Some very recent applications in ab initio computational quantum chemistry are reviewed and mainly previewed. A large number of sulphone, sulphoxide and sulphide geometric structures have been gradient optimized at the single electronic configuration self-consistent field (SCF) level using a 6-31G* (or 6-31+G* for anions) basis set. This collection allows a comparison and understanding of trends and effects in their electronic and geometric structural properties. The degree of intra- and inter-molecular hydrogen bonding involving the methyl group with the SO bond in hypervalent sulphur compounds has been characterized. A comparison of calculated dimer and 1:1 monomer-water complex structures allows a consideration of the relative importance of different hydrogen bonding situations (C-H, S-H and O-H with the SO bond) in these types of compound. A number of other hydrogen-bonded adducts involving (C-)H-O(C) and (HO-)H&-O(P) interactions, which shed light on recent experimental results, have also been studied. The homonuclear and mixed triple-bonded diatomic molecules (XYn+) with X, Y = nitrogen and oxygen form a ten-valent electron isoelectronic series (N2, NO+ and O22+) for comparison of calculated properties with experiment. The O22+ energy interaction curve shows an interesting avoided curve crossing and a metastable energy minimum, a barrier to dissociation and an exothermic bond energy. For these systems, the complete active space multi-configuration SCF method is needed for even a qualitatively correct electronic structure description of the whole curve. Relativistic effective core potentials, which replace the inert core electrons in the heavier elements, allow this study to be extended to, for example, Pt22+, Au22+ and Hg22+, as well as the whole XY2+ series with X, Y = O, S, Se and Te.