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

Intricate behaviour of one-electron potentials from the Euler equation for electron density and corresponding gradient force fields in crystals was studied. Channels of locally enhanced kinetic potential and corresponding saddle Lagrange points were found between chemically bonded atoms. Superposition of electrostatic ϕ e s r and kinetic ϕ k r potentials and electron density ρ r allowed partitioning any molecules and crystals into atomic ρ - and potential-based ϕ -basins; ϕ k -basins explicitly account for the electron exchange effect, which is missed for ϕ e s -ones. Phenomena of interatomic charge transfer and related electron exchange were explained in terms of space gaps between zero-flux surfaces of ρ - and ϕ -basins. The gap between ϕ e s - and ρ -basins represents the charge transfer, while the gap between ϕ k - and ρ -basins is a real-space manifestation of sharing the transferred electrons caused by the static exchange and kinetic effects as a response against the electron transfer. The regularity describing relative positions of ρ -, ϕ e s -, and ϕ k - basin boundaries between interacting atoms was proposed. The position of ϕ k -boundary between ϕ e s - and ρ -ones within an electron occupier atom determines the extent of transferred electron sharing. The stronger an H⋅⋅⋅O hydrogen bond is, the deeper hydrogen atom's ϕ k -basin penetrates oxygen atom's ρ -basin, while for covalent bonds a ϕ k -boundary closely approaches a ϕ e s -one indicating almost complete sharing of the transferred electrons. In the case of ionic bonds, the same region corresponds to electron pairing within the ρ -basin of an electron occupier atom.

The Effects of Chemical Bonding at Subatomic Resolution: A Case Study on α-Boron

Similar to classical asphericity shifts, aspherical deformations of the electron density in the atomic core region can result in core asphericity shifts in refinements using a Hansen-Coppens multipolar model (HCM), especially when highly precise experimental datasets with resolutions far beyond sin(θ)/λ ≤ 1.0 Å⁻¹ are employed. These shifts are about two orders of magnitude smaller than their counterparts caused by valence shell deformations, and their underlying deformations are mainly of dipolar character for 1st row atoms. Here, we analyze the resolution dependence of core asphericity shifts in α-boron. Based on theoretical structure factors, an appropriate Extended HCM (EHCM) is developed, which is tested against experimental high-resolution (sin(θ)/λ ≤ 1.6 Å⁻¹) single-crystal diffraction data. Bond length deviations due to core asphericity shifts of α-boron in the order of 4–6·10⁻⁴ Å are small but significant at this resolution and can be effectively compensated by an EHCM, although the correlation of the additional model parameters with positional parameters prevented a free refinement of all core model parameters. For high quality, high resolution data, a proper treatment with an EHCM or other equivalent methods is therefore highly recommended.

Orbital-Free Quantum Crystallographic View on Noncovalent Bonding: Insights into Hydrogen Bonds, π⋅⋅⋅π and Reverse Electron Lone Pair⋅⋅⋅π Interactions

A detailed analysis of a complete set of the local potentials that appear in the Euler equation for electron density is carried out for noncovalent interactions in the crystal of a uracil derivative using experimental X-ray charge density. The interplay between the quantum theory of atoms in molecules and crystals and the local potentials and corresponding inner-crystal electronic forces of electrostatic and kinetic origin is explored. Partitioning of crystal space into atomic basins and atomic-like potential basins led us to the definite description of interatomic interaction and charge transfer. Novel physically grounded bonding descriptors derived within the orbital-free quantum crystallography provided the detailed examination of π-stacking and intricate C=O⋅⋅⋅π interactions and nonclassical hydrogen bonds present in the crystal. The donor-acceptor character of these interactions is revealed by analysis of Pauli and von Weizsäcker potentials together with well-known functions, e. g., deformation electron density and electron localization function. In this way, our analysis throws light on aspects of these closed-shell interactions hitherto hidden from the description.

Taming the Cationic Beast: Novel Developments in the Synthesis and Application of Weakly Coordinating Anions

This Review gives a comprehensive overview of the most topical weakly coordinating anions (WCAs) and contains information on WCA design, stability, and applications. As an update to the 2004 review, developments in common classes of WCA are included. Methods for the incorporation of WCAs into a given system are discussed and advice given on how to best choose a method for the introduction of a particular WCA. A series of starting materials for a large number of WCA precursors and references are tabulated as a useful resource when looking for procedures to prepare WCAs. Furthermore, a collection of scales that allow the performance of a WCA, or its underlying Lewis acid, to be judged is collated with some advice on how to use them. The examples chosen to illustrate WCA developments are taken from a broad selection of topics where WCAs play a role. In addition a section focusing on transition metal and catalysis applications as well as supporting electrolytes is also included.

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.