In this study, we have performed ab initio computer simulations to investigate the conformational and complexation characteristics of the trimethyl ether of p-tert-butylmonodeoxycalix[4]arene (6) with a potassium ion. The structures of different conformers of 6 and their potassium complexes were optimized by using ab initio RHF/6-31G and B3LYP/6-31G(d,p) methods. The relative stability of the various conformers of the uncomplexed 6 is in following order: cone (most stable) > 1-partial-cone ~ 2i-partial-cone > 2-partial-cone ~ 1,3-alternate > 3i-partial-cone. However, the relative stability of the conformational complexes of 6 with $K^+$ is in the following order: 2-partial cone ~ 1,3-alternate > cone > 3-partial cone > 1-partial cone (least stable). The highest binding strengths of 2-partial-cone and 1,3-alternate complexes originate from two strong cation-$pi$ interactions and two strong cation-oxygen interactions in the complex of 6+$K^+$. Due to the cation-$pi$ interactions, the calculated C-C bond distances in the arenes of the $K^+$-complexes are about 0.0048 $AA$ longer than the values of their isolated hosts.