Time-Dependent Density Functional Theory (TD-DFT) has become the most widely-used theoretical approach to simulate the optical properties. The TDDFT calculations of the lowest excited states of the lanthanide and actinide triflates M(OTf)n; where (M= Ce, Th, Np, Pu, Am, Cm and Bk); (n=3 and 4) , provide an accurate description of their UV-visible spectra. The UV region is characterized by the most pointed and reduce peak of the Th(OTf)4 compound that assigned to ligand metal charge transfer (LMCT) transition. The absorption specter of Np(OTf)3 and Pu(OTf)3 is mixed of LMCT, MLCT and intra charge transfer (ICT) transitions. The HOMO-LUMO transition of Pu(OTf)3 are strongly bathochromically shifted compared with those of Np(OTf)3 and Th(OTf)4. These three complexes are capable to give a luminescence in the emission specter. The M(OTf)n where (M= Ce, Pu, Am, Cm and Bk); (n=3 and 4) are dominated in visible, ultra violet and infra read region by LMCT transition of the Ce(OTf)4 and ICT of Pu(OTf)4 , Am(OTf)3, Cm(OTf)3 and Bk(OTf)3.