How the alkali metal atoms affect electronic structure and the nonlinear optical properties of C24N24 nanocage

How do the alkali metal atoms affect electronic structure and the first hyperpolarizability (β0) of C24N24 nanocage. In this work, Mout@C24N24 (M = Li, Na, K) and Mint@C24N24 (M = Na, K) were designed and investigated in theory using density functional theory. First, two models (Mout@C24N24 and Mint@C24N24) is formed by introduction the alkali metal atoms into the C24N24 nanocage with different doping sites, the center of four nitrogen atoms and encapsulated into C24N24 nanocage. It is revealed that energy gap Egap of Mout@C24N24 and Mint@C24N24 decreased obviously in contrast to C24N24 cage due to alkali metal atoms effect. Furthermore, introduction the alkali atoms lead to Mout@C24N24 and Mint@C24N24 exhibiting considerable first hyperpolarizabilities, which were 1242, 650, 1065 au for Mout@C24N24 (M = Li, Na, K), and 4772, 106 au for Mint@C24N24 (M = Na, K), respectively. It is clearly that introduction Li over the center of four nitrogen atoms get large first hyperpolarizabilities for Mout@C24N24 (M = Li, Na, K), while the different situation is obtained for Mint@C24N24 (M = Na, K), where introduction Na atom can obtain large first hyperpolarizabilities.