The magnetic and the physical properties of some transition metals from the bulk state to the nanoparticles has been investigated in an accurate tight-binding + U model which includes the exact Coulomb correlations. With a chemical rule of d charge neutrality, this new formalism gives the local magnetic moment, explains the relaxation without requiring to the total energy. The model also computes the work function and the free electron states at the surface depending on the coordination in agreement with a Linear Muffin Tin Orbital (LMTO) calculation. Our investigation focuses on the Cobalt FCC with some explorations of the iron BCC, Nickel FCC and the Platinum.