Should negative electron affinities be used for evaluating the chemical hardness?

Spin-Polarized Conceptual Density Functional Theory from the Convex Hull

We present a new, nonarbitrary, internally consistent, and unambiguous framework for spin-polarized conceptual density-functional theory (SP-DFT). We explicitly characterize the convex hull of energy, as a function of the number of electrons and their spin, as the only accessible ground states in spin-polarized density functional theory. Then, we construct continuous linear and quadratic models for the energy. The nondifferentiable linear model exactly captures the simplicial geometry of the complex hull about the point of interest and gives exact representations for the conceptual DFT reactivity indicators. The continuous quadratic energy model is the paraboloid of maximum curvature, which most tightly encloses the point of interest and neighboring vertices. The quadratic model is invariant to the choice of coordinate system (i.e., {N, S} vs {Nα, Nβ}) and reduces to a sensible formulation of spin-free conceptual DFT in the appropriate limit. Using the quadratic model, we generalize the Parr functions {P+(r), P-(r)} (and their derivatives with respect to number of electrons) to this new spin-polarized framework, integrating the Parr function concept into the context of (spin-polarized) conceptual DFT, and extending it to include higher-order effects.

In silico evaluation of new mangiferin-based Positron Emission Tomography radiopharmaceuticals through the inhibition of metalloproteinase-9

Metalloproteinase-9 (MMP-9) is a key protein in cancer advancement and metastasis owing to its ability to degrade some extracellular matrix components. Mangiferin, a natural polyphenolic compound, has demonstrated through experimental and theoretical studies to be a great anticancer agent for the selective inhibition of MMP-9. This work aimed to evaluate the utility of several fluorinated compounds obtained from MF as possible Positron Emission Tomography (PET) radiopharmaceuticals oriented to MMP-9. Density Functional Theory calculations of MF were made to obtain the most active sites toward electrophilic and nucleophilic reactions and propose a synthetic route to produce its fluorinated derivatives. The reactivity study allowed us to propose a late-stage synthetic route based on click chemistry to obtain three fluorinated MF-based derivatives. Molecular docking calculations suggested that the derivative F-propyl-MF could be suitable as PET radiopharmaceutical owing to the establishment of a five-coordinated complex with the catalytic Zn atom belonging to the active site of MMP-9, crucial factor in the inhibition of MMP-9.

External fields in conceptual density functional theory

The necessity of the recent incorporation of new external variables in the context of conceptual DFT (CDFT) is discussed based on the ever-increasing portfolio of experimental reaction conditions in the endeavor of experimentalists to synthesize new molecules with unprecedented properties. Electric and magnetic fields (ε and B), mechanical forces (F), and confinement are proposed as valuable new variables, extending conventional CDFT and its associated response functions. A finite field approach is used to calculate the evolution of both global and local descriptors in a selected series of atomic and molecular applications, and from it derive new response function involving, with one exception, the first derivative to the field considered. The electric field results, displaying, for example, a case of a field-induced enantioselectivity in the Fukui function, may be instrumental in the recent upsurge of chemistry in oriented external electric fields. The study of atomic electronegativity and hardness in magnetic fields displays a piecewise behavior, associated to configurational jumps upon increasing field strength and reveals an overall compression of their ranges for stronger fields, which may be guiding upon investigating chemistry in extremely high fields like in white dwarfs. The evolution of the electronegativity and hardness of diatomics under mechanical force can elegantly be traced back to differences in their equilibrium distance in the neutral, cationic, and anionic state. The well-known reduction of the polarizability under confinement can be seen as a fore-runner of the increasing hardness of atoms under pressure, presently under investigation. Periodicity showing up in a spontaneous way in the variety of properties is a leitmotiv in this study, as well as the interconnections/analogies between the different response functions.

Wearable Light Sensors Based on Unique Features of a Natural Biochrome

Overexposure to complete solar radiation (combined ultraviolet, visible, and infrared) is correlated with several harmful biological consequences including hyperpigmentation, skin cancer, eye damage, and immune suppression. With limited effective therapeutic options available for these conditions, significant efforts have been directed toward promoting preventative habits. Recently, wearable solar radiometers have emerged as practical tools for managing personal exposure to sunlight. However, designing simple and inexpensive sensors that can measure energy across multiple spectral regions without incorporating electronic components remains challenging, largely due to inherent spectral limitations of photoresponsive indicators. In this work, we report the design, fabrication, and characterization of wearable radiation sensors that leverage an unexpected feature of a natural biochrome, xanthommatin-its innate sensitivity to both ultraviolet and visible through near-infrared radiation. We found that xanthommatin-based sensors undergo a visible shift from yellow to red in the presence of complete sunlight. This color change is driven by intrinsic photoreduction of the molecule, which we investigated using computational modeling and supplemented by radiation-driven formation of complementary reducing agents. These sensors are responsive to dermatologically relevant doses of erythemally weighted radiation, as well as cumulative doses of high-energy ultraviolet radiation used for germicidal sterilization. We incorporated these miniature sensors into pressure-activated microfluidic systems to illustrate on-demand activation of a wearable and mountable form factor. When taken together, our findings encompass an important advancement toward accessible, quantitative measurements of UVC and complete solar radiation for a variety of use cases.

Extending conceptual DFT to include external variables: the influence of magnetic fields

An extension of conceptual DFT to include the influence of an external magnetic field is proposed in the context of a program set up to cope with the ever increasing variability of reaction conditions and concomitant reactivity.

In silico development of new PET radiopharmaceuticals from mTOR inhibitors

Rapamycin (or sirolimus) is a macrolide that has shown to be useful as an immunosuppressant and that was studied in metabolic, neurological, or genetic disorders. Rapamycin is a specific natural inhibitor of the mechanistic target of rapamycin (mTOR) that is a kinase protein playing a pivotal role in cell growth and proliferation by activation of several metabolic processes. This work aimed to evaluate the utility of several compounds obtained from rapamycin and its semi-synthetic analogs everolimus and temsirolimus as possible radiopharmaceuticals oriented to this protein. Density Functional Theory calculations of these molecules were made and further analysis of the dual descriptor, charges populations, and of the electrostatic potential surfaces were performed. Molecular docking simulations were used to evaluate the interactions of the rapamycin with the studied candidates. They allowed us to propose two strategies for the synthesis of novel compounds based on electrophilic reactions. Molecular docking results also helped us to eliminate molecules that did not interact correctly with the target. Finally, we found for the first time, that the novel compounds synthesized through the electrophilic addition reaction that employed ¹⁸F-selectfluor, should maintain the biological activity of original compounds and could be suitable as Positron Emission Tomography radiopharmaceuticals targeting mTOR Complex1 system.

Using Fundamental Material Properties to Predict the Moisture Susceptibility of the Asphalt Binder: Polarizability and a Moisture-Induced Shear-Thinning Index

Many biomodifiers have recently been introduced to the asphalt industry to improve the performance of asphalt mixtures, rejuvenate aged asphalt, and/or partially replace asphalt binder. It is critical to screen these biomodifiers for their susceptibility to moisture damage before they are used in construction. This study develops a computational approach and a laboratory technique to predict the moisture susceptibility of modifiers used in asphalt binder mixtures. The computational approach uses the "polarizability" factor, which is one of the conceptual descriptors in density functional theory. Polarizability is indicative of the formation of instantaneous dipoles that are oriented in the applied field. A lower polarizability indicates a lower propensity of the chemical species to interact with other species in their chemical environment. The laboratory method defines a moisture-induced shear-thinning index. Moisture-induced shear-thinning measures the loss of interfacial bonds between the asphalt binder and siliceous surfaces due to water exposure. Both proposed indicators are used to evaluate and compare biomodifiers from four sources: waste vegetable oil, swine manure, algae, and a co-liquefied blend of swine manure and algae. In a comparative study, waste vegetable oil with a high content of long-chain alkanes and fatty acids showed the highest polarizability and the highest moisture-induced shear-thinning index, indicating the highest susceptibility to moisture damage. In contrast, the chemical composition of the biomodifier produced from the co-liquefaction of swine manure and algae showed the lowest polarizability and the lowest moisture-induced shear-thinning index, indicating the highest resistance to moisture damage.

Alkaline Earth Metals Activate N2 and CO in Cubic Complexes Just Like Transition Metals: A Conceptual Density Functional Theory and Energy Decomposition Analysis Study

Following the recent discovery of stable octa-coordinated alkaline earth metals with N2 and CO, the role of group II metals in the catalytic reduction of these ligands by means of density functional theory (DFT) calculations and conceptual DFT-based reactivity indices is investigated. Cubic group IV and octahedral group VI transition metal complexes as well as the free ligands are computed for reference. The outer and most accessible atoms of N2 and CO become much more nucleophilic and electrophilic in all complexes, relevant for N2 fixation, as probed by the Fukui function and local softness. Within one row of the periodic table, the alkaline earth complexes often show the strongest activation. On the contrary, the electrostatic character is found to be virtually unaffected by complexation. Trends in the soft frontier orbital and hard electrostatic character are in agreement with calculated proton affinities and energy decomposition analyses of the protonated structures, demonstrating the dominance of the soft (HOMO-LUMO) orbital interactions.

Negative Electron Affinities and Derivative Discontinuity Contribution from a Generalized Gradient Approximation Exchange Functional

Two methods to calculate negative electron affinities systematically from ground-state density functional methods are presented. One makes use of the lowest unoccupied molecular orbital energy shift provided by approximate inclusion of derivative discontinuity in the nearly correct asymptotic potential (NCAP) nonempirical, constraint-based generalized gradient approximation exchange functional. The other uses a second-order perturbation calculation of the derivative discontinuity based on the NCAP exchange-correlation potential. On a set of thirty-eight molecules, NCAP leads to a rather accurate description that is improved further through the perturbation correction. The results presented show the importance of the asymptotic behavior of the exchange-correlation potential in the calculation of negative electron affinities as well as demonstrating the versatility of the NCAP functional.

The Reactivity of Ambident Nucleophiles: Marcus Theory or Hard and Soft Acids and Bases Principle?

The model reactions CH₃ X + (NH-CH=O)M ➔ CH₃ -NH-NH═O or NH═CH-O-CH₃  + MX (M = none, Li, Na, K, Ag, Cu; X = F, Cl, Br) are investigated to demonstrate the feasibility of Marcus theory and the hard and soft acids and bases (HSAB) principle in predicting the reactivity of ambident nucleophiles. The delocalization indices (DI) are defined in the framework of the quantum theory of atoms in molecules (QT-AIM), and are used as the scale of softness in the HSAB principle. To react with the ambident nucleophile NH═CH-O^- , the carbocation H₃ C⁺ from CH₃ X (F, Cl, Br) is actually a borderline acid according to the DI values of the forming C…N and C…O bonds in the transition states (between 0.25 and 0.49), while the counter ions are divided into three groups according to the DI values of weak interactions involving M (M…X, M…N, and M…O): group I (M = none, and Me₄ N) basically show zero DI values; group II species (M = Li, Na, and K) have noticeable DI values but the magnitudes are usually less than 0.15; and group III species (M = Ag and Cu(I)) have significant DI values (0.30-0.61). On a relative basis, H₃ C⁺ is a soft acid with respect to group I and group II counter ions, and a hard acid with respect to group III counter ions. Therefore, N-regioselectivity is found in the presence of group I and group II counter ions (M = Me₄ N, Li, Na, K), while O-regioselectivity is observed in the presence of the group III counter ions (M = Ag, and Cu(I)). The hardness of atoms, groups, and molecules is also calculated with new functions that depend on ionization potential (I) and electron affinity (A) and use the atomic charges obtained from localization indices (LI), so that the regioselectivity is explained by the atomic hardness of reactive nitrogen atoms in the transition states according to the maximum hardness principle (MHP). The exact Marcus equation is derived from the simple harmonic potential energy parabola, so that the concepts of activation free energy, intrinsic activation barrier, and reaction energy are completely connected. The required intrinsic activation barriers can be either estimated from ab initio calculations on reactant, transition state, and product of the model reactions, or calculated from identity reactions. The counter ions stabilize the reactant through bridging N- and O-site of reactant of identity reactions, so that the intrinsic barriers for the salts are higher than those for free ambident anions, which is explained by the increased reorganization parameter Δr. The proper application of Marcus theory should quantitatively consider all three terms of Marcus equation, and reliably represent the results with potential energy parabolas for reactants and all products. For the model reactions, both Marcus theory and HSAB principle/MHP principle predict the N-regioselectivity when M = none, Me₄ N, Li, Na, K, and the O-regioselectivity when M = Ag and Cu(I). © 2019 Wiley Periodicals, Inc.

Atomic/Ionic Radius as Mathematical Limit of System Energy Evolution

The classical, in its nature, concept of atomic or ionic radii, although profitable in many fields, is represented by an ambiguous choice of formulations. In this work, we propose a definition of atomic and ionic radii rooted in chemical principles and conceptual density functional theories. The estimation based on electron density fundamental response functions has been successfully tested. The generalized approach has been shown to be applicable to atoms in any oxidation state. The radii display good correlation with classical estimates, such as Shannon. The atomic and ionic radii obtained according to this scheme are directly comparable between different elements, without any adjustment procedures requiring fitting constants. The definition also has a clear physical interpretation, which supports understanding of size-related phenomena and trends.

Implementing the mechanical force into the conceptual DFT framework: understanding and predicting molecular mechanochemical properties

Studying mechanochemical properties through the implementation of the mechanical force into the conceptual DFT framework (E = E[N,v,F_ext]).

Exploring chemical space with alchemical derivatives: alchemical transformations of H through Ar and their ions as a proof of concept

Alchemical derivatives have been used previously to obtain information about transformations in which the number of electrons is unchanged. Here an approach for combining changes in both the number of electrons and the nuclear charge is presented.

Evaluation of the molecular inclusion process of β-hexachlorocyclohexane in cyclodextrins

The present work aimed to study the guest–host complexes of β-hexachlorocyclohexane (β-HCH), a pesticide with high environmental stability that can cause severe health problems, with the most common cyclodextrins (α-, β-, and γ-CDs). The formation reactions of these molecular inclusion complexes were addressed in this research. The multiple minima hypersurface methodology, quantum calculations based on density functional theory and a topological exploration of the electron density based on the quantum theory of atoms in molecules approach were used to characterize the interaction spaces of the pollutant with the three CDs. Additionally, charge distribution, charge transfer and dual descriptor analyses were employed to elucidate the driving forces involved in the formation of these molecular inclusion complexes. Three types of fundamental interactions were observed: total occlusion, partial occlusion and external interaction (non-occlusion). Finally, experiments were performed to confirm the formation of the studied complexes. The most stable complexes were obtained when γ-CD was the host molecule. The interactions between the pesticide and CDs have fundamentally dispersive natures, as was confirmed experimentally by spectroscopic results. All the obtained results suggest the possibility of using CDs for the purification and treatment of water polluted with β-HCH.

The present work aimed to study the guest–host complexes of β-hexachlorocyclohexane (β-HCH), a pesticide with high environmental stability that can cause severe health problems, with the most common cyclodextrins (α-, β-, and γ-CDs).

Benchmark values of chemical potential and chemical hardness for atoms and atomic ions (including unstable anions) from the energies of isoelectronic series

We present benchmark values for the electronic chemical potential and chemical hardness from reference data for ionization potentials and electron affinities. In cases where the energies needed to compute these quantities are not available, we estimate the ionization potential of the metastable (di)anions by extrapolation along the isoelectronic series, taking care to ensure that the extrapolated data satisfy reasonable intuitive rules to the maximum possible extent. We also propose suitable values for the chemical potential and chemical hardness of zero-electron species. Because the values we report are faithful to the trends in accurate data on atomic energies, we believe that our proposed values for the chemical potential and chemical hardness are ideally suited to conceptual studies of chemical trends across the periodic table. The critical nuclear charge (Z critical) of the isoelectronic series with 2 < N < 96 has also been reported for the first time.

On understanding the chemical origin of band gaps

Conceptual DFT and quantum chemical topology provide two different approaches based on the electron density to grasp chemical concepts. We present a model merging both approaches, in order to obtain physical properties from chemically meaningful fragments (bonds, lone pairs) in the solid. One way to do so is to use an energetic model that includes chemical quantities explicitly, so that the properties provided by conceptual DFT are directly related to the inherent organization of electrons within the regions provided by topological analysis. An example of such energy model is the bond charge model (BCM) by Parr and collaborators. Bonds within an ELF-BCM coupled approach present very stable chemical features, with a bond length of ca. 1 Å and 2[Formula: see text]. Whereas the 2[Formula: see text] corroborate classical views of chemical bonding, the fact that bonds always expand along 1 Å introduces the concept of geometrical transferability and enables estimating crystalline cell parameters. Moreover, combining these results with conceptual DFT enables deriving a model for the band gap where the chemical hardness of a solid is given by the bond properties, charge, length, and a Madelung factor, where the latter plays the major role. In short, the fundamental gap of zinc-blende solids can be understood as given by a 2[Formula: see text] bond particle asymmetrically located on a 1 Å length box and electrostatically interacting with other bonds and with a core matrix. This description is able to provide semi-quantitative insight into the band gap of zinc-blende semiconductors and insulators on equal footing, as well as a relationship between band gap and compressibility. In other words, merging these different approaches to bonding enables to connect measurable macroscopic behavior with microscopic electronic structure properties and to obtain microscopic insight into the chemical origin of band gaps, whose prediction is still nowadays a difficult task. Graphical Abstract Conceptual DFT couples to quatum chemcial topology to explain the band gap of zinc-blende solids.

Structure, fragmentation patterns, and magnetic properties of small nickel oxide clusters

We report a comprehensive theoretical study of the structural and electronic properties of neutral and charged nickel oxide clusters, Ni_nO_m^0/± (n = 3–8 and m = 1–10), in the context of recent experiments of photodissociation and Ion Mobility Mass Spectrometry.

Electronegativity and redox reactions

Using the maximum hardness principle, we show that the oxidation potential of a molecule increases as its electronegativity increases and also increases as its electronegativity in its oxidized state increases.

Atomic electron affinities and the role of symmetry between electron addition and subtraction in a corrected Koopmans approach

The essential aspects of zero-temperature grand-canonical ensemble density-functional theory are reviewed in the context of spin-density-functional theory and are used to highlight the assumption of symmetry between electron addition and subtraction that underlies the corrected Koopmans approach of Tozer and De Proft (TDP) for computing electron affinities. The issue of symmetry is then investigated in a systematic study of atomic electron affinities, comparing TDP affinities with those from a conventional Koopmans evaluation and electronic energy differences. Although it cannot compete with affinities determined from energy differences, the TDP expression yields results that are a significant improvement over those from the conventional Koopmans expression. Key insight into the results from both expressions is provided by an analysis of plots of the electronic energy as a function of the number of electrons, which highlight the extent of symmetry between addition and subtraction. The accuracy of the TDP affinities is closely related to the nature of the orbitals involved in the electron addition and subtraction, being particularly poor in cases where there is a change in principal quantum number, but relatively accurate within a single manifold of orbitals. The analysis is then extended to a consideration of the ground state Mulliken electronegativity and chemical hardness. The findings further emphasize the key role of symmetry in determining the quality of the results.

Symmetry laws improve electronegativity equalization by orders of magnitude and call for a paradigm shift in conceptual density functional theory

The strict Wigner-Witmer symmetry constraints on chemical bonding are shown to determine the accuracy of electronegativity equalization (ENE) to a high degree. Bonding models employing the electronic chemical potential, μ, as the negative of the ground-state electronegativity, χ(GS), frequently collide with the Wigner-Witmer laws in molecule formation. The violations are presented as the root of the substantially disturbing lack of chemical potential equalization (CPE) in diatomic molecules. For the operational chemical potential, μ(op), the relative deviations from CPE fall between -31% ≤ δμ(op) ≤ +70%. Conceptual density functional theory (cDFT) cannot claim to have operationally (not to mention, rigorously) proven and unified the CPE and ENE principles. The solution to this limitation of cDFT and the symmetry violations is found in substituting μ(op) (i) by Mulliken's valence-state electronegativity, χ(M), for atoms and (ii) its new generalization, the valence-pair-affinity, α(VP), for diatomic molecules. Mulliken's χ(M) is equalized into the α(VP) of the bond, and the accuracy of ENE is orders of magnitude better than that of CPE using μ(op). A paradigm shift replacing the dominance of ground states by emphasizing valence states seems to be in order for conceptual DFT.

An information-theoretic resolution of the ambiguity in the local hardness

A definition of the local hardness, suitable for application in the local hard/soft acid/base principle, is derived by applying information theory.