In pursuit of negative Fukui functions: examples where the highest occupied molecular orbital fails to dominate the chemical reactivity

Does the radical GPRI strongly depend on the population scheme? A comparative study to predict radical attack on unsaturated molecules with the radical general-purpose reactivity indicator

The reactivity of 22 unsaturated molecules undergoing attack by a methyl radical (⋅CH3) have been elucidated using the condensed radical general-purpose reactivity indicator (condensed radical GPRI) appropriate for relatively nucleophilic or electrophilic molecules. Using the appropriate radical GPRI equation for electrophilic attack or nucleophilic radical attack, seven different population schemes were used to assign the most reactive atoms in each of the 22 molecules. The results show that the condensed radical GPRI is sensitive to the population scheme chosen, but less sensitive than the radical Fukui function. Therefore, the reliability of these methods depends on the population scheme. Our investigation indicates that the condensed radical GPRI is most accurate in predicting the dominant products of the methyl radical addition reactions on a variety of unsaturated molecules when the Hirshfeld, Merz-Singh-Kollman, or Voronoi deformation density population schemes are used. Furthermore, for all populations schemes in the majority of instances where the radical Fukui function failed the radical GPRI was able to identify the most reactive atom under certain reactivity conditions.

Peculiar Differences between Two Copper Complexes Containing Similar Redox-Active Ligands: Density Functional and Multiconfigurational Calculations

Transition metal complexes featuring redox-active ligands often exhibit multiple redox states, influenced by the interplay between the metal center and the ligand. This study delves into the electronic structures of two mononuclear complexes of copper with two similar redox-active urea azine ligands. The ligands differ by the replacement of an NCH3 moiety by an S atom in the ligand backbone. Experimental analysis yields pronounced electronic structural disparities between these complexes, observable in both the solution and solid phases. Conventional quantum chemical methods, such as density functional theory using different functionals (B3LYP, TPSSh, and CAM-B3LYP), remain inadequate to rationalize the observed spectroscopic anomalies. However, a multiconfigurational approach elucidates the disparate behaviors of these complexes. Multireference perturbation theory, based on complete active space self-consistent field computations, identifies Cu(I) in the case of the complex with the NCH3 containing ligands and a state with substantial Cu(II) contributions in the case of the complex with the S atom containing ligands. In contrast, DFT indicates Cu(I) in both scenarios.

Extending Conceptual Density Functional Theory toward First-Order Reduced Density Matrices: An Open Subsystems Viewpoint on the Fukui Matrix

As a matrix extension of the Fukui function, a reactivity descriptor grounded within Conceptual Density Functional Theory, the Fukui matrix extends Frontier Molecular Orbital Theory to correlated regimes with its eigendecomposition in Fukui occupations and Fukui naturals. Despite successful applications, the questions remain as to whether replacing a quantity derived from a purely density-based framework by its matrix extension is theoretically well-founded and what chemical information is contained in the corresponding eigendecomposition. In this study, we show that the matrix extension of the Fukui function is only well-defined if one also generalizes the external potential to become nonlocal, leading to the introduction of Conceptual First-Order Reduced Density Matrix Functional Theory. By interpreting the Anderson impurity model from an interacting open subsystem perspective, we show how Fukui occupations and Fukui naturals reflect the influence of an increasing (static) correlation and which characteristic patterns we should expect within a molecular context. This study represents a step in generalizing Conceptual Density Functional Theory beyond its density-based perspective.

Conceptual density functional theory based electronic structure principles

In this review article, we intend to highlight the basic electronic structure principles and various reactivity descriptors as defined within the premise of conceptual density functional theory (CDFT). Over the past several decades, CDFT has proven its worth in providing valuable insights into various static as well as time-dependent physicochemical problems. Herein, having briefly outlined the basics of CDFT, we describe various situations where CDFT based reactivity theory could be employed in order to gain insights into the underlying mechanism of several chemical processes.

High regioselectivity in the amination reaction of isoquinolinequinone derivatives using conceptual DFT and NCI analysis

DFT-derived reactivity descriptors and Non-Covalent interaction (NCI) analysis were performed to rationalize the regioselectivity in the amination reaction of some isoquinolinequinone derivatives. Statistical analysis was performed to assess robustness of atomic charges to the basis set. Various electronic population schemes including Mulliken population analysis (MPA), electrostatic method (ChelpG), Hirshfeld population analysis (HPA) and Natural population analysis (NPA) have been considered. The results revealed that NPA was the most efficient for this purpose. NCI study using the reduced density gradient (RDG) was performed for revealing weak interactions. Domains defined by isosurfaces of RDG have been integrated to quantitatively study the strength of weak interactions and their stabilities have also been examined. Steric hindrance caused by coordination of ethanol with the neighboring carbonyl prevents the nucleophilic attack on C-6 and therefore leads to preferential C-7 substitution. The quantitative study of NCI clearly demonstrates that the hydrogen bond of carbonyl (2) is more stabilizing. Consequently, the high polarity of hydrogen bond on this carbonyl may explain the high electrophilicity of C-5 compared to C-8. Our work proved that the difference in local reactivity, as well as the steric hindrance are the key elements explaining the high regioselectivity exhibited by the amination reaction.

Unifying Conceptual Density Functional and Valence Bond Theory: The Hardness-Softness Conundrum Associated with Protonation Reactions and Uncovering Complementary Reactivity Modes

In this study, we address the long-standing issue-arising prominently from conceptual density functional theory (CDFT)-of the relative importance of electrostatic, i.e., "hard-hard", versus spin-pairing, i.e., "soft-soft", interactions in determining regiochemical preferences. We do so from a valence bond (VB) perspective and demonstrate that VB theory readily enables a clear-cut resolution of both of these contributions to the bond formation/breaking process. Our calculations indicate that appropriate local reactivity descriptors can be used to gauge the magnitude of both interactions individually, e.g., Fukui functions or HOMO/LUMO orbitals for the spin-pairing/(frontier) orbital interactions and molecular electrostatic potentials (and/or partial charges) for the electrostatic interactions. In contrast to previous reports, we find that protonation reactions cannot generally be classified as either charge- or frontier orbital-controlled; instead, our results indicate that these two bonding contributions generally interplay in more subtle patterns, only giving the impression of a clear-cut dichotomy. Finally, we demonstrate that important covalent, i.e., spin pairing, reactivity modes can be missed when only a single spin-pairing/orbital interaction descriptor is considered. This study constitutes an important step in the unification of CDFT and VB theory.

Prediction of the Synthesis of Spiro Derivatives by Double Intramolecular Aromatic Electrophilic Substitution Using Reactivity Indices

The synthesis of heterocyclic spirobifluorene (SBF) analogs generally requires long and complicated synthetic pathways. Despite this synthetic effort, such structural modification allows the (opto)electronic properties of this remarkable three-dimensional node to be tuned especially for molecular electronic applications. For this reason, the development of a simple, robust, and efficient synthetic methodology to introduce various heterocycles in place of classical phenyl rings in the spirofluorene motif is highly and timely desirable. In this context, we describe herein our efforts to develop a straightforward and efficient synthesis leading to replacement of 2 phenyl rings by various heterocycles in spiro compounds from 2,2'-dibromobenzophenone. As the same procedure to form fully heterocyclic compounds failed, an original theoretical approach based mainly on the uncommon Fukui dual function was developed in order to determine clearly the limitation of this strategy and provide an efficient predictive tool. Indeed, such calculation allows prediction of the thermodynamic and kinetic aspects of the synthesis of spiro derivatives using a double aromatic electrophilic substitution. If this procedure reproduces well our experimental results focused on (heterocyclic) SBF compounds, it can be certainly adapted and generalized to other intramolecular substitutions.

How predictive could alchemical derivatives be?

The chemical space contains all possible compounds that can be imagined. Its size easily equals the number of fundamental particles in the observable universe. Rational design of compounds aims to find those sectors of the chemical space where compounds optimize a set of desired properties. Then, rational design demands tools to efficiently navigate the chemical space. Ab initio alchemical derivatives offer the possibility to navigate, without empiricism, the energy landscape through alchemical transformations. An alchemical transformation is any process, physical or fictitious, that connects to points in the chemical space. In this work, those transformations are constructed as a perturbative expansion of the energy with respect to perturbations in the stoichiometry. The response functions of that expansion are what is called alchemical derivatives. In this work we assess how effective alchemical derivatives are in predicting energy changes associated to changes in the composition. We do this by including in the expansion, for the first time, electrostatic, polarization and electron-transfer effects. The system we chose is one that challenges alchemical derivatives because none of these effects dominates its behavior. The transmutations studied here correspond to substitutional doping of Al₁₃ with up to four atoms of Si, Al_13-nSi_n. Two types of transformations are considered, those in which the number of electrons remains constant and those in which the number of electrons also changes. It is found that contrary to what has been reported before, polarization cannot be neglected. If polarization is not included, alchemical derivatives fail to predict the change of energy and the relative energy between isomers. For isoelectronic substitution of four or more atoms, the perturbative approach collapses because the strength of the perturbation becomes too strong to guarantee convergence of the series. It is shown, however, that if only one atom is mutated at a time, alchemical derivatives rank pretty well the isomers of Al_13-nSi_n according to their energy. In the case of non-isoelectronic transformations, it is observed that the series rapidly diverges with increasing number of electrons. In this situation, it becomes more important to keep the degree of transmutation of the parent system small.

On-the-Fly Computation of Frontal Orbitals in Density Matrix Expansions

We propose a method for computation of frontal (homo and lumo) orbitals in recursive polynomial expansion algorithms for the density matrix. Such algorithms give a computational cost that increases only linearly with system size for sufficiently sparse systems, but a drawback compared to the traditional diagonalization approach is that molecular orbitals are not readily available. Our method is based on the idea to use the polynomial of the density matrix expansion as an eigenvalue filter giving large separation between eigenvalues around homo and lumo [ Rubensson et al. J. Chem. Phys. 2008 , 128 , 176101 ]. This filter is combined with a shift-and-square (folded spectrum) method to move the desired eigenvalue to the end of the spectrum. In this work we propose a transparent way to select recursive expansion iteration and shift for the eigenvector computation that results in a sharp eigenvalue filter. The filter is obtained as a byproduct of the density matrix expansion, and there is no significant additional cost associated either with its construction or with its application. This gives a clear-cut and efficient eigenvalue solver that can be used to compute homo and lumo orbitals with sufficient accuracy in a small fraction of the total recursive expansion time. Our algorithms make use of recent homo and lumo eigenvalue estimates that can be obtained at negligible cost [ Rubensson et al. SIAM J. Sci. Comput . 2014 , 36 , B147 ]. We illustrate our method by performing self-consistent field calculations for large scale systems.

Theoretical study of the regioselective cyclization of enaminones in the construction of benzofurans and indoles

A theoretical study was undertaken regarding the regioselective Lewis acid-promoted intramolecular cyclization of novel enaminones 1-3 leading to the corresponding benzofurans 4-5 and indoles 6. The density functional theory (DFT) and hard and soft acids and bases (HSAB) principle provided data to describe the electronic effects of the substituents in the reactivity of the benzene ring and the enaminone moiety. The condensed and local Fukui functions for nucleophilic and electrophilic attacks of the reactants accounted for the experimentally observed preference, in regard to precursors 1-3, of the cyclization between the C6' carbon (rather than the C2' carbon) of the benzene ring and the C3 center of the enaminone moiety.

Adsorption and Corrosion Inhibition Studies of Some Selected Dyes as Corrosion Inhibitors for Mild Steel in Acidic Medium: Gravimetric, Electrochemical, Quantum Chemical Studies and Synergistic Effect with Iodide Ions

The corrosion inhibition properties of some organic dyes, namely Sunset Yellow (SS), Amaranth (AM), Allura Red (AR), Tartrazine (TZ) and Fast Green (FG), for mild steel corrosion in 0.5 M HCl solution, were investigated using gravimetric, potentiodynamic polarization techniques and quantum chemical calculations. The results showed that the studied dyes are good corrosion inhibitors with enhanced inhibition efficiencies. The inhibition efficiency of all the studied dyes increases with increase in concentration, and decreases with increase in temperature. The results showed that the inhibition efficiency of the dyes increases in the presence of KI due to synergistic interactions of the dye molecules with iodide (I⁻) ions. Potentiodynamic polarization results revealed that the studied dyes are mixed-type inhibitors both in the absence and presence of KI. The adsorption of the studied dyes on mild steel surface, with and without KI, obeys the Langmuir adsorption isotherm and involves physical adsorption mechanism. Quantum chemical calculations revealed that the most likely sites in the dye molecules for interactions with mild steel are the S, O, and N heteroatoms.

A Novel Schiff Base of 3-acetyl-4-hydroxy-6-methyl-(2H)pyran-2-one and 2,2'-(ethylenedioxy)diethylamine as Potential Corrosion Inhibitor for Mild Steel in Acidic Medium

The corrosion inhibition activity of a newly synthesized Schiff base (SB) from 3-acetyl-4-hydroxy-6-methyl-(2H)-pyran-2-one and 2,2'-(ethylenedioxy)diethylamine was investigated on the corrosion of mild steel in 1 M HCl solution using potentiodynamic polarization and electrochemical impedance spectroscopic techniques. Ultraviolet-visible (UV-vis) and Raman spectroscopic techniques were used to study the chemical interactions between SB and mild steel surface. SB was found to be a relatively good inhibitor of mild steel corrosion in 1 M HCl. The inhibition efficiency increases with increase in concentration of SB. The inhibition activity of SB was ascribed to its adsorption onto mild steel surface, through physisorption and chemisorption, and described by the Langmuir adsorption model. Quantum chemical calculations indicated the presence of atomic sites with potential nucleophilic and electrophilic characteristics with which SB can establish electronic interactions with the charged mild steel surface.

Revisiting electroaccepting and electrodonating powers: proposals for local electrophilicity and local nucleophilicity descriptors

It is shown that the electrophilicity index is also a rational choice for measuring nucleophilicity.