Vibrational spectra of molecules in the Hartree–Fock dielectric screening approach

Traditionally, the calculation of the vibrational spectra of molecules involves at one point or another a numerical differentiation procedure. Such a method has some serious drawbacks both in efficiency and in accuracy. In this paper, an alternative method based on linear response theory is presented. The second derivative of the ground-state energy is expressed in terms of the electron density response matrix by means of perturbation theory. The unperturbed wave functions are obtained from the Hartree–Fock equation. First-order perturbation theory applied to this equation leads to the Hartree–Fock linear response. As an illustration of this method the vibrational frequency of a H₂ molecule is calculated. The result is 1.348 × 10¹⁴ Hz as compared to the experimental value of 1.319 × 10¹⁴ Hz. This method is also applicable in the calculation of the phonon dispersion curves of solids.