A nonlocal, quasirelativistic density functional method, NL-SCF+QR, has been used to study the geometries and relative stabilities of the classical (I) and nonclassical (II) isomers of M(PH3)(3)H-4 with M = Fe, Ru, and Os. According to the energy calculations based on optimized geometries, the dihydrogen complex (II) is found to be most stable for Fe and Ru whereas the hydride complex (I) is the isomer of lowest energy for Os. These findings are in accordance with experimental observations. It was further found that relativistic effects are responsible for the changeover in the order of stability between I and II in going from M = Fe and Ru to M = Os. Without relativity all three metal centers would prefer conformation II. The observed preference for a dihydride complex (I) in the case of the heavier congener osmium is explained by a relativistic destabilization of the 5d orbital which makes the metal center more basic.