Molecular structures of the various conformational stereoisomers of 2,8,14,20-cyanophenyl pyrogallol[4]arenes 1 were optimized using the mPW1PW91 (hybrid Hartree-Fock density functional) calculation method. The total electronic and Gibbs free energies and the normal vibrational frequencies of the different structures from three major conformations (CHAIR, TABLE, and 1,2-Alternate) of the four stereoisomers [1(rccc), 1(rcct), 1(rctt), and 1(rtct)] were analyzed. The mPW1PW91/6-31G(d,p) calculations suggested that $1(rcct)_{1,2-A}$, 1(rctt)CHAIR, and $1(rtct)_{CHAIR}$ were the more stable conformations of the respective stereoisomers. Hydrogen bonding is the primary factor for the relative stabilities of the various conformational isomers, and maximizing the ${pi}-{pi}$ interaction between the cyanophenyl rings is the secondary factor. The calculated IR spectra of the more stable conformers [$1(rctt)_{CHAIR}$, $1(rcct)_{1,2-A}$, $1(rtct)_{CHAIR}$] were compared with the experimental IR spectrum of $1(rtct)_{CHAIR}$.