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Rattling motion of alkali metal ions through the cavities of model compounds of graphyne and graphdiyne.

We study the passage of the alkali metal ions (Li(+), Na(+), and K(+)) through some conjugated carbon-based ring systems, starting from C12H6 and C24H12 (tribenzocyclyne; TBC), which serve as model compounds for graphyne to some of the higher analogues, C26H12, C28H12, and C30H12, the model systems for graphdiyne. The motion of the ions through cyclic carbon clusters, C12 and C14, is also investigated. The potential for the motion of the ions from one side of the ring to the other through the cavities of the molecules is a symmetric double well in most cases, while it is a rather flat potential in others, arising due to the free motion of the ions through the cavities. Electrostatic potential (ESP) analyses reveal that the ions bind to the ring systems at the most negative regions of ESP. The estimated energy barriers for the motion of Li(+) through C12H6 and C24H12 are 4.7 and 4.3 kcal mol(-1), respectively, and are comparable to the barrier for the classic case of umbrella-like inversion in ammonia. Transmission of Li(+) through C26H12, C28H12, C30H12, C12, and C14 rings is barrierless. We predict that the rattling motion of Li(+) through the model compounds of graphyne and graphdiyne should be experimentally observable. We also model the effectively one-dimensional motion of the ions through the rings using discrete variable representation (DVR) and calculate the energy levels of the complexes in the symmetric double well potentials. The molecular orbital analyses and the nuclear independent chemical shift (NICS) values for the rings suggest distinct trends based on the (4n + 2/4n) π electron count, leading us to propose two neutral complexes, (C12H6)Li2 and (C24H12)Li2, that are highly stable with binding energies of 400 and 356 kcal mol(-1), respectively.