Communication: A case where the hard/soft acid/base principle holds regardless of acid/base strength

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.

The Reactivity of Ambident Nucleophiles: Marcus Theory or Hard and Soft Acids and Bases Principle?

The model reactions CH₃ X + (NH-CH=O)M ➔ CH₃ -NH-NH═O or NH═CH-O-CH₃  + MX (M = none, Li, Na, K, Ag, Cu; X = F, Cl, Br) are investigated to demonstrate the feasibility of Marcus theory and the hard and soft acids and bases (HSAB) principle in predicting the reactivity of ambident nucleophiles. The delocalization indices (DI) are defined in the framework of the quantum theory of atoms in molecules (QT-AIM), and are used as the scale of softness in the HSAB principle. To react with the ambident nucleophile NH═CH-O^- , the carbocation H₃ C⁺ from CH₃ X (F, Cl, Br) is actually a borderline acid according to the DI values of the forming C…N and C…O bonds in the transition states (between 0.25 and 0.49), while the counter ions are divided into three groups according to the DI values of weak interactions involving M (M…X, M…N, and M…O): group I (M = none, and Me₄ N) basically show zero DI values; group II species (M = Li, Na, and K) have noticeable DI values but the magnitudes are usually less than 0.15; and group III species (M = Ag and Cu(I)) have significant DI values (0.30-0.61). On a relative basis, H₃ C⁺ is a soft acid with respect to group I and group II counter ions, and a hard acid with respect to group III counter ions. Therefore, N-regioselectivity is found in the presence of group I and group II counter ions (M = Me₄ N, Li, Na, K), while O-regioselectivity is observed in the presence of the group III counter ions (M = Ag, and Cu(I)). The hardness of atoms, groups, and molecules is also calculated with new functions that depend on ionization potential (I) and electron affinity (A) and use the atomic charges obtained from localization indices (LI), so that the regioselectivity is explained by the atomic hardness of reactive nitrogen atoms in the transition states according to the maximum hardness principle (MHP). The exact Marcus equation is derived from the simple harmonic potential energy parabola, so that the concepts of activation free energy, intrinsic activation barrier, and reaction energy are completely connected. The required intrinsic activation barriers can be either estimated from ab initio calculations on reactant, transition state, and product of the model reactions, or calculated from identity reactions. The counter ions stabilize the reactant through bridging N- and O-site of reactant of identity reactions, so that the intrinsic barriers for the salts are higher than those for free ambident anions, which is explained by the increased reorganization parameter Δr. The proper application of Marcus theory should quantitatively consider all three terms of Marcus equation, and reliably represent the results with potential energy parabolas for reactants and all products. For the model reactions, both Marcus theory and HSAB principle/MHP principle predict the N-regioselectivity when M = none, Me₄ N, Li, Na, K, and the O-regioselectivity when M = Ag and Cu(I). © 2019 Wiley Periodicals, Inc.

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.

O-Regioselective Synthesis with the Silver Salt Method

The excellent O-regioselectivity of the glycosidation of the ambident 2-O-substituted 5-fluorouracil (5-FU) via the silver salt method is computationally investigated at the MP2/6-311++G(2d,p):DZP//B3LYP/6-31+G(d):DZP level of theory. The reactions studied are those between 1-bromo-1-deoxy-2,3,4,6-tetra-O-acetyl-α-d-glucopyranose and the silver salts of 5-FU, 2-O-butyl-5-FU, and 2-O-benzyl-5-FU. Two pathways are considered as follows: (A) one where the silver and bromide ion do not interact, and (B) another where the silver and bromide ion interact in the transition states. Because the O-reaction barriers are much lower (by 13.3-22.2 kcal/mol) than N-reaction barriers in both pathways, the O-regioselectivity of the silver salt method can be satisfactorily explained by either path A or path B. Furthermore, path B, where Ag and Br interact consistently, has lower activation barriers than the corresponding path A (by 6.8-17.4 kcal/mol) in both N- and O-reactions. This computational result can be attributed to the following reasons: (1) the speeding-up effect in Koenigs-Knorr reactions due to the addition of silver carbonate into the reaction mixture; (2) the halogens being pulled away by silver ions from halides, as proposed by Kornblum and co-workers; and (3) the oxocarbenium ion involvement in the glycosidation reactions. The large energy difference between N- and O-transition states originates from the association between Ag and N-(O-) of the ambident unit (-N3-C4=O4) that shows significant covalent character so that the O-reaction transition states of the silver salt method benefit from favorable ionic interaction (C+···O-) and favorable covalent interaction (Ag···N). These two favorable interactions are in agreement with the hard and soft acids and bases principle; the former is a hard-hard interaction and the latter is a soft-soft interaction.

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.

Theoretical Studies of the Glycosidation of 2-O-Substituted 5-Fluorouracil: N-Regioselective Synthesis with the Phase-Transfer-Catalysis Method

The observed N-regioselective glycosidation of 2-O-substituted 5-fluorouracil (5-FU) via the phase-transfer-catalysis (PTC) method was investigated computationally. The Gibbs free energy reaction barrier of the N-reaction between the 5-FU anion and 1-bromo-1-deoxy-2,3,4,6-tetra-O-acetyl-α-d-glucopyranose was computed at the MP2/6-311++G(2d,p)//B3LYP/6-31+G* level. The calculated transition states were, in general, quite "loose", with the ambident reaction sites at the N3- or O4-positions on 5-FU located approximately 2.0 Å from the anomeric carbon. With the S_N2 mechanism, the formation of β-glycosides was explained by the characteristics of transition states, and the N-regioselectivity was explained by three considerations: (1) the conformations of initial complexes and the structural requirement of the reactions; (2) the formation of an ionic pair between nBu₄N⁺ and 2-O-substituted 5-FU anions; and (3) the thermodynamic conversion of O-glycosides to N-glycosides. The reactions between the oxocarbenium ion and the 2-O-substituted 5-FU anions (the fast step of S_N1 mechanism) were also examined at the same level of theory. Because there were no "promoters" to extract Br in the PTC method, the S_N1 mechanism might have an unfavorably high barrier to produce oxocarbenium ion. However, both the formation of β-glycosides and the experimentally observed N-regioselectivity could also be explained by the S_N1 mechanism: The former was explained by the neighboring group participation, and the latter was explained by the formation of ionic pairs between nBu₄N⁺ and 2-O-substituted 5-FU anions. The formation of ionic pairs possibly changed the diffusion-controlled mechanism into an activation-controlled mechanism. Two factors were demonstrated by Marcus theory to play an important role for the experimentally observed N-resioselectivity in the PTC method: (1) the thermodynamic stability of N-products over O-products; (2) the formation of ionic pair between nBu₄N⁺ and 2-O-substituted 5-FU anions.

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.