  Spin-polarized DFT has been used to perform a comprehensive study of the
geometric structures and electronic properties for isolated M4X4 nano-clusters
between their two stable isomers - a planar rhombus-like 2D structure and a
cubane-like 3D structure with M = Mn, Fe, Co, Ni, Cu ; X = O, S. These two
structural patterns of the M4X4 clusters are commonly found as building blocks
in several poly-nuclear transition metal complexes in inorganic chemistry. The
effect of the van der Waals corrections to the physical properties have been
considered in the electronic structure calculations employing the empirical
Grimme's correction (DFT+D2). We report here an interesting trend in their
relative structural stability - the isolated M4O4 clusters prefer to stabilize
more in the planar structure, while the cubane-like 3D structure is more
favourable for most of the isolated M4S4 clusters than their planar 2D
counterparts. Our study reveals that this contrasting trend in the relative
structural stability is expected to be driven by an interesting interplay
between the s-d and p-d hybridization effects of the constituents' valence
electrons.
