An equation relating the strength (bondforming power) of an spd hybrid bon orbital to the angles it makes with other bond orbitals is formulated and applied in the discussion of the structures of transition-metal carbonyls and other substances by the valence-bond method. The rather simple theory gives results that agree well with those obtained by the complicated and laborious calculation of sets of orthogonal hybrid bond orbitals with maximum strength.During the last two decades there has been intense activity in the field of the synthesis of compounds of the transition metals, such as those containing carbonyl and cyclopentadienyl groups. Hundreds of these compounds have been made, and the structures of scores of them have been determined by the x-ray diffraction method. The theoretical treatment of the substances has been carried out by the molecular-orbital method, and has yielded only qualitative results. For example, the short Re-Re distance 222 pm reported for the ion Re2CI82-by Kuznetzov and Koz'min (1) was interpreted by Cotton as showing that the rhenium atoms are connected by a quadruple bond, and Cotton formulated a simple molecular-orbital theory that provided an explanation of the eclipsed configuration of the two ReCL4 groups, as follows (2): "The d.a2 y2orbital on each metal atom was assumed to be employed mainly in Re-Cl bonding and the remaining four d orbitals on each metal atom were used to form the Re-Re bond. Overlap of the d52 orbitals give rise to a a bond; overlap of corresponding pairs of the dX2 and dy4 orbitals leads to formation of a pair of r bonds. Finally, overlap of the dxy orbitals gives rise to a a bond. The eclipsed configuration is a consequence of the a component of the bond since that is the only component that is angle-dependent." Neither this nor any other molecular-orbital treatment (3) provides any significant discussion of bond angles and bond lengths or of the relative stability of alternative structures.I have now found a simple relation between the strength (the bond-forming power) of a hybrid spd bond orbital and the angles that it makes with other similar orbitals that permits the prediction to be made of bond angles, bond lengths, the relative stability of alternative structures, and other properties of compounds of the transition metals. Relation between bond strength and bond angles for spd bond orbitalsThe bond strength S of an orbital has been defined (4) as the value in the bond direction of the angular part of the wave function, with the angular wave functions normalized to 4wr. It is a reasonably good measure of the energy of the bond that can be formed by the orbital, with corrections needed, of course; for promotion of electrons, partial ionic character, deviation from electroneutrality, strain energy of bent bonds, and other factors. The values of S for some spd bond orbitals were discussed long ago (4). Hultgren (5) then discussed the problem thoroughly, with, however, the simplifying assumption that the bond orbitals have cylindrical symmetry ...