The molecular structures of thiacalix[4]biscrown-5 (1) and p-tert-butylthiacalix[4]biscrown-5 (2) and their alkali-metal-ion complexes were optimized using the DFT BLYP/6-31G(d) and mPW1PW91/6-31G(d,p) (hybrid HF-DF) calculations. The total electronic energies, the normal vibrational modes, and the Gibbs free energies of the mono- and di-topic complexes of each host with the sodium and potassium ions were analyzed. The $K^+$-complexes exhibited relatively stronger binding efficiencies than $Na^+$-complexes for both the monoand di-topic complexes of 1 and 2 comparing the efficiencies of the sodium and potassium complexes with an anisole and phenol. The mPW1PW91/6-31G(d,p) calculated distances between the oxygen atoms and the alkali metal ions were reported in the alkali-metal-ion complexes ($1{cdot}Na^+$, $1{cdot}2Na^+$, $1{cdot}K^+$, $1{cdot}2K^+$, $2{cdot}Na^+$, $2{cdot}Na^+$, $2{cdot}K^+$, $2{cdot}2K^+$). The BLYP/6-31G(d) calculated IR spectra of the host 1 and its mono-topic alkali-metal-ion complexes are compared.