Topology of the Electron Density ofd⁰Transition Metal Compounds at Subatomic Resolution

Abstract

Accurate X-ray diffraction experiments allow for a reconstruction of the electron density distribution of solids and molecules in a crystal. The basis for the reconstruction of the electron density is in many cases a multipolar expansion of the X-ray scattering factors in terms of spherical harmonics, a so-called multipolar model. This commonly used ansatz splits the total electron density of each pseudoatom in the crystal into (i) a spherical core, (ii) a spherical valence, and (iii) a nonspherical valence contribution. Previous studies, for example, on diamond and α-silicon have already shown that this approximation is no longer valid when ultrahigh-resolution diffraction data is taken into account. We report here the results of an analysis of the calculated electron density distribution in the d(0) transition metal compounds [TMCH3](2+) (TM = Sc, Y, and La) at subatomic resolution. By a detailed molecular orbital analysis, it is demonstrated that due to the radial nodal structure of the 3d, 4d, and 5d orbitals involved in the TM-C bond formation a significant polarization of the electron density in the inner electronic shells of the TM atoms is observed. We further show that these polarizations have to be taken into account by an extended multipolar model in order to recover accurate electron density distributions from high-resolution structure factors calculated for the title compounds.

Molecular QTAIM Topology Is Sensitive to Relativistic Corrections

“…There has been a lot of work on performing QTAIM calculations with electron densities that include relativity . Several researchers have investigated the changes in topology of molecules containing heavy atoms by comparing nonrelativistic calculations with various approximate relativistic calculations.…”

“…Several researchers have investigated the changes in topology of molecules containing heavy atoms by comparing nonrelativistic calculations with various approximate relativistic calculations. Eickerling et al., Fux and Reiher, and Bučinský et al . have shown explicitly the impact of relativistic effects on the electron density.…”

“…Eickerling, Batke, and Reiher have investigated how the shell structure of atoms can be identified using the Laplacian of the density. They discussed the connection to experiment in measuring the number of shells and stress the sensitivity of the magnitude of the Laplacian to the electron density, although the experimental error may be too small to draw conclusions.…”

Lanthanides and actinides: Annual survey of their organometallic chemistry covering the year 2013

“…By a detailed molecular orbital analysis, it was demonstrated that due to the radial nodal structure of the 3d, 4d, and 5d orbitals involved in the Ln C bond formation a significant polarization of the electron density in the inner electronic shells of the Ln atoms is observed. It was further shown that these polarizations have to be taken into account by an extended multipolar model in order to recover accurate electron density distributions from high-resolution structure factors calculated for [LnCH 3 ] 2+ compounds [1]. The gas-phase reactivity of methyl fluoride with selected first-row transition metal monocations (Sc + , Ti + , V + , and Zn + ) has been theoretically investigated.…”

Valence‐Shell Electron‐Pair Repulsion Theory Revisited: An Explanation for Core Polarization

“…As an example, the inclusion of core deformations in the resolution of X‐ray data is a current field of development in crystallography . Crystallographic structures are usually resolved by resorting to a multipolar approximation . In this approach, the cores are kept frozen, whereas the valence deforms to fit the experimental structure factors by using multipoles .…”