Modelling lone pairs in Group 13, 14 and 15 ceramics

Theory of lone pairs

Oxides formed from post-transition metal cations (Pb, Sn, Bi, Sb, Tl) exhibit peculiar structural behavior and trends which cannot be explained through standard ionic and covalent bonding considerations alone. Revealing the nature of the underlying interactions can help in understanding the properties of current systems and the prediction of new materials tailored for specific applications. These metals are components in a range of solid oxide fuel cells, catalysts, gas sensors, superconductors and ferroelectrics.

Structural distortions and low coordination numbers in group 13, 14 and 15 oxides are associated with an ns2 electronic configuration and the associated concept of a stereochemically active, but chemically inert, electron pair. Confusion arises in that some materials (PbO, SnO, SnS) adopt distorted crystal structures (as in the layered litharge structure illustrated above), while others (PbS, PbSe, SnTe) adopt perfectly symmetric rocksalt structures; this is despite the fact that the cations have the same formal electronic configuration in all cases.

Through a systematic theoretical examination of the electronic structure and chemical bonding of these materials in both distorted and symmetric structures we have been able to formulate an updated chemical model. This formed the basis of the PhD thesis of Dr. Aron Walsh . Support was provided through a variety of high resolution X-ray emission and adsorption spectroscopic experiments performed in both the UK and the USA.

1. The cation ns² electrons are not chemically inert, but undergo substantial covalent interactions with states of anion p character.
2. The filled antibonding states resulting from the cation s - anion p interaction are located at the top of the valence band.
3. A distortion of the lattice breaks the local site symmetry and allows for an additional bonding interaction between the high energy antibonding states and cation p character, resulting a net energetic stabilization and a driving force for asymmetry. Theses interactions are shown schematically above for PbO.
4. There is a balance between the relative binding energies of the cation s and anion p states. If they are too far apart, as is the case for Pb and S, the stabilization of the distorted structure cannot offset the lost coordination of the corresponding symmetric structure.
5. This explains why the preference for distorted structures decreases as O is substituted for S, Se, Te, or as Sn is substituted for Pb and Bi (larger cation s -anion p separations are present in each case) .

related references:

92. Walsh A, Watson G.W., Payne D.J, Edgell R.G., Guo J., Glans P.A., Learmonth T., and Smith K.E.
    Electronic structure of the alpha and delta phases of Bi₂O₃: A combined ab initio and x-ray spectroscopy study
    Physical Review B 73, 235104 (2006)
    


89. Payne D.J., Egdell R.G., Walsh A., Watson G.W., Guo J., Glans P.A., Learmonth T., Smith K.E.
    Electronic origins of structural distortions in post-transition metal oxides: Experimental and theoretical evidence for a revision of the lone pair model
    Physical Review Letters 96, 157403 (2006)
    


45. Watson G.W.
    'The structure and electronic structure of SnO'
    Journal of Chemical Physics 114, 758-763 (2001).
    


30. Watson G.W. and Parker S.C.
    'The origin of the lone pair of alpha-PbO from first principles calculations.'
    Journal of Physical Chemistry B 103, 1258-1262 (1999).
    


27. Watson G.W., Parker S.C., and Kresse G.
    'Ab initio calculation of the origin of the distortion of a-PbO.'
    Physical Review B 59, 8481-8486 (1999)