Utility of the Hard/Soft Acid−Base Principle via the Fukui Function in Biological Systems

Conceptual Density Functional Theory and Some Recent Developments

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.

Conceptual density functional theory provides descriptors (such as chemical hardness, the Fukui function, and the dual descriptor) that enable valuable computational insights into the reactivity of battery electrolyte components.

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.

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.

Alternaramide is a cyclic pentadepsipeptide isolated from marine sources that has been shown to present weak antibiotic activity against Bacillus subtilis and Staphylococcus aureus as well as inhibitory effects on inflammatory mediator expressions. Thus, this work reports the results of a computational study of the chemical reactivity and bioactivity properties of this cyclopentadepsipeptide considering a CDFT-based computational peptidology (CDFT-CP) methodology that results from the combination of the chemical reactivity descriptors that arise from conceptual density functional theory (CDFT) together with some cheminformatics tools that can be used to estimate the associated physicochemical parameters, to improve the process of virtual screening through a similarity search, and to identify the ability of the peptide to behave as a potential useful drug, complemented with an analysis of its bioactivity and pharmacokinetics indices related to the ADMET (absorption, distribution, metabolism, excretion, and toxicity) features. The results represent a new confirmation of the superiority of the MN12SX density functional in the fulfilment of the Janak and ionization energy theorems through the proposed KID procedure. This has been useful for the accurate prediction of the CDFT reactivity descriptors that help in understanding the chemical reactivity. The computational pharmacokinetics study revealed the potential ability of alternaramide as a therapeutic drug by interacting with GPCR ligands and protease inhibitors. The ADMET indices confirm this assertion through the absence of toxicity and good absorption and distribution properties.

Probing the Interplay between Electronic and Geometric Degrees-of-Freedom in Molecules and Reactive Systems

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.

Application of the condensed Fukui function to predict reactivity in core–shell transition metal nanoparticles

The chemical reactivity of a set of borophosphines of the general formula R2B-G-PY2, where G is the connector group between the Lewis acidic site, a borane group, and the Lewis basic site, a phosphine fragment, is theoretically investigated through their Lewis acidity and Lewis basicity, as well as the location of the Fukui function and the shape of the molecular electrostatic potential. The role of some global reactivity descriptors, like the vertical ionization potential, I, and the vertical electron affinity, A, is also analyzed in order to gain a deeper insight on the intrinsic chemical reactivity of these borophosphines. We also use the energies involved in the formation of the adducts between the borophosphine and the ions H- and H+ to estimate the Lewis acidity and Lewis basicity, respectively; by their nature, these energies represent local reactivity descriptors. Some of these borophosphines are able to activate the covalent bond in the hydrogen molecule. Possible paths for the hydrogen release reaction from the zwitterion R[Formula: see text]HB-G-PH[Formula: see text] are studied using the mentioned quantities, suggesting that an intramolecular hydride shift mechanism seems to be more favorable than a proton migration process. The acceptor Fukui function f+(r) proved to be useful to identify the acidic molecular sites for the interaction with the hydride ion and the relative stability of the corresponding adducts is related to the relative values of this function.

Structure, spectroscopic analyses (FT-IR and NMR), vibrational study, chemical reactivity and molecular docking study on 3,3'-((4-(trifluoromethyl)phenyl)methylene)bis(2-hydroxynaphthalene-1,4-dione), a promising anticancerous bis-lawsone derivative

BackgroundSince the last COVID-19 outbreak, several approaches have been given a try to quickly tackle this global calamity. One of the well-established strategies is the drug repurposing, which consists in finding new therapeutic uses for approved drugs. Following the same paradigm, we report in the present study, an investigation of the potential inhibitory activity of 5-FU and nineteen of its analogues against the SARS-CoV-2 main protease (3CLpro).Material and MethodsMolecular docking calculations were performed to investigate the binding affinity of the ligands within the active site of 3CLpro. The best binding candidates were further considered for molecular dynamics simulations for 100 ns to gain a time-resolved understanding of the behavior of the guest-host complexes. Furthermore, the profile of druggability of the best binding ligands was assessed based on ADMET predictions. Finally, their chemical reactivity was elucidated using different reactivity descriptors, namely the molecular electrostatic potential (MEP), Fukui functions and frontier molecular orbitals.Results and DiscussionFrom the calculations performed, four candidates (compounds 14, 15, 16 and 18) show promising results with respect to the binding affinity to the target protease, 3CLpro, the therapeutic profile of druggability and safety. These compounds are maintained inside the active site of 3CLpro thanks to a variety of noncovalent interactions, especially hydrogen bonds, involving important amino acids such as GLU166, HIS163, GLY143, ASN142, HIS172, CYS145. Molecular dynamics simulations suggest that the four ligands are well trapped within the active site of the protein over a time gap of 100 ns, ligand 18 being the most retained.ConclusionIn line with the findings reported herein, we recommend that further in-vitro and in-vivo investigations are carried out to shed light on the possible mechanism of pharmacological action of the proposed ligands.

Molecular structure, vibrational spectroscopy (FT-IR, Raman), solvent effects, molecular docking and DFT studies of 1-(4-chlorophenyl)-3-(4-ethoxyphenyl)-prop-2-en-1-one

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.

In the present work we calculated reactivity descriptors for atrazine at MP2/6-311++G(2d,2p)//B3LYP/6-311++G(2d,2p) level in order to analyze its reactivity. Reactivity descriptors such as ioniza- tion energy, molecular hardness, electrophilicity, condensed Fukui function and total energies were determined to identify changes in the reactivity of atrazine in the gas and aqueous phases. The influence of the solvent was taken into account with the PCM model. The values of the reactivity descriptors indicated that the interaction of atrazine with water diminished its reactivity in comparison with the exhibited in gas phase. Also, it was found that the electrophilic and free radical attacks were equivalent and they were located on all the cases in the ethylamine and isopropylamine groups.