Reaction of NO molecule on M-13 and M-55 clusters (M = Ru, Rh, Pd, and Ag) was theoretically investigated to elucidate why its reaction behavior depends on the position of metal element in the periodic table. DFT computations show that NO dissociative adsorption occurs on M = Ru and Rh, NO molecular adsorption occurs on M = Pd, and NO dimerization occurs on M = Ag, which agree with experimental findings. The d-band center and d-band top become lower in energy following the order Ru > Rh > Pd > Ag; this is one of the characteristic features of the periodic table. In the Ag cluster, the valence band-top consists of Ag 5s orbital and its energy is higher than the d-band top of Pd. For NO dissociative adsorption, the M-N and M-O bond strengths are crucially important at the transition state and the product, to which the metal d orbital contributes very much. Ru and Rh clusters have a high energy d-band center and d-valence band top, leading to the formation of strong M-N and M-O bonds. Pd and Ag clusters have a low energy d-band center and d-band top, leading to the formation of weak M-N and M-O bonds. Because the Ag cluster has a high energy Ss valence band that can overlap well with the pi* + pi* MO of ONNO (NO dimer) moiety due to the same symmetry, charge transfer (CT) occurs from the Ag cluster to the pi* + pi* MO, which is indispensable for NO dimerization. The 4d-valence band top of Ru and Rh clusters does not fit to the pi* + pi* MO because of the different symmetry. Though the d-valence band top of the Pd cluster can overlap with the pi* + pi* MO, its energy is low, which is not good for the CT. Thus, the reactivity of metal cluster for NO is determined by the energy and type (4d or 5s) of the valence band top, which both depend on the position of element in the periodic table; accordingly, Ru and Rh clusters are reactive for NO dissociative adsorption, the Ag cluster is reactive for NO dimerization, but the Pd cluster is not reactive for both and only NO molecular adsorption is possible.