Analytical second-order geometrical derivatives of energy for the self-consistent-charge density-functional tight-binding method

The second-order geometrical derivatives of energy for the self-consistent-charge density-functional tight-binding (SCC-DFTB) method were discussed. The derived formalism had coded and applied for calculation of harmonic vibrational frequencies for a set of 17 small and medium size molecules. A test calculations for a set of molecules for which the harmonic frequencies were available were also performed. It was found that the computational time required to evaluate the SCC-DFTB frequencies in an analytical manner was smaller than for numerical implementation.