We have presented a newly developed Davidson-like algorithm to compute selected \textit{interior} eigenstates of the Liouvillian super-operator, and a recently introduced \textit{pseudo-Hermitian} variant of the Liouville-Lanczos approach to time-dependent density-functional theory (TDDFT). The new algorithms have been released as the new version of \texttt{turboTDDFT} in the \textsc{Quantum ESPRESSO} package together with an implementation of hybrid functionals. Our implementation has been thoroughly validated against benchmark calculations performed on a few moleucles using both the original \texttt{turboTDDFT} and \texttt{Gaussian09} code. Then we have applied the new algorithms to carry on a systematic study of anthocyanins' optical properties. We have found that the Oxygen-containing side groups on the phenyl ring of these molecules play important roles to modify their optical absorption spectra, which can be understood by a so-call \textit{double-pole approximation}. We have also applied a recently proposed explicit solvent model to study the solvent effects for these molecules, using a combination of Ab-initio molecular dynamics (AIMD) and TDDFT. We have found that PBE produces too red-shifted spectra, instead B3LYP gives the spectra and the simulated colors in very good agreement with the experiment.
