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

摘要

Analytical formulation of the second-order geometrical derivatives of energy for the self-consistent-charge density-functional tight-binding (SCC-DFTB) method is presented. To test its quality and numerical performance, the derived formalism has been coded and applied for calculation of harmonic vibrational frequencies for a set of 17 small and medium size molecules. For this set, the average absolute deviation from experiment is 99 cm-1 for SCC-DFTB vs 62 cm-1 for the Moller-Plesset second-order perturbation theory with the cc-pVDZ basis set (MP2/cc-pVDZ) and 32 cm-1 for the B3LYP density functional method with the same basis set (B3LYP/cc-pVDZ), while the maximal deviation is 465 cm-1 vs 1741 cm-1 for MP2/cc-pVDZ and 112 cm-1 for B3LYP/cc-pVDZ. The SCC-DFTB results are in reasonable agreement with experiments as well as with ab initio and density-functional results, and are better than other semiempirical methods. The SCC-DFTB method allows for considerable computational time saving when compared to other methods while retaining similar overall accuracy. Data for a series of conjugated polyenes show that an analytical formulation of SCC-DFTB is noticeably faster than its numerical formulation. (C) 2004 American Institute of Physics.