Density functional theory (DFT) calculations have been carried out to study the capacity of the B 1 2 N 1 2 nanocage encapsulated with alkali metals (Li, Na, K) for the CO2 adsorption and activation. It is found that after encapsulating alkali metals, the alkali metal atoms are closer to one side of clusters instead of exactly lying at the center, and a considerable charge transfers from the inner alkali metal atoms to the B 1 2 N 1 2 cage. Besides, the HOMO–LUMO gap (HLG) values of Li@B 1 2 N 1 2 , Na@B 1 2 N 1 2 and K@B 1 2 N 1 2 are decreased to about 6 eV, being much smaller than that of the pristine B 1 2 N 1 2 . Although the geometry structure parameters and the energy differences of M06-2X are slightly different from the ones of ω B97X-D, some identical results of two kinds of functional can be obtained. CO2 can be adsorbed chemically and physically on majority bonds of all the clusters, except for some bonds with large change in bond length and bond indices. The encapsulation of alkali-metal atoms may enhance the physical and chemical adsorption of CO2 on the surface of the clusters, in which Na@B 1 2 N 1 2 and K@B 1 2 N 1 2 are the most powerful physical and chemical adsorbent for CO2, respectively. Encapsulating alkali metal atoms in the B12N12 cluster would change the cage geometry and the electronic properties. In addition, it would significantly affect the energy changes in the physical and chemical adsorption processes of CO2 adsorbed on selected adsorption sites. The calculations are performed with the ωB97X-D and the M06-2X functional, and the results of two kinds of functional are identical. [ABSTRACT FROM AUTHOR]