The relations between the harmonic frequencies of different molecules are revealed with the aid of the spring constants of atoms in molecules. Using the atomic spring constants in the related molecules, the force constants for a new molecule can be estimated. The simplest scheme to obtain the force constant of a given molecule is similar to a simple chemical reaction formula, such as A(2) + B(2) → AB, and the corresponding relation between the molecular force constants is k(AB)(-1) = (2k(A(2)))(-1) + (2k(B(2)))(-1). For a given molecule, one can design numerous schemes to obtain its force constant from the atomic spring constants in other molecules. A high degree of periodical regularity appears in the application of different kinds of schemes to the ground states. The reliable schemes for the ground electronic states can be adopted for the excited states. Over two hundred molecules with experimental data available for comparison have been tested. The discrepancies between the calculated and the experimental harmonic frequencies can reach 1% and better; the results show that the present approach is simple in theory and handy to use. The harmonic frequencies for dozens of hetero-nuclear molecules of the transition-metal elements are also predicted.