Distortions in Octahedrally Coordinated d⁰ Transition Metal Oxides:  A Continuous Symmetry Measures Approach

Abstract

More than 750 d 0 transition metal oxide octahedra have been examined in order to better understand the out-of-center distortion occurring with these cations. A continuous symmetry measures approach was used to quantify the magnitude and direction of the distortion. Using this approach we were able to divide the d 0 transition metals into three categories: strong (Mo 6+ and V 5+ ), moderate (W 6+ , Ti 4+ , Nb 5+ , and Ta 5+ ), and weak (Zr 4+ and Hf 4+ ) distorters. We also examined and discussed the directional preference of the distortion for each cation.

Oleum and Sulfuric Acid as Reaction Media: Structural Features and Thermal Behavior of RE2[W2O3(SO4)6] (RE = Sm–Gd, Ho), RE2Nb2O2(SO4)3[H(SO4)2]2 (RE = Y, Ce–Nd, Sm–Er), Sm2Nb2O2(SO4)5(S2O7), and M2Nb4O5(SO4)8 (M = Bi, Eu)

“…[24][25][26][27] This theorem is of great importance for nonlinear optical effects, and has been studied intensively with a special focus on binary and ternary oxides of d 0 ions. [28] For the binary refractory metal sulfates the decision on which theory is applicable for explaining the observed distortion effects has been ambiguous, as these compounds are polymers and not of a molecular nature. [11] However, they exhibit discrete [M=O] moieties featuring a bonding situation normally found for molecular complexes of these elements.…”

Synthesis, Crystal Structure and Hirshfeld Topology Analysis of Polymeric Silver(I) Complex with s-Triazine-Type Ligand

“…Continuous shape measure (CShM) [26,27] is the most common method used to determine the extent of distortion in a given polyhedral from an ideal shape. There are two possible ligand arrangements around the central metal ion for a hexa-coordinated metal complex: octahedral and trigonal prism.…”

Symmetry measures of the electron density

“…Shape and symmetry operation measures have been successfully applied to a number of different problems in structural chemistry. 10,11 However, a limitation to their application to problems related to chemical substitution comes from the fact that they do not correctly evaluate the chemical nature of the different constituent atoms, which is only incorporated via small effects associated to changes in bond distances and angles.…”