The stacking parameters, lattice constants, bond lengths, and bulk moduli of pyrophyllite and montmorillonites (MMTs), with alkali and alkali earth metal ions, are investigated using density functional theory with and without dispersion corrections. For pyrophyllite, it is found that the inclusion of the dispersion corrections significantly improves the agreement of the calculated values of the lattice parameters and bulk modulus with the experimental values. For the MMTs, the calculations predict that the interlayer spacing varies approximately linearly with the cation radius. The inclusion of dispersion corrections leads to sizable shifts of the interlayer spacings to shorter values. In Li-MMT, compaction of the interlayer distance triggers migration of the Li ion into the tetrahedral sheet and close coordination with basal oxygen atoms. Analysis of electron density distributions shows that the isomorphic octahedral Al3+/Mg2+ substitution in MMT causes an increase of electron density on the basal oxygen atoms of the tetrahedral sheets.