![]() ![]() ![]() To examine this we use eqn (3), by setting u G ( r ) and u G f ( r ) to HOMO and LUMO states, respectively. , GO and rGO with various numbers of O vacancies, n v, we examine whether the energy gap modulation with n v is also followed by changes in their optical activity. This is in line with the calculations for the epoxy functionalised structures with different symmetries (see the Appendix, Table 7). The effect of the breaking of symmetry is much greater, with a calculated difference of 0.385(0.513) eV. For V Ia 4 the difference is predicted by PBE0 (B3LYP) to be 36(37) meV, while for V Ia 8 it is 6(2) meV. We have found the energy gaps predicted for the structures with the same symmetry, V Ia 4 and V Ia 8, differ only very slightly from the purely epoxy functionalised structures, as shown in Table 3. The symmetry was deliberately preserved in structures V Ia 4 and V Ia 8, and broken in the case of V Ib 4, as shown in Fig. To maintain the minimisation of repulsive Coulomb forces by even distribution of adsorbates above and below the graphene lattice, a single epoxy group was replaced by two hydroxyl groups and the epoxy groups were removed in pairs. With a view to further justifying the model adopted, simula- tions were performed on a representative number of structures with hydroxyl groups present in addition to the epoxy motifs. 7i–l) are to a large extent composed of the C-2p z orbitals centered on the atoms which are the second nearest neighbours, their weak overlapping is accompanied with small values of the energy gap. Since the frontier electronic states in larger GQDs (Fig. 7c–h) are localized on the nearest neighbour C atoms and thus there is a strong overlap between the corresponding C-2p z orbitals which results in significant energy gap values. These electronic states of the three smallest quantum dots (Fig. 7 the HOMO and LUMO of all studied GQDs are mainly located at the edge of the C atoms. Orbitals above the LUMO and below the HOMO are seen to be still of sp 3 nature (not shown). Also evident is the reappearance of pristine graphene’s characteristic sp 2 hybridized p -bonds. ![]() 7(c) and (d) illustrate the HOMO and the LUMO for the structure with one O atom removed, showing both to be largely localised on C atoms (node sites), but with partial contribution of p type orbitals from the four nearest neighbouring O atoms (bridge sites). 7(a) and (b) depict the HOMO and LUMO states of fully oxidized graphene, respectively, distinctly showing the sp 3 hybridized bonds. The electronic structure of reduced graphene oxide is readily explained by detailed inspection of the Bloch functions. These clearly show the sp 2 states localized on the GQDs, positioned at energies within the band gap of GO, which is the energy gap between the highest occupied and lowest unoccupied sp 3 states. Eigenstates of the GQDs and total DOS are plotted in Fig. ![]() However, when embedded in GO, the C atoms at the boundaries of GQDs are stabilized due to binding to the surrounding GO layer. 3, produced upon partial reduction of GO, feature odd shapes which could not be preserved in the form of free nanoparticles due to a large number of under-coordinated C atoms. 47 Nanostructures with a larger fraction of zig-zag edges show a smaller energy gap than those with a similar size to mainly armchair edges. 46 Yet, both experimental and theoretical studies of graphene nanoflakes, as well as graphene nanoribbons, demonstrate a strong influence of the edges on their electronic properties. These trends differ from experimental results found for free GQDs, which show that their energy gap is inversely proportional to the diameter. E g (0) is the band gap of fully oxidized graphene and n v is the number of oxygen adatoms removed. ![]()
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