An Ab Initio Investigation of Carbon Nanorings (C_2<i>n</i>, n = 3 to 32)

In this paper, the structure and electronic stability of carbon nanorings (C 2 n , n=3 to 32) are studied in detail using the density functional theory (DFT) method. In summary, this study presents 30 nanorings with an even number of carbon molecules. These molecules showed stability with good convergence criteria using DFT and DFTB+ quantum molecular dynamics calculations. The estimation of HOMO-LUMO gaps (HLgap) converged to values between 0.34 (0.41) and 3.45 (3.39) eV for C 64 to C 10 nanorings, respectively, using the LDA and GGA approximations, showing promising electronic properties such as a wide range tuning bandgap energy. It is noteworthy that the C 6 , C 14 , C 18 , and C 22 nanorings present optical absorption in the visible region (red, yellow, and orange). All nanorings have positive vibrational frequencies, indicating that these molecules are potentially stable. There is a curve trend behavior of the form: a + bx + c / x 2 where a , b , and c are coefficients, and x denotes the number of atoms. This behavior encompasses all minimum or maximum frequencies of all nanorings. In addition to this, there are two patterns in these nanorings depending on the number of carbon atoms: larger band-gap nanorings satisfy the equation n = 4 m + 2, for m = 1, 2, 3. . . , while smaller band-gap nanorings satisfy the equation 4 m + 4, for m = 2, 3, 4. . . , with the pattern converging to a unique bandgap when n reaches 64 carbons. Even when using the more robust HSE06 hybrid functional, the gap estimation tends to decrease as the number of carbon atoms in the nanoring increases. Results indicate a trend for the binding energy of this finite-cycle carbon nanoring (C 64 ) toward the binding energy of the carbyne nanowire, around −7.0 eV for each atom. The authors hope that the proposed nanoring molecules can stimulate experimental investigations into their synthesis, which could indicate other potential technological applications.