On the transfer of theoretical multipole parameters for restoring static electron density and revealing and treating atomic anharmonic motion. Features of chemical bonding in crystals of an isocyanuric acid derivative

Abstract

The crystal and electronic structure of an isocyanuric acid derivative was studied by high-resolution single-crystal X-ray diffraction within the Hansen–Coppens multipole formalism. The observed deformation electron density shows signs of thermal smearing. The experimental picture meaningfully assigned to the consequences of unmodelled anharmonic atomic motion. Straightforward simultaneous refinement of all parameters, including Gram–Charlier coefficients, resulted in more significant distortion of apparent static electron density, even though the residual density became significantly flatter and more featureless. Further, the method of transferring multipole parameters from the model refined against theoretical structure factors as an initial guess was employed, followed by the subsequent block refinement of Gram–Charlier coefficients and the other parameters. This procedure allowed us to appropriately distinguish static electron density from the contaminant smearing effects of insufficiently accounted atomic motion. In particular, some covalent bonds and the weak π...π interaction between isocyanurate moieties were studied via the mutual penetration of atomic-like kinetic and electrostatic potential φ-basins with complementary atomic ρ-basins. Further, local electronic temperature was applied as an advanced descriptor for both covalent bonds and noncovalent interactions. Total probability density function (PDF) of nuclear displacement showed virtually no negative regions close to and around the atomic nuclei. The distribution of anharmonic PDF to a certain extent matched the residual electron density from the multipole model before anharmonic refinement. No signs of disordering of the sulfonyl group hidden in the modelled anharmonic motion were found in the PDF.

Real‐Space Interpretation of Interatomic Charge Transfer and Electron Exchange Effects by Combining Static and Kinetic Potentials and Associated Vector Fields**

“…Experimental static ED distributions were restored via multipole models for crystalline oxalic acid dihydrate (COOH) 2 × 2H 2 O, sodium chloride (NaCl), [20] high-temperature superconductor magnesium diboride (MgB 2 ), [73] and 1-{2-[2-(methoxycarbonylmethylsulfonyl)ethoxy]ethyl}-3,5-dimethylisocyanurate (ica; see Scheme S1). [64] Analysis of multipolemodeled ED and scalar fields was performed using the WinXPRO software [74] according to the published procedures. [15,75] The orbital-free local density approximation of f x r ð Þ by von Barth and Hedin was used.…”

“…Previously, we noted that according to the widely accepted classifications of the interaction types, [78][79][80] the S=O bond in ica can be formally categorized as the intermediate interaction. [64] In particular, the Laplacian of ED r 2 1 r ð Þ at the BCP is positive, the total electronic energy density h r ð Þ at the BCP has a negative value, the ratio of the absolute value of potential energy density to kinetic energy density v r ð Þ j j=g r ð Þ at the BCP is slightly less than two, while the ratio g r ð Þ=1 r ð Þ is higher than one. The behaviour of f W r ð Þ and f P r ð Þ confirms that, in fact, the S=O bond is not practically different from any other covalent ones.…”

“…The topology of f es r ð Þ [56,[59][60][61][62][63] in combination with 1-basins is widely employed for describing electrostatic contribution for various interactions in associates and crystals. [14,15,48,[64][65][66][67][68][69][70][71] Further, the gap between f es -and 1-basins is attributed to phenomena of interatomic charge (electron) transfer and can be used to estimate it. [15] However, although f k -basins (pseudoatoms) and corresponding kinetic force field have a robust physical definition, it is not clear for now how they can be exploited to retrieve chemical information.…”

“…[15] However, although f k -basins (pseudoatoms) and corresponding kinetic force field have a robust physical definition, it is not clear for now how they can be exploited to retrieve chemical information. [15,20,64,72] In this work, we generalize the described methodology to different kinds of chemical bonds present in a diverse set of selected crystals, including polar and nonpolar covalent bonds, ionic ones, and classical and nonclassical hydrogen bonds, as well as several weak to moderate intermolecular interactions. By combining the approach of superposing 1-and f-basins with the study of the behaviour of electronic potentials and corresponding forces, [15] we arrived at a phenomenological partitioning scheme of many-nuclear many-electron systems, which enables us to further understand the complex atomic structure of electron occupier revealed by different basin boundaries and phenomena of charge transfer and subsequent exchange, electron sharing, and chemical bonding.…”

“…According to Gauss‐Ostrogradsky's divergence theorem, the total integrated charges over ‐basins are equal to zero and ‐boundary can be viewed as an electrostatic shield preventing the accessibility of any external charge inside a ‐basin and any internal charge outside it. The topology of [56,59–63] in combination with ‐basins is widely employed for describing electrostatic contribution for various interactions in associates and crystals [14,15,48,64–71] . Further, the gap between ‐ and ‐basins is attributed to phenomena of interatomic charge (electron) transfer and can be used to estimate it [15] .…”