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

New Transition Metal Coordination Polymers Derived from 2-(3,5-Dicarboxyphenyl)-6-carboxybenzimidazole as Photocatalysts for Dye and Antibiotic Decomposition

Coordination polymers (CPs) are an assorted class of coordination complexes that are gaining attention for the safe and sustainable removal of organic dyes from wastewater discharge by either adsorption or photocatalytic degradation. Herein, three different coordination polymers with compositions [Ni(HL)(H2O)2·1.9H2O] (1), [Mn3(HL)(L)(μ3-OH)(H2O)(phen)2·2H2O] (2), and [Cd(HL)4(H2O)]·H2O (3) (H3L = 2-(3,5-dicarboxyphenyl)-6-carboxybenzimidazole; phen = 1,10-phenanthroline) have been synthesized and characterized spectroscopically and by single crystal X-ray diffraction. Single crystal X-ray diffraction results indicated that 1 forms a 2D layer-like framework, while 2 exhibits a 3-connected net with the Schläfli symbol of (44.6), and 3 displays a 3D supramolecular network in which two adjacent 2D layers are held by π···π interactions. All three compounds have been used as photocatalysts to catalyze the photodegradation of antibiotic dinitrozole (DTZ) and rhodamine B (RhB). The photocatalytic results suggested that the Mn-based CP 2 exhibited better photodecomposition of DTZ (91.1%) and RhB (95.0%) than the other two CPs in the time span of 45 min. The observed photocatalytic mechanisms have been addressed using Hirshfeld surface analyses.

New 5,5-(1,4-Phenylenebis(methyleneoxy)diisophthalic Acid Appended Zn(II) and Cd(II) MOFs as Potent Photocatalysts for Nitrophenols

Metal-organic frameworks (MOFs) are peculiar multimodal materials that find photocatalytic applications for the decomposition of lethal molecules present in the wastewater. In this investigation, two new d10-configuration-based MOFs, [Zn2(L)(H2O)(bbi)] (1) and [Cd2(L)(bbi)] (2) (5,5-(1,4-phenylenebis(methyleneoxy)diisophthalic acid (H2L) and 1,1'-(1,4-butanediyl)bis(imidazole) (bbi)), have been synthesized and characterized. The MOF 1 displayed a (4,6)-connected (3.43.52)(32.44.52.66.7) network topology, while 2 had a (3,10)-connected network with a Schläfli symbol of (410.511.622.72)(43)2. These MOFs have been employed as photocatalysts to photodegrade nitrophenolic compounds, especially p-nitrophenol (PNP). The photocatalysis studies reveal that 1 displayed relatively better photocatalytic performance than 2. Further, the photocatalytic efficacy of 1 has been assessed by altering the initial PNP concentration and photocatalyst dosage, which suggest that at 80 ppm PNP concentration and at its 50 mg concentration the MOF 1 can photo-decompose around 90.01% of PNP in 50 min. Further, radical scavenging experiments reveal that holes present over 1 and ·OH radicals collectively catalyze the photodecomposition of PNP. In addition, utilizing density of states (DOS) calculations and Hirshfeld surface analyses, a plausible photocatalysis mechanism for nitrophenol degradation has been postulated.

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.

Machine Learning and Quantum Calculation for Predicting Yield in Cu-Catalyzed P-H Reactions

The paper discussed the use of machine learning (ML) and quantum chemistry calculations to predict the transition state and yield of copper-catalyzed P-H insertion reactions. By analyzing a dataset of 120 experimental data points, the transition state was determined using density functional theory (DFT). ML algorithms were then applied to analyze 16 descriptors derived from the quantum chemical transition state to predict the product yield. Among the algorithms studied, the Support Vector Machine (SVM) achieved the highest prediction accuracy of 97%, with over 80% correlation in Leave-One-Out Cross-Validation (LOOCV). Sensitivity analysis was performed on each descriptor, and a comprehensive investigation of the reaction mechanism was conducted to better understand the transition state characteristics. Finally, the ML model was used to predict reaction plans for experimental design, demonstrating strong predictive performance in subsequent experimental validation.

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.

Computational Insights on the Chemical Reactivity of Functionalized and Crosslinked Polyketones to Cu2+ Ion for Wastewater Treatment

Today, the high concentrations of copper found in water resources result in an urgent problem to solve since human health and aquatic ecosystems have been affected. Functionalized crosslinked polyketone resins (XLPK) have demonstrated high performance for the uptake of heavy metals in water solutions. In addition, its green chemical synthesis makes these resins very attractive as sorbents for metal ions contained in wastewater. XLPK are not soluble in aqueous media and do not require any catalyst, solvent, or harsh conditions to carry out the uptake process. In this paper, a series of functionalized XLPK with pending amino-derivatives namely; butylamine (BA), amino 2-propanol (A2P), 4-(aminomethyl) benzoic acid (HAMC), 6-aminohexanoic acid (PAMBA), and 1,2 diamino propane (DAP) directly attached to the pyrrole backbone of the polymers and crosslinked by di-amine derivatives was investigated using Density Functional Theory (DFT) calculations. Our computational analysis revealed that dipole-dipole interactions played a crucial role in enhancing the adsorption of Cu2+ ions onto XLPKs. The negatively charged ketone moieties and functional groups within XLPKs were identified as key adsorption sites for the selective binding of Cu2+ ions. Additionally, we found that XLPKs exhibited strong electrostatic interactions primarily through the -NH2 and -C=O groups. Evaluation of the adsorption energies in XLPK-Cu(II) complexes showed that the DAP-Cu(II) complex exhibited the highest stability, attributed to strong Cu(II)-N binding facilitated by the amino moiety (-NH2). The remaining XLPKs displayed binding modes involving oxygen atoms (Cu(II)-O) within the ketone moieties in the polymer backbone. Furthermore, the complexation and thermochemical analysis emphasized the role of the coordinator atom (N or O) and the coordinating environment, in which higher entropic effects involved in the adsorption of Cu2+ ions onto XLPKs describes a lower spontaneity of the adsorption process. The adsorption reactions were favored at lower temperatures and higher pressures. These findings provide valuable insights into the reactivity and adsorption mechanisms of functionalized and crosslinked polyketones for Cu2+ uptake, facilitating the design of high-performance polymeric resins for water treatment applications.

Phenomenological description of the acidity of the citric acid and its deprotonated species: informational-theoretical study

CONTEXT

In spite of the fact that molecular acidity is a fundamental physicochemical property of molecular systems, the vast majority of theoretical studies have focused attention on monoprotic acids and on the prediction of pKa's. Polyprotic acids, represent a challenge for electronic structure calculations since the multiple acidic sites result in a vast group of species with different conformations and reactivities. In this work, Information-theoretic (IT) concepts of localizability, order and uniformity are applied to the Citric Acid and its deprotonated species through the one-electron density functionals: Shannon entropy (S), Fisher information (I) and Disequilibrium (D), respectively. We pursue the goal of characterizing the acidity of the aforementioned species with the aim to associate the IT concepts to chemical features such as the polarizability of the protonated/deprotonated species, the liability of the acidic sites, atomic electrostatic potentials, covalent bonding. IT analyses looks very promising for future studies on the acidity of specific deprotonation-sites of polyprotic acids.

METHODS

Density functional theory (DFT) calculations were performed with Gaussian 09 program. A sensitivity analysis of the IT-measures was performed for the citric acid and the citrate using B3LYP, B3PW91, BPW91, M05-2X, M06-2X and PBEPBE functionals with the 6-311++g(3df,2p), 6-311++g(d,p), 6.311+g(d,p) and aug-cc-pVDZ basis sets. The rest of the analysis was performed with the M05-2X/6-311+G(d,p) level of theory. Additionally, aqueous media was considered by use of the SMD solvent model. The IT-measures were calculated using a suite of programs developed in our laboratory jointly with the DGRID software package.

On the Use of Graphene Nanosheets for Drug Delivery: A Case Study of Cisplatin and Some of Its Analogs

Graphene (GN) nanosheets have been widely exploited in biomedical applications as potential nanocarriers for various drugs due to their distinct physical and chemical properties. In this regard, the adsorption behavior of cisplatin (cisPtCl₂) and some of its analogs on a GN nanosheet was investigated in perpendicular and parallel configurations by using density functional theory (DFT). According to the findings, the most significant negative adsorption energies (E_ads) within the cisPtX₂⋯GN complexes (where X = Cl, Br, and I) were observed for the parallel configuration, with values up to -25.67 kcal/mol at the H@GN site. Within the perpendicular configuration of the cisPtX₂⋯GN complexes, three orientations were investigated for the adsorption process, namely, X/X, X/NH₃, and NH₃/NH₃. The negative E_ads values of the cisPtX₂⋯GN complexes increased with the increasing atomic weight of the halogen atom. The Br@GN site showed the largest negative E_ads values for the cisPtX₂⋯GN complexes in the perpendicular configuration. The Bader charge transfer outcomes highlighted the electron-accepting properties of cisPtI₂ within the cisPtI₂⋯GN complexes in both configurations. The electron-donating character of the GN nanosheet increased as the electronegativity of the halogen atom increased. The band structure and density of state plots revealed the occurrence of the physical adsorption of the cisPtX₂ on the GN nanosheet, which was indicated by the appearance of new bands and peaks. Based on the solvent effect outlines, the negative E_ads values generally decreased after the adsorption process in a water medium. The recovery time results were in line with the E_ads findings, where the cisPtI₂ in the parallel configuration took the longest time to be desorbed from the GN nanosheet with values of 61.6 × 10⁸ ms at 298.15 K. The findings of this study provide better insights into the utilization of GN nanosheets in drug delivery applications.

Efficient Synthesis of Imine-Carboxylic Acid Functionalized Compounds: Single Crystal, Hirshfeld Surface and Quantum Chemical Exploration

Two aminobenzoic acid based crystalline imines (HMBA and DHBA) were synthesized through a condensation reaction of 4-aminobenzoic acid and substituted benzaldehydes. Single-crystal X-ray diffraction was employed for the determination of structures of prepared Schiff bases. The stability of super molecular structures of both molecules was achieved by intramolecular H-bonding accompanied by strong, as well as comparatively weak, intermolecular attractive forces. The comparative analysis of the non-covalent forces in HMBA and DHBA was performed by Hirshfeld surface analysis and an interaction energy study between the molecular pairs. Along with the synthesis, quantum chemical calculations were also accomplished at M06/6-311G (d, p) functional of density functional theory (DFT). The frontier molecular orbitals (FMOs), molecular electrostatic potential (MEP), natural bond orbitals (NBOs), global reactivity parameters (GRPs) and natural population (NPA) analyses were also carried out. The findings of FMOs found that Egap for HMBA was examined to be smaller (3.477 eV) than that of DHBA (3.7933 eV), which indicated a greater charge transference rate in HMBA. Further, the NBO analysis showed the efficient intramolecular charge transfer (ICT), as studied by Hirshfeld surface analysis.

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.

Development and Applications of the Density-Based Theory of Chemical Reactivity

Density functional theory, which is well-recognized for its accuracy and efficiency, has become the workhorse for modeling the electronic structure of molecules and extended materials in recent decades. Nevertheless, establishing a density-based conceptual framework to appreciate bonding, stability, function, reactivity, and other physicochemical properties is still an unaccomplished task. In this Perspective, we at first provide an overview of the four pathways currently available in the literature to tackle the matter, including orbital-free density functional theory, conceptual density functional theory, direct use of density-associated quantities, and the information-theoretic approach. Then, we highlight several recent advances of employing these approaches to realize new understandings for chemical concepts such as covalent bonding, noncovalent interactions, cooperation, frustration, homochirality, chirality hierarchy, electrophilicity, nucleophilicity, regioselectivity, and stereoselectivity. Finally, we provide a few possibilities for the future development of this relatively uncharted territory. Opportunities are abundant, and they are all ours for the taking.

Chemical and physical approaches for improved biopharmaceutical activity of amphotericin B: Current and future prospective

Over the last 50 years, the number of patients with mycotic infections has been increasing gradually. Amphotericin-B is a gold standard drug used in serious systemic fungal infections. However, limited solubility and permeability are challenging issues associated with Amphotericin-B. Chemical modification is one of the ways to get its broader applicability along with improved physicochemical properties. The review article provides a comprehensive overview of the chemical modification approach for investigation of the mechanism of action, biological activity, bioavailability, toxicity of Amphotericin B. Further, several drug delivery approaches have also been utilized to provide better therapeutic outcomes. This gives an overview of chemical approaches for the exploration of various factors associated with Amphotericin B and information on its drug delivery approaches for improved biopharmaceutical outcomes.

Recent advances on bimetallic metal-organic frameworks (BMOFs): Syntheses, applications and challenges

Bimetallic metal-organic frameworks (MOFs) possess two different metal ions as nodes in their molecular frameworks. They are prepared by either using one-pot syntheses wherein different metals are mixed with suitable...

Construction strategies to modulate the photocatalytic efficiency of Cd(ii) MOFs to photodegrade organic dyes

Two new tuned 3D Cd(ii) MOFs were synthesized and used as photocatalysts for dye degradation.

Density functional theory studies of boron clusters with exotic properties in bonding, aromaticity and reactivity

Atomic clusters are unique in many perspectives because of their size and structure features and are continuously being applied for different purposes. To unveil their unconventional properties, in this work, using neutral tetraboron clusters as illustrative examples, we study their exotic behaviors in bonding, aromaticity, and reactivity. We show that both double and triple bonds can be formed, ring current patterns can be totally different, and both electrophilic and nucleophilic reactivities can coexist simultaneously. These features are often in contrast with our conventional chemical wisdom and could enrich the possibility for their potential applications. The methodologies employed in this work can be readily applied to other systems. Our studies should help us better appreciate atomic clusters with many atypical properties and henceforth yield novel applications.

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.

Using Bases as Initiators to Isomerize Allylic Alcohols: Insights from Density Functional Theory Studies

Allylic alcohols, as common and readily available building blocks, could be converted into many widely used carbonyl compounds through isomerization reactions. However, these processes often involve expensive transition metal (TM) complexes as the catalyst. What is the bottleneck in the mechanism when no TM is used? In this study, density functional theory (DFT) was employed to explore the mechanistic patterns of allylic alcohols catalyzed using bases, such as KOH, NaOH, LiOH, tBuOK, tBuONa, tBuOLi, 1,5,7-triazabicyclo[4.4.0]dec-5-ene, 1,3,4,6,7,8-hexahydro-1-methyl-2H-pyrimido[1,2-a]pyrimidine, and 1,8-diazabicyclo[5.4.0]undec-7-ene. Our results show that bases containing metal cations follow the metal cation-assisted (MCA) mechanism, whereas organic bases without metal cations follow the ion pair-assisted (IPA) mechanism. The catalytic efficiency of bases containing metal cations is higher than that of bases without metal cations, indicating that metal cations play an important role in the reaction. Additionally, the modulation of substituents R₁ and R₂ in the substrate reveals that electron-withdrawing groups are favorable for C-H bond cleavage, and electron-donating groups are favorable for hydrogen transfer. To better understand these patterns, we applied the DFT and information-theoretic approach (ITA) to examine the impact of bases and substrate substituents on the reactivity of allylic alcohol isomerization. This work should provide a much-needed theoretical guidance to design better non-TM catalysts for the isomerization of allylic alcohols and their derivatives.

Mechanistic Insights into Formation of All-Carbon Quaternary Centers via Scandium-Catalyzed C-H Alkylation of Imidazoles with 1,1-Disubstituted Alkenes

This density functional theory (DFT) study reveals a detailed plausible mechanism for the Sc-catalyzed C-H cycloaddition of imidazoles to 1,1-disubstituted alkenes to form all-carbon quaternary stereocenters. The Sc complex binds the imidazole substrate to enable deprotonative C2-H bond activation by the Sc-bound α-carbon to afford the active species. This complex undergoes intramolecular cyclization (C═C into Sc-imidazolyl insertion) with exo-selectivity, generating a β-all-carbon-substituted quaternary center in the polycyclic imidazole derivative. The Sc-bound α-carbon deprotonates the imidazole C2-H bond to deliver the product and regenerate the active catalyst, which is the rate-determining step. Calculations illuminate the electronic effect of the ancillary Cp ligand on the catalyst activity and reveal the steric bias caused by using a chiral catalyst that induce the enantioselectivity. The insights can have implications for advancing rare-earth metal-catalyzed C-H functionalization of imidazoles.

Synthesis of All Thiophene-Based [7]Helicenes and Trithienothiepines with Isomeric Location of Sulfur Atoms Based on Intramolecular Selectivity of Deprotonation

Three unsymmetric thiophene-based [7]helicenes, namely, endo-exo-UH-1, endo-top-UH-2, and exo-top-UH-3, with different isomeric locations of sulfur atoms in two terminal thiophene rings were efficiently synthesized using dithieno[2,3-b:3',2'-d]thiophene (bb-DTT), dithieno[2,3-b:2',3'-d]thiophene (bt-DTT), and dithieno[2,3-b:3',4'-d]thiophene (bs-DTT) as building blocks via Suzuki cross-coupling and intramolecular cyclization reactions. Aside from these racemic [7]helicenes, two novel heterocyclic isomers, namely, trithienothiepines TTTP-1 and TTTP-2, were simultaneously obtained during the intramolecular cyclization. Two novel deprotonations of bi-DTTs and cyclization for synthesizing target compounds showed high selectivity and efficiently constructed both UHs and TTTPs. X-ray crystallographic analyses revealed that the UHs have typical helical molecular structures. The isomeric location of sulfur atoms in the two terminal thiophene rings in endo-exo-UH-1, endo-top-UH-2, exo-top-UH-3, and TTTP-1 allowed multiple intermolecular interactions, such as S···S, S···C, and S···H interactions, resulting in different crystal-packing patterns. Moreover, the absorption behaviors of these [7]helicenes, TTTP-1, and TTTP-2 were examined and theoretically calculated. Results indicated that the isomeric location of sulfur atoms plays a key role in tuning intramolecular π-electronic conjugation.

A theoretical study of the hydroboration of α,β-unsaturated carbonyl compounds catalyzed by a metal-free complex and subsequent C–C coupling with acetonitrile

Herein, the density functional theory (DFT) method was employed to investigate the reaction mechanism of the selective hydroboration of α,β-unsaturated carbonyl compounds catalyzed by the metal-free complex 1,3,2-diazaphospholene (DAP).

A Chemical Probe for Dark Kinase STK17B Derives Its Potency and High Selectivity through a Unique P-Loop Conformation

STK17B is a member of the death-associated protein kinase family and has been genetically linked to the development of diverse diseases. However, the role of STK17B in normal and disease pathology is poorly defined. Here, we present the discovery of thieno[3,2-d] pyrimidine SGC-STK17B-1 (11s), a high-quality chemical probe for this understudied "dark" kinase. 11s is an ATP-competitive inhibitor that showed remarkable selectivity over other kinases including the closely related STK17A. X-ray crystallography of 11s and related thieno[3,2-d]pyrimidines bound to STK17B revealed a unique P-loop conformation characterized by a salt bridge between R41 and the carboxylic acid of the inhibitor. Molecular dynamic simulations of STK17B revealed the flexibility of the P-loop and a wide range of R41 conformations available to the apo-protein. The isomeric thieno[2,3-d]pyrimidine SGC-STK17B-1N (19g) was identified as a negative control compound. The >100-fold lower activity of 19g on STK17B was attributed to the reduced basicity of its pyrimidine N1.

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.

Switching between Hückel and Möbius aromaticity: a density functional theory and information-theoretic approach study

Benziporphyrins are versatile macrocycles exhibiting aromaticity switching behaviors. The existence of both Hückel and Möbius (anti)aromaticity has been reported in these systems, whose validity is respectively governed by the [4n + 2] and [4n] π-electron rule on the macrocyclic pathway. Despite the experimental evidence on the floppiness of benziporphyrins, the switching mechanism between Hückel and Möbius structures is still not clear, as well as the factors influencing the stability of the different π-conjugation topologies. For these reasons, we performed a systematic study on A,D-di-p-benzihexaphyrins(1.1.1.1.1.1) with two redox states corresponding to [28] and [30] π-electron conjugation pathways. Whereas benzi[28]hexaphyrin obeys Möbius aromaticity, benzi[30]hexaphyrin follows Hückel aromaticity. The dynamic interconversion between Möbius and Hückel aromaticity is investigated through the rotation of a phenylene ring, which acts as the topology selector. Further analyses of the energy profiles using energy decomposition and information-theoretic approaches provide new insights into conformational stability, aromaticity and antiaromaticity for these species. Strong and opposite cross correlations between aromaticity indexes and information-theoretic quantities were found for the two macrocyclic systems with opposite global aromaticity and antiaromaticity behaviors. These results indicate that Hückel and Möbius aromaticity and antiaromaticity, though qualitatively different, are closely related and can be interchanged, and information-theoretic quantities provide a novel understanding about their relevance. Our present results should provide in-depth insights to appreciate the nature and origin about Möbius (anti)aromaticity and its close relationship with Hückel (anti)aromaticity.

Identity for Kullback-Leibler divergence in density functional reactivity theory

Density functional reactivity theory (DFRT) makes use of simple electron density functionals to appreciate chemical reactivity. The Kullback-Leibler divergence, also called information gain or relative Shannon entropy, as a key component of the DFRT framework has entertained a few fascinating applications in the recent literature. For instance, it was employed to rationalize the Hirshfeld stockholder partition of atoms in molecules. It has also been applied to both determine regioselectivity and simultaneously quantify molecular electrophilicity and nucleophilicity, the capability of atoms in molecules to accept and donate electrons. In this work, we examine the local behavior of the Kullback-Leibler divergence and present a novel identity for it. The validity of the identity is subsequently verified by the numerical results of neutral atoms from He to Kr with different choices of the reference density. Analytical properties and local behaviors of the three new functions introduced in the identity are discussed. These new local functions, together with the identity unveiled in this work, should provide new perspectives for us to further develop the DFRT framework with added insights about the local behavior of molecular physiochemical properties.

Is It Possible To Determine Oxidation States for Atoms in Molecules Using Density-Based Quantities? An Information-Theoretic Approach and Conceptual Density Functional Theory Study

The oxidation state, also called oxidation number, of atoms in molecules is a fundamental chemical concept. It is defined as the charge of an atom in a molecule after the ionic approximation of its heteronuclear bonds is applied. Even though for simple molecules the assignment of oxidation states is straightforward, redundancy and ambiguity do exist for others. In this work, we present a density-based framework to determine the oxidation state using the quantities from the information-theoretic approach. As a proof of concept, we examined six elements for a total of 49 molecules. Strong linear correlations were obtained with Shannon entropy, Ghosh-Berkowitz-Parr entropy, information gain, relative Rényi entropy of orders 2 and 3, and Hirshfeld charge. We also discovered that the crystal radius of elements plays the key role in rationalizing the system dependent nature of these strong linear correlations. The validity and effectiveness of our results were demonstrated by the examples of molecules containing elements with two or more oxidation states. Our results should be applicable to more complicated systems in assigning different oxidation states.

Shannon, Rényi, Tsallis Entropies and Onicescu Information Energy for Low-Lying Singly Excited States of Helium

Knowledge of the electronic structures of atomic and molecular systems deepens our understanding of the desired system. In particular, several information-theoretic quantities, such as Shannon entropy, have been applied to quantify the extent of electron delocalization for the ground state of various systems. To explore excited states, we calculated Shannon entropy and two of its one-parameter generalizations, Rényi entropy of order α and Tsallis entropy of order α , and Onicescu Information Energy of order α for four low-lying singly excited states (1s2s 1 S e , 1s2s 3 S e , 1s3s 1 S e , and 1s3s 3 S e states) of helium. This paper compares the behavior of these three quantities of order 0.5 to 9 for the ground and four excited states. We found that, generally, a higher excited state had a larger Rényi entropy, larger Tsallis entropy, and smaller Onicescu information energy. However, this trend was not definite and the singlet–triplet reversal occurred for Rényi entropy, Tsallis entropy and Onicescu information energy at a certain range of order α .

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.

SCI: a robust and reliable density-based descriptor to determine multiple covalent bond orders

Very recently [J. Phys. Chem. A 2018, 122 (11), 3087-3095], we proposed to employ the Pauli energy to identify and determine strong covalent interactions (SCI), whose bond order are equal to or larger than two. This is done through the signature isosurface shape between the two bonding atoms. We discovered that the signature shape for a double, triple, and quadruple covalent bond is like a dumbbell, donut (torus), and four-beats, respectively. Systems with even higher bond orders were examined and confirmed. This work is a follow-up study of our previous work. The dependence of the signature isosurface shape on the choice of methodologies and basis sets is systematically investigated. Its effectiveness and robustness in determining bond orders are highlighted again with more examples. In addition, using the molybdenum dimer in different environments, e.g., in vacuum, sandwiched between molecules, and encapsulated in the C₈₀ cage, as illustrative examples, we show that, generally speaking, bond strength and bond order are two different chemical concepts. For systems containing transition metals, it is not always true that a short metal-metal bond length corresponds to a larger bond order. Put together, these results should provide additional pieces of convincing evidence showing that the SCI index is a robust and reliable density-based descriptor to accurately determine multiple covalent bond orders.

Quantification and origin of cooperativity: insights from density functional reactivity theory

Cooperativity is a widely used chemical concept whose existence is ubiquitous in chemical and biological systems but whose quantification is still controversial and origin much less appreciated. In this work, using the interaction energy of a molecular system, which is composed of multiple copies of a building block, we propose a quantitative measurement to evaluate the cooperativity effect. This quantification approach is then applied to six molecular systems, i.e., water cluster, argon cluster, protonated water cluster, zinc atom cluster, water cluster on top of a graphene sheet, and alpha helix of glycine amino acids, each with up to 20 copies of the building block. Cooperativity is seen in all these systems. Both positive and negative cooperativity effects are observed. Employing the two energy partition schemes in density functional theory and the information-theoretic quantities such as Shannon entropy, Fisher information, information gain, etc., we then examine the origin of the cooperativity effect for these systems. Strong linear correlations between the cooperativity measure and some of these theoretical quantities have been unveiled. With these correlations, we are able to quantitatively account for their origin of cooperativity. Our results show that the interactions governing the existence and validity of the cooperativity effect are complicated. An opposite mechanism in enthalpy-entropy compensation for positive and negative cooperativity has been unveiled. These results should provide new insights and understandings from a different viewpoint about the nature and origin of cooperativity to appreciate this vastly important chemical concept.

Steric charge

Steric charge is an informative descriptor providing novel insights to appreciate the steric effect and stereoselectivity for chemical processes and transformations.