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The tri-nuclear heterometallic tetrahedral cluster [Mo–Ru–Co( µ 3 –S)(CO) 8 (Cp)COOCH 3 ] (Cp =  η 5 -C 5 H 4 ) was studied employing quantum theory of atoms in molecules (QTAIM) to examine bonding interactions, including metal–metal (M–M), metal–sulfur (M–S), metal–carbonyl (M–CO), and metal–cyclopentadienyl (M–Cp) interactions. The electron density of bonding interactions within the cluster has its topological properties calculated based on this theory. Interestingly, the computed local topological characteristics for the Mo–Ru bond show notable distinctions in comparison to the parameters for interactions involving Mo–Co and Ru–Co, since for the latter, critical points and paths were not observed. The distribution of electron density was notably affected by the presence of bridging sulfide ligands in Mo…Co, Ru…Co interactions, much more than in the Mo–Ru bond. The characteristics of the latter bond exhibited attributes typical of interactions between open-shell metals. These features included slightly positive values for ρ ( b) and ∇ 2 ρ (b) , along with small negative values of H (b) / ρ (b) approaching zero. Additionally, using the source function (SF) and electron localization function (ELF) methods, more focus has been given to the Mo–Ru bond. The core part, [Mo–Ru–Co( µ 3 –S)], was found to have a multicenter 4 c –6 e interaction. In this core, the three M–S bonds between the metal atoms and the sulfide ligand showed similar topological parameters that were typical of open-shell (covalent) interactions. Substantial π –back donation from CO to M was identified through the execution of δ (M…O CO ) delocalization index calculations.

A new theory for the study of the reactivity in Organic Chemistry, named Molecular Electron Density Theory (MEDT), is proposed herein. MEDT is based on the idea that while the electron density distribution at the ground state is responsible for physical and chemical molecular properties, as proposed by the Density Functional Theory (DFT), the capability for changes in electron density is responsible for molecular reactivity. Within MEDT, the reactivity in Organic Chemistry is studied through a rigorous quantum chemical analysis of the changes of the electron density as well as the energies associated with these changes along the reaction path in order to understand experimental outcomes. Studies performed using MEDT allow establishing a modern rationalisation and to gain insight into molecular mechanisms and reactivity in Organic Chemistry.

The electronic structure and the participation of the simplest azomethine imine (AI) in [3+2] cycloaddition (32CA) reactions have been analysed within the Molecular Electron Density Theory (MEDT) using Density Functional Theory (DFT) calculations at the MPWB1K/6-311G(d) level. Topological analysis of the electron localisation function reveals that AI has a pseudoradical structure, while the conceptual DFT reactivity indices characterises this three-atom-component (TAC) as a moderate electrophile and a good nucleophile. The non-polar 32CA reaction of AI with ethylene takes place through a one-step mechanism with moderate activation energy, 8.7 kcal·mol−1. A bonding evolution theory study indicates that this reaction takes place through a non-concerted [2n + 2τ] mechanism in which the C–C bond formation is clearly anticipated prior to the C–N one. On the other hand, the polar 32CA reaction of AI with dicyanoethylene takes place through a two-stage one-step mechanism. Now, the activation energy is only 0.4 kcal·mol−1, in complete agreement with the high polar character of the more favourable regioisomeric transition state structure. The current MEDT study makes it possible to extend Domingo’s classification of 32CA reactions to a new pseudo(mono)radical type (pmr-type) of reactivity.

Adsorption of Li and Na on pristine and defective graphene and graphene oxide (GO) is studied using density functional theory (DFT) structural and electronic calculations, quantum theory of atoms in molecules (QTAIM), and electron localization function (ELF) analyses. DFT calculations show that Li and Na adsorptions on pristine graphene are not stable at all metal coverages examined here. However, the presence of defects on graphene support stabilizes both Li and Na adsorptions. Increased Li and Na coverages cause metal nucleation and weaken adsorption. Defective graphene is associated with the presence of band gaps and, thus, Li and Na adsorptions can be used to tune these gaps. Electronic calculations show that Li– and Na–graphene interactions are Coulombic: as Li and Na coverages increase, the metal valences partially hybridize with the graphene bands and weaken metal–graphene support interactions. However, for Li adsorption on single vacancy graphene, QTAIM, ELF, and overlap populations calculations show that the Li-C bond has some covalent character. The Li and Na adsorptions on GO are significantly stronger than on graphene and strengthen upon increased coverages. This is due to Li and Na forming bonds with both carbon and oxygen GO atoms. QTAIM and ELF are used to analyze the metal–C and metal–metal bonds (when metal nucleation is present). The Li and Na clusters may contain both covalent and metallic intra metal–metal bonds: This effect is related to the adsorption support selection. ELF bifurcation diagrams show individual metal–C and metal–metal interactions, as Li and Na are adsorbed on graphene and GO, at the metal coverages examined here.

The mechanism of the DA cycloaddition reaction between the pyridine adduct of borabenzene and acetylene has been investigated using topological analysis of the electron localization function (ELF) and catastrophe theory (bonding evolution theory, BET). The study focuses on the differences in the electronic structures of C-C and C-B bonds during their formation. Additionally, the influence of electron density functionals with different constructions (B3LYP, CAM-B3LYP, B2PLYP, M06, M062X, and M052X) on the BET results was examined. The reaction proceeds through ten distinct phases. The B-C bond forms first, followed by the C-C bond. Significant differences were observed in the behavior of the non-bonding basins V(C) and V(B) compared to the V(C), V(C) basins, which precede the formation of the bonding basins V(B,C) and V(C,C). The use of different functionals results in quantitative variations in the lengths and positions of the reaction phases—for example, relative to the transition state structure. A possible qualitative influence on the overall picture of the reaction mechanism is suggested by the results obtained using the CAM-B3LYP and B2PLYP functionals, particularly in phases VI and VII.

The study utilized the molecular electron density theory to investigate the activation energies, reaction energies, and reactivity indices of the [3+2] cycloaddition reaction between 2-diazo-3,3,3-trifluoro-1-nitropropane and phenyl methacrylate. Employing electron localization function topological analysis, the molecular mechanism of the reaction was elucidated. Interestingly, the intended formation of the two single bonds does not occur simultaneously in this process. The initial step involves the formation of C2–C5 single bond, which is a prerequisite for subsequent reactions. Only after the formation of this single bond, the formation of the second C1–N3 single bond starts. This sequential bond formation sheds light on the intricate steps involved in the [3+2] cycloaddition reaction, providing a deeper understanding of its mechanism. Furthermore, a docking study conducted on the products under review uncovered significant insights. Specifically, the oxygen and nitrogen atoms within the molecules were found to enhance the interaction energy with proteins. This was exemplified by their interaction with the protease protein associated with COVID-19. The docking study not only contributes to the understanding of the products but also hints at potential bioactive properties, particularly in the context of protein interactions with crucial implications, such as those in the fight against viral infections and their impact on human health.

The study explores the application of molecular electron density theory, focusing on the [2 + 3] cycloaddition mechanisms between nitrile-imine and chalcone or thiochalcone. Density Functional Theory (DFT) calculations employing the B3LYP/6–311(d,p) methodology are utilized to determine activation and reaction energies, as well as reactivity indices. Through investigation of conceptual DFT indices, nitrile-imine is identified as a nucleophile, while chalcone and thiochalcone act as electrophiles in the reaction. The reactions exhibit both chemo- and regiospecifics, as confirmed by Parr functions, Electron Localization Function (ELF) survey, and energetic analysis, consistent with experimental results. ELF analysis suggests a two-phase mechanism for these [2 + 3] cycloadditions. Furthermore, docking studies on the resultant products reveal enhanced interaction energies with proteins due to the presence of oxygen and sulfur atoms, in their interaction with the crystal structure of COVID-19 main protease (PDB ID: 6LU7) and paves a ways for manufacturing innovation. Graphical abstract

The intramolecular Diels–Alder (IMDA) reactions of four substituted deca-1,3,9-trienes and one N-methyleneocta-5,7-dien-1-aminium with different electrophilic/nucleophilic activations have been studied within the Molecular Electron Density Theory (MEDT) and compared to their intermolecular processes. The topological analysis of the electron density and DFT-based reactivity indices reveal that substitution does not modify neither the electronic structure nor the reactivity of the reagents relative to those involved in the intermolecular processes. The analysis of the relative energies establishes that the accelerations found in the polar IMDA reactions follow the same trend as those found in the intermolecular processes. The geometries and the electronic structures of the five transition state structures involved in the IMDA reactions are highly similar to those found in the intermolecular processes. A relative interacting atomic energy (RIAE) analysis of Diels–Alder and IMDA reactions allows for the establishment of the substituent effects on the activation energies. Although the nucleophilic frameworks are destabilized, the electrophilic frameworks are further stabilized, resulting in a reduction in the activation energies. The present MEDT study demonstrates the remarkable electronic and energetic similarity between the intermolecular and intramolecular Diels–Alder reactions. Only the lower, unfavorable activation entropy associated with the latter renders it 104 times faster than the former.

[3+2] cycloaddition reactions play a crucial role in synthesizing complex organic molecules and have significant applications in drug discovery and materials science. In this study, the [3+2] cycloaddition (32CA) reactions of N-methyl-C-4-methyl phenyl-nitrone 1 and 2-propynamide 2, which have not been extensively studied before, were investigated using molecular electron density theory (MEDT) at the B3LYP/6–311++G(d,p) level of theory. According to an electron localization function (ELF) study, N-methyl-C-4-methyl phenyl-nitrone 1 is a zwitterionic species with no pseudoradical or carbenoid centers. Conceptual density functional theory (CDFT) indices were used to predict the global electronic flux from the strong nucleophilic N-methyl-C-4-methyl phenylnitrone 1 to the electrophilic 2-propynamide 2 functions. The 32CA reactions proceeded through two pairs of stereo- and regioisomeric reaction pathways to generate four different products: 3, 4, 5, and 6. The reaction pathways were irreversible owing to their exothermic characters: −136.48, −130.08, −130.99, and −140.81 kJ mol−1, respectively. The enthalpy of the 32CA reaction leading to the formation of cycloadduct 6 was lower compared with the other path owing to a slight increase in its polar character, observed through the global electron density transfer (GEDT) during the transition states and along the reaction path. A bonding evolution theory (BET) analysis showed that these 32CA reactions proceed through the coupling of pseudoradical centers, and the formation of new C-C and C-O covalent bonds did not begin in the transition states.

Noble gases (Ngs) are the least reactive elements in the periodic table towards chemical bond formation when compared with other elements because of their completely filled valence electronic configuration. Very often, extreme conditions like low temperatures, high pressures and very reactive reagents are required for them to form meaningful chemical bonds with other elements. In this personal account, we summarize our works to date on Ng complexes where we attempted to theoretically predict viable Ng complexes having strong bonding to synthesize them under close to ambient conditions. Our works cover three different types of Ng complexes, viz., non-insertion of NgXY type, insertion of XNgY type and Ng encapsulated cage complexes where X and Y can represent any atom or group of atoms. While the first category of Ng complexes can be thermochemically stable at a certain temperature depending on the strength of the Ng-X bond, the latter two categories are kinetically stable, and therefore, their viability and the corresponding conditions depend on the size of the activation barrier associated with the release of Ng atom(s). Our major focus was devoted to understand the bonding situation in these complexes by employing the available state-of-the-art theoretic tools like natural bond orbital, electron density, and energy decomposition analyses in combination with the natural orbital for chemical valence theory. Intriguingly, these three types of complexes represent three different types of bonding scenarios. In NgXY, the strength of the donor-acceptor Ng→XY interaction depends on the polarizing power of binding the X center to draw the rather rigid electron density of Ng towards itself, and sometimes involvement of such orbitals becomes large enough, particularly for heavier Ng elements, to consider them as covalent bonds. On the other hand, in most of the XNgY cases, Ng forms an electron-shared covalent bond with X while interacting electrostatically with Y representing itself as [XNg]+Y−. Nevertheless, in some of the rare cases like NCNgNSi, both the C-Ng and Ng-N bonds can be represented as electron-shared covalent bonds. On the other hand, a cage host is an excellent moiety to examine the limits that can be pushed to attain bonding between two Ng atoms (even for He) at high pressure. The confinement effect by a small cage-like B12N12 can even induce some covalent interaction within two He atoms in the He2@B12N12 complex.