Analytical second-order geometrical derivatives of energy for the self-consistent-charge density-functional tight-binding method.
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 Møller-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 1,741 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.
Witek
Henryk A
HA
Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory University, Atlanta, Georgia 30322, USA.
Irle
Stephan
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Morokuma
Keiji
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