Importance of Relativistic Effects and Electron Correlation in Structure Factors and Electron Density of Diphenyl Mercury and Triphenyl Bismuth

Abstract

This study investigates the possibility of detecting relativistic effects and electron correlation in single-crystal X-ray diffraction experiments using the examples of diphenyl mercury (HgPh2) and triphenyl bismuth (BiPh3). In detail, the importance of electron correlation (ECORR), relativistic effects (REL) [distinguishing between total, scalar and spin-orbit (SO) coupling relativistic effects] and picture change error (PCE) on the theoretical electron density, its topology and its Laplacian using infinite order two component (IOTC) wave functions is discussed. This is to develop an understanding of the order of magnitude and shape of these different effects as they manifest in the electron density. Subsequently, the same effects are considered for the theoretical structure factors. It becomes clear that SO and PCE are negligible, but ECORR and scalar REL are important in low- and medium-order reflections on absolute and relative scales-not in the high-order region. As a further step, Hirshfeld atom refinement (HAR) and subsequent X-ray constrained wavefunction (XCW) fitting have been performed for the compound HgPh2 with various relativistic and nonrelativistic wave functions against the experimental structure factors. IOTC calculations of theoretical structure factors and relativistic HAR as well as relativistic XCW fitting are presented for the first time, accounting for both scalar and spin-orbit relativistic effects.

Evaluation of dispersion type metal···π arene interaction in arylbismuth compounds – an experimental and theoretical study

“…Following this approach with slight modifications provides Ph 3 Bi with a yield of more than 80%. Crystallization from EtOH gave single crystals of the monoclinic C 2/ c polymorph 1a , which was already subject of several studies including the description of its crystal structure [39–43]. Therefore, it is somewhat surprising that the bismuth···π interaction was not noted so far.…”

“…In the literature several reports exist on the monoclinic polymorph of Ph 3 Bi ( 1a ), which crystallizes in the space group C 2/ c [39–43]. The Bi···π arene interactions range from 3.727–3.856 Å, leading to the formation of 1D ribbons in the solid state due to Bi···π arene interactions (see zig-zag (Bi–arene centroid ) ∞ chain in Fig.…”

“…Hydrogen atoms were omitted for clarity. Selected distances [Å]: Bi1–arene centroid 3.763 (violet dash line) [39–43]; b) formation of the two parallelograms connected via one edge, formed via two C–H Ph ···π (arene centroid ) intermolecular contacts with C33–H33 Ph ···π (arene centroid ) 3.030 Å (blue dashed line, γ = 10.9°); c) wire and stick model of 2D and 3D networks formed via C–H Ph ···π (arene centroid ) intermolecular contacts C14–H14 Ph ···π (arene centroid ) distances of 3.042 Å (green dashed line, γ = 19.5°), C15–H15 Ph ···π (arene centroid ) distances of 2.760 Å (black dashed line, γ = 6.4°) and C36–H36 Ph ···π (arene centroid ) distances of 2.740 Å (red dashed line, γ = 11.2°), respectively (only hydrogen atoms involved in C–H Ph ···π (arene centroid ) contacts are shown). Symmetry transformation: a = x, 1 + y , z ; b = 1 ∕ 2 – x, 3 ∕ 2 – y , – z ; c = 1 ∕ 2 – x , 5 ∕ 2 – y , – z .…”

Electronic structure theory to decipher the chemical bonding in actinide systems

“…Very few systematic studies of the effects of the relativity on the topology of the electron density exists in the literature for actinides or other heavy elements of the periodic table (e.g. see [165,166]). Amaouch et al [167] propose a QTAIM and ELF topological analyzes of the bonding in At 2 and UO 2 2+ in the framework of two-component relativistic DFT comparing scalar-relativistic and spin-orbit coupling calculations.…”

“…The main conclusion of the various studies (including non-actinides heavy elements) is that relativistic effects are not only restricted to the core electron density of heavy elements but are also clearly discernible in the outer core and the valence region within adjacent bonds [165]. In most cases scalar relativistic variants of the Hamiltonian operators as ZORA and DKH are sufficient to obtain a reasonable description of the electron density [166,168].…”