Self-Consistent Optimization of Excited States within Density-Functional Tight-Binding

摘要

We present an implementation of energies and gradients for the Delta DFTB method, an analogue of A-self-consistent-field density functional theory (Delta SCF) within density-functional tight-binding, for the lowest singlet excited state of closed-shell molecules. Benchmarks of Delta DFTB excitation energies, optimized geometries, Stokes shifts, and vibrational frequencies reveal that Delta DFTB provides a qualitatively correct description of changes in molecular geometries and vibrational frequencies due to excited-state relaxation. The accuracy of Delta DFTB Stokes shifts is comparable to that of Delta SCF-DFT, and Delta DFTB performs similarly to Delta SCF 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 Delta DFTB preserves many of the properties of its parent Delta SCF 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.