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

Henryk A. Witek, Stephan Irle, Keiji Morokuma*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

59 Scopus citations

Abstract

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 cm21 for SCC-DFTB vs 62 cm21 for the Møller-Plesset second-order perturbation theory with the cc-pVDZ basis set ~MP2/cc-pVDZ! and 32 cm21 for the B3LYP density functional method with the same basis set ~B3LYP/cc-pVDZ!, while the maximal deviation is 465 cm21 vs 1741 cm21 for MP2/cc-pVDZ and 112 cm21 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.

Original languageEnglish
Pages (from-to)5163-5170
Number of pages8
JournalJournal of Chemical Physics
Volume121
Issue number11
DOIs
StatePublished - 3 Sep 2004

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