Using the Source Function descriptor to dampen the multipole model bias in charge density studies from X-ray structure factors refinements

Accurate experimental characterization of the labile N–Cl bond in N-chloro-N′-(p-fluorophenyl)-benzamidine crystal at 17.5 K

Very low temperature can preserve the photolabile N–Cl bond in a N-chloro-N-benzamidine derivative long enough to carry on an accurate experimental X-ray charge density study.

Anharmonic motions versus dynamic disorder at the Mg ion from the charge densities in pyrope (Mg3Al2Si3O12) crystals at 30 K: six of one, half a dozen of the other

The possible occurrence of static/dynamic disorder at the Mg site in pyrope (Mg₃Al₂Si₃O₁₂), with or without anharmonic contribution to the thermal vibrations even at low temperatures, has been largely debated but conclusions were contrasting. Here a report is given on the experimental charge density distribution, ρ_EXP, of synthetic pyrope at T = 30 K, built through a Stewart multipolar expansion up to l = 5 and based on a very precise and accurate set of in-home measured single-crystal X-ray diffraction amplitudes with a maximum resolution of 0.44 Å. Local and integral topological properties of ρ_EXP are in substantial agreement with those of ρ_THEO, the corresponding DFT-grade quantum charge density of an ideal pyrope crystal, and those derived from synchrotron investigations of chemical bonding in olivines. Relevant thermal atomic displacements, probably anharmonic in nature, clearly affect the whole structure down to 30 K. No significant (> 2.5σ) residual Fourier peaks are detectable from the ρ_EXP distribution around Mg, after least-squares refinement of a multipole model with anharmonic thermal motion at the Mg site. Experimental findings were confirmed by a full analysis of normal vibration modes of the DFT-optimized structure of the perfect pyrope crystal. Mg undergoes wide displacements from its equilibrium position even at very low temperatures, as it is allocated in a ∼ 4.5 Å large dodecahedral cavity and involved in several soft phonon modes. Implications on the interplay among static/dynamic disorder of Mg and lattice vibrational degrees of freedom are discussed.

Source Function applied to experimental densities reveals subtle electron-delocalization effects and appraises their transferability properties in crystals

The Source Function (SF), introduced in 1998 by Richard Bader and Carlo Gatti, is succinctly reviewed and a number of paradigmatic applications to in vacuo and crystal systems are illustrated to exemplify how the SF may be used to discuss chemical bonding in both conventional and highly challenging cases. The SF enables the electron density to be seen at a point determined by source contributions from the atoms or a group of atoms of a system, and it is therefore well linked to the chemist's awareness that any local property and chemical behaviour is to some degree influenced by all the remaining parts of a system. The key and captivating feature of the SF is that its evaluation requires only knowledge of the electron density (ED) of a system, thereby enabling a comparison of ab initio and X-ray diffraction derived electron density properties on a common and rigorous basis. The capability of the SF to detect electron-delocalization effects and to quantify their degree of transferability is systematically explored in this paper through the analysis and comparison of experimentally X-ray derived Source Function patterns in benzene, naphthalene and (±)-8'-benzhydrylideneamino-1,1'-binaphthyl-2-ol (BAB) molecular crystals. It is shown that the SF tool recovers the characteristic SF percentage patterns caused by π-electron conjugation in the first two paradigmatic aromatic molecules in almost perfect quantitative agreement with those obtained from ab initio periodic calculations. Moreover, the effect of chemical substitution on the degree of transferability of such patterns to the benzene- and naphthalene-like moieties of BAB is neatly shown and quantified by the observed systematic deviations, relative to benzene and naphthalene, of only those SF contributions from the substituted C atoms. Finally, the capability of the SF to reveal electron-delocalization effects is challenged by using a promolecule density, rather than the proper quantum mechanical density, to determine the changes in SF patterns along the cyclohexene, 1,3-cyclohexadiene and benzene molecule series. It is shown that, differently from the proper quantum density, the promolecular density is unable to reproduce the SF trends anticipated by the increase of electron delocalization along the series, therefore ruling out the geometrical effect as being the only cause for the observed SF patterns changes.

Insights on spin polarization through the spin density source function

The source function for the spin density s(r) is introduced, allowing the H and O influence on s(r) to be disentangled.

Understanding how spin information is transmitted from paramagnetic to non-magnetic centers is crucial in advanced materials research and calls for novel interpretive tools. Herein, we show that the spin density at a point may be seen as determined by a local source function for such density, operating at all other points of space. Integration of the local source over Bader's quantum atoms measures their contribution in determining the spin polarization at any system's location. Each contribution may be then conveniently decomposed in a magnetic term due to the magnetic natural orbital(s) density and in a reaction or relaxation term due to the remaining orbitals density. A simple test case, ³B₁ water, is chosen to exemplify whether an atom or group of atoms concur or oppose the paramagnetic center in determining a given local spin polarization. Discriminating magnetic from reaction or relaxation contributions to such behaviour strongly enhances chemical insight, though care needs to be paid to the large sensitivity of the latter contributions to the level of the computational approach and to the difficulty of singling out the magnetic orbitals in the case of highly correlated systems. Comparison of source function atomic contributions to the spin density with those reconstructing the electron density at a system's position, enlightens how the mechanisms which determine the two densities may in general differ and how diverse may be the role played by each system's atom in determining each of the two densities. These mechanisms reflect the quite diverse portraits of the electron density and electron spin density Laplacians, hence the different local concentration/dilution of the total and (α–β) electron densities throughout the system. Being defined in terms of an observable, the source function for the spin density is also potentially amenable to experimental determination, as customarily performed for its electron density analogue.

On the nature of Ni···Ni interaction in a model dimeric Ni complex

A new dinuclear complex (NiC(5)H(4)SiMe(2)CHCH(2))(2) (2) was prepared by reacting nickelocene derivative [(C(5)H(4)SiMe(2)CH=CH(2))(2)Ni] (1) with methyllithium (MeLi). Good quality crystals were subjected to a high-resolution X-ray measurement. Subsequent multipole refinement yielded accurate description of electron density distribution. Detailed inspection of experimental electron density in Ni···Ni contact revealed that the nickel atoms are bonded and significant deformation of the metal valence shell is related to different populations of the d-orbitals. The existence of the Ni···Ni bond path explains the lack of unpaired electrons in the complex due to a possible exchange channel.