Topological aspects of chemical bonding in superconductors

The topological aspects of chemical bonding in superconductors are discussed using the King and Rouvray (1977) graph-theory derived approach to chemical bonding topology. It is argued that the much higher critical temperatures of the copper oxide superconductors, relative to superconductors based on metal cluster structures, can be related to the much higher ionic character and, thus, much lower polarizability of metal-oxygen bonds relative to metal-metal bonds. An assumption that Tc scales linearly with the hole concentration leads to a simple formula for estimating the critical temperature of members of homologous series such as (MIII)2(MII)2Ca(n-1)Cu(n)O(5+2n-1+x), (MIII = Bi, MII = Sr; or MIII - Tl, MII = Ba). This formula suggests that the maximum Tc obtainable from copper oxide superconductors will be far below room temperature and probably no more than 180 K.