Shared and closed-shell O-O interactions in silicates

Bond paths of maximum electron density spanning O-O edges shared between equivalent or quasiequivalent MO_n (n > 4) coordination polyhedra are not uncommon electron density features displayed by silicates. On the basis of the positive values for the local electronic energy density, H(r _c), at the bond critical points, r_c, they qualify as weak "closed-shell" interactions. As observed for M-O bonded interactions (M = first and second row metal atoms), the electron density, ρ(r _c), and the Laplacian of the electron density increase in a regular way as the separation between the O atoms, R(O-O), decreases. A simple model, based on R(O-O) and the distances of the Si atoms from the midpoint between adjacent pairs of O atoms, partitions the O-O bond paths in the high-pressure silica polymorph coesite into two largely disjoint domains, one with and one without bond paths. The occurrence of O-O bond paths shared in common between equivalent coordination polyhedra suggests that they may be grounded in some cases on factors other man bonded interactions, particularly since they are often displayed by inert procrystal representations of the electron density. In these cases, it can be argued that the accumulation of the electron density along the paths has its origin, at least in part, in the superposition of the peripheral electron density distributions of the metal M atoms occupying the edge-sharing polyhedra. On the other hand, the accumulation of electron density along the paths may stabilize a structure by shielding the adjacent M atoms in the edge-sharing polyhedra. For closed-shell Li-O, Na-O, and Mg-O interactions, H(r_c) is positive and increases as the value of ρ(r_c) increases, unlike the "shared" Be-O, B-O, C-O, Al-O, Si-O, P-O, and S-O interactions, where H(r_c) is negative and decreases as ρ(r_c) increases. The H(r_c) values for the weak closed-shell O-O interactions also increase as ρ(r_c) increases, as observed for the closed-shell M-O interactions. On the basis of the bond critical point properties and the negative H(r_c) value, the O-O interaction comprising the O₂ molecule in silica III qualifies as a shared interaction.