Revealing electron delocalization through the source function.

The source function (SF) introduced in late 90s by Bader and Gatti quantifies the influence of each atom in a system in determining the amount of electron density at a given point, regardless of the atom's remote or close location with respect to the point. The SF may thus be attractive for studying directly in the real space somewhat elusive molecular properties, such as "electron conjugation" and "aromaticity", that lack rigorous definitions as they are not directly associated to quantum-mechanical observables. In this work, the results of a preliminary test aimed at understanding whether the SF descriptor is capable to reveal electron delocalization effects are corroborated by further examination of the previously investigated benzene, 1,3-cyclohexadiene, and cyclohexene series and by extending the analysis to some benchmark organic systems with different unsaturated bond patterns. The SF can actually reveal, order, and quantify π-electron delocalization effects for formal double, single conjugated, and allylic bonds, in terms of the influence of distant atoms on the electron density at given bond critical points. In polycyclic aromatic hydrocarbons, the SF neatly reveals the mutual influence of the benzenoid subunits. In naphthalene it provides a rationale for the changes observed in the local aromatic character of one ring when the other is partially hydrogenated. The SF analysis describes instead biphenyl as made up by two weakly interacting benzene rings, only slightly perturbed by the combination of mutual steric and electronic effects. Eventually, a new SF-based indicator of local aromaticity is introduced, which shows excellent correlation with the aromatic index developed by Matta and Hernández-Trujillo, based on the delocalization indices. At variance with this latter and other commonly employed quantum-mechanical (local) aromaticity descriptors, the SF-based indicator does not require the knowledge of the pair density, nor the system wave function, being therefore promising for applications to experimentally derived charge density distributions.

Conformational polymorphism in a Schiff-base macrocyclic organic ligand: an experimental and theoretical study.

Polymorphism in the highly flexible organic Schiff-base macrocycle ligand 3,6,9,17,20,23-hexa-azapentacyclo(23.3.1.1(11,15).0(2,6).0(16,20))triaconta-1(29),9,11,13,15(30),23,25,27-octaene (DIEN, C(24)H(30)N(6)) has been studied by single-crystal X-ray diffraction and both solid-state and gas-phase density functional theory (DFT) calculations. In the literature, only solvated structures of the title compound are known. Two new polymorphs and a new solvated form of DIEN, all obtained from the same solvent with different crystallization conditions, are presented for the first time. They all have P\bar 1 symmetry, with the macrocycle positioned on inversion centres. The two unsolvated polymorphic forms differ in the number of molecules in the asymmetric unit Z', density and cohesive energy. Theoretical results confirm that the most stable form is (II°), with Z' = 1.5. Two distinct molecular conformations have been found, named `endo' or `exo' according to the orientation of the imine N atoms, which can be directed towards the interior or the exterior of the macrocycle. The endo arrangement is ubiquitous in the solid state and is shared by two independent molecules which constitute an invariant supramolecular synthon in all the known crystal forms of DIEN. It is also the most stable arrangement in the gas phase. The exo form, on the other hand, appears only in phase (II°), which contains both the conformers. Similarities and differences among the occurring packing motifs, as well as solvent effects, are discussed with the aid of Hirshfeld surface fingerprint plots and correlated to the results of the energy analysis. A possible interconversion path in the gas phase between the endo and the exo conformers has been found by DFT calculations; it consists of a two-step mechanism with activation energies of the order of 30-40 kJ mol(-1). These findings have been related to the empirical evidence that the most stable phase (II°) is also the last appearing one, in accordance with Ostwald's rule.

Detection and kinetics of the single-crystal to single-crystal complete transformation of a thiiranium ion into thietanium ion.

The conversion of a di-tert-butyl-methylthiiranium ion into thietanium ion, that is reported in the literature as taking place spontaneously at 25 degrees C in a CD(2)Cl(2) solution, has been discovered to occur quantitatively at room temperature (RT) also in the crystalline state. The ring enlargement reaction is accompanied, in the solid phase, by a modest deterioration of the quality of the sample under investigation, and all three specimens here studied by in situ crystallography maintained their single-crystal nature up to 100% conversion. The rearrangement reaction implies the breaking of a C-S bond and the formation of a new bond of the same type, together with the migration of a methyl group. The extent of the corresponding atomic displacements has been measured by comparing the initial and final crystal structures. Several intermediate stages of the process have been investigated and characterized by the site occupancy factor of the episulfonium ion. The RT temporal evolution of this factor and that of the unit-cell volume indicate multi-step kinetics, with processes of simple molecular reorientation or displacement before and after the main, central stage, where the conversion reaction takes place. The overall kinetics is well described by an Avrami-Erofeev equation, with exponent m = 1.75(3) and rate coefficient k = 10.4(3) x 10(-8) s(-1) at 25 degrees C. Ab initio calculations in the gas phase predict a three-step mechanism resulting in a slightly spontaneous reaction with an overall decrease of entropy.