Using UB3LYP/6-31G*(d) density functional level of theory, the structural, electronic, optical and magnetic properties of \( {\text{B}}_{24} {\text{N}}_{24} \), \( {\text{Li}}@{\text{B}}_{24} {\text{N}}_{24} \), \( {\text{Na}}@{\text{B}}_{24} {\text{N}}_{24} \) and \( {\text{K}}@{\text{B}}_{24} {\text{N}}_{24} \) cages were studied when M (Li, Na, K) atoms locate at center of \( {\text{B}}_{24} {\text{N}}_{24} \) cage. Results illustrate that the capsulation of M atom in \( {\text{B}}_{24} {\text{N}}_{24} \) cage increases the bond length of B–N. In addition, the stability of \( {\text{M}}@{\text{B}}_{24} {\text{N}}_{24} \) cages corresponds to size of atomic radius of M atom. \( {\text{B}}_{24} {\text{N}}_{24} \) cage becomes magnetic by the capsulation of the M atom in \( {\text{B}}_{24} {\text{N}}_{24} \) cage. \( {\text{K}}@{\text{B}}_{24} {\text{N}}_{24} \) and \( {\text{Na}}@{\text{B}}_{24} {\text{N}}_{24} \) cages have a minimum (0.976 \( \mu_{\text{B}} \)) and maximum (1.185 \( \mu_{\text{B}} \)) values of total magnetic moment, respectively. Numerical results show that polarizabilities values of \( {\text{K}}@{\text{B}}_{24} {\text{N}}_{24} \) and \( {\text{Na}}@{\text{B}}_{24} {\text{N}}_{24} \) molecules are about 1.6 times bigger than that of \( {\text{B}}_{24} {\text{N}}_{24} \) molecule.

使用UB3LYP / 6-31G *（d）密度泛函理论水平，\（{\ text {B}} _ {24} {\ text {N}} _ {24}的结构，电子，光学和磁性\），\（{\ text {Li}} @ {\ text {B}} _ {24} {\ text {N}} _ {24} \），\（{\ text {Na}} @ {\文本{B}} _ {24} {\文本{N}} _ {24} \）和\（{\文本{K}} @ {\文本{B}} _ {24} {\文本{N} } _ {24} \）个笼子是在M（Li，Na，K）个原子位于\（{\ text {B}} _ {24} {\ text {N}} _ {24} \）的中心时研究的笼。结果表明\（{\ text {B}} _ {24} {\ text {N}} _ {24} \）笼中M原子的封装增加了B–N的键长。此外，\（{\ text {M}} @ {\ text {B}} _ {24} {\ text {N}} _ {24} \）的稳定性笼形对应于M原子的原子半径的大小。\（{\ text {B}} _ {24} {\ text {N}} _ {24} \）笼由于\（{\ text {B}} _ {24} {\ text {N}} _ {24} \）笼子。\（{\ text {K}} @ {\ text {B}} _ {24} {\ text {N}} _ {24} \）和\（{\ text {Na}} @ {\ text {B }} _ {24} {\ text {N}} _ {24} \）笼的最小值（0.976 \（\ mu _ {\ text {B}} \））和最大值（1.185 \（\ mu _ {\ text {B}} \））的总磁矩值。数值结果表明\（{\ text {K}} @ {\ text {B}} _ {24} {\ text {N}} _ {24} \）和\（{\ text {Na} } @ {\ text {B}} _ {24} {\ text {N}} _ {24} \）分子比\（{\ text {B}} _ {24} {\ text {N}} _ {24} \）分子大1.6倍。