Relationship between Dipole Moments and Harmonic Vibrational Frequencies in Diatomic Molecules

Electric dipole moments and harmonic vibrational frequencies are two of the most important molecular properties in many fields of chemistry and physics. With the aid of classical physics, an empirical relationship between them was obtained for diatomic molecules as μ_d = kq²/(R_eμ_Aω_e²)^1/2, where k is a constant and μ_d, q, R_e, μ_A, and ω_e are the dipole moment, atomic charge, equilibrium bond length, reduced mass, and equilibrium vibrational frequency, respectively. This relation also provides the atomic charge q as a function of molecular dipole moment. Comparisons with over 60 molecules were made to test this relationship. For typical ionic molecules such as the alkali halides, the predicted dipole moments are in good agreement with the observed data assuming the atomic charges are 1 e. For general polar molecules, the estimated atomic charges obtained from the electric dipole moments are in good agreement with ab initio results for natural bond orbital and/or Mulliken populations.