Are phosphide nano-cages better than nitride nano-cages? A kinetic, thermodynamic and non-linear optical properties study of alkali metal encapsulated X12Y12 nano-cages

Density functional theory calculations have been performed for alkali metal encapsulated X12Y12 nano-cages (X = B, Al and Y = N, P) to evaluate their stability, boundary crossing barriers and optical (linear and non-linear) properties. The adsorption energies of alkali metals in nano-cages are calculated, and correlated with the size of the nano-cages and alkali atoms. Distortion (expansion) of the nano-cages caused by alkali metal encapsulation was estimated through distortion energy. The distortion energies show good correlation with the diameter of the nano-cages. Kinetic barriers for the movement of alkali metals through nano-cages (boundary crossing barriers) are quantitatively measured. This manuscript presents the first ever study on boundary crossing barriers for alkali metal atoms through any spherical surface. The translation of alkali metals through the boundary of nano-cages presents a new approach for encapsulation of alkali metal atoms ((particularly lithium)) in nano-cages. The linear and non-linear optical properties of alkali metal encapsulated nano-cages are calculated. A quite remarkable non-linear optical response is calculated for lithium and potassium encapsulated boron phosphide (B12P12 or BP) nano-cages. In general, the non-linear optical response of phosphide nano-cages is two to three orders of magnitude higher than those of the corresponding nitride nano-cages. The calculated first hyperpolarizability of the K@BP nano-cage is 5.7 x 10(5) a.u., a value comparable to that of the best NLO material reported in the literature. The electronic structures of nano-cages including the HOMO-LUMO gap, TDOS, PDOS and excitation energies are analyzed to rationalize the extraordinary NLO response of the phosphide nano-cages. The NLO response of the K@BP nano-cage is primarily attributed to a very low excitation energy (0.5 eV). Interaction of nitrogen and phosphorus (of the nano-cages) with alkali metals differs between aluminum and boron nano-cages. Interaction of lone pair containing atoms with alkali metals in aluminum nano-cages generates diffuse excess electrons, whereas no such diffuse excess electrons are generated in boron nano-cages. UV-Vis and infra-red spectral characteristics for these encapsulated nano-cages are presented as a reference for future studies.