CHEMPHYSCHEM ARTICLES DOI: 10.1002/cphc.201301137
A Time-Dependent DFT Study of the Absorption and Fluorescence Properties of Graphene Quantum Dots Meilian Zhao, Feng Yang, Ying Xue, Dan Xiao,* and Yong Guo*[a] Absorption and fluorescence spectra of graphene quantum dots (GQDs) have been computed by using time-dependent density functional theory (TDDFT). Different functionals, including PBE, TPSSh, B3LYP, PBE0, CAM-B3LYP, and LC-wPBE, have been tested and B3LYP/6-31G(d) has been proven to be the most accurate method for our work. The bulk solvent effects of toluene and dichloromethane have been assessed by using the polarizable continuum model (PCM). The absorption wavelength of GQDs in solvents is red-shifted compared with that in the gas phase. Edge functionalization effects analysis shows
that a small number of substituted groups on GQDs induce a small redshift whereas a large redshift occurs when the edges of GQDs are all decorated. Little difference in the fluorescent emission was observed in solvents and in the gas phase. Molecular orbital transition and transition density matrix analysis have been performed. The electronic transition mainly occurs in the middle part of the structure of C132. The strong absorption of C132 corresponds to a S0 !S3 transition and the fluorescence emission is ascribed to a S1!S0 transition, which indicates that Kasha’s rule is obeyed.
1. Introduction Since it was discovered in 2004, graphene[1] has attracted tremendous interest. Graphene, which consists of a single atomic layer of graphite, is a unique type of semiconductor with a zero fundamental band gap. Cutting the graphene sheet into small pieces, for example, in the form of graphene nanoribbons and graphene quantum dots (GQDs), can induce band gaps. It is expected to result in many interesting phenomena not obtainable in other semiconductor materials.[2] Recently, many groups have made great efforts to fabricate graphenes with finite size (GQDs) by bottom-up and top-down synthesis approaches.[3] Notably, it is reported that large, stable colloidal GQDs with a uniform and tunable size, for example, GQDs that consist of graphene moieties with 132, 168, and 170 conjugated carbon atoms, labeled C132, C168, and C170, respectively, have been successfully synthesized by using a solution-chemistry approach.[4] These GQDs have attracted considerable attention because their band gap can be tuned depending on their size. The large optical absorptivity and widely tunable band gap of GQDs makes them attractive materials for optical and optoelectrical devices.[3b, 5] The absorption and emission properties of GQDs in various solvents have been studied experimentally. Mueller et al.[6] reported the absorption and photoluminescence spectra of C132
[a] M. Zhao, F. Yang, Prof. Y. Xue, Prof. D. Xiao, Prof. Y. Guo College of Chemistry, Sichuan University Key Laboratory of Green Chemistry and Technology in Ministry of Education Chengdu 610064 (P.R. China) Tel:(+86) 28-85418330 Fax: (+ 86) 28-85412907 E-mail: [email protected] [email protected] Supporting Information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.201301137.
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in toluene and dichloromethane and found that C132 shows fluorescence (l 670 nm) when excited at l = 510 nm at room temperature in toluene and dichloromethane. Their group also measured the absorption of C132, C168, and C170 in dichloromethane and found that C168 and C170 have absorption edges that appear at significantly longer wavelengths than C132.[4b] Yan et al.[4a] found that the large, solution-processable C168 can be applied as a sensitizer in nanocrystalline solar cells because of the large molar extinction coefficient (em) in dichloromethane; the absorption maximum appears at l = 591 nm with em = 1.0 105 m1 cm1. Functionalized GQDs (C132 and C168) have been synthesized[7] and the band gaps were determined by the red edge of the absorption spectra. In addition to these reports, Schumacher[8] studied the theoretical structural and electronic properties of the ground state and the UV/Vis absorption spectral characteristics of C168 in the gas phase, he explained the optical selection rules in C168 and found that lowest optically bright transitions are degenerate. However, effects of the chemical environment, such as the solvent and even the size and functionalization, on the spectral characteristics of GQDs have not been discussed theoretically; in addition, the detailed absorption and fluorescence processes of C132 need to be explained from a theoretical computational point of view. To date, many theoretical investigations into the excited states by TDDFT have been published. TDDFT, which was proposed by Gross et al.[9] more than two decades ago, has been successfully applied to accurately describe electronic excitations and predict absorption and emission spectral characteristics.[8, 10] Tretiak et al.[10a] reported the absorption in carbon nanotube by applying DFT and TDDFT. Li et al.[11] adopted TDDFT to study the fluorescence of C60 derivatives. TDDFT calculations also provide a two-dimensional real-space analysis of ChemPhysChem 2014, 15, 950 – 957
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CHEMPHYSCHEM ARTICLES transition densities that represent coherent electronic transitions between ground and electronically excited states.[12] The transition densities provide a panoramic view of electron–hole coherence and exciton delocalization in each of the studied systems.[10c] Moreover, a TDDFT methodology allowing excited-state optimization with the inclusion of bulk solvent effects has been proposed recently.[13] Many PCM/TDDFT computational studies have appeared in the last years[14] and PCM/TDDFT has been shown to present good results compared with experimental values. Jacquemin et al.[14c] reported that the inclusion of solvent effects is essential to describe the excited-state properties of 1,8-naphthalimide. Cheshmedzhieva et al.[14e] adopted PCM/ TDDFT to analyze the absorption and fluorescence spectra of a series of substituted N-hexyl-1,8-naphthalimides, the results are in good agreement with the experimental data. Herein, we compare the difference between the absorption of C132, C168, and C170 under various conditions to establish the impact of solvent and size on the spectral properties of the GQDs. In addition, we also studied the absorption process of GQDs with functionalized groups synthesized by Li et al.[7] to elucidate the effect of the functionalized groups on the excitation. The fluorescence of C132 in the gas phase, toluene, and dichloromethane are also investigated. Furthermore, we predict the fluorescence of C168 and C170 in toluene and dichloromethane. It is valuable to elucidate the electron transition during the absorption and fluorescence emission processes and interpret the nature of the photophysical behavior of the newly synthesized GQDs. To the best of our knowledge, this is the first effort to model the theoretical absorption and fluorescence emission processes of GQDs with different sizes in solvents.
Computational Details The GQDs and functionalized GQDs analyzed in this work are shown in Figures 1 and 2. All calculations were carried out by using the Gaussian 09 program package.[15] The DFT and TDDFT computations were performed by applying different functionals, including a pure gradient approximation (GGA) functional (PBE[16]), two hybrid-GGA functionals (B3LYP[17] and PBE0[18]), hybrid metaGGA (TPSSh[19]), and two long-range-corrected functionals (CAMB3LYP[20] and LC-wPBE[21]). The 6-31G(d) basis set was selected to combine with these functionals throughout all calculations. The bulk solvent effects on both the geometries and transition energies were evaluated by means of the PCM approach in its integral equation formalism form.[13a, 14b] To determine the absorption wavelength, the ground-state geometries, S0 of the GQDs, were first optimized and the vibrational frequencies in the energy minima were also calculated to make sure that there were no imaginary frequencies. Side groups that shielded the GQDs[4b] were replaced by H atoms herein because they are largely uninvolved in the photophysics of the GQDs.[8] The geometry optimizations were calculated without symmetry constraints (Cartesian coordinates of S0 for C132, C168, and C170 are shown in the Supporting Information). Then vertical electronic excitation energies were calculated by using TDDFT at the optimized groundstate geometries; ten lowest singlet excited states for each GQD were considered. The simplest way to take into account the effects 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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Figure 1. Molecular structures of the GQDs investigated. Dark gray spheres represent carbon atoms and light gray spheres hydrogen atoms.
of solvents on absorption maxima calculations was to use the socalled nonequilibrium solutions (linear response solvation), which is suitable for the study of absorption processes.[13a] Indeed the absorption process presents a short characteristic time, so only the solvent electronic distribution can adapt to the new excited electronic structure of the solute, whereas molecular motions of the solvent are frozen during the process. To simulate the fluorescence, the geometry of the lowest singlet state, S1, was optimized by using TDDFT starting with the groundstate geometry. The fluorescence electronic transitions were calculated as vertical de-excitation based on the optimized geometries of the excited state. Fluorescence calculations in solution were conducted by using the equilibrium solutions, that is, by considering a full solvent relaxation.[13a] Most fluorescence measurements are carried out at room temperature and the PCM equilibrium model should be adequate to simulate such measurements.
2. Results and Discussion 2.1. Comparison of Different Functionals Here we compare the absorption maximum lmax of C132 in toluene calculated by using different functionals, including PBE, TPSSh, B3LYP, PBE0, CAM-B3LYP, and LC-wPBE, combined with the 6-31G(d) basis set. From Table 1, we see that the PBE and TPSSh functionals underestimate the excitation energy, they predict lmax values that are about 134 and 47 nm longer than the experimental data (lmax = 560 nm),[6] respectively. However, PBE0 and the long-range-corrected functionals, CAM-B3LYP and LC-wPBE, overestimate the excitation energy, giving waveChemPhysChem 2014, 15, 950 – 957
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www.chemphyschem.org from pure GGA to long-range-corrected hybrids have different amounts (a) of HF exchange in the exchange-correlation functional, that is, PBE (a = 0), TPSSh (a = 10 %), B3LYP (a = 20 %), PBE0 (a = 25 %), CAM-B3LYP (a = 20–65 %), and LC-wPBE (a = 0–100 %). The long-range-corrected functionals behave as typical hybrid or GGA at short range but at the same time they have increased amounts of HF at longer distances, up to a maximum value of 65 % for CAM-B3LYP and 100 % for LC-wPBE. With the increasing component of HF exchange in the functional, the band gap increases, so PBE gives the longest wavelength and LC-wPBE gives the shortest wavelength. The result (lmax = 565.75 nm) obtained by B3LYP with the proper amount of HF at 6-31G(d) level is in perfect agreement with the experimental value (lmax = 560 nm) reported by Muller et al.[6] In addition, the fluorescence wavelength (l = 668.46 nm) of C132 in toluene calculated by using B3LYP/6-31G(d) also best reflects the experimental data (l = 670 nm). It has been demonstrated that the B3LYP hybrid functional is considered to be one of the most accurate functionals in computational chemistry and reproduces electronic excitations in large conjugated systems well.[8, 10a, 11, 22] The data calculated at the B3LYP/6-31G(d) level for the excited states of C60 derivatives and C168 best reflect available experimental data.[8, 11] Therefore, the following discussions for the absorption and fluorescence are based on B3LYP/6-31G(d). 2.2. Absorption Spectra
Figure 2. Molecular structure of the functionalized GQDs investigated. Black, dark gray, and light gray spheres represent oxygen, carbon, and hydrogen atoms, respectively. Structures 1–6 were synthesized by Yan’s group,[7] 7–10 were designed by us for comparison.
Table 1. Vertical excitation energies (Eabs), wavelengths (labs), and oscillator strengths (f) for the absorption maximum of GQD C132 in toluene calculated by using different functionals combined with the 6-31G(d) basis set.[a] Functional
Eabs [eV]
lmax [nm]
f
PBE TPSSh B3LYP PBE0 CAM-B3LYP LC-wPBE
1.788 2.044 2.192 2.301 2.812 3.311
693.52 606.59 565.75 538.82 440.96 374.45
2.3683 3.0121 3.4935 3.7931 5.4105 6.7435
[a] The experimental value of lmax for C132 in toluene is 560 nm.[6]
lengths that are about 21, 119, and 186 nm shorter, respectively, than the experimental value. The DFT functionals ranging 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
In the first step of this section, we calculate the lowest ten vertical excitation energies of C132 in the gas phase, the calculations are all performed at the TDDFT level with B3LYP functionals, combined with 6-31G(d) basis set. It shows a sharp strong absorption with lmax = 543.10 nm for C132, which corresponds to the S0 !S3 transition, see Table 2. Next we investigated the solvent effects of toluene and dichloromethane on the UV/Vis absorption spectra of C132 by using PCM model. The strong absorption wavelengths with lmax corresponding to S0 !S3 transition are lmax = 565.75 nm in toluene and lmax = 563.30 nm in dichloromethane. Compared with the absorption wavelength in the gas phase, we find the wavelengths are red-shifted in solvents and the absorption intensity is stronger in solvent than in the gas phase (see Table 2). However, the absorption wavelengths are very close in toluene and dichloromethane. To illustrate the polarity effect of the solvent, for comparison we also calculated the absorption spectra of C132 in water, which has strong polarity, and found a lmax value of 559.90 nm with an oscillator strength of f = 3.2221. These results show that the polarity of the solvent does not seem to significantly alter the lmax value of C132. Yan et al.[4b, 6] reported that the UV/Vis absorption of C132 in toluene and dichloromethane is nearly the same with lmax values of about 560 nm. However, we see that the oscillator strengths of S0 !S1 and S0 !S2 for C132 are very small (Table 2), and CAM-B3LYP also gives the same trends. The transitions are dipole forbidden but vibration-electronic coupling, which allows a borrowing of intensity from an energetically close bright state and makes the transitions weakly allowed.[23] ChemPhysChem 2014, 15, 950 – 957
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To provide further insight into the opoelectronic trends, we conducted a two-dimensional real-space analysis of density GQD Transition Gas phase Toluene Dichloromethane matrices that represented the Eabs [eV] labs [nm] f Eabs [eV] labs [nm] f Eabs [eV] labs [nm] f electronic transition between S0 !S1 1.920 645.81 0.0000 1.920 645.79 0.0002 1.920 645.79 0.0011 the ground state and an elecS0 !S2 1.981 625.91 0.0326 1.978 626.94 0.0758 1.978 626.83 0.0689 C132 tronically excited state for C132 2.283 543.10 2.4879 2.192 565.75 3.4935 2.201 563.30 3.3788 S0 !S3 in toluene. We investigated the 2.344 528.87 0.0506 2.288 541.80 1.5197 2.296 540.05 1.4393 S0 !S4 1.710 725.01 0.0000 1.710 725.05 0.0000 1.710 725.15 0.0000 S0 !S1 four lowest singlet excited states 1.765 702.45 0.0000 1.764 702.79 0.0000 1.764 702.94 0.0000 S0 !S2 of C132 in toluene. The plots of C168 2.084 594.92 1.9548 2.001 619.49 2.9633 2.010 616.86 2.8393 S0 !S3 the coordinate density matrices 2.084 594.88 1.9547 2.002 619.46 2.9643 2.010 616.84 2.8397 S0 !S4 were performed by using Mul1.695 731.54 0.0000 1.695 731.63 0.0001 1.694 731.92 0.0002 S0 !S1 1.749 709.03 0.0203 1.746 710.15 0.0550 1.745 710.39 0.0493 S0 !S2 tiwfn software[24] for free, see C170 2.053 604.01 1.9251 1.972 628.63 2.9544 1.980 626.16 2.8303 S0 !S3 Figure 4. The horizontal and verS0 !S4 2.069 599.35 1.8933 1.988 623.58 2.8586 1.996 621.16 2.7415 tical axes represent the number of carbon atom in C132, the hydrogen atoms are not included as they contribute little to the electron delocalizations of the These absorption spectra are expected to begin on the low large conjugated systems. The contour plots show that atoms energy side with very weak bands.[4b, 6] In addition, we analyzed the transitions between the molec1–55 labeled in Figure 1 are the primary sites of electron tranular orbitals of C132 in toluene. In the electronic structure calsitions. The transition-density matrix analysis illustrates that the culations we were able to identify those optical transitions that electronic transition mainly occurs in the middle part of the are dominated by transitions between molecular orbitals from structure of C132. a simple shell-structure analysis shown in Figure 3. We find C168 and C170 were used to examine the effect of size on that the molecular orbitals (the orbital lower than the highest the absorption, they show a sharp strong absorption at lmax = 594.92 and 604.01 nm in the gas phase, respectively. The aboccupied molecular orbital (HOMO1), HOMO, the lowest unsorption wavelengths present redshifts with the increasing size of the three GQDs (Table 2). We also find that the absorption wavelengths corresponding to the transitions of S0 !S3 and S0 !S4 are very close and have similar oscillator strengths, therefore, we deduce that the strong absorptions lmax of C168 and C170 arise from the two transitions. In addition, the transitions of S0 !S1 and S0 !S2 for GQDs (C168 and C170) are also weakly allowed.[4b] Moreover, solvent effects on the absorption of C168 and C170 are similar to that of C132, that is, the lmax value is 619.49 in toluene and 616.86 nm in dichloromethane for C168, which indicates the redshifts in lmax in solvents compared with that in the gas phase (see Table 2). For functionalized GQDs C132 and C168 (Figure 2), we calculated the UV/Vis absorption in the gas phase, toluene, and dichloromethane. The maximum absorption wavelength lmax corresponding to the S0 !S3 transitions for the substituted C132 Figure 3. Molecular orbitals of C132 in toluene in the ground-state (S0) geand S0 !S3 and S0 !S4 transitions for substituted C168 are ometry. summarized in Table 3. The lmax of functionalized GQDs show redshifts in solvents compared with in the gas phase. occupied molecular orbital (LUMO), and LUMO + 1) constitute The results obtained for GDQs in toluene are discussed in the P shell of C132 for both conduction and valence band. The detail. C132 structures with PhOMe at different sites on the four lowest singlet transitions are dominated by the four fronedge (GQDs 3–5 in Figure 2) have the same lmax value (see tier molecular (P shell) orbitals. Each state can be represented Table 3). C168 structures with PhOMe and PhCOOH at the by two pairs of molecular orbital transitions, with each transisame site on the edge (GQDs 1 and 2 in Figure 2) have lmax tion capturing about 50 % of the state character. The S0 !S3 values of 623.33 and 624.34 nm, respectively. The lmax values of functionalized C132 and C168 show small redshifts (about transition corresponding to the strong absorption is found to 8 nm in GQDs 3–5) when compared with the corresponding have mostly P-to-P shell character and could be described by hydrogenated GQDs. C132 with a different number of OH or the molecular orbital transitions, in which HOMO1!LUMO COOH groups on the edge were also investigated (GQDs 6–10 accounts for 50.5 % and HOMO!LUMO + 1 accounts for in Figure 2). From Table 3, we see that the lmax of GQDs show 48.9 % from the calculations by using B3LYP/6-31G(d). Table 2. Vertical excitation energies (Eabs), wavelengths (labs), and oscillator strengths (f) for the lowest four excited states of GQDs in the gas phase, toluene, and dichloromethane calculated by using B3LYP at the 6-31G(d) level.
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Figure 4. Contour plots of coordinate density matrices for the lowest four excitation energies (S0 !S1, S0 !S2, S0 ! S3, and S0 !S4) of C132 in toluene calculated at the B3LYP/6-31G(d) level. Each plot depicts probabilities of an electron moving from one molecular position (horizontal axis) to another (vertical axis) upon electronic excitation.
to 2.307 eV (GQD 7 in Figure 2) when a small number of functionalized groups are substituted on the edge. Therefore, the lmax values present a slight redshift. When the edge of C132 is completely decorated with OH groups (GQD 10 in Figure 2), the band gap is reduced to 2.097 eV and thus presents a large redshift (about 55 nm) in lmax. In addition, we analyzed the transitions between the molecular orbitals of these functionalized GQDs (Figure 5) and find that a n!p* transition exists in the COOH-substituted C132. The O in OH-substituted C132 is involved in the electron transition, but these effects are very small because they play a minor part in the electron transition. The electron transition of GQD 10 that shows a large redshift is inclined to occur in half of the structure. It is different from the electron transition of C132, which occurs in the middle part of the structure.
Table 3. The maximum absorption energies (E), wavelengths (lmax), and oscillator strengths (f) for the functionalized GQDs in the gas phase, toluene, and dichloromethane calculated by using B3LYP at the 6-31G(d) level. GQD
1 2 3 4 5 6 7 8 9 10
Transition S0 !S3 S0 !S4 S0 !S3 S0 !S4 S0 !S3 S0 !S3 S0 !S3 S0 !S3 S0 !S3 S0 !S3 S0 !S3 S0 !S3
Gas phase E [eV] lmax [nm]
f
Toluene E [eV] lmax [nm]
f
2.069 2.079 2.063 2.076 2.244 2.244 2.245 2.272 2.228 2.280 2.255 2.028
2.2555 1.9279 2.2470 1.9013 3.0700 2.8860 3.2602 2.4954 2.7195 2.4909 2.4456 1.5239
1.989 1.997 1.986 1.995 2.160 2.160 2.161 2.181 2.141 2.189 2.168 1.998
3.2458 2.9402 3.2446 2.9191 4.0004 3.8185 4.1985 3.4938 3.6627 3.5023 3.4277 2.9436
599.34 596.39 600.91 597.38 552.45 552.49 552.21 545.69 556.61 543.76 549.76 611.38
623.33 620.81 624.34 621.44 573.96 573.91 573.73 568.56 579.05 566.48 571.79 620.54
small redshifts as the number of OH or COOH groups was increased, for example, the lmax of C132 with one and ten OH groups at the edge are lmax = 566.68 and 571.79 nm, respectively, and an extraordinarily large redshift occurs in GQD 10 (lmax = 620.54 nm) with OH groups substituted at all edge sites of C132. The redshift in lmax could be explained from the band gaps, which is related to the UV/Vis absorption spectra. It has been demonstrated that in conjugated polymer systems, electron-withdrawing groups lower the LUMO levels and electrondonating substituted groups generally raise the HOMO levels.[25] Our calculations indicate that the band gaps of the functionalized GQDs are reduced slightly from 2.335 eV (C132) 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Dichloromethane E [eV] lmax [nm]
f
2.3. Fluorescence Spectra
The structure optimization of the lowest excited state S1 of C132 in the gas phase was performed at the TD-B3LYP/631G(d) level of theory, the solvent effect was considered by using the PCM model. By comparing with the fluorescence calculated in the gas phase (l = 668.40 nm), we find that the solvent has little effect on the fluorescence wavelength (see Table 4). The fluorescence wavelength of C132 in toluene was calculated to be l = 668.46 nm at the B3LYP/6-31G(d) level, which is in good agreement with the experimental value of l = 670 nm, ascribed to the S1!S0 transition. This result is consistent with the work reported by Mueller et al.[6, 26] We conclude that the fluorescence emission process of C132 obeys Kasha’s rule, which states that only the lowest singlet-excited state of a molecule is fluorescent. The fluorescence from S1 to S0 is a p!p* transition. During this de-excitation process, the LUMO! HOMO1 transition contributes 48.2 % and the LUMO + 1! HOMO transition accounts for 49.9 %. 1.997 2.005 1.995 2.005 2.167 2.167 2.168 2.190 2.149 2.198 2.173 2.016
620.98 618.27 621.40 618.49 572.20 572.20 571.88 566.01 576.93 564.07 570.50 615.08
3.1371 2.8182 3.1393 2.8092 3.9046 3.7162 4.1140 3.3830 3.5644 3.3839 3.3454 2.9644
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Figure 5. Molecular orbitals of functionalized C132 (GQD 5, 6, 8, and 10) in toluene in the ground-state (S0) geometry.
bility of intersystem crossing,[6] Table 4. Fluorescence emitting energies (E), wavelengths (l), and oscillator strengths (f) for C132, C168, and that is, GQD C132 at states S2 C170 in toluene and dichloromethane calculated by using B3LYP at the 6-31G(d) level. and S3 is much likely to relax into triplet states. So we conMedium Transition C132 C168 C170 clude that the fluorescence E [eV] l [nm] f E [eV] l [nm] f E [eV] l [nm] f emission is due to the transition 1.855 668.46 0.0003 1.656 748.60 0.0000 1.642 755.28 0.0001 toluene S1!S0 corresponding to S1!S0, which 1.855 668.52 0.0038 1.655 748.91 0.0000 1.641 755.65 0.0007 dichloromethane S1!S0 shows that Kasha’s rule is obeyed in our studied system. Due to the small oscillator strength of the lowest excited state, the emission spectra are From the details discussed above, we get a summary for the expected to show a very small radiative rate constant and absorption and emission processes for C132 in toluene. In the a very low emission quantum yield, which is confirmed by the absorption process, it is prone to induce a S0 !S3 transition beexperimental findings that the emission quantum yield of cause it has the largest oscillator strength, and the transitions C132 in toluene is determined to be 2 %.[6] to S1 and S2 are weakly allowed because of the very small oscillator strengths. However, during the emission process, due to In addition, we predict that the fluorescence of GQDs C168 the small difference in energy gaps between S3, S2, and S1, the and C170 in toluene and dichloromethane follows Kasha’s rule. The calculations show that the fluorescence wavelengths presnonradiative transition is fast so internal conversion is superior ent redshifts with the increasing size of GQDs, however, the to fluorescence emission for the high-lying excited state in polarity of solvents has little effect on the fluorescence waveC132, whereas for the large-sized GQD the electrons are delolength of C168 and C170, which is similar to the results obcalized over a large area, which significantly reduces the sintained for C132 (see Table 4). Moreover, the very small oscillaglet–triplet splitting and thus considerably increases the proba 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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CHEMPHYSCHEM ARTICLES tor strength indicates a very low emission quantum yield for C168 and C170, especially for C168 because it has high molecular symmetry.
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[6] [7]
3. Conclusions Herein, we report the absorption and fluorescence spectra of GQDs by using TDDFT procedures, the bulk solvent effects are taken into consideration for both geometry optimizations and transition-energy calculations by using a PCM model. The agreement obtained between theoretical and experimental wavelengths by using B3LYP/6-31G(d) is satisfactory for the absorption and fluorescence processes. The strong absorptions with lmax correspond to S0 !S3 transition for C132 and to S0 !S3 and S0 !S4 transitions for C168 and C170. We find that the wavelengths were red-shifted in solvents when compared with the absorption wavelength in the gas phase. Edge-functionalized C132 and C168 show small redshifts in lmax when a small number of functional groups were substituted on the edge and a large redshift occurred when the edge was fully substituted. The fluorescence of C132 corresponding to a p!p* transition is due to the S1!S0 transition, which shows that Kasha’s rule is obeyed. Little difference in the fluorescent emission was observed in toluene and dichloromethane. In addition, we analyzed the molecular-orbital transition and transition-density matrix to visually study the spatial span and primary sites of electron transitions. It turns out that the first 55 carbon atoms (see Figure 1) have a large probability of being involved in the transitions. The results we report have important consequences for optical applications of GQDs.
[8] [9] [10]
[11] [12]
[13]
[14]
Acknowledgements We greatly appreciate the Natural Science Foundation of China (grants 21075083, 21345001) for supporting this work. [15]
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Received: November 29, 2013 Published online on March 3, 2014
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A Time-Dependent DFT Study of the Absorption and Fluorescence Properties of Graphene Quantum Dots Meilian Zhao, Feng Yang, Ying Xue, Dan Xiao,* and Yong Guo*[a] Absorption and fluorescence spectra of graphene quantum dots (GQDs) have been computed by using time-dependent density functional theory (TDDFT). Different functionals, including PBE, TPSSh, B3LYP, PBE0, CAM-B3LYP, and LC-wPBE, have been tested and B3LYP/6-31G(d) has been proven to be the most accurate method for our work. The bulk solvent effects of toluene and dichloromethane have been assessed by using the polarizable continuum model (PCM). The absorption wavelength of GQDs in solvents is red-shifted compared with that in the gas phase. Edge functionalization effects analysis shows
that a small number of substituted groups on GQDs induce a small redshift whereas a large redshift occurs when the edges of GQDs are all decorated. Little difference in the fluorescent emission was observed in solvents and in the gas phase. Molecular orbital transition and transition density matrix analysis have been performed. The electronic transition mainly occurs in the middle part of the structure of C132. The strong absorption of C132 corresponds to a S0 !S3 transition and the fluorescence emission is ascribed to a S1!S0 transition, which indicates that Kasha’s rule is obeyed.
1. Introduction Since it was discovered in 2004, graphene[1] has attracted tremendous interest. Graphene, which consists of a single atomic layer of graphite, is a unique type of semiconductor with a zero fundamental band gap. Cutting the graphene sheet into small pieces, for example, in the form of graphene nanoribbons and graphene quantum dots (GQDs), can induce band gaps. It is expected to result in many interesting phenomena not obtainable in other semiconductor materials.[2] Recently, many groups have made great efforts to fabricate graphenes with finite size (GQDs) by bottom-up and top-down synthesis approaches.[3] Notably, it is reported that large, stable colloidal GQDs with a uniform and tunable size, for example, GQDs that consist of graphene moieties with 132, 168, and 170 conjugated carbon atoms, labeled C132, C168, and C170, respectively, have been successfully synthesized by using a solution-chemistry approach.[4] These GQDs have attracted considerable attention because their band gap can be tuned depending on their size. The large optical absorptivity and widely tunable band gap of GQDs makes them attractive materials for optical and optoelectrical devices.[3b, 5] The absorption and emission properties of GQDs in various solvents have been studied experimentally. Mueller et al.[6] reported the absorption and photoluminescence spectra of C132
[a] M. Zhao, F. Yang, Prof. Y. Xue, Prof. D. Xiao, Prof. Y. Guo College of Chemistry, Sichuan University Key Laboratory of Green Chemistry and Technology in Ministry of Education Chengdu 610064 (P.R. China) Tel:(+86) 28-85418330 Fax: (+ 86) 28-85412907 E-mail: [email protected] [email protected] Supporting Information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.201301137.
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in toluene and dichloromethane and found that C132 shows fluorescence (l 670 nm) when excited at l = 510 nm at room temperature in toluene and dichloromethane. Their group also measured the absorption of C132, C168, and C170 in dichloromethane and found that C168 and C170 have absorption edges that appear at significantly longer wavelengths than C132.[4b] Yan et al.[4a] found that the large, solution-processable C168 can be applied as a sensitizer in nanocrystalline solar cells because of the large molar extinction coefficient (em) in dichloromethane; the absorption maximum appears at l = 591 nm with em = 1.0 105 m1 cm1. Functionalized GQDs (C132 and C168) have been synthesized[7] and the band gaps were determined by the red edge of the absorption spectra. In addition to these reports, Schumacher[8] studied the theoretical structural and electronic properties of the ground state and the UV/Vis absorption spectral characteristics of C168 in the gas phase, he explained the optical selection rules in C168 and found that lowest optically bright transitions are degenerate. However, effects of the chemical environment, such as the solvent and even the size and functionalization, on the spectral characteristics of GQDs have not been discussed theoretically; in addition, the detailed absorption and fluorescence processes of C132 need to be explained from a theoretical computational point of view. To date, many theoretical investigations into the excited states by TDDFT have been published. TDDFT, which was proposed by Gross et al.[9] more than two decades ago, has been successfully applied to accurately describe electronic excitations and predict absorption and emission spectral characteristics.[8, 10] Tretiak et al.[10a] reported the absorption in carbon nanotube by applying DFT and TDDFT. Li et al.[11] adopted TDDFT to study the fluorescence of C60 derivatives. TDDFT calculations also provide a two-dimensional real-space analysis of ChemPhysChem 2014, 15, 950 – 957
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CHEMPHYSCHEM ARTICLES transition densities that represent coherent electronic transitions between ground and electronically excited states.[12] The transition densities provide a panoramic view of electron–hole coherence and exciton delocalization in each of the studied systems.[10c] Moreover, a TDDFT methodology allowing excited-state optimization with the inclusion of bulk solvent effects has been proposed recently.[13] Many PCM/TDDFT computational studies have appeared in the last years[14] and PCM/TDDFT has been shown to present good results compared with experimental values. Jacquemin et al.[14c] reported that the inclusion of solvent effects is essential to describe the excited-state properties of 1,8-naphthalimide. Cheshmedzhieva et al.[14e] adopted PCM/ TDDFT to analyze the absorption and fluorescence spectra of a series of substituted N-hexyl-1,8-naphthalimides, the results are in good agreement with the experimental data. Herein, we compare the difference between the absorption of C132, C168, and C170 under various conditions to establish the impact of solvent and size on the spectral properties of the GQDs. In addition, we also studied the absorption process of GQDs with functionalized groups synthesized by Li et al.[7] to elucidate the effect of the functionalized groups on the excitation. The fluorescence of C132 in the gas phase, toluene, and dichloromethane are also investigated. Furthermore, we predict the fluorescence of C168 and C170 in toluene and dichloromethane. It is valuable to elucidate the electron transition during the absorption and fluorescence emission processes and interpret the nature of the photophysical behavior of the newly synthesized GQDs. To the best of our knowledge, this is the first effort to model the theoretical absorption and fluorescence emission processes of GQDs with different sizes in solvents.
Computational Details The GQDs and functionalized GQDs analyzed in this work are shown in Figures 1 and 2. All calculations were carried out by using the Gaussian 09 program package.[15] The DFT and TDDFT computations were performed by applying different functionals, including a pure gradient approximation (GGA) functional (PBE[16]), two hybrid-GGA functionals (B3LYP[17] and PBE0[18]), hybrid metaGGA (TPSSh[19]), and two long-range-corrected functionals (CAMB3LYP[20] and LC-wPBE[21]). The 6-31G(d) basis set was selected to combine with these functionals throughout all calculations. The bulk solvent effects on both the geometries and transition energies were evaluated by means of the PCM approach in its integral equation formalism form.[13a, 14b] To determine the absorption wavelength, the ground-state geometries, S0 of the GQDs, were first optimized and the vibrational frequencies in the energy minima were also calculated to make sure that there were no imaginary frequencies. Side groups that shielded the GQDs[4b] were replaced by H atoms herein because they are largely uninvolved in the photophysics of the GQDs.[8] The geometry optimizations were calculated without symmetry constraints (Cartesian coordinates of S0 for C132, C168, and C170 are shown in the Supporting Information). Then vertical electronic excitation energies were calculated by using TDDFT at the optimized groundstate geometries; ten lowest singlet excited states for each GQD were considered. The simplest way to take into account the effects 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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Figure 1. Molecular structures of the GQDs investigated. Dark gray spheres represent carbon atoms and light gray spheres hydrogen atoms.
of solvents on absorption maxima calculations was to use the socalled nonequilibrium solutions (linear response solvation), which is suitable for the study of absorption processes.[13a] Indeed the absorption process presents a short characteristic time, so only the solvent electronic distribution can adapt to the new excited electronic structure of the solute, whereas molecular motions of the solvent are frozen during the process. To simulate the fluorescence, the geometry of the lowest singlet state, S1, was optimized by using TDDFT starting with the groundstate geometry. The fluorescence electronic transitions were calculated as vertical de-excitation based on the optimized geometries of the excited state. Fluorescence calculations in solution were conducted by using the equilibrium solutions, that is, by considering a full solvent relaxation.[13a] Most fluorescence measurements are carried out at room temperature and the PCM equilibrium model should be adequate to simulate such measurements.
2. Results and Discussion 2.1. Comparison of Different Functionals Here we compare the absorption maximum lmax of C132 in toluene calculated by using different functionals, including PBE, TPSSh, B3LYP, PBE0, CAM-B3LYP, and LC-wPBE, combined with the 6-31G(d) basis set. From Table 1, we see that the PBE and TPSSh functionals underestimate the excitation energy, they predict lmax values that are about 134 and 47 nm longer than the experimental data (lmax = 560 nm),[6] respectively. However, PBE0 and the long-range-corrected functionals, CAM-B3LYP and LC-wPBE, overestimate the excitation energy, giving waveChemPhysChem 2014, 15, 950 – 957
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www.chemphyschem.org from pure GGA to long-range-corrected hybrids have different amounts (a) of HF exchange in the exchange-correlation functional, that is, PBE (a = 0), TPSSh (a = 10 %), B3LYP (a = 20 %), PBE0 (a = 25 %), CAM-B3LYP (a = 20–65 %), and LC-wPBE (a = 0–100 %). The long-range-corrected functionals behave as typical hybrid or GGA at short range but at the same time they have increased amounts of HF at longer distances, up to a maximum value of 65 % for CAM-B3LYP and 100 % for LC-wPBE. With the increasing component of HF exchange in the functional, the band gap increases, so PBE gives the longest wavelength and LC-wPBE gives the shortest wavelength. The result (lmax = 565.75 nm) obtained by B3LYP with the proper amount of HF at 6-31G(d) level is in perfect agreement with the experimental value (lmax = 560 nm) reported by Muller et al.[6] In addition, the fluorescence wavelength (l = 668.46 nm) of C132 in toluene calculated by using B3LYP/6-31G(d) also best reflects the experimental data (l = 670 nm). It has been demonstrated that the B3LYP hybrid functional is considered to be one of the most accurate functionals in computational chemistry and reproduces electronic excitations in large conjugated systems well.[8, 10a, 11, 22] The data calculated at the B3LYP/6-31G(d) level for the excited states of C60 derivatives and C168 best reflect available experimental data.[8, 11] Therefore, the following discussions for the absorption and fluorescence are based on B3LYP/6-31G(d). 2.2. Absorption Spectra
Figure 2. Molecular structure of the functionalized GQDs investigated. Black, dark gray, and light gray spheres represent oxygen, carbon, and hydrogen atoms, respectively. Structures 1–6 were synthesized by Yan’s group,[7] 7–10 were designed by us for comparison.
Table 1. Vertical excitation energies (Eabs), wavelengths (labs), and oscillator strengths (f) for the absorption maximum of GQD C132 in toluene calculated by using different functionals combined with the 6-31G(d) basis set.[a] Functional
Eabs [eV]
lmax [nm]
f
PBE TPSSh B3LYP PBE0 CAM-B3LYP LC-wPBE
1.788 2.044 2.192 2.301 2.812 3.311
693.52 606.59 565.75 538.82 440.96 374.45
2.3683 3.0121 3.4935 3.7931 5.4105 6.7435
[a] The experimental value of lmax for C132 in toluene is 560 nm.[6]
lengths that are about 21, 119, and 186 nm shorter, respectively, than the experimental value. The DFT functionals ranging 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
In the first step of this section, we calculate the lowest ten vertical excitation energies of C132 in the gas phase, the calculations are all performed at the TDDFT level with B3LYP functionals, combined with 6-31G(d) basis set. It shows a sharp strong absorption with lmax = 543.10 nm for C132, which corresponds to the S0 !S3 transition, see Table 2. Next we investigated the solvent effects of toluene and dichloromethane on the UV/Vis absorption spectra of C132 by using PCM model. The strong absorption wavelengths with lmax corresponding to S0 !S3 transition are lmax = 565.75 nm in toluene and lmax = 563.30 nm in dichloromethane. Compared with the absorption wavelength in the gas phase, we find the wavelengths are red-shifted in solvents and the absorption intensity is stronger in solvent than in the gas phase (see Table 2). However, the absorption wavelengths are very close in toluene and dichloromethane. To illustrate the polarity effect of the solvent, for comparison we also calculated the absorption spectra of C132 in water, which has strong polarity, and found a lmax value of 559.90 nm with an oscillator strength of f = 3.2221. These results show that the polarity of the solvent does not seem to significantly alter the lmax value of C132. Yan et al.[4b, 6] reported that the UV/Vis absorption of C132 in toluene and dichloromethane is nearly the same with lmax values of about 560 nm. However, we see that the oscillator strengths of S0 !S1 and S0 !S2 for C132 are very small (Table 2), and CAM-B3LYP also gives the same trends. The transitions are dipole forbidden but vibration-electronic coupling, which allows a borrowing of intensity from an energetically close bright state and makes the transitions weakly allowed.[23] ChemPhysChem 2014, 15, 950 – 957
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To provide further insight into the opoelectronic trends, we conducted a two-dimensional real-space analysis of density GQD Transition Gas phase Toluene Dichloromethane matrices that represented the Eabs [eV] labs [nm] f Eabs [eV] labs [nm] f Eabs [eV] labs [nm] f electronic transition between S0 !S1 1.920 645.81 0.0000 1.920 645.79 0.0002 1.920 645.79 0.0011 the ground state and an elecS0 !S2 1.981 625.91 0.0326 1.978 626.94 0.0758 1.978 626.83 0.0689 C132 tronically excited state for C132 2.283 543.10 2.4879 2.192 565.75 3.4935 2.201 563.30 3.3788 S0 !S3 in toluene. We investigated the 2.344 528.87 0.0506 2.288 541.80 1.5197 2.296 540.05 1.4393 S0 !S4 1.710 725.01 0.0000 1.710 725.05 0.0000 1.710 725.15 0.0000 S0 !S1 four lowest singlet excited states 1.765 702.45 0.0000 1.764 702.79 0.0000 1.764 702.94 0.0000 S0 !S2 of C132 in toluene. The plots of C168 2.084 594.92 1.9548 2.001 619.49 2.9633 2.010 616.86 2.8393 S0 !S3 the coordinate density matrices 2.084 594.88 1.9547 2.002 619.46 2.9643 2.010 616.84 2.8397 S0 !S4 were performed by using Mul1.695 731.54 0.0000 1.695 731.63 0.0001 1.694 731.92 0.0002 S0 !S1 1.749 709.03 0.0203 1.746 710.15 0.0550 1.745 710.39 0.0493 S0 !S2 tiwfn software[24] for free, see C170 2.053 604.01 1.9251 1.972 628.63 2.9544 1.980 626.16 2.8303 S0 !S3 Figure 4. The horizontal and verS0 !S4 2.069 599.35 1.8933 1.988 623.58 2.8586 1.996 621.16 2.7415 tical axes represent the number of carbon atom in C132, the hydrogen atoms are not included as they contribute little to the electron delocalizations of the These absorption spectra are expected to begin on the low large conjugated systems. The contour plots show that atoms energy side with very weak bands.[4b, 6] In addition, we analyzed the transitions between the molec1–55 labeled in Figure 1 are the primary sites of electron tranular orbitals of C132 in toluene. In the electronic structure calsitions. The transition-density matrix analysis illustrates that the culations we were able to identify those optical transitions that electronic transition mainly occurs in the middle part of the are dominated by transitions between molecular orbitals from structure of C132. a simple shell-structure analysis shown in Figure 3. We find C168 and C170 were used to examine the effect of size on that the molecular orbitals (the orbital lower than the highest the absorption, they show a sharp strong absorption at lmax = 594.92 and 604.01 nm in the gas phase, respectively. The aboccupied molecular orbital (HOMO1), HOMO, the lowest unsorption wavelengths present redshifts with the increasing size of the three GQDs (Table 2). We also find that the absorption wavelengths corresponding to the transitions of S0 !S3 and S0 !S4 are very close and have similar oscillator strengths, therefore, we deduce that the strong absorptions lmax of C168 and C170 arise from the two transitions. In addition, the transitions of S0 !S1 and S0 !S2 for GQDs (C168 and C170) are also weakly allowed.[4b] Moreover, solvent effects on the absorption of C168 and C170 are similar to that of C132, that is, the lmax value is 619.49 in toluene and 616.86 nm in dichloromethane for C168, which indicates the redshifts in lmax in solvents compared with that in the gas phase (see Table 2). For functionalized GQDs C132 and C168 (Figure 2), we calculated the UV/Vis absorption in the gas phase, toluene, and dichloromethane. The maximum absorption wavelength lmax corresponding to the S0 !S3 transitions for the substituted C132 Figure 3. Molecular orbitals of C132 in toluene in the ground-state (S0) geand S0 !S3 and S0 !S4 transitions for substituted C168 are ometry. summarized in Table 3. The lmax of functionalized GQDs show redshifts in solvents compared with in the gas phase. occupied molecular orbital (LUMO), and LUMO + 1) constitute The results obtained for GDQs in toluene are discussed in the P shell of C132 for both conduction and valence band. The detail. C132 structures with PhOMe at different sites on the four lowest singlet transitions are dominated by the four fronedge (GQDs 3–5 in Figure 2) have the same lmax value (see tier molecular (P shell) orbitals. Each state can be represented Table 3). C168 structures with PhOMe and PhCOOH at the by two pairs of molecular orbital transitions, with each transisame site on the edge (GQDs 1 and 2 in Figure 2) have lmax tion capturing about 50 % of the state character. The S0 !S3 values of 623.33 and 624.34 nm, respectively. The lmax values of functionalized C132 and C168 show small redshifts (about transition corresponding to the strong absorption is found to 8 nm in GQDs 3–5) when compared with the corresponding have mostly P-to-P shell character and could be described by hydrogenated GQDs. C132 with a different number of OH or the molecular orbital transitions, in which HOMO1!LUMO COOH groups on the edge were also investigated (GQDs 6–10 accounts for 50.5 % and HOMO!LUMO + 1 accounts for in Figure 2). From Table 3, we see that the lmax of GQDs show 48.9 % from the calculations by using B3LYP/6-31G(d). Table 2. Vertical excitation energies (Eabs), wavelengths (labs), and oscillator strengths (f) for the lowest four excited states of GQDs in the gas phase, toluene, and dichloromethane calculated by using B3LYP at the 6-31G(d) level.
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Figure 4. Contour plots of coordinate density matrices for the lowest four excitation energies (S0 !S1, S0 !S2, S0 ! S3, and S0 !S4) of C132 in toluene calculated at the B3LYP/6-31G(d) level. Each plot depicts probabilities of an electron moving from one molecular position (horizontal axis) to another (vertical axis) upon electronic excitation.
to 2.307 eV (GQD 7 in Figure 2) when a small number of functionalized groups are substituted on the edge. Therefore, the lmax values present a slight redshift. When the edge of C132 is completely decorated with OH groups (GQD 10 in Figure 2), the band gap is reduced to 2.097 eV and thus presents a large redshift (about 55 nm) in lmax. In addition, we analyzed the transitions between the molecular orbitals of these functionalized GQDs (Figure 5) and find that a n!p* transition exists in the COOH-substituted C132. The O in OH-substituted C132 is involved in the electron transition, but these effects are very small because they play a minor part in the electron transition. The electron transition of GQD 10 that shows a large redshift is inclined to occur in half of the structure. It is different from the electron transition of C132, which occurs in the middle part of the structure.
Table 3. The maximum absorption energies (E), wavelengths (lmax), and oscillator strengths (f) for the functionalized GQDs in the gas phase, toluene, and dichloromethane calculated by using B3LYP at the 6-31G(d) level. GQD
1 2 3 4 5 6 7 8 9 10
Transition S0 !S3 S0 !S4 S0 !S3 S0 !S4 S0 !S3 S0 !S3 S0 !S3 S0 !S3 S0 !S3 S0 !S3 S0 !S3 S0 !S3
Gas phase E [eV] lmax [nm]
f
Toluene E [eV] lmax [nm]
f
2.069 2.079 2.063 2.076 2.244 2.244 2.245 2.272 2.228 2.280 2.255 2.028
2.2555 1.9279 2.2470 1.9013 3.0700 2.8860 3.2602 2.4954 2.7195 2.4909 2.4456 1.5239
1.989 1.997 1.986 1.995 2.160 2.160 2.161 2.181 2.141 2.189 2.168 1.998
3.2458 2.9402 3.2446 2.9191 4.0004 3.8185 4.1985 3.4938 3.6627 3.5023 3.4277 2.9436
599.34 596.39 600.91 597.38 552.45 552.49 552.21 545.69 556.61 543.76 549.76 611.38
623.33 620.81 624.34 621.44 573.96 573.91 573.73 568.56 579.05 566.48 571.79 620.54
small redshifts as the number of OH or COOH groups was increased, for example, the lmax of C132 with one and ten OH groups at the edge are lmax = 566.68 and 571.79 nm, respectively, and an extraordinarily large redshift occurs in GQD 10 (lmax = 620.54 nm) with OH groups substituted at all edge sites of C132. The redshift in lmax could be explained from the band gaps, which is related to the UV/Vis absorption spectra. It has been demonstrated that in conjugated polymer systems, electron-withdrawing groups lower the LUMO levels and electrondonating substituted groups generally raise the HOMO levels.[25] Our calculations indicate that the band gaps of the functionalized GQDs are reduced slightly from 2.335 eV (C132) 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Dichloromethane E [eV] lmax [nm]
f
2.3. Fluorescence Spectra
The structure optimization of the lowest excited state S1 of C132 in the gas phase was performed at the TD-B3LYP/631G(d) level of theory, the solvent effect was considered by using the PCM model. By comparing with the fluorescence calculated in the gas phase (l = 668.40 nm), we find that the solvent has little effect on the fluorescence wavelength (see Table 4). The fluorescence wavelength of C132 in toluene was calculated to be l = 668.46 nm at the B3LYP/6-31G(d) level, which is in good agreement with the experimental value of l = 670 nm, ascribed to the S1!S0 transition. This result is consistent with the work reported by Mueller et al.[6, 26] We conclude that the fluorescence emission process of C132 obeys Kasha’s rule, which states that only the lowest singlet-excited state of a molecule is fluorescent. The fluorescence from S1 to S0 is a p!p* transition. During this de-excitation process, the LUMO! HOMO1 transition contributes 48.2 % and the LUMO + 1! HOMO transition accounts for 49.9 %. 1.997 2.005 1.995 2.005 2.167 2.167 2.168 2.190 2.149 2.198 2.173 2.016
620.98 618.27 621.40 618.49 572.20 572.20 571.88 566.01 576.93 564.07 570.50 615.08
3.1371 2.8182 3.1393 2.8092 3.9046 3.7162 4.1140 3.3830 3.5644 3.3839 3.3454 2.9644
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Figure 5. Molecular orbitals of functionalized C132 (GQD 5, 6, 8, and 10) in toluene in the ground-state (S0) geometry.
bility of intersystem crossing,[6] Table 4. Fluorescence emitting energies (E), wavelengths (l), and oscillator strengths (f) for C132, C168, and that is, GQD C132 at states S2 C170 in toluene and dichloromethane calculated by using B3LYP at the 6-31G(d) level. and S3 is much likely to relax into triplet states. So we conMedium Transition C132 C168 C170 clude that the fluorescence E [eV] l [nm] f E [eV] l [nm] f E [eV] l [nm] f emission is due to the transition 1.855 668.46 0.0003 1.656 748.60 0.0000 1.642 755.28 0.0001 toluene S1!S0 corresponding to S1!S0, which 1.855 668.52 0.0038 1.655 748.91 0.0000 1.641 755.65 0.0007 dichloromethane S1!S0 shows that Kasha’s rule is obeyed in our studied system. Due to the small oscillator strength of the lowest excited state, the emission spectra are From the details discussed above, we get a summary for the expected to show a very small radiative rate constant and absorption and emission processes for C132 in toluene. In the a very low emission quantum yield, which is confirmed by the absorption process, it is prone to induce a S0 !S3 transition beexperimental findings that the emission quantum yield of cause it has the largest oscillator strength, and the transitions C132 in toluene is determined to be 2 %.[6] to S1 and S2 are weakly allowed because of the very small oscillator strengths. However, during the emission process, due to In addition, we predict that the fluorescence of GQDs C168 the small difference in energy gaps between S3, S2, and S1, the and C170 in toluene and dichloromethane follows Kasha’s rule. The calculations show that the fluorescence wavelengths presnonradiative transition is fast so internal conversion is superior ent redshifts with the increasing size of GQDs, however, the to fluorescence emission for the high-lying excited state in polarity of solvents has little effect on the fluorescence waveC132, whereas for the large-sized GQD the electrons are delolength of C168 and C170, which is similar to the results obcalized over a large area, which significantly reduces the sintained for C132 (see Table 4). Moreover, the very small oscillaglet–triplet splitting and thus considerably increases the proba 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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[6] [7]
3. Conclusions Herein, we report the absorption and fluorescence spectra of GQDs by using TDDFT procedures, the bulk solvent effects are taken into consideration for both geometry optimizations and transition-energy calculations by using a PCM model. The agreement obtained between theoretical and experimental wavelengths by using B3LYP/6-31G(d) is satisfactory for the absorption and fluorescence processes. The strong absorptions with lmax correspond to S0 !S3 transition for C132 and to S0 !S3 and S0 !S4 transitions for C168 and C170. We find that the wavelengths were red-shifted in solvents when compared with the absorption wavelength in the gas phase. Edge-functionalized C132 and C168 show small redshifts in lmax when a small number of functional groups were substituted on the edge and a large redshift occurred when the edge was fully substituted. The fluorescence of C132 corresponding to a p!p* transition is due to the S1!S0 transition, which shows that Kasha’s rule is obeyed. Little difference in the fluorescent emission was observed in toluene and dichloromethane. In addition, we analyzed the molecular-orbital transition and transition-density matrix to visually study the spatial span and primary sites of electron transitions. It turns out that the first 55 carbon atoms (see Figure 1) have a large probability of being involved in the transitions. The results we report have important consequences for optical applications of GQDs.
[8] [9] [10]
[11] [12]
[13]
[14]
Acknowledgements We greatly appreciate the Natural Science Foundation of China (grants 21075083, 21345001) for supporting this work. [15]
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Received: November 29, 2013 Published online on March 3, 2014
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