Theoretical Chemistry Accounts

, Volume 129, Issue 3, pp 331–342

Time-dependent density functional theory gradients in the Amsterdam density functional package: geometry optimizations of spin-flip excitations

Regular Article

DOI: 10.1007/s00214-010-0819-2

Cite this article as:
Seth, M., Mazur, G. & Ziegler, T. Theor Chem Acc (2011) 129: 331. doi:10.1007/s00214-010-0819-2


An implementation of time-dependent density functional theory (TDDFT) energy gradients into the Amsterdam density functional theory program package (ADF) is described. The special challenges presented by Slater-type orbitals in quantum chemical calculation are outlined with particular emphasis on details that are important for TDDFT gradients. Equations for the gradients of spin-flip TDDFT excitation energies are derived. Example calculations utilizing the new implementation are presented. The results of standard calculations agree well with previous results. It is shown that starting from a triplet reference, spin-flip TDDFT can successfully optimize the geometry of the four lowest singlet states of CH2 and three other isovalent species. Spin-flip TDDFT is used to calculate the potential energy curve of the breaking of the C–C bond of ethane. The curve obtained is superior to that from a restricted density functional theory calculation, while at the same time the problems with spin contamination exhibited by unrestricted density functional theory calculations are avoided.


Time-dependent density functional theory Analytical gradients Slater-type orbitals Spin-flip 

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of ChemistryUniversity of CalgaryCalgaryCanada
  2. 2.Department of Computational Methods in ChemistryJagiellonian UniversityKrakòwPoland

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