X α local spin density calculations were performed for a body of 112 molecules containing fluorine and second-row elements, silicon, phosphorus, sulphur and chlorine. The parameter α was treated as a variable and adapted to each molecule, depending upon the number and type of bonds involved. The X α atomization energies are in acceptable agreement with their experimental counterparts. The standard deviations, 5.6 and 6.2 kcal mol −1 for the X α(6-31G ∗∗) and X α(3-21G) methods, respectively, compare well with those obtained earlier for molecules containing only first-row elements. Compared to the sophisticated self-consistent hybrid B3LYP model, used here with a 6-311G(d,p) basis, our simplified approach permits considerable savings of computer time. It is shown that the 3-21G orbital basis generally offers a reasonable compromise between accuracy and economy.