Bonding and antibonding characters of the first order reduced density matrix. A new look at two charge-shift bonds.

This article reports a new way of analyzing chemical bonds based on the use of gradient of a first order reduced density matrix (1-RDM) map to partition bonds into atomic core, valence, and dorsal regions that can be further characterized as bonding or antibonding. These classifications are directly related to the familiar language of molecular orbital analysis. Analyses based on these quantities and the critical points of the 1-RDM performed on two charge-shift bonds show that although they share common features, there are fundamental differences in these interactions that are detected neither by density-based analysis nor by valence bond theory. The results suggest the gradient of 1-RDM as a valuable tool in bond analysis.

Theoretical determination of half-wave potentials for phenanthroline-, bipyridine-, acetylacetonate-, and glycinate-containing copper (II) complexes.

We report a protocol for the evaluation of theoretical half-wave potential (E1/2) using a set of 22 mixed chelate copper (II) complexes containing 1,10-phenanthroline and 2,2'-bipyridine derivatives as primary ligands, and acetylacetonate or glycinate as secondary ligands (formally from the Casiopeínas® family) for which accurate experimental values were determined in a 2/5 mixture of ethanol/water. We have calibrated the BP86, PBE, PBE0, B3LYP, M06-2X, and ω-B97XD functionals, using the Los Alamos LANL2DZ and Stuttgart-Köln SDDAll effective core potentials for the Cu and Fe atoms and the 6-311+G* basis set for the C, H, O, and N atoms. To address the solvent effects, we have saturated the first solvation shell with up to 9 water molecules for the explicit model and compared it with the Continuum Like-Polarizable Continuum Model (CPCM) implicit solvent scheme. We found that the PBE/LANL2DZ-6-311+G* protocol (with the CPCM implicit solvent scheme with an effective dielectric constant ε = 64.9121 for the 2/5 mixture of ethanol/water) yields the overall best performance. The theoretical values are compared with experimental data, three of which are reported here for the first time. We find good correlations between the theoretical and experimental E1/2 values for the 2,2'-bipyridine derivatives (R2 = 0.987, MAE = 86 mV) and 1,10-phenanthroline derivatives (R2 = 0.802, MAE = 58.4 mV). The correlation trends have been explained in terms of the copper atom's ability to be reduced in the presence of the ligands. The Gibbs free energy differences at 298 K obtained for the redox reactions show that the more flexible secondary ligands (acetylacetonate) lead to larger entropic contributions which, as expected, increase the average MAE values as compared with the more rigid ligands (glycine). The present protocol yields lower MAEs as compared with previous approaches for similar mixed and flexible Cu(II) complexes.

Electronic charge density analysis of Li-doped polyacetylene: molecular vs periodic descriptions and nature of Li-to-chain bonding.

A detailed analysis of the electronic structure and charge distribution around the trigonal site of Li-doped polyacetylene is reported using finite chain and periodic descriptions of the polymer. Atoms-in-molecules (AIM) analysis is done to characterize the nature of the bond between Li and the polymer backbone through the location of the bond critical points and computation of the total charge on the atomic basins around the doping site. We find that the Li atom donates practically one electron to the π-system, in accordance with the classical Su-Schriffer-Heeger model. However, despite that the Li atom is equidistant from the three closest C atoms in the geometric soliton, a single Li-C bond critical point is found. The AIM quantitative analysis of the electronic density reveals that the Li(+) ion is immersed into the polymer π-cloud in a way that resembles a metallic bonding interaction.