Raman-active modes of even-numbered cycloparaphenylenes: Comparisons between experiments and density functional theory (DFT) calculations with group theory arguments

[6]-, [8]-, [10]-, and [12]cycloparaphenylenes (CPPs), the smallest even-numbered carbon nanohoops synthesized to date, are probed by Raman spectroscopy. For the highly symmetric even [n]CPPs, group theory predicts that there are 133 Raman-active modes in total for n ≥ 8, 73 for [6]CPP, and 100 for [4]CPP. The Raman-active modes of these even-numbered CPPs are identified by comparing experimental results with theoretical Raman spectra calculated using density functional theory (DFT). Taking advantage of the symmetry arguments in these symmetric molecules allows the assignment of the observed Raman peaks, as well as the identification of their dependence on the sizes of the CPPs.