Rodolfo O. Esquivel

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. We have shown that the information-theoretical characterization of the chemical course of the reaction is in complete agreement with its phenomenological behavior in passing from reactants to products. In addition, we were able to detect the main differences between the two reaction mechanisms. This type of informational analysis serves to provide tools to help understand the chemical reactivity of the two simplest Diels-Alder reactions, which permits the establishment of a connection between the quantum changes that molecular systems exert along reaction coordinates and standard physicochemical phenomenology. In the present study, we have shown that every reaction stage has a family of subsequent structures that are characterized not solely by their phenomenological behavior but also by informational properties of their electronic density distribution (localizability, order, uniformity). Moreover, we were able to describe the main differences between endo-adduct and exo-adduct pathways. With the advent of new experimental techniques, it is in principle possible to observe the structural changes in the transient regions of chemical reactions. Indeed, through this work we have provided the theoretical concepts needed to unveil the concurrent processes associated with chemical reactions.

Molecular similarity based on information entropies and distances

A similarity index based on the concept of an information distance is evaluated for a series of diatomic molecules. The results show that the momentum space information distance is a good indicator of the extent of charge separation present in a molecule. The Shannon entropy in position space is shown to decrease with increasing charge separation and as such is presented as a measure of the structure or extent of electron localization in a system. The concept of a local Shannon entropy over an atomic basin is introduced and it is shown how this quantity may be used to examine the local behavior of electron densities.

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. These results emphasize the difference in the mechanisms inherent in the different perspectives, the similarity between the statistical, information entropic, and idempotency views, and provides further evidence for the use of information theoretic based quantities in studies of electron correlation.

Information uncertainty-type inequalities in atomic systems

The one-electron Shannon information entropy sum is reformulated in terms of a single entropic quantity dependent on a one-electron phase space quasiprobability density. This entropy is shown to form an upper bound for the entropy of the one-electron Wigner distribution. Two-electron entropies in position and momentum space, and their sum, are introduced, discussed, calculated, and compared to their one-electron counterparts for neutral atoms. The effect of electron correlation on the two-electron entropies is examined for the helium isoelectronic series. A lower bound for the two-electron entropy sum is developed for systems with an even number of electrons. Calculations illustrate that this bound may also be used for systems with an odd number of electrons. This two-electron entropy sum is then recast in terms of a two-electron phase space quasiprobability density. We show that the original Bialynicki-Birula and Mycielski information inequality for the N-electron wave function may also be formulated in terms of an N-electron phase space density. Upper bounds for the two-electron entropies in terms of the one-electron entropies are reported and verified with numerical calculations.

A numerical study of molecular information entropies

Abstract Molecular information entropies are computed by means of a three-dimensional numerical integration from wavefunctions expanded in a variety of Gaussian basis sets at different levels. The results substantiate the use of the entropy sum as a measure of basis set quality. This sum is also shown to be sensitive to electron correlation. The previously observed trends for atomic systems computed from Slater-type orbitals are seen to be present in the results from wavefunctions expanded in Gaussian-type orbitals.

Quantum entanglement in helium

We compute the entanglement of the ground state and several singlet and triplet excited states of the helium atom using high-quality, state-of-the-art wavefunctions. The behaviour of the entanglement of the helium eigenstates is similar to that observed in some exactly soluble two-electron systems. In particular, the amount of entanglement exhibited by the eigenstates tends to increase with energy.

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.

Shannon entropy of chemical changes: SN2 displacement reactions

The Shannon entropies along the intrinsic reaction coordinates (IRC) of two SN2 reactions were calculated at the RHF/6-31++G** level. The resulting entropic profiles were compared with the corresponding energy profiles. The Shannon entropy profiles in position and momentum space, as well as their sum, show interesting features about the bond forming and breaking process that are not apparent from the conventional reaction energy profile.

An information-entropic study of correlated densities of the water molecule

The Shannon entropy of the water molecule was calculated at different correlation levels including full configuration interaction (CI) for the D95 basis set. The results show that an analysis of both the position and momentum space entropy yields insights into the characteristics of different correlated methods from the density perspective and provides an alternative way of interpreting the wave function. Various changes in the electronic densities intrinsic to these correlation methods are also related to concepts within the information entropy framework.