The gate-opening adsorption mechanism and sigmoidal adsorption isotherm were theoretically investigated taking CO, adsorption into porous coordination polymers, [Fe(ppt)(2)](n) (PCP-N, Hppt = 3-(2-pyrazinyl)-5-(4-pyridyl)-1,2,4-triazole) and [Fe(dpt)(2)](n) (PCP-C, Hdpt = 3-(2-pyridiny1)-5-(4-pyridy1)-1,2,4-triazole) as examples, where the hybrid method consisting of dispersion-corrected DFT or infinite PCP and a post-Hartree-Fock (SCS-MP2 and CCSD(T)) method for the cluster model was employed. PCP-N has site I (one-dimensional channel), site II (small aperture to site I), and site III (small pore) useful for CO2 adsorption. CO2 adsorption at site I occurs in a one by one manner with a Langmuir adsorption isotherm. CO2 adsorption at sites II and III occurs through a gate-opening adsorption mechanism, because the crystal deformation energy (EDEF) at these sites is induced largely by the first CO2 adsorption but induced much less by the subsequent CO2 adsorption. Interestingly, nine CO2 molecules are adsorbed simultaneously at these sites because a large EDEF cannot be overcome by adsorption of one CO2 molecule but can be by simultaneous adsorption of nine CO2 molecules. For such CO2 adsorption, the Langmuir-Freundlich sigmoidal adsorption isotherm was derived from the equilibrium equation for CO2 adsorption. A very complicated CO2 adsorption isotherm, experimentally observed, is reproduced by combination of the Langmuir and Langmuir Freundlich adsorption isotherms. In PCP-C, CO2 adsorption occurs only at site I with the Langmuir adsorption isotherm. Sites II and III of PCP-C cannot be used for CO2 adsorption because a very large EDEF cannot be overcome by simultaneous adsorption of nine CO2 molecules. Factors necessary for gate-opening adsorption mechanism are discussed on the basis of differences between PCP-N and PCP-C.