Time-Dependent Density Functional Theory Excited-State Forces with the Gaussian and Augmented Plane Wave Method

Augmented plane wave methods enable an efficient description of atom-centered or localized features of the electronic density, circumventing high energy cutoffs and thus prohibitive computational costs of pure plane wave formulations. To complement existing implementations for ground-state properties and excitation energies, we present the extension of the Gaussian and augmented plane wave method to excited-state nuclear gradients within the CP2K program package. Benchmarks for a test set of 35 small molecules demonstrate that maximum errors in the nuclear forces for excited states of singlet and triplet spin multiplicity are smaller than 0.1 eV/Å. The method is furthermore applied to the calculation of the zero-phonon line of defective hexagonal boron nitride. This spectral feature is reproduced with an error of 0.2 eV in comparison to GW-Bethe-Salpeter reference computations and of 0.4 eV in comparison to experimental measurements. Accuracy assessments and applications thus demonstrate the potential use of the outlined developments for large-scale applications on excited-state properties of extended systems.