Relationship between Dipole Moments and Harmonic Vibrational Frequencies in Diatomic Molecules

Abstract

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 μd = kq(2)/(ReμAωe(2))(1/2), where k is a constant and μd, q, Re, μA, and ωe 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.

A data-driven approach to determine dipole moments of diatomic molecules

“…Therefore, we find that it is essential to add ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi mR e o e 2 p as a feature in describing the dipole moment of a diatomic molecule. It can be shown that this feature is related to the was first introduced by Hou and Bernath 10,11 as an empirical relationship, and we use this here to define the ionic character of a molecular bond.…”

“…30 Surprisingly, eqn (10) and (11) lead to different results for the ionic character of the molecules in the database, as shown in Fig. 4, where it is noticed that the distribution of the ionic character following eqn (11) appears to the complement to the one obtained from eqn (10). This is related to the fact that the model of Hou and Bernath (eqn (10)) systematically leads to a larger ionic character than the model of Hannay an Smyth.…”

“…20 The models of Pauling and Mulliken have been accepted by the physical chemistry community and taught in elementary chemistry courses for a long time, despite the fact that neither one of those is fully satisfactory. Recently, Hou and Bernath, 10,11 after studying the experimentally determined dipole moments of an extensive group of molecules and using quantum chemistry calculations, have suggested that the electric dipole moment of a molecule should be given as…”

“…where q is the effective charge and R e denotes the equilibrium bond length of the molecule, does not capture the proper physics of the dipole moment in many molecules. 10,11 They also demonstrated that the dipole moment of some molecules can be predicted from the effective charge (obtained from quantum chemistry calculations) and spectroscopic constants of molecules. In the 2000s the big data-driven science paradigm emerged in the scientific community.…”

“…Comparison of the histograms of ionic characters and dipole moments in the whole dataset (shown in grey) and the ML-learned subset of 118 molecules (shown in blue). Panel (a) and (b) show the ionic characters calculated from eqn(10) and(11), respectively. Panel (c) plots the histogram of the dipole moment of the molecules.…”