The structure of the silicate species is determined using the Hartree-Fock method, and the Si-29 NMR magnetic shielding constants are subsequently calculated using the coupled perturbed Hartree-Fock method with gauge including atomic orbitals. The silicate monomer is modeled as a neutral fully protonated species, H4SiO4 and as a monoanion-potassium cation pair, H3SiO4-K+. Hydration by up to four and two water molecules, respectively, is also considered. For both types of environment the Si-29 NMR chemical shift is within -71.0 +/- 0.5 ppm. The effect of symmetry and degree of condensation is studied for silicate oligomers forming chains (dimer, trimer), rings (trimer, tetramer, pentamer, hexamer), and cages (prismatic hexamer, cubic octamer, hexagonal dodecamer). Lowering the symmetry lowers the shielding. The shift of a Q-unit " depends on the adjacent bond angles : delta(TMS)(Q ") = -61.23n[rho(SiOSi)] - 60.45 (4 - n)[rho(SiOH)] + 6.58, with rho(alpha) = cos alpha/(cos alpha - 1). In addition the tetrahedral tetramer is studied. Previous tentative assignments of the signal at -97.3 ppm to this species can be ruled out. It is likely to be due to one of the double-ring structures with 8, 10, or 12 tetrahedra.