The time-dependent density functional theory(TDDFT)has become as an effective theoretical tool to calculate the excitation energies and Stokes shift of relatively large systems due to the implementation of analytical first geometrical derivatives of TDDFT excited-state energy [1,2,3] in some quantum chemistry packages.To develop the computationally efficient theoretical tools to obtain the vibrational frequencies,vibrational spectra,vibrationally-resolved electronic and Resonance Raman scattering spectroscopes as well as explore the excited-state potential surfaces,the analytical high-order energy derivatives of the excited states are required.In this talk,I will show you our groups efforts in the following two fields.One is to formulate the analytic second-order energy derivatives of TDDFT excited states for the molecules in gap phase [4,5] and condensed phase [6,7],and implement the algorithms into Q-CHEM software package.Another is to develop the time-dependent correlation function approaches for vibrationally-resolved electronic and resonance Raman spectroscopies with inclusion of Duschinsky rotation and Herzberg-Teller effects [8,9].Some benchmark tests and the applications to some realistic systems will be shown.By integrating the analytical energy derivatives approaches and the effective quantum dynamics approaches,I will show that the computational bottlenecks on the calculations of some molecular excited-state properties are breakdown.