Even though molecules are fundamentally quantum entities, the concept of a molecule retains certain classical attributes concerning its constituents. This includes the empirical separability of a molecule into its three-dimensional, rigid structure in Euclidean space, a framework often obtained through experimental methods like X-Ray crystallography. In this work, we delve into the mathematical implications of partitioning a molecule into its constituent parts using the widely recognized Atoms-In-Molecules (AIM) schemes, aiming to establish their validity within the framework of Information Theory concepts. We have uncovered information-theoretical justifications for employing some of the most prevalent AIM schemes in the field of Chemistry, including Hirshfeld (stockholder partitioning), Bader\'s (topological dissection), and the quantum approach (Hilbert\'s space definition). In the first approach we have applied the generalized principle of minimum relative entropy derived from the Sharma-Mittal two-parameter functional, avoiding the need for an arbitrary selection of reference promolecular atoms. Within the ambit of topological-information partitioning, we have demonstrated that the Fisher information of Bader\'s atoms conform to a comprehensive theory based on the Principle of Extreme Physical Information avoiding the need of employing the Schwinger\'s principle, which has been proven to be problematic. For the quantum approach we have presented information-theoretic justifications for conducting Löwdin symmetric transformations on the density matrix to form atomic Hilbert spaces generating orthonormal atomic orbitals with maximum occupancy for a given wavefunction.

The C-X bond cleavage in different methyl halides (CH3X; X = Cl, Br, I) mediated by 5,6-dimethylbenzimidazole-bis(dimethylglyoximate)cobalt(II) (CoIICbx) was theoretically investigated in the present work. An SN2-like mechanism was considered to simulate the chemical process where the cobalt atom acts as the nucleophile and the halogen as the leaving group. The reaction path was computed by means of the intrinsic reaction coordinate method and analyzed in detail through the reaction force formalism, the quantum theory of atoms in molecules (QTAIM), and the calculation of one-electron density derived quantities, such as the source function (SF) and the spin density. A thorough comparison of the results with those obtained in the same reaction occurring in presence of 5,6-dimethylbenzimidazole-bis(dimethylglyoximate)cobalt(I) (CoICbx) was conducted to reveal the main differences between the two cases. The reactions mediated by CoIICbx were observed to be endothermic and possess higher activation energies in contrast to the reactions where the CoICbx complex is present. The latter was supported by the reaction force results, which suggest a relationship between the activation energy and the ionization potentials of the different nucleophiles present in the cleavage reaction. Moreover, the SF results indicates that the lower axial ligand (i.e., 5,6-dimethylbenzimidazole) exclusively participates on the first stage of the reaction mediated by the CoIICbx complex, while for the CoICbx case, it appears to have an important role along the whole process. Finally, the QTAIM charge analysis indicates that oxidation of the cobalt atom occurs in both cases; at the same time, it suggests the formation of an uncommon two-center one-electron bond in the CoIICbx case. The latter was confirmed by means of electron localization calculations, which resulted in a larger electron count at the Co-C interatomic region for the CoICbx case upon comparison with its CoIICbx counterpart.

The π-conjugated supramolecular polymers (SMP) have gained vast popularity in materials chemistry and biomedicine due to their spectacular self-assembling behaviour. A detailed account of the electronic structure and bonding through quantum theory of atoms-in-molecules, non-covalent interactions, and energy decomposition analysis (EDA) in the oligomers of perylene, perylene diimide (PDI), and thionated-PDI (t-PDI) is presented. The oligomers of all three molecules show a slip angle of θ≈62° thus forming H-aggregates. The stacking pattern in perylene oligomers prefers a slip-stacked brick-layer order, while the bulkier PDI and t-PDI prefer a parallel step-wise pattern in their oligomers. Successive addition of monomers leads to a consequent rise in the association energy, although to a much greater extent in PDI and t-PDI than in perylene. While the major contribution to this association energy comes from the dispersion interactions in all three systems, the steric interactions in t-PDI quench the cooperativity in its SMP formation. A detailed analysis of the non-covalent interactions reveals the presence of π-π, π-hole⋅⋅⋅O=C, and π-hole⋅⋅⋅S=C electrostatic interactions playing a crucial role in the self-assembly process, which can be further implemented on developing force field-based methods for understanding the self-assembling mechanism in higher degree of oligomers.

The computational modeling supported with experimental results can explain the overall structural packing by predicting the hydrogen bond interactions present in any cocrystals (active pharmaceutical ingredients + coformer) as well as salts. In this context, the hydrogen bonding synthons, physiochemical properties (chemical reactivity and stability), and drug-likeliness behavior of proposed nicotinamide-oxalic acid (NIC-OXA) salt have been reported by using vibrational spectroscopic signatures (IR and Raman spectra) and quantum chemical calculations. The NIC-OXA salt was prepared by reactive crystallization method. X-ray powder diffraction (XRPD) and differential scanning calorimetry (DSC) techniques were used for the characterization and validation of NIC-OXA salt. The spectroscopic signatures revealed that (N7-H8)/(N23-H24) of the pyridine ring of NIC, (C═O), and (C-O) groups of OXA were forming the intermolecular hydrogen bonding (N-H⋯O-C), (C-H⋯O═C), and (N-H⋯O═C), respectively, in NIC-OXA salt. Additionally, the quantum theory of atoms in molecules (QTAIM) showed that (C10-H22⋯O1) and (C26-H38⋯O4) are two unconventional hydrogen bonds present in NIC-OXA salt. Also, the natural bond orbital analysis was performed to find the charge transfer interactions and revealed the strongest hydrogen bonds (N7-H8⋯O5)/(N23-H24⋯O2) in NIC-OXA salt. The frontier molecular orbital (FMO) analysis suggested more reactivity and less stability of NIC-OXA salt in comparison to NIC-CA cocrystal and NIC. The global and local reactivity descriptors calculated and predicted that NIC-OXA salt is softer than NIC-CA cocrystal and NIC. From MESP of NIC-OXA salt, it is clear that electrophilic (N7-H8)/(N23-H24), (C6═O4)/(C3═O1) and nucleophilic (C10-H22)/(C26-H38), (C6-O5)/(C3-O2) reactive groups in NIC and OXA, respectively, neutralize after the formation of NIC-OXA salt, confirming the presence of hydrogen bonding interactions (N7-H8⋯O5-C6) and (N23-H24⋯O2-C3). Lipinski\'s rule was applied to check the activeness of salt as an orally active form. The results shed light on several features of NIC-OXA salt that can further lead to the improvement in the physicochemical properties of NIC.

The ability of B atoms on two different molecules to engage with one another in a noncovalent diboron bond is studied by ab initio calculations. Due to electron donation from its substituents, the trivalent B atom of BYZ2 (Z=CO, N2 , and CNH; Y=H and F) has the ability to in turn donate charge to the B of a BX3 molecule (X=H, F, and CH3 ), thus forming a B⋅⋅⋅B diboron bond. These bonds are of two different strengths and character. BH(CO)2 and BH(CNH)2 , and their fluorosubstituted analogues BF(CO)2 and BF(CNH)2 , engage in a typical noncovalent bond with B(CH3 )3 and BF3 , with interaction energies in the 3-8 kcal/mol range. Certain other combinations result in a much stronger diboron bond, in the 26-44 kcal/mol range, and with a high degree of covalent character. Bonds of this type occur when BH3 is added to BH(CO)2 , BH(CNH)2 , BH(N2 )2 , and BF(CO)2 , or in the complexes of BH(N2 )2 with B(CH3 )3 and BF3 . The weaker noncovalent bonds are held together by roughly equal electrostatic and dispersion components, complemented by smaller polarization energy, while polarization is primarily responsible for the stronger ones.

Amide metathesis has been used to generate the first structurally characterized boryl complexes of calcium and strontium, {(Me3 Si)2 N}M{B(NDippCH)2 }(thf)n (M=Ca, n=2; M=Sr, n=3), through the reactions of the corresponding bis(amides), M{N(SiMe3 )2 }2 (thf)2 , with (thf)2 Li- {B(NDippCH)2 }. Most notably, this approach can also be applied to the analogous potassium amide K{N(SiMe3 )2 }, leading to the formation of the solvent-free borylpotassium dimer [K{B(NDippCH)2 }]2 , which is stable in the solid state at room temperature for extended periods (48 h). A dimeric structure has been determined crystallographically in which the K+ cations interact weakly with both the ipso-carbons of the flanking Dipp groups and the boron centres of the diazaborolyl heterocycles, with K⋅⋅⋅B distances of >3.1 Å. These structural features, together with atoms in molecules (QTAIM) calculations imply that the boron-containing fragment closely approaches a limiting description as a \"free\" boryl anion in the condensed phase.

Quantum theory of atoms in molecules and the orbital-free density functional theory (DFT) are combined in this work to study the spatial distribution of electrostatic and quantum electronic forces acting in stable crystals. The electron distribution is determined by electrostatic electron mutual repulsion corrected for exchange and correlation, their attraction to nuclei and by electron kinetic energy. The latter defines the spread of permissible variations in the electron momentum resulting from the de Broglie relationship and uncertainty principle, as far as the limitations of Pauli principle and the presence of atomic nuclei and other electrons allow. All forces are expressed via kinetic and DFT potentials and then defined in terms of the experimental electron density and its derivatives; hence, this approach may be considered as orbital-free quantum crystallography. The net force acting on an electron in a crystal at equilibrium is zero everywhere, presenting a balance of the kinetic Fkin(r) and potential forces F(r). The critical points of both potentials are analyzed and they are recognized as the points at which forces Fkin(r) and F(r) individually are zero (the Lagrange points). The positions of these points in a crystal are described according to Wyckoff notations, while their types depend on the considered scalar field. It was found that F(r) force pushes electrons to the atomic nuclei, while the kinetic force Fkin(r) draws electrons from nuclei. This favors formation of electron concentration bridges between some of the nearest atoms. However, in a crystal at equilibrium, only kinetic potential vkin(r) and corresponding force exhibit the electronic shells and atomic-like zero-flux basins around the nuclear attractors. The force-field approach and quantum topological theory of atoms in molecules are compared and their distinctions are clarified.

[Ni{2-H2NC(=O)C5H4N}2(H2O)2][Ni{2,6-(O2C)2C5H3N}2]·4.67H2O, a new complex salt containing a bis(2,6-dicarboxypyridine)nickel(II) anion and a bis(2-amidopyridine)diaquanickel(II) cation, was synthesized and characterized. The crystal is stabilized by an extensive network of hydrogen bonds. Alternate layers of anions and cations/water molecules parallel to (010) can be distinguished. Computational studies of the network packing of the title compound by high-level DFT-D/B3LYP calculations indicate stabilization of the networks with conventional and non-conventional intermolecular O-H...O, N-H...O and C-H...O hydrogen bonds along with π-stacking contacts. Due to the presence of water molecules and the importance of forming hydrogen bonds with the involvement of water clusters to the stability of the crystal packing, the importance and role of these water clusters, and the quantitative stability resulting from the formation of hydrogen bonds and possibly other noncovalent bonds such as π-stacking are examined. The binding energies obtained by DFT-D calculations for these contacts indicate that hydrogen bonds, especially O-H...O and N-H...O, control the construction of the crystalline packing. Additionally, the results of Bader\'s theory of AIM for these interactions agree reasonably well with the calculated energies.

High-level ab initio calculations show that the MCl3 - anions comprising Group 2B M atoms Zn, Cd, and Hg form a stable complex with the CN- anion, despite the like charge of the two ions. The complexation occurs despite a negative π-hole region above the M atom of MCl3 - . The dimerization distorts the planar geometry of MCl3 - into a pyramidal shape which reduces the negative potential above the M atom, facilitating a close approach of the two anions, with R(M⋅⋅⋅C)∼2 Å, and an overall attractive electrostatic attraction within the dimer. In the gas phase, this dimer is less stable than the pair of separated ions by some 30 kcal/mol. However, the dissociation must surmount an energy barrier of roughly 25 kcal/mol which occurs at an intermolecular distance of 4 Å. In aqueous solution, the dimerization process is exothermic and barrier-free, with a binding energy in the 11-18 kcal/mol range.