Distribution and Topology of the Electron Density in an Aluminosilicate Compound from High-Resolution X-ray Diffraction Data: the Case of Scolecite

Tracing electron density changes in langbeinite under pressure

Pressure is well known to dramatically alter physical properties and chemical behaviour of materials, much of which is due to the changes in chemical bonding that accompany compression. Though it is relatively easy to comprehend this correlation in the discontinuous compression regime, where phase transformations take place, understanding of the more subtle continuous compression effects is a far greater challenge, requiring insight into the finest details of electron density redistribution. In this study, a detailed examination of quantitative electron density redistribution in the mineral langbeinite was conducted at high pressure. Langbeinite is a potassium magnesium sulfate mineral with the chemical formula [K2Mg2(SO4)3], and crystallizes in the isometric tetartoidal (cubic) system. The mineral is an ore of potassium, occurs in marine evaporite deposits in association with carnallite, halite and sylvite, and gives its name to the langbeinites, a family of substances with the same cubic structure, a tetrahedral anion, and large and small cations. Single-crystal X-ray diffraction data for langbeinite have been collected at ambient pressure and at 1 GPa using a combination of in-house and synchrotron techniques. Experiments were complemented by theoretical calculations within the pressure range up to 40 GPa. On the basis of changes in structural and thermal parameters, all ions in the langbeinite structure can be grouped into 'soft' (potassium cations and oxygens) and 'hard' (sulfur and magnesium). This analysis emphasizes the importance of atomic basins as a convenient tool to analyse the redistribution of electron density under external stimuli such as pressure or temperature. Gradual reduction of completeness of experimental data accompanying compression did not significantly reduce the quality of structural, electronic and thermal parameters obtained in experimental quantitative charge density analysis.

Experimental observation of charge-shift bond in fluorite CaF2

On the basis of a multipole refinement of single-crystal X-ray diffraction data collected using an Ag source at 90 K to a resolution of 1.63 Å^-1, a quantitative experimental charge density distribution has been obtained for fluorite (CaF₂). The atoms-in-molecules integrated experimental charges for Ca²⁺ and F^- ions are +1.40 e and -0.70 e, respectively. The derived electron-density distribution, maximum electron-density paths, interaction lines and bond critical points along Ca²⁺...F^- and F^-...F^- contacts revealed the character of these interactions. The Ca²⁺...F^- interaction is clearly a closed shell and ionic in character. However, the F^-...F^- interaction has properties associated with the recently recognized type of interaction referred to as `charge-shift' bonding. This conclusion is supported by the topology of the electron localization function and analysis of the quantum theory of atoms in molecules and crystals topological parameters. The Ca²⁺...F^- bonded radii - measured as distances from the centre of the ion to the critical point - are 1.21 Å for the Ca²⁺ cation and 1.15 Å for the F^- anion. These values are in a good agreement with the corresponding Shannon ionic radii. The F^-...F^- bond path and bond critical point is also found in the CaF₂ crystal structure. According to the quantum theory of atoms in molecules and crystals, this interaction is attractive in character. This is additionally supported by the topology of non-covalent interactions based on the reduced density gradient.

Experimental determination of electrostatic properties of Na-X zeolite from high resolution X-ray diffraction

High-resolution single crystal X-ray diffraction is used for the first time to obtain the charge density distribution in dehydrated Na-X zeolite. The electron density is extracted according to the Hansen & Coppens multipolar-model, from which Pval-κ-type atomic charges are derived. In order to compare the experimental electron density with theoretical calculations on zeolites and other minerals, a topological analysis is performed to derive AIM charges and electron density properties at bond critical points. The results are compared with that described in the literature. Finally, the electrostatic potential is evaluated in a periodic, mean field approach (disordered cation distribution in the Fd3[combining macron] space group) and for a given distribution of the cations (space group P1). The electrostatic energy is, then, derived in the neighbourhood of cation sites where the molecules are usually physisorbed.

Point atomic multipole moments for simulation of electrostatic potential and field in all-siliceous zeolites

Calibration method of atomic multipole moments (AMMs) is presented with respect to geometries of all-siliceous zeolite models obtained with X-ray diffraction (XRD) methods. Mulliken atomic charges and AMMs are calculated for all-siliceous types possessing small size elementary unit cells at the hybrid density functional theory (DFT) (B3LYP) and general gradient approximation (GGA) Perdew-Burke-Ernzerhof (PBE) levels and then used to fit the dependences versus geometry variables for the Mulliken charges and versus special coordinate for the AMMs. Fitted and exact charges and AMMs are used to compute electrostatic potential (EP) and electric field (EF) for all-siliceous zeolites with CRYSTAL. A possibility of application of the point AMMs to quantum mechanical/molecular mechanics computations or classic simulation of physical adsorption is evaluated. The considered models expand over wide range of structural parameters and could be applied even to amorphous all-siliceous systems.

Bonded interactions and the crystal chemistry of minerals: a review

Connections established during last century between bond length, radii, bond strength, bond valence and crystal and molecular chemistry are briefly reviewed followed by a survey of the physical properties of the electron density distributions for a variety of minerals and representative molecules, recently generated with first-principles local energy density quantum mechanical methods. The structures for several minerals, geometry-optimized at zero pressure and at a variety of pressures were found to agree with the experimental structures within a few percent. The experimental Si–O bond lengths and the Si–O–Si angle, the Si–O bond energy and the bond critical point properties for crystal quartz are comparable with those calculated for the H6Si2O7disilicic acid molecule, an indication that the bonded interactions in silica are largely short ranged and local in nature. The topology of model experimental electron density distributions for first and second row metal M atoms bonded to O, determined with high resolution and high energy synchrotron single crystal X-ray diffraction data are compared with the topology of theoretical distributions calculated with first principles methods. As the electron density is progressively accumulated between pairs of bonded atoms, the distributions show that the nuclei are progressively shielded as the bond lengths and the bonded radii of the atoms decrease. Concomitant with the decrease in the M–O bond lengths, the local kinetic energy,G(rc), the local potential energy,V(rc), and the electronic energy density,H(rc) =G(rc) +V(rc), evaluated at the bond critical points,rc, each increases in magnitude with the local potential energy dominating the kinetic energy density in the internuclear region for intermediate and shared interactions. The shorter the bonds, the more negative the local electronic energy density, the greater the stabilization and the greater the shared character of the intermediate and shared bonded interactions. In contrast, the local kinetic energy density increases with decreasing bond length for closed shell interactions withG(rc) dominatingV(rc) in the internuclear region, typical of an ionic bond. ...

Experimental bond critical point and local energy density properties determined for Mn-O, Fe-O, and Co-O bonded interactions for tephroite, Mn2SiO4, fayalite, Fe2SiO4, and Co2SiO4 olivine and selected organic metal complexes: comparison with properties calculated for non-transition and transition metal M-O bonded interactions for silicates and oxides

Bond critical point (bcp) and local energy density properties for the electron density (ED) distributions, calculated with first-principle quantum mechanical methods for divalent transition metal Mn-, Co-, and Fe-containing silicates and oxides are compared with experimental model ED properties for tephroite, Mn 2SiO 4, fayalite, Fe 2SiO 4, and Co 2SiO 4 olivine, each determined with high-energy synchrotron single-crystal X-ray diffraction data. Trends between the experimental bond lengths, R(M-O), (M = Mn, Fe, Co), and the calculated bcp properties are comparable with those observed for non-transition M-O bonded interactions. The bcp properties, local total energy density, H( r c), and bond length trends determined for the Mn-O, Co-O, and Fe-O interactions are also comparable. A comparison is also made with model experimental bcp properties determined for several Mn-O, Fe-O, and Co-O bonded interactions for selected organometallic complexes and several oxides. Despite the complexities of the structures of the organometallic complexes, the agreement between the calculated and model experimental bcp properties is fair to good in several cases. The G( r c)/rho( r c) versus R(M-O) trends established for non-transition metal M-O bonded interactions hold for the transition metal M-O bonded interactions with G( r c)/rho( r c) increasing in value as H( r c) becomes progressively more negative in value, indicating an increasing shared character of the interaction as G( r c)/rho( r c) increases in value. As observed for the non-transition metal M-O bonded interactions, the Laplacian, nabla (2)rho( r c), increases in value as rho( r c) increases and as H( r c) decreases and becomes progressive more negative in value. The Mn-O, Fe-O, and Co-O bonded interactions are indicated to be of intermediate character with a substantial component of closed-shell character compared with Fe-S and Ni-S bonded interactions, which show greater shared character based on the | V( r c)|/ G( r c) bond character indicator. The atomic charges conferred on the transition metal atoms for the three olivines decrease with increasing atomic number from Mn to Fe to Co as the average M-O bond lengths decrease from 2.219 to 2.168 to 2.128 A, respectively.