Using DFT B3LYP/6-31+G(d,p)//B3LYP/6-31G(d,p) calculation method, stable molecular structures were optimized for the p-tert-butylcalix[4]arene functionalized at lower rim by cage-annulated crown ether (1) in two different conformers and their potassium-ion complexes. Cone conformer of free host 1 was slightly more stable than partial-cone conformer. For two different kinds of complexation mode, the potassium ion in benzene-rings (bz) pocket showed comparable complexation efficiency with the cation in cage-annulated crown-ether (cr) for the cone and partial-cone conformers of 1. The complex (1${ullet}K^+$) in the cr-binding mode for the partial-cone conformer was more stable than the cone conformer for B3LYP/6-31G(d,p) geometry optimization. However, $1_{(cone)}{ullet}K^+$(cr) showed lower single-point energy than the $1_{(pc)}{ullet}K^+$(cr) for B3LYP/6- 31+G(d,p) calculation method.