The low-charge dioctahedral 2:1 phyllosilicates are an important group of clay minerals that have a low degree of cation substitution and very weak interlayer interatomic interactions which are difficult to reproduce with quantum mechanical calculations. In order to study the crystallographic properties of these compounds with density functional theory (DFT) quantum-mechanical methods, an optimization of norm-conserving pseudopotentials of Al, Si, O, H and Na atoms has been carried out, and an optimization of the cutoff radii of the basis sets has been accomplished. Crystallographic properties and vibrational stretching frequencies of the OH groups, ν(OH), have been calculated, being consistent with previous computational and experimental results. All frequencies can be related to the different molecular environment of the OH groups. The effect of octahedral Fe3+ substitution on the ν(OH) frequency is reproduced. Several configurations of cation substitutions and interlayer cation (IC) positions are studied in low-charge dioctahedral 2:1 phyllosilicates, such as Al4(Si7−xAlx)O20(OH)4Nax, with x = 0.25, 0.50 and 0.75, indicating that the IVAl3+ is highly dispersed and the IC tends to be in the substituted ditrigonal hole. For the Al4(Si7Al)O20(OH)4Na composition, the trans-vacant form is more stable than the cis-vacant one.