Analytical excited state forces for the time‐dependent density‐functional tight‐binding method

An analytical formulation for the geometrical derivatives of excitation energies within the time‐dependent density‐functional tight‐binding (TD‐DFTB) method is presented. The derivation is based on the auxiliary functional approach proposed in [Furche and Ahlrichs, J Chem Phys 2002, 117, 7433]. To validate the quality of the potential energy surfaces provided by the method, adiabatic excitation energies, excited state geometries, and harmonic vibrational frequencies were calculated for a test set of molecules in excited states of different symmetry and multiplicity. According to the results, the TD‐DFTB scheme surpasses the performance of configuration interaction singles and the random phase approximation but has a lower quality than ab initio time‐dependent density‐functional theory. As a consequence of the special form of the approximations made in TD‐DFTB, the scaling exponent of the method can be reduced to three, similar to the ground state. The low scaling prefactor and the satisfactory accuracy of the method makes TD‐DFTB especially suitable for molecular dynamics simulations of dozens of atoms as well as for the computation of luminescence spectra of systems containing hundreds of atoms. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2007

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