We report a theoretical study of the structural and electronic properties of the rccc and rctt conformers of several pyrogallol[4]arenes, R-Pyg[4]arenes (i.e. R = fluoroethyl, methyl, t-butyl, phenyl, tolyl and p-fluorophenyl) carried out by employing the HF-DFT hybrid B3LYP functional. Comparison of the B3LYP energies of the two stereoisomers showed that the rccc conformer is more stable than its rctt counterpart for all the derivatives considered. However, calculations made with the double-hybrid Grimme's B97D functional confirmed the experimental observation that the relative stability depends on the type of the R substituents. These results clearly suggest that the B97D functional together with large enough basis sets (i.e. split-valence plus polarisation and diffuse functions) is sufficiently accurate for the purpose of describing the conformational features of these compounds. Computed electrostatic potential maps of the rccc of the different R-Pyg[4]arenes showed that a negative potential is present within the cavity of these compounds. In addition, it is observed that the size of this negative electrostatic potential depends on the electron-donating or electron-withdrawing character of the R substituents.