The 6-31 G* and 6-31 G·· basis sets previously introduced for first-row atoms have been extended through thesecond-row of the periodic table. Equilibrium geometries for one-heavy-atom hydrides calculated for the twobasissets and using Hartree-Fock wave functions are in good agreement both with each other and with theexperimental data. HF/6-31G· structures, obtained for two-heavy-atom hydrides and for a variety ofhypervalent second-row molecules, are also in excellent accord with experimental equilibrium geometries. Nolarge deviations between calculated and experimental single bond lengths have been noted, in contrast toprevious work on analogous first-row compounds, where limiting Hartree-Fock distances were in error by upto a tenth of an angstrom. Equilibrium geometries calculated at the HF /6-31 G level are consistently in betteragreement with the experimental data than are those previously obtained using the simple split-valance 3-21Gbasis set for both normal- and hypervalent compounds. Normal-mode vibrational frequencies derived from 6-31G· level calculations are consistently larger than the corresponding experimental values, typically by%-15%; they are of much more uniform quality than those obtained from the 3-21G basis set.Hydrogenation energies calculated for normal- and hypervalent compounds are in moderate accord withexperimental data, although in some instances large errors appear. Calculated energies relating to thestabilities of single and multiple bonds are in much better accord with the experimental energy differences.