Density functional theory calculations have been carried out on the trigonal complexes OsO3E and MCl3E (M = V, Ta) and the square pyramidal systems MCl4E (M = Cr, Mo, W, Re) for E = O, S, Se, and Te as well as (C5H5)ReO3. All complexes were fully optimized, and the calculated geometrical parameters are in reasonable agreement with gas-phase electron diffraction data where available. The calculated M-E bond energies decrease from oxygen to tellurium, from bottom to top in a metal triad, and from left to right in a transition series. The trend setting factor is the donation from the d(sigma) metal orbital to the p(sigma) acceptor orbital on the chalcogen atom. The contribution from the chalcogen to metal pi back-donation has a maximum for sulfur and selenium. However in relative terms, the contribution from the pi back-donation to the total M-E bond energy increases from oxygen to tellurium. Comparisons are made to previous calculations and experimental data on M-E bond strengths.