Modeling Molecular Acidity with Electronic Properties and Hammett Constants for Substituted Benzoic Acids

Simultaneous identification of strong and weak interactions with Pauli energy, Pauli potential, Pauli force, and Pauli charge

Strong and weak interatomic interactions in chemical and biological systems are ubiquitous, yet how to identify them on a unified theoretical foundation is still not well established. Recently, we proposed employing Pauli energy-based indexes, such as strong covalent interaction and bonding and noncovalent interaction indexes, in the framework of density functional theory for the purpose. In this work, we extend our previous theoretical work by directly employing Pauli energy, Pauli potential, Pauli force, and Pauli charge to simultaneously identify both strong covalent bonding and weak noncovalent interactions. Our results from this work elucidate that using their signature isosurfaces, we can identify different types of interactions, either strong or weak, including single, double, triple, and quadruple covalent bonds, ionic bond, metallic bond, hydrogen bonding, and van der Waals interaction. We also discovered strong linear correlations between Pauli energy derived quantities and different covalent bond orders. These qualitative and quantitative results from our present study solidify the viewpoint that a unified approach to simultaneously identify both strong and weak interactions is possible. In our view, this work signifies one step forward towards the goal of establishing a density-based theory of chemical reactivity in density functional theory.

Directionality and additivity effects of molecular acidity and aromaticity for substituted benzoic acids under external electric fields

Our recent study [M. Li et al.Phys. Chem. Chem. Phys., 2023, 25, 2595-2605] unveiled that the impact of an external electric field on molecular acidity and aromaticity for benzoic acid is directional, which can be understood using changes in frontier orbitals and partial charges. However, it is unclear if the effect will disappear when substituting groups are present and whether new patterns of changes will show up. In this work, as a continuation of our efforts to appreciate the impact of external electric fields on physiochemical properties, we find that the directionality effect is still in place for substituted benzoic acid derivatives and that there exists the additivity effect with respect to the number of substituent groups, regardless of the direction of the applied field and the type of substituting groups. We confirm the findings using electron-donating and electron-accepting groups with the electric field applied either parallelly or perpendicularly to the carboxyl group along the benzene ring. The directionality and additivity effects uncovered from this work should enrich the body of our knowledge about the impact of external electric fields on physiochemical properties and could be applicable to other systems and properties as well.

Topological analysis of information-theoretic quantities in density functional theory

We have witnessed considerable research interest in the recent literature about the development and applications of quantities from the information-theoretic approach (ITA) in density functional theory. These ITA quantities are explicit density functionals, whose local distributions in real space are continuous and well-behaved. In this work, we further develop ITA by systematically analyzing the topological behavior of its four representative quantities, Shannon entropy, two forms of Fisher information, and relative Shannon entropy (also called information gain or Kullback-Leibler divergence). Our results from their topological analyses for 103 molecular systems provide new insights into bonding interactions and physiochemical properties, such as electrophilicity, nucleophilicity, acidity, and aromaticity. We also compare our results with those from the electron density, electron localization function, localized orbital locator, and Laplacian functions. Our results offer a new methodological approach and practical tool for applications that are especially promising for elucidating chemical bonding and reactivity propensity.

Discovery of potent Plasmodium falciparum protein kinase 6 (PfPK6) inhibitors with a type II inhibitor pharmacophore

Malaria is a devastating disease that causes significant global morbidity and mortality. The rise of drug resistance against artemisinin-based combination therapy demonstrates the necessity to develop alternative antimalarials with novel mechanisms of action. We report the discovery of Ki8751 as an inhibitor of essential kinase PfPK6. 79 derivatives were designed, synthesized and evaluated for PfPK6 inhibition and antiplasmodial activity. Using group efficiency analyses, we established the importance of key groups on the scaffold consistent with a type II inhibitor pharmacophore. We highlight modifications on the tail group that contribute to antiplasmodial activity, cumulating in the discovery of compound 67, a PfPK6 inhibitor (IC50 = 13 nM) active against the P. falciparum blood stage (EC50 = 160 nM), and compound 79, a PfPK6 inhibitor (IC50 < 5 nM) with dual-stage antiplasmodial activity against P. falciparum blood stage (EC50 = 39 nM) and against P. berghei liver stage (EC50 = 220 nM).

Impacts of external fields on aromaticity and acidity of benzoic acid: a density functional theory, conceptual density functional theory and information-theoretic approach study

The impact of external fields on the molecular structure and reactivity properties has been of considerable interest in the recent literature. Benzoic acid as one of the most widely used compounds in medicinal and materials sciences is known for its dual propensity in aromaticity and acidity. In this work, we systematically investigate the impact of a uniform external electric field on these properties. We apply density functional theory, conceptual density functional theory, and an information-theoretic approach to appreciate the change pattern of aromaticity and acidity properties in external fields with different strengths. Our results show that they possess different change patterns under external fields, which can be satisfactorily rationalized by variations in reactivity descriptors and partial charges. The surprising yet novel results from this study should enrich the body of our knowledge about the impact of external fields for different kinds of electronic properties and provide guidance and foundation for future studies of this phenomenon in other molecular systems.

Machine learning methods for pKa prediction of small molecules: Advances and challenges

The acid-base dissociation constant (pK_a) is a fundamental property influencing many ADMET properties of small molecules. However, rapid and accurate pK_a prediction remains a great challenge. In this review, we outline the current advances in machine-learning-based QSAR models for pK_a prediction, including descriptor-based and graph-based approaches, and summarize their pros and cons. Moreover, we highlight the current challenges and future directions regarding experimental data, crucial factors influencing pK_a and in silico prediction tools. We hope that this review can provide a practical guidance for the follow-up studies.

Quantifications and Applications of Relative Fisher Information in Density Functional Theory

Though density functional theory is widely accepted as one of the most successful developments in theoretical chemistry in the past few decades, the knowledge of how to apply this new electronic structure theory, to help us better understand chemical processes and transformations, is still an unaccomplished task. The information-theoretic approach is emerging as a viable option for that purpose in the recent literature, providing new insights about steric effect, cooperativity, electrophilicity, nucleophilicity, stereoselectivity, homochirality, etc. In this work, based on the result from a recent paper by one of us [ J. Chem. Phys, 2019, 151, 141103], we present two quantifications of the relative Fisher information and discuss their physiochemical properties and possible applications. To that end, their analytical properties have been elucidated. They have also been applied to six categories of systems to illustrate their applicability. A better descriptor to quantify the single bond rotation barrier has been obtained. The relative Fisher information can also simultaneously determine electrophilicity and nucleophilicity, and effectively describe helical structures with different homochiral and heterochiral propensities. As integral parts of the information-theoretic approach, these newly introduced quantities will provide us with more analytical tools toward the long-term goal of crafting a chemical reactivity theory in the density-based language.

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.

Reactivity Parameters and Substitution Effect in Organic Acids

We investigate a few density functional theory-based reactivity indices of chemistry, with a view to arrive at an intercomparison and also consider their applications toward the problems of chemical significance. In particular, we propose to use the concepts of fugality and atom-atom polarizability to study the acidic strength of para-substituted benzoic acid derivatives. The nature of the variations and trends in the correlation of reactivity parameters and pK_a values is shown to provide an insight into the applicability of these concepts to such reactions.

Analysis of the Gas Phase Acidity of Substituted Benzoic Acids Using Density Functional Concepts

A theoretical study of the effect of the substituent Z on the gas phase acidity of substituted benzoic acids ZC₆H₄COOH in terms of density functional theory descriptors (chemical potential, softness and Fukui function) is presented. The calculated gas phase Δ_acidG° values obtained were close to the experimental ones reported in the literature. The good relationship between the Δ_acidG° values and the electronegativity of ZC₆H₄COOH and its fragments, suggested a better importance of the inductive than polarizability contributions. The balance of inductive and resonance contributions of the substituent in the acidity of substituted benzoic acids showed that the highest inductive and resonance effects were for the -SO₂CF₃ and -NH₂ substituents in the para- and ortho-position, respectively. The Fukui function confirmed that the electron-releasing substituent attached to the phenyl ring of benzoic acid decreased the acidity in the trend ortho > meta > para, and the electron-withdrawing substituent increased the acidity in the trend ortho < meta < para.

Baird's Rule in Substituted Fulvene Derivatives: An Information-Theoretic Study on Triplet-State Aromaticity and Antiaromaticity

Originated from the cyclic delocalization of electrons resulting in extra stability and instability, aromaticity and antiaromaticity are important chemical concepts whose appreciation and quantification are still much of recent interest in the literature. Employing information-theoretic quantities can provide us with more insights and better understanding about them, as we have previously demonstrated. In this work, we examine the triplet-state aromaticity and antiaromaticity, which are governed by Baird's 4n rule, instead of Hückel's 4n + 2 rule for the singlet state. To this end, we have made use of 4 different aromaticity indexes and 8 information-theoretic quantities, examined a total of 22 substituted fulvene derivatives, and compared the results both in singlet and triplet states. It is found that cross-correlations of these two categories of molecular property descriptors enable us to better understand the nature and propensity of aromaticity and antiaromaticity for the triplet state. Our results have not only demonstrated the existence and validity of Baird's rule but also shown that Hückel's rule and Baird's rule indeed share the same theoretical foundation because with these cross-correlation patterns we are able to distinguish them from each other simultaneously in both singlet and triplet states. Our results should provide new insights into the nature of aromaticity and antiaromaticity in the triplet state and pave the road toward new ways to quantify this pair of important chemical concepts.

Molecular acidity: An accurate description with information-theoretic approach in density functional reactivity theory

Molecular acidity is one of the important physiochemical properties of a molecular system, yet its accurate calculation and prediction are still an unresolved problem in the literature. In this work, we propose to make use of the quantities from the information-theoretic (IT) approach in density functional reactivity theory and provide an accurate description of molecular acidity from a completely new perspective. To illustrate our point, five different categories of acidic series, singly and doubly substituted benzoic acids, singly substituted benzenesulfinic acids, benzeneseleninic acids, phenols, and alkyl carboxylic acids, have been thoroughly examined. We show that using IT quantities such as Shannon entropy, Fisher information, Ghosh-Berkowitz-Parr entropy, information gain, Onicescu information energy, and relative Rényi entropy, one is able to simultaneously predict experimental pKa values of these different categories of compounds. Because of the universality of the quantities employed in this work, which are all density dependent, our approach should be general and be applicable to other systems as well. © 2017 Wiley Periodicals, Inc.

Effects of para-substituents of styrene derivatives on their chemical reactivity on platinum nanoparticle surfaces

Stable platinum nanoparticles were successfully prepared by the self-assembly of para-substituted styrene derivatives onto the platinum surfaces as a result of platinum-catalyzed dehydrogenation and transformation of the vinyl groups to the acetylene ones, forming platinum-vinylidene/-acetylide interfacial bonds. Transmission electron microscopic measurements showed that the nanoparticles were well dispersed without apparent aggregation, suggesting sufficient protection of the nanoparticles by the organic capping ligands, and the average core diameter was estimated to be 2.0 ± 0.3 nm, 1.3 ± 0.2 nm, and 1.1 ± 0.2 nm for the nanoparticles capped with 4-tert-butylstyrene, 4-methoxystyrene, and 4-(trifluoromethyl)styrene, respectively, as a result of the decreasing rate of dehydrogenation with the increasing Taft (polar) constant of the para-substituents. Importantly, the resulting nanoparticles exhibited unique photoluminescence, where an increase of the Hammett constant of the para-substituents corresponded to a blue-shift of the photoluminescence emission, suggesting an enlargement of the HOMO-LUMO band gap of the nanoparticle-bound acetylene moieties. Furthermore, the resulting nanoparticles exhibited apparent electrocatalytic activity towards oxygen reduction in acidic media, with the best performance among the series of samples observed with the 4-tert-butylstyrene-capped nanoparticles due to an optimal combination of the nanoparticle core size and ligand effects on the bonding interactions between platinum and oxygen species.

Quantifying electro/nucleophilicity by partitioning the dual descriptor

Translating local electro/nucleophilicities into the language of reactive sites is an appealing theoretical challenge that could be conducive to strengthen the collaborative dialogue between experimentalists and quantum chemists. The usual schemes for such condensation, relying on atomic charges, may however lead to important information loss, due to a sometimes inappropriate averaging of the reactivity anisotropy. In this article, we present instead an approach based on the dual descriptor Δf, which aims at partitioning real space into nonoverlapping reactive domains that feature a constant Δf sign. This strategy enables not only to identify the nucleo/electrophilic regions inside a molecule but also to quantify meaningful properties (mean value, volume, electron population…). Its interest is then illustrated on two specific chemical problems: the measure of σ-holes in the context of halogen bonds, and of the electrophilicity of organic carbocations, casting the light on the versatility of this method.

Scaling properties of information-theoretic quantities in density functional reactivity theory

A number of strong linear correlations between information-theoretic quantities and electron populations for atoms, molecules, and atoms-in-molecules have been disclosed.

Density functional reactivity theory study of SN2 reactions from the information-theoretic perspective

Strong linear correlations were unveiled between barrier heights of bimolecular nucleophilic substitution (S_N2) reactions and quantities from the information-theoretic approach.

Predicting pKa in Implicit Solvents: Current Status and Future Directions

Computational prediction of condensed phase acidity is a topic of much interest in the field today. We introduce the methods available for predicting gas phase acidity and pKas in aqueous and non-aqueous solvents including high-level electronic structure methods, empirical linear free energy relationships (LFERs), implicit solvent methods, explicit solvent statistical free energy methods, and hybrid implicit–explicit approaches. The focus of this paper is on implicit solvent methods, and we review recent developments including new electronic structure methods, cluster-continuum schemes for calculating ionic solvation free energies, as well as address issues relating to the choice of proton solvation free energy to use with implicit solvation models, and whether thermodynamic cycles are necessary for the computation of pKas. A comparison of the scope and accuracy of implicit solvent methods with ab initio molecular dynamics free energy methods is also presented. The present status of the theory and future directions are outlined.

MOLECULAR ACIDITY OF BUILDING BLOCKS OF BIOLOGICAL SYSTEMS: A DENSITY FUNCTIONAL REACTIVITY THEORY STUDY

An accurate prediction of the molecular acidity by employing ab initio or density functional approaches for typical molecular systems is still challenging. Recently, we proposed to utilize two quantum descriptors, molecular electrostatic potential (MEP) and the sum of valence natural atomic orbital (NAO) energies on the nucleus of both the acidic atom and leaving proton, to quantitatively evaluate the pKa values. This new approach has been validated by a number of organic and inorganic systems and justified within the framework of density functional reactivity theory (DFRT). In this work, we apply the approach to building blocks of biological systems, namely, 20 natural α-amino acids and 5 DNA/RNA bases, together with a few other biologically relevant species. Our results show that there exists a strong linear correlation between MEP on the nucleus of the N atom and the sum of N 2p NAO energies, with the correlation coefficient R2 = 0.99. Also, we observe that both MEP on the nitrogen nucleus and the sum of N 2p NAO energies correlate well with experimental pKa values, with the correlation coefficient equal to 0.91. Using this established model, we predicted the trend of pKa changes of amino acids in proteins with different dielectric constants. We also applied the model to predict pKa values for dipeptides. Implications of these linear relationships to understand functions and reactivity of biological systems are discussed as well.

A theoretical study on the gas-phase protonation of pyridine and phosphinine derivatives

In this paper, we study the protonation of pyridine and phosphinine derivatives. In particular, the geometries, the amount of charge transfer, and the nature of the created N-H and P-H bonds are discussed, underlying the fundamental differences between the phosphorus and the nitrogen atoms as proton acceptors. Conceptual density functional theory and Bader's quantum theory of atoms-in-molecules are notably used to rationalize these trends and to predict the overall energies of these prototype gas-phase acid-base reactions.

Application of variable anti-connectivity index to active sites. Modelling pK(a) values of aliphatic monocarboxylic acids

A partial distance-weighted variable anti-connectivity topological index was introduced for modelling pK(a) values of 31 aliphatic carboxylic acids and haloalkyl-carboxylic acids. The partial distance-weighted variable anti-connectivity index showed superior modelling capabilities compared with the index calculated from the complete graph, because it is capable of accounting correctly for the intramolecular interactions of unconnected vertices to specific bond strengths (active site), thereby improving the RMS(CV) error by about 30% (0.221 pK(a) units).