The singlet-singlet electronic spectrum of the anti conformer of n-tetrasilane has been studied using multiconfigurational wave functions (CASSCF), second-order perturbation theory (CASPT2), and its multistate extension (MS-CASPT2), in conjunction with large ANO-type basis sets including Rydberg functions. The calculations include the 4s, 4p, and 3d members of the Rydberg series converging on the first ionization. Mixing of valence and Rydberg states observed in the CASSCF wave functions is not fully rectified by single-reference CASPT2 theory, whereas the MS-CASPT2 method separates the valence and Rydberg states effectively. At the MS-CASPT2 level, six valence excited states have been found below the lowest Rydberg transition, predicted at 7.40 eV. In terms of natural orbitals, they correspond to single electron promotions from the a-symmetry HOMO to four sigma* and two pi* valence orbitals. Vertical dipole-allowed valence transition energies (oscillator strengths) are computed at 6.33 eV (1.12), 6.68 eV (0.01), and 6.96 eV (0.15), for excitation to 1(1)B(u), 1(1)A(u), and 2(1)B(u), states, respectively. Three vertical dipole-forbidden valence transitions are predicted to be interleaved among them at 6.55 eV (2(1)A(g)), 6.87 eV (3(1)A(g)), and 7.10 eV (1(1)B(g)). The results are consistent with the available experimental data and are easily rationalized in terms of a simple Huckel model of sigma delocalization.