Bonded Radii and the Contraction of the Electron Density of the Oxygen Atom by Bonded Interactions

Donor Radii in Rare-Earth Complexes

We present a set of donor radii for the rare-earth cations obtained from the analysis of structural data available in the Cambridge Structural Database (CSD). Theoretical calculations using density functional theory (DFT) and wave function approaches (NEVPT2) demonstrate that the Ln-donor distances can be broken down into contributions of the cation and the donor atom, with the minimum in electron density (ρ) that defines the position of (3,-1) critical points corresponding well with Shannon's crystal radii (CR). Subsequent linear fits of the experimental bond distances for all rare earth cations (except Pm3+) afforded donor radii (rD) that allow for the prediction of Ln-donor distances regardless of the nature of the rare-earth cation and its oxidation state. This set of donor radii can be used to rationalize structural data and identify particularly weak or strong interactions, which has important implications in the understanding of the stability and reactivity of complexes of these metal ions. A few cases of incorrect atom assignments in X-ray structures were also identified using the derived rD values.

Revised radii of the univalent Cu, Ag, Au and Tl cations

Radii of Cu⁺, Ag⁺, Au⁺ and Tl⁺ cations are determined by the additive method from interatomic distances in molecular and/or crystalline halides, oxides, chalcogenides and cyanides with different coordinations of atoms, and then recalculated for the 6-coordination number. The averaged (from 74 structures) values of revised radii are equal to r(Cu⁺) = 0.74 Å, r(Ag⁺) = 0.99 Å, r(Au⁺) = 0.92 Å, r(Tl⁺) = 1.22 Å, which are consistent with radii calculated from direct cation-cation contacts in ultimately compressed metals.

Ionic radii of hydrated sodium cation from QTAIM

The sodium cation is ubiquitous in aqueous chemistry and biological systems. Yet, in spite of numerous studies, the (average) distance between the sodium cation and its water ligands, and the corresponding ionic radii, are still controversial. Recent experimental values in solution are notably smaller than those from previous X-ray studies and ab initio molecular dynamics. Here we adopt a "bottom-up" approach of obtaining these distances from quantum chemistry calculations [full MP2 with the 6-31++G(d,p) and cc-pVTZ basis-sets] of gas-phase Na⁺(H₂O)_n clusters, as a function of the sodium coordination number (CN = 2-6). The bulk limit is obtained by the polarizable continuum model, which acts to increase the interatomic distances at small CN, but has a diminishing effect as the CN increases. This extends the CN dependence of the sodium-water distances from crystal structures (CN = 4-12) to lower CN values, revealing a switch between two power laws, having a small exponent at small CNs and a larger one at large CNs. We utilize Bader's theory of atoms in molecules to bisect the Na⁺-O distances into Na⁺ and water radii. Contrary to common wisdom, the water radius is not constant, decreasing even more than that of Na⁺ as the CN decreases. We also find that the electron density at the bond critical point increases exponentially as the sodium radius decreases.

A Variety of Bond Analysis Methods, One Answer? An Investigation of the Element-Oxygen Bond of Hydroxides Hn XOH

There is a great variety of bond analysis tools that aim to extract information on the bonding situation from the molecular wavefunction. Because none of these can fully describe bonding in all of its complexity, it is necessary to regard a balanced selection of complementary analysis methods to obtain a reliable chemical conclusion. This is, however, not a feasible approach in most studies because it is a time-consuming procedure. Therefore, we provide the first comprehensive comparison of modern bonding analysis methods to reveal their informative value. The element-oxygen bond of neutral H_n XOH model compounds (X=Li, Be, B, C, N, O, F, Na, Mg, Al, Si, P, S, Cl) is investigated with a selection of different bond analysis tools, which may be assigned into three different categories: i) real space bonding indicators (quantum theory of atoms in molecules (QTAIM), the electron localizability indicator (ELI-D), and the Raub-Jansen index), ii) orbital-based descriptors (natural bond orbitals (NBO), natural resonance theory (NRT), and valence bond (VB) calculations), and iii) energy analysis methods (energy decomposition analysis (EDA) and the Q-analysis). Besides gaining a deep insight into the nature of the element-oxygen bond across the periodic table, this systematic investigation allows us to get an impression on how well these tools complement each other. Ionic, highly polarized, polarized covalent, and charge-shift bonds are discerned from each other.

Revisiting the I{\overline {\bf 1}} structures of high-temperature Ca-rich plagioclase feldspar - a single-crystal neutron and X-ray diffraction study

The I{\overline 1} structures of four natural Ca-rich plagioclase feldspars formed at high temperature were analysed using single-crystal neutron and X-ray diffraction. The neutron time-of-flight Laue diffractometer at the ORNL Spallation Neutron Source (Tennessee, USA) combined with a single-crystal X-ray diffraction instrument were able to reveal some new details about these already intensively studied structures. The split oxygen atoms refined from the neutron diffraction data show the underlying mechanism of Ca-Na ordering and the anisotropic P{\overline 1} ordering along the c-axis. The compositional ranges covered by the samples studied are quite rare for I{\overline 1} structures. The incommensurately modulated e2 structure of some plagioclase samples can easily be confused with an I{\overline 1} structure from the diffraction pattern, which puts some previously published I{\overline 1} structures into question. An incomplete phase diagram for Ca-rich plagioclase feldspar is proposed to explain the rarity of the I{\overline 1} structure in this compositional range, and a time-temperature-transformation diagram for the composition ∼An₆₆ is provided accordingly.

Oxygen Packing Fraction and the Structure of Silicon and Germanium Oxide Glasses

The recently proposed relationship between the oxygen volume fraction and topological ordering in solid and liquid oxide glasses at high pressure is examined with Bader's atoms-in-molecules (AIM) theory using glass structures generated from first principles molecular dynamics calculations. It is shown that the atomic (O/Si and O/Ge) volume ratio derived from AIM theory is not constant with pressure. This finding is due to the continuous change in the electron topology under compression. Unlike crystalline solids, there is no distinctive transition pressure for Si-O and Ge-O coordination in a glass; instead, the changes are gradual and continuous over a broad pressure range. Therefore, relating a unique Si-O or Ge-O coordination number to the properties of the glass at a given pressure is difficult.

Predicting the lattice parameters for the A I A II B II 2F7 disordered cubic fluoride pyrochlores

A simple calculation scheme based on the Ahrens ionic radii system is proposed for predicting the lattice parameters of the A I A II B II 2F7 disordered cubic fluoride pyrochlores.

Isoelectronic Theory for Cationic Radii

Ionic radii play a central role in all branches of chemistry, in geochemistry, solid-state physics, and biophysics. While authoritative compilations of experimental radii are available, their theoretical basis is unclear, and no quantitative derivation exists. Here we show how a quantitative calculation of ionic radii for cations with spherically symmetric charge distribution is obtained by charge-weighted averaging of outer and inner radii. The outer radius is the atomic (covalent) radius, and the inner is that of the underlying closed-shell orbital. The first is available from recent experimental compilations, whereas the second is calculated from a "modified Slater theory", in which the screening (S) and effective principal quantum number (n*) were previously obtained by fitting experimental ionization energies in isoelectronic series. This reproduces the experimental Shannon-Prewitt "effective ionic radii" (for coordination number 6) with mean absolute deviation of 0.025 Å, approximately the accuracy of the experimental data itself. The remarkable agreement suggests that the calculation of other cationic attributes might be based on similar principles.

On the effective ionic radii for ammonium

A set of effective ionic radii corresponding to different coordination numbers (CNs) and compatible with the radii system by Shannon [Acta Cryst. (1976), A32, 751-767] has been derived for ammonium: 1.40 Å (CN = IV), 1.48 Å (CN = VI), 1.54 Å (CN = VIII) and 1.67 Å (CN = XII). The bond-valence parameters r0 = 2.3433 Å and B = 0.262 Å have been determined for ammonium-fluorine bonds.