Charge transfer and chemical potential in 1,3-dipolar cycloadditions

Insights into Hildebrand Solubility Parameters - Contributions from Cohesive Energies or Electrophilicity Densities?

We introduce certain concepts and expressions from conceptual density functional theory (DFT) to study the properties of the Hildebrand solubility parameter. The original form of the Hildebrand solubility parameter is used to qualitatively estimate solubilities for various apolar and aprotic substances and solvents and is based on the square root of the cohesive energy density. Our results show that a revised expression allows the replacement of cohesive energy densities by electrophilicity densities, which are numerically accessible by simple DFT calculations. As an extension, the reformulated expression provides a deeper interpretation of the main contributions and, in particular, emphasizes the importance of charge transfer mechanisms. All calculated values of the Hildebrand parameters for a large number of common solvents are compared with experimental values and show good agreement for non- or moderately polar aprotic solvents in agreement with the original formulation of the Hildebrand solubility parameters. The observed deviations for more polar and protic solvents define robust limits from the original formulation which remain valid. Likewise, we show that the use of machine learning methods leads to only slightly better predictability.

In silico evaluation of new mangiferin-based Positron Emission Tomography radiopharmaceuticals through the inhibition of metalloproteinase-9

Metalloproteinase-9 (MMP-9) is a key protein in cancer advancement and metastasis owing to its ability to degrade some extracellular matrix components. Mangiferin, a natural polyphenolic compound, has demonstrated through experimental and theoretical studies to be a great anticancer agent for the selective inhibition of MMP-9. This work aimed to evaluate the utility of several fluorinated compounds obtained from MF as possible Positron Emission Tomography (PET) radiopharmaceuticals oriented to MMP-9. Density Functional Theory calculations of MF were made to obtain the most active sites toward electrophilic and nucleophilic reactions and propose a synthetic route to produce its fluorinated derivatives. The reactivity study allowed us to propose a late-stage synthetic route based on click chemistry to obtain three fluorinated MF-based derivatives. Molecular docking calculations suggested that the derivative F-propyl-MF could be suitable as PET radiopharmaceutical owing to the establishment of a five-coordinated complex with the catalytic Zn atom belonging to the active site of MMP-9, crucial factor in the inhibition of MMP-9.

One-Bond-Nucleophilicity and -Electrophilicity Parameters: An Efficient Ordering System for 1,3-Dipolar Cycloadditions

Diazoalkanes are ambiphilic 1,3-dipoles that undergo fast Huisgen cycloadditions with both electron-rich and electron-poor dipolarophiles but react slowly with alkenes of low polarity. Frontier molecular orbital (FMO) theory considering the 3-center-4-electron π-system of the propargyl fragment of diazoalkanes is commonly applied to rationalize these reactivity trends. However, we recently found that a change in the mechanism from cycloadditions to azo couplings takes place due to the existence of a previously overlooked lower-lying unoccupied molecular orbital. We now propose an alternative approach to analyze 1,3-dipolar cycloaddition reactions, which relies on the linear free energy relationship lg k₂(20 °C) = s_N(N + E) (eq 1) with two solvent-dependent parameters (N, s_N) to characterize nucleophiles and one parameter (E) for electrophiles. Rate constants for the cycloadditions of diazoalkanes with dipolarophiles were measured and compared with those calculated for the formation of zwitterions by eq 1. The difference between experimental and predicted Gibbs energies of activation is interpreted as the energy of concert, i.e., the stabilization of the transition states by the concerted formation of two new bonds. By linking the plot of lg k₂ vs N for nucleophilic dipolarophiles with that of lg k₂ vs E for electrophilic dipolarophiles, one obtains V-shaped plots which provide absolute rate constants for the stepwise reactions on the borderlines. These plots furthermore predict relative reactivities of dipolarophiles in concerted, highly asynchronous cycloadditions more precisely than the classical correlations of rate constants with FMO energies or ionization potentials. DFT calculations using the SMD solvent model confirm these interpretations.

1,3 Dipolar Cycloaddition of Münchnones: Factors behind the Regioselectivity

The 1,3 dipolar cycloaddition reactions of münchnones and alkenes provide an expedite synthetic way to substituted pyrroles, an exceedingly important structural motif in the pharmaceutical and material science fields of research. The factors governing their regioselectivity rationalization are not well understood. Using several approaches, we investigate a set of 14 reactions (featuring two münchnones, 12 different alkenes, and two alkynes). The Natural Bond Theory and the Non-Covalent Interaction Index analyses of the noncovalent interaction energies fail to predict the experimental major regioisomer. Employing global cDFT descriptors or local ones such as the Fukui function and dual descriptor yields similarly inaccurate predictions. Only the local softness pairing, within Pearson's Hard and Soft Acids and Bases principle, constitutes a reliable predictor for the major reaction product. By taking into account an estimator for the steric effects, the correct regioisomer is predicted. Steric effects play a major role in driving the regioselectivity, as was corroborated by energy decomposition analysis of the transition states.

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.

In silico development of new PET radiopharmaceuticals from mTOR inhibitors

Rapamycin (or sirolimus) is a macrolide that has shown to be useful as an immunosuppressant and that was studied in metabolic, neurological, or genetic disorders. Rapamycin is a specific natural inhibitor of the mechanistic target of rapamycin (mTOR) that is a kinase protein playing a pivotal role in cell growth and proliferation by activation of several metabolic processes. This work aimed to evaluate the utility of several compounds obtained from rapamycin and its semi-synthetic analogs everolimus and temsirolimus as possible radiopharmaceuticals oriented to this protein. Density Functional Theory calculations of these molecules were made and further analysis of the dual descriptor, charges populations, and of the electrostatic potential surfaces were performed. Molecular docking simulations were used to evaluate the interactions of the rapamycin with the studied candidates. They allowed us to propose two strategies for the synthesis of novel compounds based on electrophilic reactions. Molecular docking results also helped us to eliminate molecules that did not interact correctly with the target. Finally, we found for the first time, that the novel compounds synthesized through the electrophilic addition reaction that employed ¹⁸F-selectfluor, should maintain the biological activity of original compounds and could be suitable as Positron Emission Tomography radiopharmaceuticals targeting mTOR Complex1 system.

1,3-Dipolar Cycloadditions by a Unified Perspective Based on Conceptual and Thermodynamics Models of Chemical Reactivity

The main aim in the present report is to gain a deeper understanding of typical 1,3-dipolar cycloadditions by means of three chemical reactivity models in a unified perspective: conceptual density functional theory, distortion/interaction, and reaction force analysis. The focus is to explore the information provided by each reactivity model and how they complement or reinforce each other. Our results showed that the Bell-Evans-Polanyi (BEP) relationship is fulfilled, which is consistent with the Hammond-Leffler postulate. The electronic chemical potential based analysis classifies the reactions as HOMO-, HOMO/LUMO-, and LUMO-controlled reactions as the activation energy increases. It seems likely that HOMO-controlled reaction shifts into LUMO-controlled one as the transition state (TS) position does from early into late. Therefore, the transition from HOMO- (and early TS) into LUMO-controlled (and late TS) is paid by shifting the overall energy change into an endothermic direction, thus supporting the fulfillment of the BEP principle. While thermodynamic models unveil that the distortion or structural rearrangements mainly drive the activation barriers rather than interaction or electronic rearrangements in accord with the distortion/interaction and reaction force analysis, respectively. It is also found that both models are consistent when energy associated with structural and electronic reordering from reaction force analysis is respectively confronted with destabilizing (distortion and Pauli repulsion) and stabilizing (electrostatic and orbital interactions) contributions from the distortion/interaction model, which, on the other hand, increases as low activation barrier and high exothermicity are converted into the high barrier and low exothermicity along with the BEP relation. Finally, the reaction force constant reveals that all 1,3-dipolar cycloaddition reactions proceed by a synchronous single-step mechanism, unveiling that the degree of synchronicity is quite the same in all reactions, confirming the statement that BEP is fulfilled for similar reactions proceeding by a quite alike degree of synchronicity.

Temperature-Dependent Approach to Electronic Charge Transfer

A charge transfer model is developed within the framework of the grand canonical ensemble through the analysis of the behavior of the fractional charge as a function of the chemical potential of the bath when the temperature and the external chemical potential are kept fixed. Departing from the fact that, before the interaction between two species, each one has a zero fractional charge, one can identify two situations after the interaction occurs where the fractional charge of at least one of the species is different from zero, indicating that there has been charge transference. One of them corresponds to the case when one of the species is immersed in a bath conformed by the other one, while the other is related to the case in which both species are present in equal amounts (stoichiometric proportion). Correlations between the fractional charges and average energies, thus obtained with experimental equilibrium constants, kinetic rate constants, hydration constants, and bond enthalpies, indicate that, although at the experimental temperatures, they are very small quantities, they have chemically meaningful information. Additionally, in the stoichiometric case, one also finds a rather good correlation between the equalized chemical potential and the one obtained from experimental information for a test set of diatomic and triatomic molecules.

Evaluation of the molecular inclusion process of β-hexachlorocyclohexane in cyclodextrins

The present work aimed to study the guest–host complexes of β-hexachlorocyclohexane (β-HCH), a pesticide with high environmental stability that can cause severe health problems, with the most common cyclodextrins (α-, β-, and γ-CDs). The formation reactions of these molecular inclusion complexes were addressed in this research. The multiple minima hypersurface methodology, quantum calculations based on density functional theory and a topological exploration of the electron density based on the quantum theory of atoms in molecules approach were used to characterize the interaction spaces of the pollutant with the three CDs. Additionally, charge distribution, charge transfer and dual descriptor analyses were employed to elucidate the driving forces involved in the formation of these molecular inclusion complexes. Three types of fundamental interactions were observed: total occlusion, partial occlusion and external interaction (non-occlusion). Finally, experiments were performed to confirm the formation of the studied complexes. The most stable complexes were obtained when γ-CD was the host molecule. The interactions between the pesticide and CDs have fundamentally dispersive natures, as was confirmed experimentally by spectroscopic results. All the obtained results suggest the possibility of using CDs for the purification and treatment of water polluted with β-HCH.

The present work aimed to study the guest–host complexes of β-hexachlorocyclohexane (β-HCH), a pesticide with high environmental stability that can cause severe health problems, with the most common cyclodextrins (α-, β-, and γ-CDs).

How Biochemical Environments Fine-Tune a Redox Process: From Theoretical Models to Practical Applications

In this study, we give a new physical insight into how enzymatic environments influence a redox process. This is particularly important in a biochemical context, in which oxidoreductase enzymes and low-molecular-weight cofactors create a microenvironment, fine-tuning their specific redox potential. We present a new theoretical model, quantitatively backed up by quantum chemically calculated data obtained for key biological sulfur-based model reactions involved in preserving the cellular redox homeostasis during oxidative stress. We show that environmental effects can be quantitatively predicted from the thermodynamic cycle linking ΔΔ G(OX/RED)_ref-ligand values to the differential interaction energy ΔΔ G_int of the reduced and oxidized species with the environment. Our obtained data can be linked to hydrogen-bond patterns found in protein active sites. The thermodynamic model is further understood in the framework of molecular orbital theory. The key insight of this work is that the intrinsic properties of neither a redox couple nor the interacting environment (e.g., ligand) are enough by themselves to uniquely predict reduction potentials. Instead, system-environment interactions need to be considered. This study is of general interest as redox processes are pivotal to empower, protect, or damage organisms. Our presented thermodynamic model allows a pragmatically evaluation on the expected influence of a particular environment on a redox process, necessary to fully understand how redox processes take place in living organisms.

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.

Computational Screening of New Orthogonal Metal-Free Dipolar Cycloadditions of Mesomeric Betaines

Computational strategies have gained increasing impact in the de novo design of large molecular sets targeted to a desired application. Herein, DFT-assisted theoretical analyses of cycloadditions, involving mesoionic dipoles and strained cycloalkynes, unveil a series of unexplored mesomeric betaines as vastly superior candidates for orthogonal applications. Thus, isosydnones; thiosydnones; and a six-membered homolog, 6-oxo-1,3-oxazinium-4-olate, exhibit enhanced reactivity with respect to sydnone, which is the archetypal mesoionic ring employed so far in orthogonal chemistry. These compounds were found by assessing energy barriers and transition structures, which are largely governed by electron fluxes from dipolarophile to dipole and noncovalent interactions. Charge-transfer analysis also accounts for previous experimental and theoretical results gathered in the literature, and provides a rationale for further substitution variations. The above naked dipoles release only CO₂ as a byproduct through retro-Diels-Alder of the resulting cycloadducts. These results should invite practitioners to look at such underestimated dipoles and could also help to minimize the number of experiments.

On the outside looking in: rethinking the molecular mechanism of 1,3-dipolar cycloadditions from the perspective of bonding evolution theory. The reaction between cyclic nitrones and ethyl acrylate

Understanding the molecular mechanism of 1,3-dipolar cycloadditions using the bonding evolution theory.