Nelson Flores-Gallegos

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.

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.

Natural atomic probabilities in quantum information theory

Quantum Information Theory has witnessed a great deal of interest in the recent years since its potential for allowing the possibility of quantum computation through quantum mechanics concepts such as entanglement, teleportation and cryptography. In Chemistry and Physics, von Neumann entropies may provide convenient measures for studying quantum and classical correlations in atoms and molecules. Besides, entropic measures in Hilbert space constitute a very useful tool in contrast with the ones in real space representation since they can be easily calculated for large systems. In this work, we show properties of natural atomic probabilities of a first reduced density matrix that are based on information theory principles which assure rotational invariance, positivity, and N- and v-representability in the Atoms in Molecules (AIM) scheme. These (natural atomic orbital-based) probabilities allow the use of concepts such as relative, conditional, mutual, joint and non-common information entropies, to analyze physical and chemical phenomena between atoms or fragments in quantum systems with no additional computational cost. We provide with illustrative examples of the use of this type of atomic information probabilities in chemical process and systems.

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.

Theoretic-information entropies analysis of nanostructures: ab initio study of PAMAM precursors and dendrimers G0 to G3

Information theory in conjugated and in Hilbert spaces is employed to analyse the growing behaviour of nanostructures. Shannon entropies in position and momentum spaces require costly and time-consuming computations as the size of the molecules increases in contrast with information entropies in Hilbert space, which are shown to be highly advantageous for analysing large molecules. In this work, ab initio electronic structure calculations at the Hartree–Fock (HF), MP2 and B3LYP levels of theory were performed to analyse the initial steps towards growing nanostructured molecules of polyamidoamine (PAMAM) dendrimers, starting from the monomers, dimers, trimers and tetramers up to generations G0 (with 84 atoms), G1 (228 atoms), G2 (516 atoms) and G3 (1092 atoms). This was achieved by using selected physical descriptors such as the radius of gyration, the asphericity factor, the moments of inertia, the dipole moments, the total energies and chemical reactivity indices such as the hardness, softness and the electrophilicity index at the HF/3-21G* level of theory. For the chemical indices, higher level calculations at the B3LYP/6-311++ G** and MP2/6-311+ G* levels were also performed in order to account for the effects of electron correlation. Information-theoretic measures of the Shannon type in conjugated space were employed to characterise the G0–PAMAM precursors and G0. Hilbert space entropies of the Shannon and Kullback type were employed to provide theoretic-information evidence of the validity of the dense-core model of PAMAM precursors and dendrimers G0 to G3.

Ab Initio Study of Selected PAMAM Dendrimers: von Neumann Entropies Analysis

Quantum information theory is employed to analyze the growing behavior of nanostructured molecules through marginal H-type von Neumann informational entropies. This is achieved by performing ab initio electronic structure calculations at the Hartree-Fock level of theory to characterize the initial steps towards growing Polyamidoamine (PAMAM) dendrimers, starting from conformational structures of polymeric precursors up to generations G0 (with 84 atoms), G1 (228 atoms), G2 (516 atoms), and G3 (1092 atoms). Several physical descriptors like radius of gyration, asphericity factor, moments of inertia and dipole moments, along with chemical reactivity indexes such as total energies, hardness and electrophilicity are employed to provide evidence for the validity of dense-core model of dendrimers.