The luminescence emission of graphene quantum dots (GQDs) is around the visible range, so it could be used as light-emitting diodes or biological markers. Also, the diameter of the GQDs determines the luminescence emission by the variation of the energy gap. For this reason, it is important to establish models that help us to estimate the size of the GQDs. In particular, the radial breathing mode (RBM) allows the correlation of the diameter in some nanostructures with a specific vibrational frequency that could be obtained by Raman spectroscopy. For this reason, we performed the calculation of the RBM in GQDs using the density functional theory. We performed the calculations with different exchange and correlation (XC) functionals to compare the values obtained and select which XC functional could be more accurate in the calculation of the RBM. Also, we found that in the case of the energy gap the values obtained from the various functionals are very similar for standard XC functionals. By contrast, the RBM within the local density approximation is very similar to the other XC functionals, but with small differences to that obtained within the generalized gradient approximation (GGA) to the XC functional. Finally, we found that the dependency of the RBM behavior on the diameter could be described by the inverse of its radius as in the case of nanowires.
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