Topological Analysis of the Fukui Function. In: Chauvin R, Lepetit C, Silvi B, Alikhani E, editors. Applications of Topological Methods in Molecular Chemistry. Cham: Springer International Publishing; 2016. pp. 227-41. [DOI: 10.1007/978-3-319-29022-5_8]

Photoswitchable nonlinear optical properties of azobenzene-based supramolecular complexes: insights from density functional theory

Density functional theory (DFT) calculations were performed for a series of supramolecular assemblies containing azobenzene (Azo-X where X = I, Br and H) and alkoxystilbazole subunits to evaluate their electronic, linear and nonlinear optical properties. These assemblies are derivatives of azobenzene, obtained by the substitution of electron-withdrawing and electron-donating groups onto the molecular skeleton. The interaction energies (E_int) of all the designed supramolecular complexes (IA-IF, IIA-IIF and IIIA-IIIF) range from -1.0 kcal mol^-1 to -7.7 kcal mol^-1. The electronic properties of these hydrogen/halogen bond driven supramolecular assemblies such as vertical ionization energies (VIE), HOMO-LUMO energy gap (G_H-L), excitation energies, density of states (DOS) and natural population (NPA) analyses were also computed. The non-covalent interaction index (NCI) and quantum theory of atoms in molecules (QTAIM) analyses were also performed to validate the nature of inter- and intra-molecular interactions in these complexes. A substantial enhancement in the first hyperpolarizability (β₀) values of the designed supramolecular complexes was observed, which is driven by the charge transfer from the pyridyl moiety of alkoxystilbazole to Azo-X. The highest β₀ value of 1.3 × 10⁴ au was observed for the supramolecular complex of p-nitro substituted azobenzene with alkoxystilbazole (ID complex). Moreover, the results show that the substitution of electron-withdrawing groups on Azo-X can also bring larger β₀ values for such complexes. It was confirmed on a purely theoretical basis that both the types of noncovalent interactions present and the substituent group incorporated influence the nonlinear optical (NLO) response of the systems. Furthermore, the β₀ values of the E (trans) and Z (cis) forms were compared to demonstrate the two-way photoinduced switching mechanism.

Molecular interactions from the density functional theory for chemical reactivity: Interaction chemical potential, hardness, and reactivity principles

In the first paper of this series, the authors derived an expression for the interaction energy between two reagents in terms of the chemical reactivity indicators that can be derived from density functional perturbation theory. While negative interaction energies can explain reactivity, reactivity is often more simply explained using the “|dμ| big is good” rule or the maximum hardness principle. Expressions for the change in chemical potential (μ) and hardness when two reagents interact are derived. A partial justification for the maximum hardness principle is that the terms that appear in the interaction energy expression often reappear in the expression for the interaction hardness, but with opposite sign.

Molecular Interactions From the Density Functional Theory for Chemical Reactivity: The Interaction Energy Between Two-Reagents

Reactivity descriptors indicate where a reagent is most reactive and how it is most likely to react. However, a reaction will only occur when the reagent encounters a suitable reaction partner. Determining whether a pair of reagents is well-matched requires developing reactivity rules that depend on both reagents. This can be achieved using the expression for the minimum-interaction-energy obtained from the density functional reactivity theory. Different terms in this expression will be dominant in different circumstances; depending on which terms control the reactivity, different reactivity indicators will be preferred.

Links among the Fukui potential, the alchemical hardness and the local hardness of an atom in a molecule

This paper presents a brief summary of the difficulty that resides in the definition of the elusive concept of local chemical hardness. We argue that a definition of local hardness should be useful to a reactivity principle and not just as a mere definition. We then continue with a formal discussion about the benefits and difficulties of using the Fukui potential, which is interpreted as an alchemical derivative (alchemical hardness), as descriptor of local hardness of molecules. Computational evidence shows that the alchemical hardness is at least as good a descriptor as the combination of other two well-stabilized descriptors of local hardness, such as the Fukui function and grand canonical local hardness. Although our results are auspicious for the alchemical hardness as descriptor of local hardness, we finish by calling the attention of the community on the importance of discussing the raison d'être of a local hardness function and its main characteristics. We suggest that an axiomatic construction of local hardness could be they way of constructing a local hardness which is both useful and free of arbitrariness.

Kick-Fukui: A Fukui Function-Guided Method for Molecular Structure Prediction

Here, we introduce a hybrid method, named Kick-Fukui, to explore the potential energy surface (PES) of clusters and molecules using the Coulombic integral between the Fukui functions in the first screening of the best individuals. In the process, small stable molecules or clusters whose combination has the stoichiometry of the explored species are used as assembly units. First, a small set of candidates has been selected from a large and stochastically generated (Kick) population according to the maximum value of the Coulombic integral between the Fukui functions of both fragments. Subsequently, these few candidates are optimized using a gradient method and density functional theory (DFT) calculations. The performance of the program has been evaluated to explore the PES of various systems, including atomic and molecular clusters. In most cases studied, the global minimum (GM) has been identified with a low computational cost. The strategy does not allow to identify the GM of some silicon clusters; however, it predicts local minima very close in energy to the GM that could be used as the initial population of evolutionary algorithms.

New insights in chemical reactivity from quantum chemical topology

Based on the quantum chemical topology of the modified electron localization function ELF_x , an efficient and robust mechanistic methodology designed to identify the favorable reaction pathway between two reactants is proposed. We first recall and reshape how the supermolecular interaction energy can be evaluated from only three distinct terms, namely the intermolecular coulomb energy, the intermolecular exchange-correlation energy and the intramolecular energies of reactants. Thereafter, we show that the reactivity between the reactants is driven by the first-order variation in the coulomb intermolecular energy defined in terms of the response to changes in the number of electrons. Illustrative examples with the formation of the dative bond B-N involved in the BH₃ NH₃ molecule and the typical formation of the hydrogen bond in the canonical water dimer are presented. For these selected systems, our approach unveils a noticeable mimicking of E_dual onto the DFT intermolecular interaction energy surface calculated between the both reactants. An automated reaction-path algorithm aimed to determine the most favorable relative orientations when the two molecules approach each other is also outlined.

Partitioning a Molecule into the Atomic Basins and the Resultant Atomic Charges from Quantum Chemical Topology Analysis of the Kohn-Sham Potential

Quantum chemical topology (QCT) solidifies the chemical basic concepts demonstrating how a molecular system is intrinsically partitioned into its components and what the interaction lines between them are. Here, QCT analysis using a Kohn-Sham one-electron potential (KSpot) in KS equation as a scalar function is initiated and explored, showing KSpot and its resultant electron force lines have novel spatial features which reveal that an atom in a molecule is a spatial basin governed by its nucleus as a 3D-attractor that terminates all the electron force lines defined by the negative gradient of KSpot and that a chemical bond line is just a minimum path of KSpot for the electron motion. Particularly, the atomic charges from this KSpot QCT analysis are moderate and good, having much lower dependence on basis sets chosen for computation. This may provide a platform for the study of molecular structures and properties, intra- and intermolecular electrostatic interaction, energy decomposition, and construction of force field.

Predicting Deprotonation Sites Using Alchemical Derivatives

An alchemical transformation is any process, physical or fictitious, that connects two points in the chemical space. A particularly important transformation is the vanishing of a proton, whose energy can be linked to the proton dissociation enthalpy of acids. In this work we assess the reliability of alchemical derivatives in predicting the proton dissociation enthalpy of a diverse series of mono- and polyprotic molecules. Alchemical derivatives perform remarkably well in ranking the proton affinity of all molecules. Additionally, alchemical derivatives could be use also as a predictive tool because their predictions correlate quite well with calculations based on energy differences and experimental values. Although second-order alchemical derivatives underestimate the dissociation enthalpy, the deviation seems to be almost constant. This makes alchemical derivatives extremely accurate to evaluate the difference in proton affinity between two acid sites of polyprotic molecule. Finally, we show that the reason for the underestimation of the dissociation enthalpy is most likely the contribution of higher-order derivatives.

Orbital-Weighted Dual Descriptor for the Study of Local Reactivity of Systems with (Quasi-) Degenerate States

An alternative response function, based on the dual descriptor in terms of Koopmans' approximation, is hereby proposed for the description of chemical reactivity in systems with (quasi-) degenerate frontier molecular orbitals. This descriptor is constructed from Fukui functions that include contributions from different orbitals, i.e., orbital-weighted Fukui functions. The methodology is applied to three case studies: the first case consists of a series of benchmark organic and inorganic molecules from which the dual descriptor, based only on frontier orbitals, is not appropriate to describe their reactivity. The second case deals with the proper description of chemical reactivity in Diels-Alder reactions between fullerene C₆₀ and cyclopentadiene (CP), revealing the importance of considering secondary orbital interactions for an adequate regioselectivity description. The third, and last case, consists of a series of polycyclic aromatic hydrocarbons (PAHs) possessing molecular orbital degeneracy. By means of analyzing of this descriptor, an alternative approach to the description of aromaticity is proposed. In all cases, the proposed index called "orbital-weighted dual descriptor" has proven to accurately describe the chemical reactivity and aromaticity of the studied systems.

Interpreting Aromaticity and Antiaromaticity through Bifurcation Analysis of the Induced Magnetic Field

In all molecules, a current density is induced when the molecule is subjected to an external magnetic field. In turn, this current density creates a particular magnetic field. In this work, the bifurcation value of the induced magnetic field is analyzed in a representative set of aromatic, non-aromatic and antiaromatic monocycles, as well as a set of polycyclic hydrocarbons. The results show that the bifurcation value of the ring-shaped domain adequately classifies the studied molecules according to their aromatic character. For aromatic and nonaromatic molecules, it is possible to analyze two ring-shaped domains, one diatropic (inside the molecular ring) and one paratropic (outside the molecular ring). Meanwhile, for antiaromatic rings, only a diatropic ring-shaped domain (outside the molecular ring) is possible to analyze, since the paratropic domain (inside the molecular ring) is irreducible with the maximum value (attractor) at the center of the molecular ring. In some of the studied cases, i. e., in heteroatomic species, bifurcation values do not follow aromaticity trends and present some inconsistencies in comparison to ring currents strengths, showing that this approximation provides only a qualitative estimation about (anti)aromaticity.

Electron localization function from density components

This work addresses the decomposition of the Electron Localization Function (ELF) into partial density contributions using an appealing split of kinetic energy densities. Regarding the degree of the electron localization, the relationship between ELF and its usual spin-polarized formula is discussed. A new polarized ELF formula, built from any subsystems of the density, and a localization function, quantifying the measure of electron localization for only a subpart of the total system are introduced. The methodology appears tailored to describe the electron localization in bonding patterns of subsystems, such as the local nucleophilic character. Beyond these striking examples, this work opens up opportunities to describe any electronic properties that depend only on subparts of the density in atoms, molecules, or solids. © 2016 Wiley Periodicals, Inc.