Structure and Bonding in SnWO₄, PbWO₄, and BiVO₄:  Lone Pairs vs Inert Pairs

Abstract

Three ternary oxides, SnWO4, PbWO4, and BiVO4, containing p-block cations with ns2np0 electron configurations, so-called lone pair cations, have been studied theoretically using density functional theory and UV-visible diffuse reflectance spectroscopy. The computations reveal significant differences in the underlying electronic structures that are responsible for the varied crystal chemistry of the lone pair cations. The filled 5s orbitals of the Sn2+ ion interact strongly with the 2p orbitals of oxygen, which leads to a significant destabilization of symmetric structures (scheelite and zircon) favored by electrostatic forces. The destabilizing effect of this interaction can be significantly reduced by lowering the symmetry of the Sn2+ site to enable the antibonding Sn 5s-O 2p states to mix with the unfilled Sn 5p orbitals. This interaction produces a localized, nonbonding state at the top of the valence band that corresponds closely with the classical notion of a stereoactive electron lone pair. In compounds containing Pb2+ and Bi3+ the relativistic contraction of the 6s orbital reduces its interaction with oxygen, effectively diminishing its role in shaping the crystal chemical preferences of these ions. In PbWO4 this leads to a stabilization of the symmetric scheelite structure. In the case of BiVO4 the energy of the Bi 6s orbital is further stabilized. Despite this stabilization, the driving force for a stereoactive lone pair distortion appears to be enhanced. The energies of structures exhibiting distorted Bi3+ environments are competitive with structures that possess symmetric Bi3+ environments. Nevertheless, the "lone pair" that results associated with a distorted Bi3+ environment in BiVO4 is more diffuse than the Sn2+ lone pair in beta-SnWO4. Furthermore, the distortion has a much smaller impact on the electronic structure near the Fermi level.

Optical absorption of divalent metal tungstates: Correlation between the band-gap energy and the cation ionic radius

“…As well, the correlation we found can be used to make a back-of-the-envelope fairly well with previous experiments [15,16,18] supporting the correctness of the predictions made for the other four compounds, which however should de tested by future experiments and ab initio calculations. Finally, the lines drawn in Fig.…”

“…In this equation E U is the Urbach's energy, which is related to the steepness of the absorption tail, and 0 U A k E = for a direct band-gap [18], being k a characteristic parameter of each material. Fig.…”

First-principles studies of lone-pair-induced distortions in epitaxial phases of perovskiteSnTiO3andPbTiO3

“…36,[52][53][54] However, when comparing the ELF plots of the structurally similar P 4mm, Amm2 and Cm phases for the ATiO 3 perovskite structure -all non-centrosymmetric and polar, but with different directions of the unit-cell polarization vector -we did not observe any noticeable distinctions among them. Alternatively, following an approach of Watson and coworkers 20,22,23,55,56 that utilizes energy-resolved, or partial, electron charge density maps to visualize specific regions of the EDOS that are associated with the asymmetric nature of lone pairs allowed us to resolve the distinctions among these phases, as discussed in detail in section III B.…”

“…Just as described in the previous paragraph, in all polar phases, we observe asymmetric charge density distributions associated with stereochemical electron lone pair activity while, in non-polar P m3m phases, such charge density distributions have spherical symmetry. Using the same arguments as in the investigation of tungsten-based AWO 4 (A = Sn, Pb) compounds, 36 we interpret these visualization results as the Sn 2+ lone pairs being "more compact" and the Pb 2+ ones "more diffuse. "…”

“…This band gap reduction could be attributed to the stronger interaction between the Sn(5s) and O(2p) orbitals compared to that of Pb(6s) and O(2p), which leads to a more pronounced upward shift of the antibonding s-p hybrids that constitute the top of the valence band. 36 It is also noteworthy that the weakness of the A(s)-O(p) interactions in PbTiO 3 , as well as their relative insensitivity to the direction of the polar structural distortion, results in the flatness of the VBM level inside this ±2% epitaxial strain interval (see filled-circle curve in Fig. 2).…”