Expression and interactions of stereo-chemically active lone pairs and their relation to structural distortions and thermal conductivity

Stereo-chemically active lone pairs are typically described as an important non-bonding effect, and large interest has centered on understanding the derived effect of lone pair expression on physical properties such as the thermal conductivity. To manipulate such properties, it is essential to understand the conditions that lead to lone pair expression and to provide a quantitative chemical description. Here we first use density functional theory calculations to establish the presence of stereo-chemically active lone pairs on antimony in $\text{MnSb}_{2}\text{O}_{4}$. The lone pairs are formed through a similar mechanism to those in binary post-transition metal compounds in an oxidation state of two less than their main group number, where the degree of orbital interaction determines the expression of the lone pair. In $\text{MnSb}_{2}\text{O}_{4}$ the Sb lone pairs interact through a void space in the crystal structure, and they minimize their mutual repulsion by introducing a deflection angle. This angle increases significantly with decreasing Sb-Sb distance, thus showing the highly destabilizing nature of the lone pair interactions. Analysis of the chemical bonding in the structure shows that it is dominated by polar covalent interactions. A database search of related ternary chalcogenide structures shows that for structures with a lone pair the degree of lone pair expression is largely determined by whether the antimony-chalcogen units are connected or not, suggesting a cooperative effect. Isolated $\text{SbX}_3$ units have larger X-Sb-X bond angles, and therefore weaker lone pair expression than connected units. Since increased lone pair expression is equivalent to an increased orbital interaction (covalent bonding), which typically leads to increased heat conduction, this can explain the previously established correlation between larger bond angles and lower thermal conductivity.