Abstract: By treating a weakly coupled pair of atomic systems A and B using time-dependent quantum-mechanical perturbation theory, an expression of tunneling conductance and an expression of chemical-bond interaction energy can be obtained. By comparing those two expressions, a universal relation between tunneling conductance and chemical-bond interaction energy is established. This relation was repeatedly verified by numerous experiments. Because tunneling conductance can be expressed by the Bardeen surface integral, which often results in simple analytic results, the above equivalence relation can provide a new approximate analytic theory on the chemical bond and magnetic phenomena.