Time-Dependent Density Functional Tight Binding: New Formulation and Benchmark of Excited States

A new formulation of time-dependent density functional tight binding (TD-DFTB) is reported in this paper. It is derived from the application of the linear response theory to the ground state DFTB Hamiltonian, without the introduction of additional parameters for the description of the excited states. The method is validated for several sets of organic compounds, against the best theoretical estimates from the literature, density functional theory, semiempirical methods, and experimental data. The comparison shows that TD-DFTB gives reliable results both for singlet and triplet excitation energies. In addition, the application of TD-DFTB to open-shell systems shows promising results.