Structure and Optical Properties of Alkali-Metal Ion (Li⁺, Na⁺, K⁺, Rb⁺, and Cs⁺) Endohedral Cyclo[18]carbon

With growing interest in carbon-based materials for energy storage and active research in the field of advanced optoelectronic devices, ten complexes are designed with cyclo[18]carbon (C₁₈) inside and outside complexing alkali metal ion (M⁺ = Li⁺, Na⁺, K⁺, Rb⁺, and Cs⁺), respectively, referred to as M⁺@C₁₈ ⁱⁿ and M⁺@C₁₈ ^out, and careful analysis of their structure, binding interaction between M⁺ and C₁₈, as well as optical properties of stable endohedral complexes M⁺@C₁₈ ⁱⁿ is performed. The effects of atomic number of alkali metals on structure, binding interaction, electronic absorption spectrum, and molecular (hyper)polarizability of the M⁺@C₁₈ ⁱⁿ are studied using accurate (time-dependent) density functional theory calculations. The research suggests that the binding modes and strengths of different M⁺ with C₁₈ are different but there is no evident difference in electronic absorption spectra of the complexes. The polarizability and second hyperpolarizability of M⁺@C₁₈ ⁱⁿ containing different alkali-metal ions are close due to the similarity of ionic properties but their first hyperpolarizability differs greatly by reason of discrepancy in molecular symmetry. The similarities and differences in structure, fragment interaction, electronic absorption spectrum, and (hyper)polarizability of M⁺@C₁₈ ⁱⁿ are explored using advanced wavefunction analysis methods.