We
present an implementation of energies and gradients for the
ΔDFTB method, an analogue of Δ-self-consistent-field density
functional theory (ΔSCF) within density-functional tight-binding,
for the lowest singlet excited state of closed-shell molecules. Benchmarks
of ΔDFTB excitation energies, optimized geometries, Stokes shifts,
and vibrational frequencies reveal that ΔDFTB provides a qualitatively
correct description of changes in molecular geometries and vibrational
frequencies due to excited-state relaxation. The accuracy of ΔDFTB
Stokes shifts is comparable to that of ΔSCF-DFT, and ΔDFTB
performs similarly to ΔSCF with the PBE functional for vertical
excitation energies of larger chromophores where the need for efficient
excited-state methods is most urgent. We provide some justification
for the use of an excited-state reference density in the DFTB expansion
of the electronic energy and demonstrate that ΔDFTB preserves
many of the properties of its parent ΔSCF approach. This implementation
fills an important gap in the extended framework of DFTB, where access
to excited states has been limited to the time-dependent linear-response
approach, and affords access to rapid exploration of a valuable class
of excited-state potential energy surfaces
