  Graphene quantum dots (GQDs) represent single layers up to dozens of graphene
layers smaller than 30 nm. GQDs are newish molecules that have aroused great
interest in research because of their exceptional and manageable optical,
electrical, chemical, and structural properties. In this work, we report
electrostatic potential energy maps, or molecular electrostatic potential
surfaces, illustrate the charge distributions of GQDs three-dimensionally.
Knowledge of the charge distributions can be used to determine how GQDs
interact with one another. To analyze the distribution of molecular charges
accurately, a large number of electrostatic potential energy values must be
calculated. The best way to transmit these data is to visualize them as in the
electrostatic potential map. A ZINDO semi-empirical quantum chemistry method
then imposes the calculated data onto an electron density model of the GQDs
derived from the Schr\"odinger equation. To make the electrostatic potential
energy data of GQDs easy to interpret, a color spectrum, with red as the lowest
electrostatic potential energy value and blue as the highest, is employed to
convey the varying intensities of the electrostatic potential energy values.
The results of the four GQD models suggest that the energy of the ionization
potential lies in a range of -7.20 eV to -5.31 eV and the electron affinity is
-2.65 to -0.24 eV.
