A statistical analysis of magic numbers of valence electrons in small clusters of transition metals using the Cambridge Crystal Structure Database

Abstract

Distribution of small clusters of transition metals M n with n = 3 to 6 metal atoms over the number of valence electrons in metallopolyhedra, N val, has been analysed using the Cambridge Crystal Structure Database (10 sets, total 923 crystal structures). The occurrence of peaks related to magic numbers N val has been found for trinuclear (48e), tetranuclear (60e) and hexanuclear (86e) carbonyl clusters of metals of the Fe and Co subgroups. However, similar distributions for pentanuclear carbonyl clusters of the same metals, for tri- and tetranuclear carbonyl-phosphine derivatives of metals of the Ni subgroup, and also for the M 4(μ 3-X) 4 type clusters with mixed cubane-like frameworks (where X is a halogen or chalcogen) are more uniform and exhibit no predominance of specific “magic” numbers. Among tri- and tetranuclear metal complexes of the Cu subgroup, the more common and typical are those with no metal-metal bonds, in which every metal atom has a 17-, 18-, or 19-electron valence shell. On going from metals of the Fe and Co subgroups to post-transition elements, the strength of metal-metal bonds and the descriptive ability of magic numbers decline. The following magic numbers were found for octahedral “inorganic” clusters of early transition metals: N val = 74 for clusters of the M 6(μ 3-X) 12 type (where X is a halogen) and a more strictly obeyed number N val=84 valid for more rigid frameworks M 6(μ 3-X) 8, (X is halogen or chalcogen).