement characterizing the system in the limit cases corresponding to (i) the united-atom representation and (ii) the asymptotic region when atoms dissociate are discussed in detail. It is also shown that the behaviour of the electronic entanglement as a function of the reaction coordinate R exhibits remarkable correspondences with the phenomenological description of the physically meaningful regimes comprising the processes under study. In particular, the extrema of the total energies and the electronic entanglement are shown to be associated with the main physical changes experienced by the molecular spatial electronic density, such as charge depletion and accumulation or bond cleavage regions. These structural changes are characterized by several selected descriptors of the density, such as the Laplacian of the electronic molecular distributions (LAP), the molecular electrostatic potential (MEP) and the atomic electric potentials fitted to the MEP.

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. New density-based structures related to the bond-forming and bond-breaking regions are proposed. Our results support the concept of a continuum of transient of Zewail and Polanyi for the transition state rather than a single state, which is also in agreement with reaction-force analyses.

Minimum-cross-entropy estimation of atomic charge densities from scattering factors

Tight model-independent approximations to the one-particle atomic density , derived from very few values of the form factor , are obtained by means of the minimum-cross-entropy technique. For completeness, the accuracy of the approximations is analysed within a Hartree-Fock framework.

Atomic and Molecular Complexities: Their Physical and Chemical Interpretations

Within the present work on the meaning, interpretation and applications of the complexity measures, different order-uncertainty planes embodying relevant information-theoretical magnitudes are studied in order to analyse the information content of the position and momentum electron densities of several atomic (neutrals, singly-charged ions, isoelectronic series) and molecular (closed shells, radicals, isomers) systems. The quantities substaining those planes are the exponential and the power Shannon entropies, the disequilibrium, the Fisher information and the variance. Each plane gives rise to a measure of complexity, determined by the product of its components. In the present work, the values of the so-called Lopez-Ruiz, Mancini and Calbet (LMC), Fisher-Shannon (FS) and Cramer-Rao (CR) complexities will be provided in both conjugated spaces and interpreted from physical and chemical points of view. Computations for atoms were carried out within a Hartree-Fock framework, while for molecules by means of CISD(T)/6-311++G(3df, 2p) wave functions. In order to have a complete information-theoretical description of these systems, it appears relevant to consider simultaneously the results in both spaces.

Information-theoretical complexity for the hydrogenic abstraction reaction

In this work, we have investigated the complexity of the hydrogenic abstraction reaction by means of information functionals such as disequilibrium (D), exponential entropy (L), Fisher information (I), power entropy (J) and joint information-theoretic measures, i.e. the I–D, D–L and I–J planes and the Fisher–Shannon and López–Mancini–Calbet (LMC) shape complexities. The analysis of the information-theoretical functionals of the one-particle density was computed in position (r) and momentum (p) space. The analysis revealed that all of the chemically significant regions can be identified from the information functionals and most of the information-theoretical planes, i.e. the reactant/product regions (R/P), the transition state (TS), including those that are not present in the energy profile such as the bond cleavage energy region (BCER), and the bond breaking/forming regions (B–B/F). The analysis of the complexities shows that, in position as well as in the joint space, the energy profile of the abstraction reaction bears the same information-theoretical features as the LMC and FS measures. We discuss why most of the chemical features of interest, namely the BCER and B–B/F, are lost in the energy profile and that they are only revealed when particular information-theoretical aspects of localizability (L or J), uniformity (D) and disorder (I) are considered.