The nature of the bonding of H2 to the Cr(L)5 complex (L = CO, PH3) has been investigated by means of ab initia Molecular Orbital (MO) - Linear Combination of Atomic Orbitals (LCAO) calculations. The use of a constrained orbital variation technique has made it possible to establish the importance of the different bonding mechanisms. In particular, the H2→Cr donation and the Cr→H2 back donation have been studied for complexes with CO or PH3 ligands coordinated to the Cr atom. We found that the presence of the poor πaccepting PH3 ligands greatly increases the back donation and the degree of H2 activation. © 1991 Accademia nazionale dei Lincei.