Abstract:The implementation of the n-center electron delocalization indices, n-DIs, and n-order electron localization indices, n-LIs, within the framework of the quantum theory of atoms in molecules, QTAIM, is performed. n-DIs are shown to be very useful to study the local aromaticity in monocyclic and polycyclic compounds. Total and p n-DIs from n ¼ 4 to 7 were computed for a series of typical 4, 5, 6, and 7-center aromatic and antiaromatic rings. For n ! 5 the p n-DI accounts for the 95% of the total n-DI and can be employed alone to measure the aromaticity. A scaling factor on the n-DIs is required in order to compare the aromaticity of [5c-6e] and [6c-6e] rings, the same correction allows to estimate the relative aromatic stabilization of polycyclic compounds using the sum of its values for individual rings. This is called Effective Scaled Electron Delocalization, ESED. The comparison with other aromaticity indices reflects a good correlation between ESED and both resonance energies, and HOMA indices. The most important differences between scaled p n-DIs and NICS(0) indices are found for compounds that contain rings with different number of centers or p electrons.

Conjugated circuits have been employed to accurately reproduce the aromatic stabilization, London susceptibility, and ring current maps in polycyclic aromatic hydrocarbons, PAHs, focusing on polybenzenoids. Starting from a wave function ansatz, constructed as a superposition of Kekulé valence bond structures, the conjugated circuit resonance energy is derived using the second quantization formulation. Approximated expressions for the resonance energy, London susceptibility, and ring electron current intensity have been obtained. In these expressions, the benzene molecule is employed as a reference for the calculation in a graph theoretical fashion of properties in larger polybenzenoids. Comparison of the results obtained with conjugated circuits with those obtained using more accurate quantum chemical methods reflects the power of the conjugated circuit concept as a quantitative tool for the study of magnetic properties in PAHs. Besides the usefulness of this methodology for understanding and interpreting both the aromatic stabilization and the magnetic behavior of small and medium size PAHs, it provides a straightforward alternative way for the computation of these properties in giant PAHs for which ab initio calculations are not applicable.

A study of the intramolecular hydrogen bond (IHB) in 1,2-ethanediol and 1,2-dihydroxybenzene (catechol) was carried out using the QTAIM theory. Atomic and bond properties defined within this theory were calculated for different donor-acceptor distances, H d Á Á ÁO a , in both molecules, and different H-O a -C-C dihedral angles for 1,2-dihydroxybenzene, optimising the remaining geometry. Though no conformer of both compounds present IHB, it appears when the H d Á Á ÁO a distance is reduced in both molecules or when the H-O a -C-C angle is rotated in 1,2-dihydroxybenzene. The evolution of integrated and local properties follows the criteria of Koch and Popelier for hydrogen bond formation when the interatomic distance is modified, but display the opposite trends when the IHB is formed by rotating the dihedral angle.

The suitability of implicitly dispersion-corrected functionals, namely the M06-2X, for the determination of interaction energies and electron polarization densities in adsorption studies of aromatic molecules on carbon allotropes surfaces is analysed by comparing the results with those obtained using explicit dispersion through Grimme's empirical corrections. Several models of increasing size for the graphene sheet together with one-dimensional curved carbon structures, (5,5), (6,6) and (7,7) armchair single-walled nanotubes, and two-dimensional curved carbon structures, C60 fullerene, have been considered as substrates in this work, whereas pyridine has been chosen as an example for the adsorbed aromatic molecule. Comparison with recent experimental estimations of the adsorption energy and calculations using periodic boundary conditions on a supercell of 72 carbon atoms indicates that a finite model containing ninety six carbon atoms (C96) approaches quite well the adsorption on a graphene sheet. Analysis of the interaction energy components reveals that the M06-2X functional accounts for most of the dispersion energy implicitly, followed far by wB97X and B3LYP, whereas B97 and BLYP do not differ too much from HF. It has been found that M06-2X corrects only the energy component associated to dispersion and leaves the rest, electrostatic, Pauli and induction "unaltered" with respect to the other DFT functionals investigated. Moreover, only the M06-2X functional reflects the effect of dispersion on the electron polarization density, whereas for the remaining functionals the polarization density does not differ too much from the HF density. This makes the former functional more suitable a priori for the calculation of electron density related properties in these adsorption complexes.

The aim of this review is to describe the main physicochemical characteristics of diverse types of humic‐metal‐phosphate acid complexes. The effects of these complexes on phosphorus (P) fixation in soils with different pH values and physicochemical features and on plant phosphorus uptake are also discussed. Humic‐metal‐phosphate complexes have apparent stability constants in the same range as those of metal‐humic complexes, in solutions with diverse pH and ionic‐strength values. Likewise, the molecular‐size distribution of humic‐metal‐phosphate complexes as a function of pH is similar to that of potassium or sodium humates and metal‐humic complexes. Humic‐metal‐phosphate complexes are able to decrease phosphate fixation in soils and increase plant growth and phosphate uptake. Phosphorus fertilizers containing humic‐metal‐phosphate complexes proved to be efficient to improve plant growth and P uptake with respect to conventional fertilizers such as single superphosphate. The values of parameters related to plant phosphorus‐utilization efficiency (PUt E) suggest that the regulation of root acquisition of phosphate from these complexes could involve the interregulation of a system for the optimization of metabolic P utilization in the shoot and another system involving stress responses of roots under phosphorus deficiency.