Excited-State Forces with the Gaussian and Augmented\nPlane Wave Method for the Tamm–Dancoff Approximation of Time-Dependent\nDensity Functional Theory

Augmented plane wave\nmethods enable an efficient description of\natom-centered or localized features of the electronic density, circumventing\nhigh energy cutoffs and thus prohibitive computational costs of pure\nplane wave formulations. To complement existing implementations for\nground-state properties and excitation energies, we present the extension\nof the Gaussian and augmented plane wave method to excited-state nuclear\ngradients within the Tamm–Dancoff approximation of time-dependent\ndensity functional theory and its implementation in the CP2K program\npackage. Benchmarks for a test set of 35 small molecules demonstrate\nthat maximum errors in the nuclear forces for excited states of singlet\nand triplet spin multiplicity are smaller than 0.1 eV/Å. The\nmethod is furthermore applied to the calculation of the zero-phonon\nline of defective hexagonal boron nitride. This spectral feature is\nreproduced with an error of 0.6 eV in comparison to GW–Bethe–Salpeter\nreference computations and 0.4 eV in comparison to experimental measurements.\nAccuracy assessments and applications thus demonstrate the potential\nuse of the outlined developments for large-scale applications on excited-state\nproperties of extended systems.