Approaching the reactivity of anions in battery electrolytes via conceptual density functional theory

Conceptual Density Functional Theory and Some Recent Developments

The Buckminster fullerene C₆₀ molecule was analyzed from the point of view of global and local reactivity. In particular, the dual descriptor--a local reactivity descriptor derived from conceptual density functional theory--was used to describe local reactivity in this molecule. One of the main advantages of using such a descriptor is the simplicity of obtaining accurate information about the local reactivity required to form covalent bonds without needing to perform calculations at higher levels of theory. The descriptor was adapted to the correct symmetry of this molecule in equilibrium so that the isosurface belongs to the totally symmetrical irreducible representation of the respective group of symmetry. Unlike global and some other local reactivity descriptors, correlation effects and basis sets are not critically important when using the dual descriptor because local reactivity is conserved at a qualitative level.

The oxygen-evolving complex (OEC) of Photosystem II catalyzes the water-splitting reaction using solar energy. Thus, understanding the reaction mechanism will inspire the design of biomimetic artificial catalysts that convert solar energy to chemical energy. Conceptual Density Functional Theory (CDFT) focuses on understanding the reactivity of molecules and the atomic contribution to the overall nucleophilicity and electrophilicity of the molecule using quantum descriptors. However, this method has not been applied to the OEC before. Here, we use Fukui functions and the dual descriptor to provide quantitative measures of the nucleophilicity and electrophilicity of oxygens in the OEC for different models in different S states. Our results show that the μ-oxo bridges connected to terminal Mn4 are nucleophilic, and those in the cube formed by Mn1, Mn2, and Mn3 are mostly electrophilic. The dual descriptors of the bridging oxygens in the OEC showed a similar reactivity to that of bridging oxygens in Mn model compounds. However, the terminal water W1, which is bound to Mn4, showed very strong reactivity in some of the S3 models. Thus, our calculations support the model that proposes the formation of the O2 molecule through nucleophilic attack by a terminal water.

We extend the framework of conceptual density functional theory (DFT) to include fourth-order energy derivatives. We present the series of quantum reactivity descriptors at this order for the canonical and the grand canonical ensembles. After introducing a direct computational methodology, we investigate and describe the quartic curvature λ and the third-order Fukui function f(3)(r). These higher-order descriptors capture nonlinear aspects of electronic reactivity that go beyond the conventional concepts of chemical potential, hardness, or Fukui functions. The global descriptor λ, obtained via finite-difference approximations of frontier orbital energies, quantifies the curvature of the chemical hardness and offers insight into the electronic (in)stability of molecular systems under charge perturbations. The local descriptor f(3)(r), derived as the third-order response of the electron density, reveals spatially resolved regions of charge-transfer sensitivity. We apply these descriptors to a series of push-pull organic molecules and open-shell systems, demonstrating their ability to highlight differences in internal charge transfer character and electronic delocalization. The results support the use of fourth-order conceptual DFT tools as chemically meaningful indicators of reactivity beyond the harmonic regime.

The chemical hardness concept and its realization within the conceptual density functional theory is approached with innovative perspectives, such as the electronegativity and hardness equalization of atoms in molecules connected with the softness kernel, in order to examine the structure-reactivity equalization ansatz between the electronic sharing index and the charge transfer either in the additive or geometrical mean picture of bonding. On the other hand, the maximum hardness principle presents a relation with the chemical stability of the hardness concept. In light of the inverse relation between hardness and polarizability, the minimum polarizability principle has been proposed. Additionally, this review includes important applications of the chemical hardness concept to solid-state chemistry. The mentioned applications support the validity of the electronic structure principles regarding chemical hardness and polarizability in solid-state chemistry.

Many useful concepts developed within density functional theory provide much insight for the understanding and prediction of chemical reactivity, one of the main aims in the field of conceptual density functional theory. While approximate evaluations of such concepts exist, the analytical and efficient evaluation is, however, challenging, because such concepts are usually expressed in terms of functional derivatives with respect to the electron density, or partial derivatives with respect to the number of electrons, complicating the connection to the computational variables of the Kohn-Sham one-electron orbitals. Only recently, the analytical expressions for the chemical potential, one of the key concepts, have been derived by Cohen, Mori-Sánchez, and Yang, based on the potential functional theory formalism. In the present work, we obtain the analytical expressions for the real-space linear response function using the coupled perturbed Kohn-Sham and generalized Kohn-Sham equations, and the Fukui functions using the previous analytical expressions for chemical potentials of Cohen, Mori-Sánchez, and Yang. The analytical expressions are exact within the given exchange-correlation functional. They are applicable to all commonly used approximate functionals, such as local density approximation (LDA), generalized gradient approximation (GGA), and hybrid functionals. The analytical expressions obtained here for Fukui function and linear response functions, along with that for the chemical potential by Cohen, Mori-Sánchez, and Yang, provide the rigorous and efficient evaluation of the key quantities in conceptual density functional theory within the computational framework of the Kohn-Sham and generalized Kohn-Sham approaches. Furthermore, the obtained analytical expressions for Fukui functions, in conjunction with the linearity condition of the ground state energy as a function of the fractional charges, also lead to new local conditions on the exact functionals, expressed in terms of the second-order functional derivatives. We implemented the expressions and demonstrate the efficacy with some atomic and molecular calculations, highlighting the importance of relaxation effects.

The regioselectivity of the 1,3-dipolar cycloaddition of a model nitrone with a set of dipolarophiles, presenting diverse electronic effects, is analyzed using conceptual density functional theory (DFT) methods. We deviate from standard approaches based on frontier molecular orbitals and formulations of the local hard/soft acid/base principle and use instead the dual descriptor. A detailed analysis is carried out to determine the influence of the way to calculate the dual descriptor, the computational procedure, basis set and choice of method to condensate the values of this descriptor. We show that the qualitative regioselectivity predictions depend on the choice of "computational conditions", something that indicates the danger of using black-box computational set-ups in conceptual DFT studies.

The hard/soft acid-base principle has long been known to be an excellent predictor of chemical reactivity. The Fukui function, a reactivity descriptor from conceptual density functional theory, has been shown to be related to the local softness of a system. The usefulness of the Fukui function is explored and demonstrated herein for three common biological problems: ligand docking, active site detection, and protein folding. In each type of study, a scoring function is developed based on the local HSAB principle using atomic Fukui indices. Even with necessary approximations for its use in large systems, the Fukui function remains a useful descriptor for predicting chemical reactivity and understanding chemical systems.

In this study, we address the long-standingissue—arisingprominently from conceptual density functional theory (CDFT)—ofthe relative importance of electrostatic, i.e., “hard–hard”,versus spin-pairing, i.e., “soft–soft”, interactionsin determining regiochemical preferences. We do so from a valencebond (VB) perspective and demonstrate that VB theory readily enablesa clear-cut resolution of both of these contributions to the bondformation/breaking process. Our calculations indicate that appropriatelocal reactivity descriptors can be used to gauge the magnitude ofboth interactions individually, e.g., Fukui functions or HOMO/LUMOorbitals for the spin-pairing/(frontier) orbital interactions andmolecular electrostatic potentials (and/or partial charges) for theelectrostatic interactions. In contrast to previous reports, we findthat protonation reactions cannot generally be classified as eithercharge- or frontier orbital-controlled; instead, our results indicatethat these two bonding contributions generally interplay in more subtlepatterns, only giving the impression of a clear-cut dichotomy. Finally,we demonstrate that important covalent, i.e., spin pairing, reactivitymodes can be missed when only a single spin-pairing/orbital interactiondescriptor is considered. This study constitutes an important stepin the unification of CDFT and VB theory.

Highly Hazardous Pesticides (HHPs) pose severe risks to human health and the environment, making it essential to understand their molecular stability and degradation pathways. In this study, the Quantum Theory of Atoms in Molecules (QTAIM) was applied to four representative organophosphate pesticides, allowing the identification of electronically weak bonds as intrinsic sites of lability. These findings are consistent with reported hydrolytic, oxidative, enzymatic, and microbial degradation routes. Importantly, QTAIM descriptors proved largely insensitive to solvation, confirming their intrinsic character within the molecular electronic structure. To complement QTAIM, conceptual DFT (Density Functional Theory) reactivity indices were analyzed, revealing that solvent effects induce more noticeable variations in global and local descriptors than in topological parameters. In addition, a Topological Analysis of the Fukui Function (TAFF) was performed, which mapped nucleophilic, electrophilic, and radical susceptibilities directly onto QTAIM basins. The TAFF analysis confirmed that bonds identified as weak by QTAIM (notably P–O, P–S, and P–N linkages) also coincide with the most reactive sites, thereby reinforcing their mechanistic role in degradation pathways. This integrated framework highlights the robustness of QTAIM, the sensitivity of global and local reactivity descriptors to solvation revealed by conceptual DFT, and the complementary insights provided by TAFF, contributing to risk assessment, remediation strategies, and the rational design of safer pesticides.

Objective: It is known that the electronegativities of functional groups can be significantly to used predict the reaction mechanisms and to explain inductive effects of chemical compounds. Method: Bratsch equation is one of the most important equations used to calculate the electronegativities of functional groups. Conclusion: In the present study, some important comments and contributions related to Bratsch's group electronegativity equation are presented. In addition, it is proposed that absolute electronegativity should be considered in comparison of inductive effects of functional groups. Keywords: Bratsch equation, chemical hardness, conceptual density functional theory, electronegativity, group electronegativity, sanderson's electronegativity equalization principle.

Metal hexafluorides hydrolyze at ambient temperature to deposit compounds having fluorine-to-oxygen ratios that depend upon the identity of the metal. Uranium-hexafluoride hydrolysis, for example, deposits uranyl fluoride (UO2F2), whereas molybdenum hexafluoride (MoF6) and tungsten hexafluoride deposit trioxides. Here, we pursue general strategies enabling the prediction of depositing compounds resulting from multi-step gas-phase reactions. To compare among the three metal-hexafluoride hydrolyses, we first investigate the mechanism of MoF6 hydrolysis using hybrid density functional theory (DFT). Intermediates are then validated by performing anharmonic vibrational simulations and comparing with infrared spectra [McNamara et al., Phys. Chem. Chem. Phys. 25, 2990 (2023)]. Conceptual DFT, which is leveraged here to quantitatively evaluate site-specific electrophilicity and nucleophilicity metrics, is found to reliably predict qualitative deposition propensities for each intermediate. In addition to the nucleophilic potential of the oxygen ligands, several other contributing characteristics are discussed, including amphoterism, polyvalency, fluxionality, steric hindrance, dipolar strength, and solubility. To investigate the structure and composition of pre-nucleation clusters, an automated workflow is presented for the simulation of particle growth. The workflow entails a conformer search at the density functional tight-binding level, structural refinement at the hybrid DFT level, and computation of a composite free-energy profile. Such profiles can be used to estimate particle nucleation kinetics. Droplet formation is also considered, which helps to rationalize the different UO2F2 particle morphologies observed under varying levels of humidity. Development of predictive methods for simulating physical and chemical deposition processes is important for the advancement of material manufacturing involving coatings and thin films.

Conceptual Density Functional Theory

Review for "Temperature and External Fields 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.