Anharmonic Thermal Motion Modelling in the Experimental XRD Charge Density Determination of 1-Methyluracil at T = 23 K

The experimental electron density distribution (EDD) of 1-methyluracil (1-MUR) was obtained by single crystal X-ray diffraction (XRD) experiments at 23 K. Four different structural models fitting an extensive set of XRD data to a resolution of (sinθ/λ)max = 1.143 Å−1 are compared. Two of the models include anharmonic temperature factors, whose inclusion is supported by the Hamilton test at a 99.95% level of confidence. Positive Fourier residuals up to 0.5 eÅ–3 in magnitude were found close to the methyl group and in the region of hydrogen bonds. Residual density analysis (RDA) and molecular dynamics simulations in the solid-state demonstrate that these residuals can be likely attributed to unresolved disorder, possibly dynamical and long–range in nature. Atomic volumes and charges, molecular moments up to hexadecapoles, as well as maps of the molecular electrostatic potential were obtained from distributed multipole analysis of the EDD. The derived electrostatic properties neither depend on the details of the multipole model, nor are significantly affected by the explicit inclusion of anharmonicity in the least–squares model. The distribution of atomic charges in 1-MUR is not affected by the crystal environment in a significant way. The quality of experimental findings is discussed in light of in-crystal and gas-phase quantum simulations.

Experimental Charge Density Analysis and Electrostatic Properties of Crystalline 1,3-Bis(Dimethylamino)Squaraine and Its Dihydrate from Low Temperature (T = 18 and 20 K) XRD Data

Multipolar refinements of structural models fitting extensive sets of X-ray diffraction (XRD) data from single crystals of 1,3-bis(dimethylamino)squaraine [SQ, C8H12N2O2] and its dihydrate [SQDH, C8H12N2O2·2H2O], collected at very low T (18 ± 1 K for SQ, 20 ± 1 K for SQDH), led to an accurate description of their crystal electron density distributions. Atomic volumes and charges have been estimated from the experimental charge densities using the Quantum Theory of Atoms in Molecules (QTAIM) formalism. Our analysis confirms the common representation (in the literature and textbooks) of the squaraine central, four-membered squarylium ring as carrying two positive charges, a representation that has been recently questioned by some theoretical calculations: the integrated total charge on the C4 fragment is estimated as ca. +2.4e in SQ and +2.2e in SQDH. The topology of the experimental electron density for the SQ squaraine molecule is modified in the dihydrated crystal by interactions between the methyl groups and the H2O molecules in the crystal. Maps of the molecular electrostatic potential in the main molecular planes in both crystals clearly reveal the quadrupolar charge distribution of the squaraine molecules. Molecular quadrupole tensors, as calculated with the PAMoC package using both Stewart and QTAIM distributed multipole analysis (DMA), are the same within experimental error.

Is It Conjugated or Not? The Theoretical and Experimental Electron Density Map of Bonding in p-CH3CH2COC6H4-C≡C-C≡C-p-C6H4COCH3CH2

The electron density of p-CH3CH2COC6H4-C≡CC≡C-p-C6H4COCH3CH2 has been investigated on the basis of single-crystal X-ray diffraction data collected to high resolution at 100 K and from theoretical calculations. An analysis of the X-ray data of the diyne showed interesting “liquidity” of electron distribution along the carbon chain compared to 1,2-diphenylacetylene. These findings are compatible with the results of topological analysis of Electron Localization Function (ELF), which has also revealed a larger (than expected) concentration of the electron density at the single bonds. Both methods indicate a clear π-type or “banana” character of a single bond and a significant distortion from the typical conjugated structure of the bonding in the diyne with a small contribution of cumulenic structures.

Orbital-free quantum crystallography: view on forces in crystals

Quantum theory of atoms in molecules and the orbital-free density functional theory (DFT) are combined in this work to study the spatial distribution of electrostatic and quantum electronic forces acting in stable crystals. The electron distribution is determined by electrostatic electron mutual repulsion corrected for exchange and correlation, their attraction to nuclei and by electron kinetic energy. The latter defines the spread of permissible variations in the electron momentum resulting from the de Broglie relationship and uncertainty principle, as far as the limitations of Pauli principle and the presence of atomic nuclei and other electrons allow. All forces are expressed via kinetic and DFT potentials and then defined in terms of the experimental electron density and its derivatives; hence, this approach may be considered as orbital-free quantum crystallography. The net force acting on an electron in a crystal at equilibrium is zero everywhere, presenting a balance of the kinetic F kin( r ) and potential forces F ( r ). The critical points of both potentials are analyzed and they are recognized as the points at which forces F kin( r ) and F ( r ) individually are zero (the Lagrange points). The positions of these points in a crystal are described according to Wyckoff notations, while their types depend on the considered scalar field. It was found that F ( r ) force pushes electrons to the atomic nuclei, while the kinetic force F kin( r ) draws electrons from nuclei. This favors formation of electron concentration bridges between some of the nearest atoms. However, in a crystal at equilibrium, only kinetic potential v kin( r ) and corresponding force exhibit the electronic shells and atomic-like zero-flux basins around the nuclear attractors. The force-field approach and quantum topological theory of atoms in molecules are compared and their distinctions are clarified.

The many flavours of halogen bonds – message from experimental electron density and Raman spectroscopy

Experimental electron-density studies based on high-resolution diffraction experiments allow halogen bonds between heavy halogens to be classified. The topological properties of the electron density in Cl...Cl contacts vary smoothly as a function of the interaction distance. The situation is less straightforward for halogen bonds between iodine and small electronegative nucleophiles, such as nitrogen or oxygen, where the electron density in the bond critical point does not simply increase for shorter distances. The number of successful charge–density studies involving iodine is small, but at least individual examples for three cases have been observed. (a) Very short halogen bonds between electron-rich nucleophiles and heavy halogen atoms resemble three-centre–four-electron bonds, with a rather symmetric heavy halogen and without an appreciable σ hole. (b) For a narrow intermediate range of halogen bonds, the asymmetric electronic situation for the heavy halogen with a pronounced σ hole leads to rather low electron density in the (3,−1) critical point of the halogen bond; the properties of this bond critical point cannot fully describe the nature of the associated interaction. (c) For longer and presumably weaker contacts, the electron density in the halogen bond critical point is only to a minor extent reduced by the presence of the σ hole and hence may be higher than in the aforementioned case. In addition to the electron density and its derived properties, the halogen–carbon bond distance opposite to the σ hole and the Raman frequency for the associated vibration emerge as alternative criteria to gauge the halogen-bond strength. We find exceptionally long C—I distances for tetrafluorodiiodobenzene molecules in cocrystals with short halogen bonds and a significant red shift for their Raman vibrations.