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

The Journal of Chemical Physics
Henryk A WitekKeiji Morokuma

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 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.

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Citations

May 3, 2013·The Journal of Chemical Physics·Hiroya NakataShinichiro Nakamura
Nov 21, 2015·Journal of Chemical Theory and Computation·Chien-Pin ChouHenryk A Witek
May 25, 2016·Physical Chemistry Chemical Physics : PCCP·Yoshio Nishimoto, Dmitri G Fedorov
Jun 24, 2019·The Journal of Chemical Physics·Rafał PodeszwaHenryk A Witek
Aug 24, 2018·The Journal of Chemical Physics·Natacha GilletTomáš Kubař
Oct 10, 2018·Journal of Computational Chemistry·Hiroya Nakata, Dmitri G Fedorov
Nov 24, 2012·Journal of Computational Chemistry·Marcus V P dos SantosRicardo L Longo
Sep 23, 2018·Journal of Molecular Modeling·Chien-Pin ChouStephan Irle
Jun 14, 2019·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Alejandro Santana-BonillaGianaurelio Cuniberti
Oct 23, 2020·The Journal of Chemical Physics·Vladimir BačićAgnieszka Kuc
Sep 26, 2009·The Journal of Physical Chemistry. a·Michael GausMarcus Elstner
Nov 7, 2020·Advances in Physics: X·Fernand SpiegelmanMathias Rapacioli
Dec 4, 2012·Journal of Chemical Theory and Computation·Michael GausMarcus Elstner
Jun 1, 2018·Journal of Chemical Theory and Computation·Xiaoyu XieAlessandro Troisi
May 13, 2011·Journal of the American Chemical Society·Dmitry V KazachkinEric Borguet
Nov 22, 2012·The Journal of Physical Chemistry. a·Steve KaminskiMarcus Elstner
Mar 8, 2011·Journal of Chemical Theory and Computation·Fabio Trani, Vincenzo Barone
Apr 9, 2013·Journal of Chemical Theory and Computation·Vincenzo BaroneGiovanni Scalmani
Sep 10, 2013·Journal of Chemical Theory and Computation·Antonio GamboaFernand Spiegelman
Sep 9, 2014·Journal of Chemical Theory and Computation·Hiroya NakataShinichiro Nakamura
Apr 14, 2007·The Journal of Physical Chemistry. a·Edyta MałolepszaStephan Irle
Jun 8, 2007·The Journal of Physical Chemistry. a·B HourahineTh Frauenheim

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