Excited singlet state structures believed to be responsible for the Franck-Condon-allowed and the strongly Stokes-shifted (blue) emissions in linear permethylated oligosilanes (SinMe(2n+2)) have been found and characterized with time-dependent density functional (TD-DFT) methods for chain lengths 4 <= n <= 16. For chain lengths with n > 7, the S1 relaxed structures closely resemble the S0 equilibrium structures where all valence angles are tetrahedral and all backbone dihedral angles are transoid. At chain lengths with n < 8 more strongly distorted structures with one long Si-Si bond built from silicon 3p orbitals are encountered. The large Stokes shift is due more to a large destabilization of the ground state than the relaxation in the S1 excited state. For n > 7, both types of minima were located, exactly reproducing the borderline between the large-radius and the small-radius self-trapped excitons known from experiments.