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Article

Tuning Optical Excitations of Graphene Quantum Dots Through Selective Oxidation: Effect of Epoxy Groups

by
Igor V. Ershov
1,*,
Anatoly A. Lavrentyev
2,
Dmitry L. Romanov
2 and
Olga M. Holodova
1
1
Department of Physics, Don State Technical University, Rostov-on-Don 344000, Russia
2
Department of Electrical Engineering and Electronics, Don State Technical University, Rostov-on-Don 344000, Russia
*
Author to whom correspondence should be addressed.
C 2025, 11(3), 51; https://doi.org/10.3390/c11030051
Submission received: 6 June 2025 / Revised: 1 July 2025 / Accepted: 11 July 2025 / Published: 14 July 2025
(This article belongs to the Special Issue Carbon-Based Polymer Composites: Synthesis, Processing, Characterization and Applications (2nd Edition))
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Abstract

Graphene quantum dots (GQDs) have strong potential in optoelectronics, particularly in LEDs, photodetectors, solar cells, and nanophotonics. While challenges remain in efficiency and scalability, advances in functionalization and hybrid material integration could soon make them commercially viable for next-generation optoelectronic devices. In this work, we assess the stability of various epoxy positions and their impact on the electronic and optical properties of GQDs. The oxygen binding energies and the potential barrier heights at different positions of epoxy groups at the edges and in the core of the GQD were estimated. The effect of possible transformations of epoxy groups into other edge configurations on the structural and optical properties of GQDs was evaluated. The results demonstrate that the functionalization of the GQD surface and edges with an epoxy groups at varying binding sites can result in substantial modification of the electronic structure and absorption properties of the GQDs. The prospects of low temperature annealing for controlling optical properties of epoxidized GQDs were discussed. The present computational work offers atomistic insights that can facilitate the rational design of optoelectronic systems based on GQD materials.

Graphical Abstract

1. Introduction

Graphene quantum dots are currently extensively studied systems as promising carbon nanomaterials due to their potential applications including bioimaging [1], photovoltaics [2], and optoelectronics [3]. Among the most attractive properties of GQDs are their high stability, low cost, high solubility in various solvents and low toxicity [4,5,6]. These properties make them much more desirable for many applications compared with inorganic semiconductor quantum dots. GQDs hold significant promise in optoelectronics due to their unique optical and electronic properties, including tunable bandgap, high photoluminescence, excellent charge carrier mobility, and solution processability [7].
However, pristine quantum dots still face several challenges, including a limited absorption range, low photoluminescence quantum yield, and broad emission bands. Covalent functionalization can address many of these limitations and unlock new applications of GQDs in optoelectronics. For example, it was experimentally shown that adsorption of various functional groups on the surface of graphene quantum dots can increase the quantum yield from 13 to 94% [8,9,10]. Functionalization has also been demonstrated as a powerful method of bandgap engineering in graphene nanoribbons [11].
Various oxygen functional groups, such as epoxy, hydroxyl, and carboxyl, are adsorbed on the basal planes or at the edges of GQDs [12,13,14]. The epoxy and hydroxyl groups are the main chemical species present at the basal planes of GQDs [15]. Several studies have shown that it is possible to oxidize the graphene surface exclusively with epoxy groups [16,17,18,19], and the oxidized surface can recover to the pristine form via a desorption reaction. Thus, with the help of epoxy group adsorption, it is possible to perform functionalization without irreversible damage to the underlying carbon lattice.
Numerous theoretical studies have shown that selective functionalization of GQDs can significantly change their optoelectronic properties [12,20]. It was previously experimentally shown that epoxidation of epitaxial graphene can be completely reversed and that epoxy groups do not etch graphene even at saturated coverages [16,17,18]. Atomic radicals have sufficient energy to overcome the kinetic and thermodynamic barriers associated with covalent reactions on the basal plane of graphene but lack the energy required to break the C-C sigma bonds that would destroy the carbon lattice [17]. This offers good perspectives for selective functionalization by controlling the reaction temperature, since epoxy groups with different stabilities will desorb at different temperatures without irreversible disruption of the carbon backbone. In the case of graphene quantum dots, in addition to the basal surface, oxygen adsorption can occur at the edges; thus, the stability of different adsorption positions of epoxy groups directly affects the structure of quantum dots at different temperatures. Epoxy groups form sp3-hybridized bonds with the carbons of GQD, warping the planar structure of the carbon backbone, and disrupt the integrity and the structural symmetry of the conjugated π-electron system through modification of electronic wavefunction spatial distribution [20]. This makes the adsorption of epoxy groups of greatest interest for tuning the optical properties of GQDs compared to other oxygen-containing groups. There have been numerous theoretical works to date on the structural, electronic, and optical properties of epoxy graphene [21,22,23,24] and graphene quantum dots [25,26,27]. However, the effect of individual non-equivalent oxygen binding sites at the edges and on the basal plane and their stability on the optical properties of quantum dots is still poorly understood. The question of possible transitions between different binding sites at finite temperatures and the dependence of optical properties on the concentration of epoxy groups is also far from being answered.
In this work, we predict the performance of epoxidized GQDs by using density functional theory (DFT) to describe the impact of different oxygen adsorption sites and oxygen coverage on the system geometry and the consequent effects on the electronic and optical properties of GQDs. The stability of all possible non-equivalent positions of epoxy groups at the edges and on the basal surface of the quantum dot was analyzed, and the energy barriers and possible transformations of epoxy groups into hydroxyl and ether groups were estimated. It was demonstrated that the optoelectronic properties of GQDs are predominantly influenced by the specific epoxide positions rather than by the degree of oxygen coverage.

2. Materials and Methods

GQDs can be characterized as medium-to-large-sized polycyclic aromatic hydrocarbons (PAHs), which demonstrate discrete absorption and emission spectra due to quantum confinement, as compared to graphene sheets [28]. In the present work, we used the experimentally well-characterized PAH C48H18 [29,30] with mixed zigzag and armchair edges as a model of real graphene quantum dots.
Covalent modification of the GQD plane and edges requires the presence of high energy reactants, such as strong acids or radicals. Chen et al. [31] showed that epoxy and hydroxyl groups can be formed by direct attack of graphitic sheets with •O• and •OH radicals. To establish the mechanisms of oxygen adsorption at various positions of GQDs, a series of quantum mechanical calculations were carried out. First, for qualitative assessment of the reactivity of various regions of GQDs with respect to the nucleophilic and free radical attack to the charge density, we calculated Fukui functions f+(r) and f0(r)) within the density functional theory framework, as follows [32]:
f + r → = ρ N + 1 r → − ρ N r → , f 0 r → = 1 2 ρ N + 1 r → − ρ N − 1 r → ,
where ρN is the electronic density of the neutral N-electron quantum dot, ρN+1 is the density of the anion generated from adding one electron to the N-electron system, and ρN+1 is the density of the cation.
Figure S1 shows an isosurface for positive values of the f+(r) function, indicating reactivity towards nucleophilic attack. As can be seen from Figure S1, the regions that are most susceptible to nucleophilic addition are located at the edges of the GQD. The positions in the quantum dot most susceptible to a radical attack were investigated using the f0(r) function, as plotted in Figure S1. As in the case of nucleophilic addition, the edge carbon atoms appeared to be the most susceptible to a radical attack.
After determining the most reactive regions of the GQD, we performed the global energy minimum search for the adsorption of atomic oxygen on the C48H18 quantum dot using the global geometry optimization and ensemble generator (GOAT) implemented in the ORCA 6.01 software package [33] with extended semiempirical tight-binding Hamiltonian GFN-xTB [34].
For the most energetically favorable positions of epoxy groups at the edges and basal plane of the quantum dot, the energy barriers between these positions were calculated through the transition state search [35] within the dispersion-corrected density functional theory framework [36,37]. The results obtained within the GGA-PBE approximation appeared qualitatively in perfect agreement with the results obtained by the semiempirical dispersion-corrected tight-binding method. The obtained potential energy profiles, which demonstrate possible oxygen pathways through the lowest available potential barriers, are presented in Figure S2. The structures with highest binding energy are presented in Figure 1. In the C48H18 structure, thirteen non-equivalent epoxy positions can be distinguished, including six at the edge and seven on the basal surface (Figure 1).
The ground-state energies of the most favorable oxygen positions were further calculated within the DFT framework at the higher level of theory using the hybrid exchange-correlation functional (B3LYP/def2-SVP) with Grimme D3 atom-pairwise dispersion correction [38,39] (Table 1). The binding energy per oxygen atom for various positions and number of epoxy groups was estimated using the following expression:
E b = E G O Q D − E G Q D − N E O / N ,
where EGOQD is the ground-state total energy of the oxidized GQD, EGQD is the total energy of the pristine GQD, EO is the total energy of the triplet oxygen atom, and N is the total number of oxygen atoms in the GQD.
Excited state energies and optical absorption spectra were calculated for the optimized GQDs with oxygen groups using the simplified time-dependent density functional theory approach (sTD-DFT) [40,41]. The Pople 6-311G (d,p) split-valence triple-zeta basis set with polarization functions on heavy atoms and hydrogen was used in the calculations. In the sTD-DFT formalism, the response term of the semi-local density functional is neglected to avoid expensive numerical integration, and two-electron integrals are approximated by short-range damped Coulomb interactions of transition charge density monopoles, which are obtained from a Löwdin population analysis [40,41,42]. In combination with global hybrid density functionals, the sTD-DFT approach has shown good quantitative agreement with experiments for compounds with a valence-dominated response, such as conjugated π-systems [41,42]. The absorption spectra were simulated using the calculated transition energies and oscillator strengths with a full width at half maximum of 0.15 eV.

3. Results and Discussion

Table 1 shows the estimated values of the adsorption (binding) energy of oxygen atoms for various positions related to the number of epoxy groups. The analysis of Table 1 and the potential energy profile (Figure S2) for the oxygen pathway from the edge towards the center of the quantum dot shows that the most energetically favorable are the oxygen binding positions at the edge denoted as Ph, A, and D. The Ph position has the highest binding energy and is formed by the substitution of an edge hydrogen atom and subsequent formation of a hydroxyl (phenol) group (Figure 1b). However, considering the optical properties, hydroxyl groups at the edges have practically no effect on the absorption spectrum of graphene quantum dots, which was confirmed by our calculations (see Figure S3), so these functional groups are not of practical interest in the present work.
The second highest binding energy position of single oxygen is the epoxy group at the K-region on zigzag edge [30] denoted as position A (Figure 1c), which has about 1.6 eV lower binding energy compared to phenol position. Binding position A is the most energetically favorable position of epoxy group in the GQD in agreement with previous predictions and theoretical studies [26,30]. The binding energy of the epoxy group at position A in Figure S2 is taken as the zero reference point. The second energy-favorable binding position of the epoxy group is position D (Figure 1d), located near the armchair bay region. The binding energy of the epoxy group in position D is only 0.09 eV lower than in position A. Neither position A nor D practically distort the planar structure of the quantum dot, which partially explains their highest stability. Analysis of the potential energy profile (Figure S2) also allows us to conclude that position A is separated from the neighboring local minima (position B) by potential barriers of about 1.5 eV high. The transition to the phenolic position Ph is also bounded by a potential barrier of more than 1.5 eV high. Position D, in turn, is characterized by the slightly lower barriers of the order of 1.3 eV between adjacent minima (positions C and E).
Edge-binding positions B and C, as can be seen from the potential energy profile, appear to be unstable at finite temperatures, since at small perturbations (activation energy about 40–50 meV) they transform to the more stable and energy favorable configurations B’ and C’. Configurations B’ and C’ are actually no longer epoxy groups, because oxygen in the bridge positions breaks the C-C bond in the six-member ring forming cyclic ether; therefore, the given configurations can be formally called “ether”. Epoxy-binding position E, which is located in the bay region (Figure 1e), is somewhat more stable; however, it is also relatively easy to transform to the more favorable ether configuration (the potential barrier is only 0.1 eV), which is denoted as E’ (Figure 1f). All ether configurations demonstrate almost equal binding energies, which are higher compared to their epoxy counterparts. Formation of ether groups is accompanied by strong local distortion of the GQD planar structure, which is illustrated in Figure 1f for the configuration E’. Among all non-equivalent epoxy positions at the edges, the least energetically favorable is the position F at the bottom of the bay region (Figure 1a). Oxygen in this position breaks the C-C bond, which dramatically distorts the planar structure of the GQD, resulting in a decrease in the oxygen binding energy by more than 1.3 eV compared to the reference value (pos. A).
Moving to the positions inside the quantum dot, on its basal surface, the three most favorable positions, namely α, δ, and η should be considered (Figure 2). Position δ is the most favorable of the three; however, its binding energy is more than 1 eV lower than the reference value (pos. A) and it is separated from the neighboring local minimum E by a potential barrier of 0.64 eV. The minimal potential barriers for the positions η and α were found to be 0.69 eV and 0.71 eV, respectively (Figure S2). The other epoxy positions inside the quantum dot were found to be less stable due to smaller binding energies and lower potential barriers.
Thus, epoxidation of GQDs occurs more easily at the edges than on the basal plane. The latter is in agreement with previous studies [24,25,26]. It was proposed that oxygen functional groups at the edge of a GQD cause a greater deformation of the conjugated π-electron system, resulting in larger binding energies and longer C–C bonds than in the other configurations [26]. In Table 2, the average C-C and C-O bond lengths for the different configurations of the oxidized GQD are presented. The average C-C bond lengths of the two most stable epoxy edge configurations increased by about 7.8% upon oxidation, while the average C-C bond lengths of the two energy favorable basal-oxidized configurations increased by 6.8% and 7.2%, respectively.
As it was shown in previous theoretical studies [25,26] electronic states associated with epoxy groups appear deep inside the valence band of the GQD and hybridization has virtually no effect on its frontier molecular orbitals. However, the band gaps (HOMO-LUMO gaps) of the GQD considerably change with the position of the epoxy functional group (Figure 3a). Figure 3a shows that HOMO-LUMO gaps for the edge epoxy configurations gradually decrease with decreasing oxygen binding energy, compared to the gap of the non-oxidized quantum dot, while the energy gaps of the basal-oxidized configurations, on the contrary, increase up to 3.22 eV for the less favorable position α. Thus, the variation of the bandgap at different positions of the epoxy group is about 0.8 eV. There are several reasons for such variation. Primarily, adsorbed oxygen forms sp3-bonds with planar carbon network, which causes localization of electron densities and local distortion of the GQD’s planar structure around the binding sites, resulting in the redistribution of electron densities and variation of molecular orbitals’ energy levels. This structural deformation is size dependent; it is less pronounced in large graphene sheets and becomes significant in graphene quantum dots.
Oxygen in epoxy positions perturbs the spatial distribution and symmetry of the frontier molecular orbitals (Figure 3b) which results in the localization of the charge density around the binding sites. This localization is least pronounced for the most favorable oxygen positions A and D, for which the electron density distribution is practically unchanged in comparison with the non-oxidized GQD. At the same time, a significant electron localization is observed in the lowest unoccupied molecular orbitals of the basal-oxidized GQDs in positions η and α. These features are directly reflected in the absorption spectra of oxidized GQDs, as presented in Figure 4.
Figure 4 shows the calculated absorption spectra of six mono-epoxides and one mono-ether configuration. The calculated and experimental energies of excited states in the non-oxidized C48H18 quantum dot along with the calculated absorption spectrum are presented in Table S1 and Figure S3. Typically, large polycyclic aromatic molecules feature three characteristic optical bands α, p, and β with increasing intensity in the absorption edge [43]. However, in the case of C48H18 quantum dots, the α- and p-bands are formed by symmetry-forbidden dark states (Table S1), which is explained by the degenerate HOMO/HOMO-1 and LUMO/LUMO+1 orbitals (Figure 3a). The α-band in PAH is typically formed by the first singlet excited state S1, while the p-band is due to the S0 → S2 transition. As can be seen from Figure S3, the C48H18 quantum dot features an intense absorption band centered around 400 nm which is caused by the excitation of degenerate singlet states 1Bb and 1Ba (in Platt’s notation [44]) or β and β’ bands in Clar’s notation [43]. The calculated β- and β’-band energies (S0 → S4 and S0 → S5 transitions in Table S1) were found to be in good agreement with the experimental data.
In contrast to the non-oxidized quantum dot, the spectra of singly oxidized GQDs demonstrate new absorption bands and red shift of the absorption edge. In case of edge-oxidized mono-epoxides (Figure 4a–c) and ether configuration E’ (Figure 4d) the absorption edge is formed by the activated S2 excitations (p-bands), which mainly originate from HOMO→LUMO transitions [43] (S0 → S2 transitions in Table S2). The main absorption band in the visible range is formed by the two nondegenerate singlet excitations 1Bb and 1Ba with high oscillator strengths. The S0 → S1 transitions in all edge-oxidized structures demonstrate very small values of the transition dipole moment, and consequently negligibly small oscillator strengths. The energies of the S2 excitations decrease with decreasing binding energy, while the oscillator strengths for the corresponding transitions increase, reaching a value of 0.25 for the E configuration (Table S2). The energies of the main absorption band in the visible range, as in the case of the p-band, decrease with the oxygen binding energy lowering. Moreover, with decreasing oxygen binding energy, a broadening of the main absorption band and a corresponding decrease in its intensity were observed. In the case of oxygen conversion from the epoxy E configuration to the more stable ether configuration E’, the adsorption spectrum demonstrates blue shift due to the increased energy of the S2 and S3 states. The absorption spectrum of the ether group at the B’ position is shown in Figure S3c. Thus, the formation of ether configurations at the edges results in minor changes in the absorption spectrum compared to epoxy groups. The absorption spectra of the GQD with epoxy groups on the basal plane are shown in Figure 4e–g. The spectra demonstrate continuous absorption in the wavelength range from UV to 500 nm due to a greater number of excitations activated upon the oxygen adsorption. In particular, the absorption bands in the visible range are formed by the intense excitations which involve the more distant molecular orbitals HOMO-2 and LUMO+2 (Table S2). It should also be noted that the very small values of the oscillator strengths for the transitions S0 → S2 form weak p-bands, as well as relatively small oscillator strengths of the 1Bb excited states (β band), while the 1Ba excitations appear to be almost twice as intense. At the same time, it should be noted that there is an increase in the probability of transitions involving the S1 state for the configuration δ (Table S2). Thus, adsorption of a single oxygen atom can significantly change the absorption spectrum of the pristine GQD.
In order to study the effect of oxygen coverage on the optical properties of quantum dots we studied structures with two, three, four, six, and nine epoxy groups. The C48H18O2 structures with two adsorbed oxygen atoms are presented in Figure 5. Similar to mono-epoxides, we performed calculations for the edge-oxidized and basal-oxidized structures. The six most favorable edge-oxidized and three basal-oxidized conformations are shown in Figure 5.
As in the case of mono-epoxides, the most energetically favorable epoxy-conformation (Table 1) is the AA configuration with two oxygen atoms adsorbed on C-C bonds of the two equivalent K-regions (Figure 5). The second highest binding energy conformation DD-1 with two oxygen atoms adsorbed on the same zigzag edge in ortho-positions has only 0.03 eV lower binding energy than the reference (AA) configuration. For the other isomers with edge oxidation, except for the last one (AD-3), the oxygen binding energy falls within 0.09 eV compared to the reference value (Table 1). All edge-oxidized configurations retain their planar structure upon oxygen adsorption. The basal-oxidized configurations showed the highest binding energies when two oxygen atoms were attached to a single carbon hexagon on the opposite sides of the basal plane. The binding energies of the three most favorable basal-oxidized configurations were found to be almost identical and, on average, about 0.85 eV less than the reference edge-configuration. Oxygen adsorption on the central hexagon of the GQD (ηη configuration) results in the minimal distortion of its plane, while in the other two configurations, more prominent deformation occurs (Figure 5).
The optical absorption spectra of the C48H18O2 GQDs are presented in Figure 6 and Figure 7. As in the case of the edge-oxidized mono-epoxides, we observe a shift of the absorption edge to the long-wavelength region with decreasing oxygen binding energy in the edge-oxidized C48H18O2 GQDs (Figure 6a–d) due to an increase in the S2 excitation energy. However, this trend is broken when we come to the DD-2 conformation, which has the highest optical gap, where we observe a single narrow absorption peak with high absorbance, centered at 430 nm (Figure 6e), formed by two nearly degenerate states, namely 1Bb and 1Ba, similar to the pristine GQD. This can be explained by the symmetry change in the π-electron system due to the formation of the point group Cs. The latter is confirmed by the degenerate HOMO/HOMO-1 and LUMO/LUMO+1 (Figure S4a) and the HOMO and LUMO charge density distribution (Figure S5b). The AD-1 conformation with the para-configuration of the epoxy groups exhibits the lowest optical gap of 2.2 eV, which is in accordance with the lowest value of the corresponding HOMO-LUMO gap (Figure S5a).
The absorption spectra of the basal-oxidized configurations with two oxygen atoms exhibit several interesting features. For example, the absorption spectrum of the ηη-configuration lies exclusively in the ultraviolet region (Figure 7a), since the first six excitations are either optically forbidden or have negligibly small oscillator strengths (Table S2). The first bright state S7 involves HOMO-2 and LUMO+1 orbitals. The αδ-conformation was found to have the lowest optical gap 2.64 eV, which is formed by the bright p-band (S2 excitation).
Figure 8 shows the structures of the C48H18O3 quantum dots with three adsorbed epoxy groups in order of decreasing oxygen binding energy. The most energetically favorable epoxy conformation with three adsorbed oxygen atoms turned out to be the AAA configuration, in which oxygen is bonded to all available K-regions. In the remaining two edge configurations, oxygen is attached in various combinations to positions D. The two most energetically favorable configurations of quantum dots with three epoxy groups on the basal surface are labeled in Figure 8 as ηηη and δδη, respectively. As we can see from Figure 8, three oxygen atoms tend to agglomerate from both sides of a single carbon hexagon. The binding energy for the most favorable configuration ηηη is 2.32 eV (Table 1); thus, we can conclude that the agglomeration of epoxy groups on the basal plane increases the binding energy per single oxygen atom.
The optical absorption spectra of the C48H18O3 GQDs are presented in Figure 9. The absorption spectrum of the most stable AAA configuration in the visible range is characterized by a single narrow intense absorption band centered at a wavelength of 380 nm (Figure 9a). This band is formed by the degenerate S5 and S6 states (β and β’ bands), similarly as in the case of the pristine GQD, being shifted to the boundary between the visible and ultraviolet region. The other transitions in the AAA configuration appeared to be symmetry-forbidden. The analysis of the frontier molecular orbitals’ energies in the AAA conformation (Figure S5) revealed the presence of degenerate HOMO/HOMO-1 and LUMO/LUMO+1 orbitals and, as a consequence an increased value of the HOMO-LUMO gap (Table 1). Our calculations showed that the absorption spectrum of the AAA configuration is nearly identical to that of hexa-peri-hexabenzocoronene (HBC) (Table S1). The latter can be explained by the fact that the epoxy groups in the positions of K-regions bind the π-electrons located on them making the π-electron network of the oxidized GQD identical to that of HBC. The DDD-2 configuration exhibits an intense absorption band in the visible region similar to that of the AAA configuration, centered at 400 nm and formed by nearly degenerate β and β’ bands (Figure 9c). The p-band is very weak in this configuration. Absorption spectrum of DDD-1 configuration (Figure 9b) is characterized by a lower value of the optical gap and the presence of a p-band of moderate intensity at the absorption edge. Absorption spectra of the two most favorable basal-oxidized configurations (Figure 9d,e) reveal the same trends which were observed in the C48H18O2 basal-oxidized quantum dots. In the higher symmetry configuration ηηη, the absorption edge is formed by the sharp narrow absorption band with moderate absorbance, centered at 390 nm and formed by degenerate β and β’ states. As one can see from the distribution of the frontier molecular orbitals (Figure S6) the HOMO and HOMO-1 orbitals are degenerate, while the LUMO and LUMO+1 orbitals have very close eigenvalues, in this connection, the ηηη configuration shows the largest HOMO-LUMO gap (3.50 eV) of all triple-epoxidized GQDs. The lower symmetry configuration δδη features p, β, and β’ bands with comparable absorbance. Thus, it can be concluded that the intensity of the β and β’ bands decreases with the increasing oxygen concentration at the basal plane of GQDs.
Figure 10 illustrates the structures of the C48H18 quantum dots with four, six and nine epoxy groups adsorbed on the edges. As in the case of three adsorbed epoxy groups, the most favorable are the structures in which oxygen is bonded at positions A and D on the zigzag edges. The highest binding energy per single oxygen atom (as in the AAA configuration) was found in the 6D configuration, with six epoxy groups uniformly arranged at the edges in the D positions (Table 1). This structure also demonstrates a high degree of planarity of the carbon backbone (Figure 10). The structure with complete edge oxidation by nine epoxy groups demonstrated the lowest oxygen binding energy, which is attributed to the considerable deformation of the GQD basal plane.
Figure 11 shows the optical absorption spectra of quantum dots with four, six, and nine epoxy groups adsorbed at the edges. The 6D structure with the highest binding energy demonstrates strong absorption at a wavelength of 365 nm (Figure 11d), due mainly to the degenerate β and β’ bands (S3 and S4 excitations), as well as two degenerate excited states S5 and S6 (Table S2). The wavelength of this absorption band is almost exactly the same as the main absorption band in HBC (Table S1). A similar absorption spectrum is exhibited by the structure with complete edge oxidation (Figure 11e). The absorption edge is centered at a wavelength of 410 nm and is formed by two excitations S8 and S9, which involve HOMO-2 and LUMO+2 molecular orbitals. Among the structures with four epoxide groups, the most stable appeared to be the configurations with oxygen atoms adsorbed at the D positions (4D-1 and 4D-2) and the mixed structure AADD. The latter demonstrate continuous absorption covering nearly the whole visible spectrum up to 600 nm (Figure 11c). It is interesting to note that in this spectrum, the p-band, centered at 514 nm, exhibits higher absorbance than the β and β’ bands. In the spectra with four epoxy groups, it can be observed that with decreasing oxygen binding energy, the optical gap decreases and the intensity of the p-bands increases with a simultaneous decrease in the intensity of the β and β’ bands.
To explain the stability and optical properties of different structures upon the attachment of epoxy groups, Clar’s rule can be used [45,46]. Figure S7 shows the Clar’s structures for the pristine C48H18 quantum dot and the two most stable edge-epoxidized structures, i.e., C48H18O3 and C48H18O6. As can be seen from Figure S7a, the C48H18 GQD is characterized by seven aromatic sextets and three K-regions with six π-electrons which cannot be included in a sextet. These outer π-electrons form three double bonds with increased reactivity. In case of the AAA epoxy configuration of the C48H18O3 GQD, all the three K-regions are passivated, and the outer π-electrons form covalent bonds with oxygen atoms; thus, the π-electron subsystem with seven aromatic sextets becomes fully benzenoid (Figure S7b). According to Clar’s sextet rule [45], if the π-electrons can all be grouped into sextets, then particularly high stabilization energy and consequently low reactivity is observed. The same fully benzenoid π-electron structure is characteristic of the HBC molecule. The similarity in the shapes and energies of the absorption edges of the AAA configuration and HBC now becomes clear. If we now turn to the 6D configuration of the C48H18O6 structure, which also has the maximum binding energy, we can also see that oxygen in the epoxide groups passivates six K-regions (all D positions), which results in the formation of fully benzenoid triangular structure with six aromatic sextets (Figure S7c). This aromatic core structure is completely identical to that of the fully benzenoid tribenzocoronene. The resulting fully benzenoid structures appeared to be highly planar. In contrast to the two previous cases, at passivation of all K-regions around the periphery of the quantum dot, which is the case in the C48H18O9 structure, only three aromatic sextets remain (Figure S7d). The resulting structure is not fully benzenoid, which reduces the binding energy. The same considerations allow us to explain the stability of configurations with four epoxy groups. The fourth oxygen atom disrupts the hexagonal structure of seven sextets, resulting in a more stable six-sextet triangular structure (Figure S7c).

4. Conclusions

In the present work, we have performed DFT calculations, including linear-response time-dependent theory, to study the effect of different oxygen adsorption sites and oxygen coverage on the structural, electronic, and optical properties of GQDs. We analyzed the stability of all possible non-equivalent positions of epoxy groups at the edges and on the basal surface of the quantum dot. The energy barriers and possible transformations of epoxy groups into hydroxyl and ether groups were also estimated. The calculations revealed that epoxy groups located at different positions on the edges and basal surface of the GQD exhibited varied binding stabilities. In particular, it has been shown that epoxy groups are likely to adsorb on the zigzag edges at the K-regions. The oxygen binding energy at these positions appears to be more than 1 eV larger than at the basal surface, and the energy barriers are higher than 1.5 eV. It has been demonstrated that the agglomeration of epoxy groups on the basal plane results in an increase in the binding energy per single oxygen atom. As a consequence, epoxy groups exhibit a tendency to agglomerate from both sides of a single carbon hexagon.
Analysis of potential energy profiles for epoxy groups suggests that, during the annealing process at a specific temperature, along with desorption, oxygen can migrate from positions on the basal surface inside the quantum dot to the edges due to climbing relatively low potential barriers without irreversible damage to the underlying carbon backbone. This opens up prospects for selective oxidation and control of optical properties of quantum dots by low-temperature annealing. During annealing, there is a high probability of oxygen configurations that result in the formation of a fully benzenoid aromatic core. In this case, GQDs will demonstrate the greatest stability and planarity while exhibiting minimal reactivity. The optical properties will undergo changes, including an increase in the optical gap due to orbital degeneracy and the emergence of forbidden transitions.
The present findings demonstrate that the functionalization of the GQD surface and edges with an epoxy groups at varying binding sites can result in substantial modification of the electronic structure and absorption properties of the GQDs. The effect of epoxy groups on the optoelectronic properties of quantum dots is manifested in several ways. Firstly, the planar structure of the carbon backbone is distorted, particularly at basal oxidation. Secondly, the integrity and structural symmetry of the conjugated π-electron system becomes disrupted. These effects result in the brightening of initially dark excitations, the variation of excitation energy and intensity, and the broadening of the absorption spectra. In particular, it has been shown that the optical gap can decrease by up to 1.5 times upon adsorption of single oxygen to different epoxy-positions. We should also note that the formation of ether groups on the edges results in minor changes in the absorption spectrum compared to epoxy groups, and the presence of hydroxyl (phenolic) groups on the edges has virtually no effect on the optical properties of GQDs. It was also shown that increasing the oxygen concentration at the edges in most cases results in an increase in the intensity of the absorption edge, while increasing the concentration in the GQD core results in a decrease in the intensity of the main absorption band. At the same time, it was found that in some configurations of epoxy groups on the basal surface, for example in configuration δ, the probability of transitions involving the S1 state increases. This can result in an enhancement of the luminescence quantum yield due to an increase in the transition moments for the first excited state.
The degree of oxygen coverage at the edges was found to have a virtually negligible effect on the optical gap width. This is most clearly observed when comparing the absorption spectra of symmetric structures with three, six, and nine epoxy groups with the pristine non-oxidized GQD. This study highlights the tunability of the optoelectronic properties of GQDs by selective adsorption of epoxy functional groups. In this regard, it is essential to further develop and refine technologies for precision control over the adsorption of various functional groups to obtain quantum dots with the desired optoelectronic properties.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/c11030051/s1, Figure S1: Isosurface for positive values of the f + (r) and f 0 (r) Fukui function; Figure S2: Potential energy profiles with energy barriers for the oxygen atom at the edge and basal plane of the GQD within GGA-PBE+D approximation; Figure S3: Optical absorption spectra of the C48H18 GQD non-oxidized (a), oxidized with hydroxyl (phenol) group (b), and oxidized with formation of ether group at position B’; Figure S4: UV/Vis and normalized photoluminescence emission spectrum of the C48H18 GQD; Figure S5: Ground-state energy levels and energy gaps for the C48H18O2 GQDs frontier molecular orbitals (a) and charge density distribution of HOMOs and LUMOs (b); Figure S6: Ground-state energy levels and energy gaps for the C48H18O3 GQDs frontier molecular orbitals (a) and charge density distribution of HOMOs and LUMOs (b); Figure S7: Clar structures for the pristine C48H18 quantum dot (a), the two most stable edge-epoxidized structures, namely C48H18O3 (b) and C48H18O6 (c), and complete zigzag edge epoxidized structure C48H18O9 (d) Table S1: Singlet–singlet transitions in the C42H18-D6 (HBC) and C48H18-D3 PAH molecules calculated using a simplified TD-DFT approach with a hybrid B3LYP XC functional; Table S2: Singlet–singlet transitions in C48H18 GQDs with epoxy groups in edge positions; Table S3: Singlet–singlet transitions in C48H18 GQDs with epoxy groups on the basal plane of the GQD.

Author Contributions

Conceptualization, I.V.E. and A.A.L.; methodology, I.V.E.; software, D.L.R.; validation, A.A.L. and I.V.E.; formal analysis, O.M.H.; investigation, I.V.E.; resources, A.A.L.; data curation, I.V.E.; writing—original draft preparation, I.V.E.; writing—review and editing, A.A.L.; visualization, D.L.R. and O.M.H.; supervision, A.A.L.; project administration, I.V.E.; funding acquisition, I.V.E. and A.A.L. All authors have read and agreed to the published version of the manuscript.

Funding

This work is supported by the Russian Science Foundation (project 25-23-00378), https://rscf.ru/en/project/25-23-00378/.

Data Availability Statement

The original contributions presented in this study are included in the article/Supplementary Material. Further inquiries can be directed to the corresponding author.

Acknowledgments

The authors would like to acknowledge Efremenko I.N. and Beskopylny A.N. for the organization and support of high-performance computations, and to thank Bazhin I.V. for providing the software infrastructure and useful discussions.

Conflicts of Interest

The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

Abbreviations

The following abbreviations are used in this manuscript:
GQDGraphene quantum dot
DFTDensity functional theory
LEDLight-emitting diode
PAHPolycyclic aromatic hydrocarbons
GGAGeneralized gradient approximation
sTD-DFTSimplified time-dependent DFT
HOMOHighest occupied molecular orbital
LUMOLowest unoccupied molecular orbital

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Carbon 11 00051 g001
Figure 1. Structure of the C48H18 GQD with possible oxygen adsorption sites (a) and energetically favorable positions of oxygen atom at the edges of the GQD: (b) pos. Ph, (c) pos. A, (d) pos. D, (e) pos. E, and (f) pos. E’.
Figure 1. Structure of the C48H18 GQD with possible oxygen adsorption sites (a) and energetically favorable positions of oxygen atom at the edges of the GQD: (b) pos. Ph, (c) pos. A, (d) pos. D, (e) pos. E, and (f) pos. E’.
Carbon 11 00051 g001
Carbon 11 00051 g002
Figure 2. The three most favorable binding positions of epoxy groups on the basal plane inside the GQD: (a) pos. δ, (b) pos. η, (c) pos. α.
Figure 2. The three most favorable binding positions of epoxy groups on the basal plane inside the GQD: (a) pos. δ, (b) pos. η, (c) pos. α.
Carbon 11 00051 g002
Carbon 11 00051 g003
Figure 3. Ground-state energy levels and energy gaps for the C48H18O GQDs frontier molecular orbitals (a) and charge density distribution of HOMOs and LUMOs for the C48H18O GQDs with different binding sites of epoxy group (b).
Figure 3. Ground-state energy levels and energy gaps for the C48H18O GQDs frontier molecular orbitals (a) and charge density distribution of HOMOs and LUMOs for the C48H18O GQDs with different binding sites of epoxy group (b).
Carbon 11 00051 g003
Carbon 11 00051 g004
Figure 4. Absorption spectra of the C48H18O GQDs in decreasing order of oxygen binding energy with edge oxygen-binding positions: (a) pos. A, (b) pos. D, (c) pos. E, and (d) pos. E’, and with oxygen binding positions inside the GQDs: (e) pos. δ, (f) pos. η, and (g) pos. α.
Figure 4. Absorption spectra of the C48H18O GQDs in decreasing order of oxygen binding energy with edge oxygen-binding positions: (a) pos. A, (b) pos. D, (c) pos. E, and (d) pos. E’, and with oxygen binding positions inside the GQDs: (e) pos. δ, (f) pos. η, and (g) pos. α.
Carbon 11 00051 g004
Carbon 11 00051 g005
Figure 5. Energetically favorable binding positions (left—most favorable) of two oxygen atoms at the edges and on the basal plane of the C48H18 GQD.
Figure 5. Energetically favorable binding positions (left—most favorable) of two oxygen atoms at the edges and on the basal plane of the C48H18 GQD.
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Carbon 11 00051 g006
Figure 6. Optical absorption spectra of the C48H18O2 GQDs with edge oxygen-binding positions in decreasing order of oxygen binding energy: (a) pos. AA, (b) pos. DD-1, (c) pos. AD-1, (d) pos. AD-2, (e) pos. DD-2, and (f) pos. AD-3.
Figure 6. Optical absorption spectra of the C48H18O2 GQDs with edge oxygen-binding positions in decreasing order of oxygen binding energy: (a) pos. AA, (b) pos. DD-1, (c) pos. AD-1, (d) pos. AD-2, (e) pos. DD-2, and (f) pos. AD-3.
Carbon 11 00051 g006
Carbon 11 00051 g007
Figure 7. Optical absorption spectra of the C48H18O2 with oxygen positions inside the GQDs: (a) pos. ηη, (b) pos. αδ, and (c) pos. δδ.
Figure 7. Optical absorption spectra of the C48H18O2 with oxygen positions inside the GQDs: (a) pos. ηη, (b) pos. αδ, and (c) pos. δδ.
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Carbon 11 00051 g008
Figure 8. Energetically most favorable binding positions (left—most favorable) of three oxygen atoms at the edges and on the basal plane of the C48H18 GQD.
Figure 8. Energetically most favorable binding positions (left—most favorable) of three oxygen atoms at the edges and on the basal plane of the C48H18 GQD.
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Carbon 11 00051 g009
Figure 9. Optical absorption spectra of the C48H18O3 GQDs in decreasing order of oxygen binding energy with three edge oxygen binding positions: (a) pos. AAA, (b) pos. DDD-1, (c) pos. and DDD-2, and with oxygen binding positions inside the GQDs: (d) pos. ηηη and (e) pos. δδη.
Figure 9. Optical absorption spectra of the C48H18O3 GQDs in decreasing order of oxygen binding energy with three edge oxygen binding positions: (a) pos. AAA, (b) pos. DDD-1, (c) pos. and DDD-2, and with oxygen binding positions inside the GQDs: (d) pos. ηηη and (e) pos. δδη.
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Carbon 11 00051 g010
Figure 10. Binding positions of four, six, and nine epoxy groups at the edges of the C48H18 GQD.
Figure 10. Binding positions of four, six, and nine epoxy groups at the edges of the C48H18 GQD.
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Carbon 11 00051 g011
Figure 11. Absorption spectra of the C48H18O4 GQDs with four edge oxygen-binding positions: (a) pos. 4D-1, (b) pos. 4D-2, and (c) pos. AADD; C48H18O6 GQD with six edge oxygen-binding positions (d) pos. 6D; and completely edge-oxidized C48H18O9 GQD (e).
Figure 11. Absorption spectra of the C48H18O4 GQDs with four edge oxygen-binding positions: (a) pos. 4D-1, (b) pos. 4D-2, and (c) pos. AADD; C48H18O6 GQD with six edge oxygen-binding positions (d) pos. 6D; and completely edge-oxidized C48H18O9 GQD (e).
Carbon 11 00051 g011
Table 1. Binding energy of an oxygen atom, energy difference relative to the most favorable epoxy configuration, and HOMO-LUMO gap for the GQD with epoxy groups.
Table 1. Binding energy of an oxygen atom, energy difference relative to the most favorable epoxy configuration, and HOMO-LUMO gap for the GQD with epoxy groups.
Oxygen PositionsBinding Energy, eVEnergy Difference, eVHOMO-LUMO Gap, eV
C48H18O edge-oxidized
A–2.950.002.90
D–2.86+0.092.78
E–1.95+1.002.44
E’ (ether)–2.77+0.182.76
B’ (ether)–2.78+0.172.85
Ph–4.54–1.593.07
C48H18O basal-oxidized
δ–1.88+1.073.01
η–1.76+1.193.00
α–1.72+1.233.22
C48H18O2 edge-oxidized
AA–2.960.003.04
DD-1–2.93+0.032.85
AD-1–2.89+0.072.51
AD-2–2.87+0.092.66
DD-2–2.87+0.093.00
AD-3–2.77+0.192.78
C48H18O2 basal-oxidized
ηη–2.12+0.843.37
αδ–2.11+0.852.94
δδ–2.10+0.863.29
C48H18O3 edge-oxidized
AAA–2.970.003.43
DDD-1–2.93+0.042.70
DDD-2–2.92+0.053.01
C48H18O3 basal-oxidized
ηηη–2.32+0.653.50
δδη–2.26+0.712.95
C48H18O4 edge-oxidized
4D-1–2.950.002.93
4D-2–2.93+0.022.80
AADD–2.91+0.042.69
C48H18O6 edge-oxidized
6D–2.97–3.57
C48H18O9 edge-oxidized
all A and D–2.77–3.15
Table 2. Average C-C and C-O bond lengths of epoxy groups attached to different sites of the GQD.
Table 2. Average C-C and C-O bond lengths of epoxy groups attached to different sites of the GQD.
ADEE’δηα
Average C-C bond length (Å)Oxidized1.4781.4771.5632.3291.5241.5141.554
Initial1.3711.3721.4251.4251.4221.4181.424
C-C bond stretching (%)7.87.79.7637.26.89.1
Average C-O bond length (Å)1.4301.4321.4181.3741.4381.4381.428
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Ershov, I.V.; Lavrentyev, A.A.; Romanov, D.L.; Holodova, O.M. Tuning Optical Excitations of Graphene Quantum Dots Through Selective Oxidation: Effect of Epoxy Groups. C 2025, 11, 51. https://doi.org/10.3390/c11030051

AMA Style

Ershov IV, Lavrentyev AA, Romanov DL, Holodova OM. Tuning Optical Excitations of Graphene Quantum Dots Through Selective Oxidation: Effect of Epoxy Groups. C. 2025; 11(3):51. https://doi.org/10.3390/c11030051

Chicago/Turabian Style

Ershov, Igor V., Anatoly A. Lavrentyev, Dmitry L. Romanov, and Olga M. Holodova. 2025. "Tuning Optical Excitations of Graphene Quantum Dots Through Selective Oxidation: Effect of Epoxy Groups" C 11, no. 3: 51. https://doi.org/10.3390/c11030051

APA Style

Ershov, I. V., Lavrentyev, A. A., Romanov, D. L., & Holodova, O. M. (2025). Tuning Optical Excitations of Graphene Quantum Dots Through Selective Oxidation: Effect of Epoxy Groups. C, 11(3), 51. https://doi.org/10.3390/c11030051

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