Synergy of machine learning and density functional theory calculations for predicting experimental Lewis base affinity and Lewis polybase binding atoms

Investigation of Lewis acid-base interactions has been conducted by ab initio calculations and machine learning (ML) models. This study aims to resolve two critical tasks that have not been quantitatively investigated. First, ML models developed from density functional theory (DFT) calculations predict experimental BF3 affinity with Pearson correlation coefficients around 0.9 and mean absolute errors around 10 kJ mol-1. The ML models are trained by DFT-calculated BF3 affinity of more than 3000 adducts, with input features readily obtained by rdkit. Second, the ML models have the capability of predicting the relative strength of Lewis base binding atoms in Lewis polybases, which is either an extremely challenging task to conduct experimentally or a computationally expensive task for ab initio methods. The study demonstrates and solidifies the potential of combining DFT calculations and ML models to predict experimental properties, especially those that are scarce and impractical to empirically acquire.

Kinetic Characterization of Cerium and Gallium Ions as Inhibitors of Cysteine Cathepsins L, K, and S

Heavy metal ions can disrupt biological functions via multiple molecular mechanisms, including inhibition of enzymes. We investigate the interactions of human papain-like cysteine endopeptidases cathepsins L, K, and S with gallium and cerium ions, which are associated with medical applications. We compare these results with zinc and lead, which are known to inhibit thiol enzymes. We show that Ga³⁺, Ce³⁺, and Ce⁴⁺ ions inhibit all tested peptidases with inhibition constants in the low micromolar range (between 0.5 µM and 10 µM) which is comparable to Zn²⁺ ions, whereas inhibition constants of Pb²⁺ ions are one order of magnitude higher (30 µM to 150 µM). All tested ions are linear specific inhibitors of cathepsin L, but cathepsins K and S are inhibited by Ga³⁺, Ce³⁺, and Ce⁴⁺ ions via hyperbolic inhibition mechanisms. This indicates a mode of interaction different from that of Zn²⁺ and Pb²⁺ ions, which act as linear specific inhibitors of all peptidases. All ions also inhibit the degradation of insoluble elastin, which is a common target of these peptidases in various inflammatory diseases. Our results suggest that these ions and their compounds have the potential to be used as cysteine cathepsin inhibitors in vitro and possibly in vivo.

Molecular interactions from the density functional theory for chemical reactivity: Interaction chemical potential, hardness, and reactivity principles

In the first paper of this series, the authors derived an expression for the interaction energy between two reagents in terms of the chemical reactivity indicators that can be derived from density functional perturbation theory. While negative interaction energies can explain reactivity, reactivity is often more simply explained using the “|dμ| big is good” rule or the maximum hardness principle. Expressions for the change in chemical potential (μ) and hardness when two reagents interact are derived. A partial justification for the maximum hardness principle is that the terms that appear in the interaction energy expression often reappear in the expression for the interaction hardness, but with opposite sign.

On the Prediction of Lattice Energy with the Fukui Potential: Some Supports on Hardness Maximization in Inorganic Solids

Using perturbation theory within the framework of conceptual density functional theory, we derive a lower bound for the lattice energy of the ionic solids. The main element of the lower bound is the Fukui potential in the nuclei of the molecule corresponding to the unit formula of the solid. Thus, we propose a model to calculate the lattice energy in terms of the Fukui potential. Our method, which is extremely simple, performs well as other methods using the crystal structure information of alkali halide solids. The method proposed here correlates surprisingly well with the experimental data on the lattice energy of a diverse series of solids having even a non-negligible covalent characteristic. Finally, the validity of the maximum hardness principle (MHP) is assessed, showing that in this case, the MHP is limited.

Molecular Interactions From the Density Functional Theory for Chemical Reactivity: The Interaction Energy Between Two-Reagents

Reactivity descriptors indicate where a reagent is most reactive and how it is most likely to react. However, a reaction will only occur when the reagent encounters a suitable reaction partner. Determining whether a pair of reagents is well-matched requires developing reactivity rules that depend on both reagents. This can be achieved using the expression for the minimum-interaction-energy obtained from the density functional reactivity theory. Different terms in this expression will be dominant in different circumstances; depending on which terms control the reactivity, different reactivity indicators will be preferred.

Links among the Fukui potential, the alchemical hardness and the local hardness of an atom in a molecule

This paper presents a brief summary of the difficulty that resides in the definition of the elusive concept of local chemical hardness. We argue that a definition of local hardness should be useful to a reactivity principle and not just as a mere definition. We then continue with a formal discussion about the benefits and difficulties of using the Fukui potential, which is interpreted as an alchemical derivative (alchemical hardness), as descriptor of local hardness of molecules. Computational evidence shows that the alchemical hardness is at least as good a descriptor as the combination of other two well-stabilized descriptors of local hardness, such as the Fukui function and grand canonical local hardness. Although our results are auspicious for the alchemical hardness as descriptor of local hardness, we finish by calling the attention of the community on the importance of discussing the raison d'être of a local hardness function and its main characteristics. We suggest that an axiomatic construction of local hardness could be they way of constructing a local hardness which is both useful and free of arbitrariness.

Competition between N and O: use of diazine N-oxides as a test case for the Marcus theory rationale for ambident reactivity

The preferred site of alkylation of diazine N-oxides by representative hard and soft alkylating agents was established conclusively using the 1H-15N HMBC NMR technique in combination with other NMR spectroscopic methods. Alkylation of pyrazine N-oxides (1 and 2) occurs preferentially on nitrogen regardless of the alkylating agent employed, while O-methylation of pyrimidine N-oxide (3) is favoured in its reaction with MeOTf. As these outcomes cannot be explained in the context of the hard/soft acid/base (HSAB) principle, we have instead turned to Marcus theory to rationalise these results. Marcus intrinsic barriers (ΔG ‡ 0) and Δr G° values were calculated at the DLPNO-CCSD(T)/def2-TZVPPD/SMD//M06-2X-D3/6-311+G(d,p)/SMD level of theory for methylation reactions of 1 and 3 by MeI and MeOTf, and used to derive Gibbs energies of activation (ΔG ‡) for the processes of N- and O-methylation, respectively. These values, as well as those derived directly from the DFT calculations, closely reproduce the observed experimental N- vs. O-alkylation selectivities for methylation reactions of 1 and 3, indicating that Marcus theory can be used in a semi-quantitative manner to understand how the activation barriers for these reactions are constructed. It was found that N-alkylation of 1 is favoured due to the dominant contribution of Δr G° to the activation barrier in this case, while O-alkylation of 3 is favoured due to the dominant contribution of the intrinsic barrier (ΔG ‡ 0) for this process. These results are of profound significance in understanding the outcomes of reactions of ambident reactants in general.

Selective Metal-Ligand Bond-Breaking Driven by Weak Intermolecular Interactions: From Metamagnetic Mn(III)-Monomer to Hexacyanoferrate(II)-Bridged Metamagnetic Mn2Fe Trimer

Metal-ligand coordination interactions are usually much stronger than weak intermolecular interactions. Nevertheless, here, we show experimental evidence and theoretical confirmation of a very rare example where metal-ligand bonds dissociate in an irreversible way, helped by a large number of weak intermolecular interactions that surpass the energy of the metal-ligand bond. Thus, we describe the design and synthesis of trinuclear Mn₂Fe complex {[Mn(L)(H₂O)]₂Fe(CN)₆},^2- starting from a mononuclear Mn(III)-Schiff base complex: [Mn(L)(H₂O)Cl] (1) and [Fe(CN)₆]^4- anions. This reaction implies the dissociation of Mn(III)-Cl coordination bonds and the formation of Mn(III)-NC bonds with the help of several intermolecular interactions. Here, we present the synthesis, crystal structure, and magnetic characterization of the monomeric Mn(III) complex [Mn(L)(H₂O)Cl] (1) and of compound (H₃O)[Mn(L)(H₂O)₂]{[Mn(L)(H₂O)]₂Fe(CN)₆}·4H₂O (2) (H₂L = 2,2'-((1E,1'E)-(ethane-1,2-diylbis(azaneylylidene))bis(methaneylylidene))bis(4-methoxyphenol)). Complex 1 is a monomer where the Schiff base ligand (L) is coordinated to the four equatorial positions of the Mn(III) center with a H₂O molecule and a Cl^- ion at the axial sites and the monomeric units are assembled by π-π and hydrogen-bonding interactions to build supramolecular dimers. The combination of [Fe(CN)₆]^4- with complex 1 leads to the formation of linear Mn-NC-Fe-CN-Mn trimers where two trans cyano groups of the [Fe(CN)₆]^4- anion replace the labile chloride from the coordination sphere of two [Mn(L)(H₂O)Cl] complexes, giving rise to the linear anionic {[Mn(L)(H₂O)]₂Fe(CN)₆}^2- trimer. This Mn₂Fe trimer crystallizes with an oxonium cation and a mononuclear [Mn(L)(H₂O)₂]⁺ cation, closely related to the precursor neutral complex [Mn(L)(H₂O)Cl]. In compound 2, the Mn₂Fe trimers are assembled by several hydrogen-bonding and π-π interactions to frame an extended structure similar to that of complex 1. Density functional theoretical (DFT) calculations at the PBE1PBE-D3/def2-TZVP level show that the bond dissociation energy (-29.3 kcal/mol) for the Mn(III)-Cl bond is smaller than the summation of all the weak intermolecular interactions (-30.1 kcal/mol). Variable-temperature magnetic studies imply the existence of weak intermolecular antiferromagnetic couplings in both compounds, which can be can cancelled with a critical field of ca. 2.0 and 2.5 T at 2 K for compounds 1 and 2, respectively. The magnetic properties of compound 1 have been fit with a simple S = 2 monomer with g = 1.959, a weak zero-field splitting (|D| = 1.23 cm^-1), and a very weak intermolecular interaction (zJ = -0.03 cm^-1). For compound 2, we have used a model with an S = 2 monomer with ZFS plus an S = 2 antiferromagnetically coupled dimer with g = 2.009, |D| = 1.21 cm^-1, and J = -0.42 cm^-1. The metamagnetic behavior of both compounds is attributed to the weak intermolecular π-π and hydrogen-bonding interactions.

Ambident Nucleophilic Substitution: Understanding Non-HSAB Behavior through Activation Strain and Conceptual DFT Analyses

The ability to understand and predict ambident reactivity is key to the rational design of organic syntheses. An approach to understand trends in ambident reactivity is the hard and soft acids and bases (HSAB) principle. The recent controversy over the general validity of this principle prompted us to investigate the competing gas-phase SN 2 reaction channels of archetypal ambident nucleophiles CN- , OCN- , and SCN- with CH3 Cl (SN 2@C) and SiH3 Cl (SN 2@Si), using DFT calculations. Our combined analyses highlight the inability of the HSAB principle to correctly predict the reactivity trends of these simple, model reactions. Instead, we have successfully traced reactivity trends to the canonical orbital-interaction mechanism and the resulting nucleophile-substrate interaction energy. The HOMO-LUMO orbital interactions set the trend in both SN 2@C and SN 2@Si reactions. We provide simple rules for predicting the ambident reactivity of nucleophiles based on our Kohn-Sham molecular orbital analysis.

An electronic temperature definition for the reactive electronic species: Conciliating practical approaches in conceptual chemical reactivity theory with a rigorous ensemble formulation

By working under the framework of the Helmholtz potential as a functional of the equilibrium density matrix, in this contribution, we provide theoretical evidence about a particular thermodynamic situation, where electronic species display their highest susceptibility to exchange electrons to or from surroundings. This situation is denominated as the electronic temperature condition. Neutral chemical species display their lowest possible hardness value at the electronic temperature condition, and remarkably, under this circumstance, the exchange of any amount of electronic charge will necessarily be translated into a net increase in the corresponding chemical hardness. Chemical response functions defined as partial derivatives of the Helmholtz potential with respect to the (average) number of electrons and evaluated at the electronic temperature condition provide comparable results than those obtained from the coarse quadratic approximation to the exact dependence of the electronic energy vs the number of electrons, including composite quantities as the electrophilicity index. In this context, we show that the exact Helmholtz potential dependence with respect to the number of electrons can accurately be approximated by "temperature dependent" polynomial fits (up to fourth order), evaluated at the electronic temperature condition.

High affinity interactions of Pb2+ with synaptotagmin I

Lead (Pb) is a potent neurotoxin that disrupts synaptic neurotransmission. We report that Synaptotagmin I (SytI), a key regulator of Ca2+-evoked neurotransmitter release, has two high-affinity Pb2+ binding sites that belong to its cytosolic C2A and C2B domains. The crystal structures of Pb2+-complexed C2 domains revealed that protein-bound Pb2+ ions have holodirected coordination geometries and all-oxygen coordination spheres. The on-rate constants of Pb2+ binding to the C2 domains of SytI are comparable to those of Ca2+ and are diffusion-limited. In contrast, the off-rate constants are at least two orders of magnitude smaller, indicating that Pb2+ can serve as both a thermodynamic and kinetic trap for the C2 domains. We demonstrate, using NMR spectroscopy, that population of these sites by Pb2+ ions inhibits further Ca2+ binding despite the existing coordination vacancies. Our work offers a unique insight into the bioinorganic chemistry of Pb(ii) and suggests a mechanism by which low concentrations of Pb2+ ions can interfere with the Ca2+-dependent function of SytI in the cell.

Local electrophilicity

In this work some possibilities for deriving a local electrophilicity are studied. First, we consider the original definition proposed by Chattaraj, Maiti, and Sarkar (J Phys Chem A 107:4973, 2003), in which the local electrophilicity is given by the product of the global electrophilicity, and the Fukui function for charge acceptance is derived by two different approaches, making use of the chain rule for functional derivatives. We also modify the proposals based on the electron density so as to have a definition with the same units of the original definition, which also introduces a dependence in the Fukui function for charge donation. Additionally, we also explore other possibilities using the tools of information theory and the temperature dependent reactivity indices of the density functional theory of chemical reactivity. The poor results obtained from the last two approaches lead us to conjecture that this is due to the fact that the global electrophilicity is not a derivative, like most of the other reactivity indices. The conclusion is that Chattaraj's suggestion seems to be the simplest, but at the same time a very reliable approach to this important property.

Elementary Derivation of the "|Δμ| Big Is Good" Rule

Thirty years ago, Parr and Yang postulated that favorable chemical processes are associated with large changes in the electronic chemical potential or, equivalently, the electronegativity. They called this the "|Δμ| big is good" rule and noted that if the rule could be justified, then it "would constitute a validation of frontier theory from first principles." We provide a simple and insightful justification for the "|Δμ| big is good" rule, with special emphasis on electron-transfer reactions. Furthermore, we show that it implies Pearson's hard/soft acid/base principle mathematically and confirm this result with numerical examples. This supports Parr's intuition that many other reactivity precepts arise as corollaries to the more fundamental "|Δμ| big is good" rule. In all of this, it is essential to consider the intensive nature of the chemical potential.

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

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

The protection effects of (1E,6E)-1,7-diphenylhepta-1,6-diene-3,5-dione, a curcumin analogue, against operative liver injury in rats

The relationship between the chemistry characteristic and the hepatoprotective effects of (1E,6E)-1,7-diphenylhepta-1,6-diene-3,5-dione (DDD), a curcumin analogue, in operative liver injury rats was investigated to reveal the mechanism of hepatic protection effects of DDD. DDD (1.2-4.8mmol/kg) was administrated 10min before reperfusion phase in hepatic ischemia-reperfusion injury (IRI) rats. DDD (4.8mmol/kg) administrated 10min before ischemia and N-acetylcysteine (NAC) (4.8mmol/kg) administrated 10min before reperfusion were included for comparative studies. The plasma liver enzyme activities, histopathological indices and markers of lipid peroxide were determined to evaluate the hepatic protection effects. Effects of DDD on succinate dehydrogenase (SDH) activity were also investigated. DDD showed dose-dependent hepatocyte protections when administrated 10min before reperfusion stages in hepatic IRI rats. DDD showed almost equivalent hepatoprotective effects when administrated 10min before ischemia phase demonstrating that DDD acted on the reperfusion stages selectively against the hepatic IRI, instead of ischemia phase. NAC was not effective against hepatic IRI when treated 10min before reperfusion because of the higher pKa of NAC. In additional, DDD had no effect on the SDH both in hepatic IRI rats and in mitochondria. In conclusion, DDD had dose-dependent hepatocyte protections in the reperfusion stages in hepatic IRI rats, while the observed hepatocyte protections of DDD did not involve SDH activities. β-Diketone structures of DDD were crucial for the hepatocyte protections. The abilities of DDD to clear up the unsaturated aldehydes related with the enolate nucleophilicity and the pKa. DDD might be a promising candidate to treat hepatic IRI.

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

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

Intermolecular interactions in organic crystals: gaining insight from electronic structure analysis by density functional theory

Conceptual density functional theory is exploited to extend the HSAB (hard and soft acids and bases) principle for investigating the locality and regioselectivity of intermolecular interactions in organic crystals.