The transition metal hydride cations, TMH+ (TM = first transition metal row, Sc, Ti, V, Cr, Mn, Co, Ni, Cu, and Zn), have been studied using valence bond (VB) theory to elucidate the bonding in these systems through VB concepts. Although the bonds appear extremely covalent by virtue of charge distribution, this appearance conceals key contributions to bonding, such as covalent-ionic resonance energy (RECS) and relaxation energy of the inactive electrons (Delta E-relax(inactive)). The RECS term is seen to increase from ScH+ toward ZnH+, becoming significant in the late TMH+ molecules. The Delta E-relax(inactive) term, which accountsfor the nonbonding 3d(n) electrons and the 3s(2)3p(6) core electrons, is always significant. Furthermore, fdr all of the bonds from CrH+ to CuH+, the relaxation term makes a major contribution to the bond energy. It appears therefore, that in these TM-Ht bonds, the spin pairing of the bonding electrons can act as a trigger for the nonbonding and adjacent core electrons to relax their Pauli repulsion and thereby strengthen the binding of TM+ and H. As a result of the general weakness of TM bonds, the relaxation is expected to frequently be an important bonding contribution. The major function of the inactive and core electrons shows that the traditional role of "covalency" must be reassessed in a systematic manner.