The authors investigate the common qualitative idea that a solid is particularly stable if the electron states are filled up to some energy band gap. Such ideas have previously been advanced to explain the occurrence of a certain family of M5X4 compounds (M=transition metal, X=chalcogen) only for particular ranges of valence electron concentration (VEC). In these materials octahedral metal clusters condense to form infinite chains. The authors study the stability of such chains against break-up on two models, (i) a regular octahedral chain and (ii) the chain of the compound Nb 5Te4 and discuss the question of why only the compounds with 2.4