Comparative analysis of absorption resonances between carbynes and cyclo[ n ]carbons.

Two approaches are presented here to analyze the absorption resonances between carbynes and cyclo[ n ]carbons, namely the analytical tight-binding model to calculate the optical selection rules of cumulenic atomic rings and chains and the ab initio time-dependent density functional theory for the optical investigation of polyynic carbon ring and chains. The optical absorption spectra of the carbon ring match that of the finite chain when their eigen energies align following the N ring = 2 N chain + 2 rule, which states that the number of atoms in an atomic ring N ring is twice the number of atoms on a finite chain N chain with two additional atoms. Two representative atomic chains are chosen for our numerical calculations, specifically carbynes with N = 7 and 8 carbon atoms as optical resonance spectra match to a recently synthesized carbon ring called cyclo$[18]$carbon. Despite the mismatch in resonance peaks, molecular orbital transitions of both carbynes N = 7 and 8 and cyclo[ n ]carbons reveal a wave function symmetry change from inversion to reflection and vice versa for allowed molecular orbital transitions, which results in electron density redistribution along the polyynic carbyne axis or the cyclo[ n ]carbons circumference. Our investigation of the correlation of optical absorption peaks between carbynes and cyclo[ n ]carbons is a step towards enhancing the reliability of allotrope identification in advanced molecular device spectroscopy. Moreover, this work could facilitate the non-invasive, rapid and crucial assessment of these sensitive 1D allotropes by providing accurate descriptions of their electronic and optical properties, particularly in controlled synthesis environments.