We present the result of a fragment-based energy decomposition analysis on some molecule-surface interactions. The analysis allows us to quantify the Pauli repulsion, its relief, and the attractive orbital interaction energy. In a metal, the existence of incompletely occupied energy bands causes significant relief of the Pauli repulsion due to escape of antibonding electrons to unoccupied states at the Fermi energy. This is the key electronic structure feature of metals that causes metal-molecule bond energies to be stronger and dissociation barriers of chemisorbed molecules to be much lower than those in comparable systems with no or one metal atom. As examples, we discuss the energy decomposition for the activated dissociation of hydrogen on the Cu surface and its unactivated dissociation on Pd, and for the (activated) chemisorption of N-2 on W. We show that in all cases the relief of Pauli repulsion is of crucial importance for the chemisorption energy and for the low (or nonexistent) dissociation barriers. The barrier to the chemisorption well for nitrogen on tungsten is clearly related to a late relief of the Pauli repulsion. The relief of Pauli repulsion is important in lowering the barrier to dissociation of H-2 on both Cu and Pd, but the difference in barrier heights for Cu and Pd appears to not be due to stronger relief of Pauli repulsion on Pd but primarily to the Pauli repulsion itself being stronger on Cu than on Pd, the relief energy being quite comparable on the two metals.