Quantum chemistry of highly symmetrical molecules and free space clusters, plus almost spherical cages of C and B atoms

In early work by one of us, the forerunner of modern density functional theory (DFT), namely the Thomas-Fermi (TF) statistical method, was employed in conjunction with a one-centre expansion, to treat tetrahedral and octahedral molecules, such as GeH$_4$ and SF$_6$. This led at equilibrium to rather remarkable scaling properties, especially connected with the nuclear-nuclear potential energy $V_{nn}$, which correlated strongly with the number of electrons. A fully quantum-mechanical generalization of these TF results has recently been provided by Krishtal \emph{et al.}, and their results are also summarized. Some attention is devoted to both positive and negative molecular ions at equilibrium, mainly focussing on SiH$_4$ in relation to available experimental findings. While the above molecules can all be synthesized, we then pay substantial attention to very recent quantum-chemical studies on free-space clusters. Particular attention is here drawn to oxygen clusters, the motivation being to gain insight into some solid-state properties predicted for the molecular solid CO$_2$, first of all at ambient pressure. More briefly, almost spherical cages of C and B atoms are referred to.