Electron Pair Repulsion Responsible for the Peculiar Edge Effects and

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Electron Pair Repulsion Responsible for the Peculiar Edge Effects and Surface Chemistry of Black Phosphorous Xiang-Peng Kong, Xiaomei Shen, Joonkyung Jang, and Xingfa Gao J. Phys. Chem. Lett., Just Accepted Manuscript • Publication Date (Web): 07 Feb 2018 Downloaded from http://pubs.acs.org on February 7, 2018

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The Journal of Physical Chemistry Letters

Electron Pair Repulsion Responsible for the Peculiar Edge Effects and Surface Chemistry of Black Phosphorous Xiang-Peng Kong,† Xiaomei Shen,† Joonkyung Jang,*,‡ and Xingfa Gao*,†,§ †

College of Chemistry and Chemical Engineering, Jiangxi Normal University, Nanchang, 330022, China

‡

Department of Nanoenergy Engineering, Pusan National University, Busan 46241, Republic of Korea

§

CAS Key Laboratory for Biomedical Effects of Nanomaterials and Nanosafety, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China

ABSTRACT: The electronic and optical properties of black phosphorus (black-P) are significantly modulated by fabricating the edges of this two-dimensional material. Electron lone pairs (ELPs) are ubiquitous in black-P but their role in creating the edge effects of black-P is poorly understood. Using the first-principle calculation, we report ELPs of black-P turn out to experience severe Coulomb repulsion and play a central role in creating the edge effects of black-P. We discover the outermost P atoms of the zigzag edges of black-PQDs are free of the Coulomb repulsion, but the P atoms of the armchair edges do experience the Coulomb repulsion. The Coulomb repulsion serves as a new chemical driving force to make electron-donor-acceptor bonds with chemical groups bearing vacant orbitals. Our results provide insights into the mechanism responsible for the peculiar edge effects of black-P and highlight the opportunity to use the ELPs of black-P for their damage-free surface functionalization.

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ince the first synthesis of monolayer and few-layer black phosphorus (black-Ps),1 these two-dimensional (2D) materials have attracted much interest because of their intrinsic semiconducting nature,2 moderately-large band gaps (2.0 eV to 0.3 eV inversely proportional to thickness),3-5 and sufficiently high thermal6 and charge conductivities.7 These favorable properties distinguish black-Ps from other 2D materials such as the gapless graphene8 and the large-gaped transition-metal dichalcogenides,9-10 endowing black-Ps with versatility in various electronics11 and photonic 12-13 applications. The electronic properties of 2D black-Ps can be further modulated by tailoring them into one dimensional ribbons14-15 or zero dimensional quantum dots.16-17 These edge-containing materials have more flexible electro-optical responses18-20 and higher application potentials.21 The edges of black-P and their effects on the electronic properties of black-P have been addressed before.22 Black-P has two basic edge configurations, armchair and zigzag, just like graphene (Figure 1a). The HOMO-LUMO (H-L) energy gaps of black-P quantum dots (black-PQDs) sensitively decrease with increasing their armchair edges but remain almost unchanged with the increase of their zigzag edges.23 This peculiar energy gap and edge relationship differs from that of graphene quantum dots (GQDs): the H-L gaps of GQDs sensitively decrease with the increase of their zigzag, not armchair, edges.24 The edge effects on the electronic and chemical properties of graphene have been comprehensively studied.25-34 However, the mechanism responsible for the peculiar edge effects of black-P has been poorly understood. Besides creating and engineering the edges, surface derivatization can be also used to tune the electronic properties of black-P and to protect black-P from unwanted chemical erosions.35-37 However, because all P atoms of black-P are chemically saturated without free valences, the formation of shared-electron covalent bonds on the surfaces of black-Ps will unavoidably cause severe changes to the pristine bond connectivity and electronic properties of black-Ps.38-40 A new chemical driving force of black-P for their damage-free derivatization is thus highly desirable.41-42 Here, we perform the density functional theory (DFT) calculation to study the edge effects of monolayer black-P. By examining both black-P and blue-phosphorus (blue-P)—a newly emerging phase of phosphorus,43-45 we demonstrate that the electron lone pairs (ELPs) of black-P have severe Coulomb repulsion. The difference in the armchair- and zigzag-edge effects of black-P arises from the difference in relieving the Coulomb repulsion of the ELPs along different edges. We show the relief of the Coulomb repulsion can be a chemical driving force for the damage-free surface functionalization of black-P, in which black-P acts as electron donors, making electron-donor-acceptor bonds with external ligands.

Figure 1. Black-PQD (a) and blue-PQD (b) with edge P atoms passivated by hydrogens. The armchair and zigzag edges of both (a) and (b) are labelled; the electron lone pairs (ELPs) of selected P atoms are drawn; in both a) and b), the P atoms in sub-planes A and B are shown in purple and brown, respectively. In (a), the electron pair repulsion between P1 and P4 and that between P7 and P4 are labeled, and armchair P atom P1 and zigzag P atom P8 are marked. In b), the atomic distance between P1 and P2 and that between P3 and P4 are marked. The insets of (a) and (b) show the corresponding top-view structures, in which the numbers label the lengths of the armchair (na) and zigzag edges (nz). We use [na, nz] to represent the black- and blue-PQDs with the armchair edge lengths of na and the zigzag edge lengths of nz.

Figure 2a shows the H-L energy gaps of the black-PQDs calculated with the spin-restricted B3LYP/6-31G(d,p) method (see Table S1 of the supporting information, SI, for the numeric gap values). All their edges have been passivated by hydrogen atoms. The energy gap decreases when the lengths of armchair (na) and zigzag edges (nz) increase, which is similar to the case of GQDs.24 A large H-L energy gap usually corresponds to a large chemical stability of the system. Therefore, black-PQDs of smaller sizes are more chemically stable. Interestingly, the energy gaps of black-PQDs are more sensitive to their armchair edge length na than to zigzag edge length nz. This is opposite to the case of GODs. Such inverse dependence of H-L gap on na and nz is clearly illustrated in Figure 2c, in which the energy gaps of the extreme structures black-PQDs [1, n] and [n, 1] are plotted. The gap of black-PQD [n, 1] rapidly reduces from 5.5 eV to 2.7 eV when the n increases from 1 to 30; on the contrary, the gap of black-PQD [1, n] has a much slower decreasing tendency, which just decreases from 5.5 eV to 4.5 eV as the n increases from 1 to 30 (Figure 2c). When n further increases to above 30, the H-L gaps of both black-PQD [1, n] and black-PQD [n, 1] plateau and converge to 4.5 and 2.7 eV, respectively. Such feature of black-PQD differs from that of GQD, whose energy


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The Journal of Physical Chemistry Letters gap approaches zero when its zigzag edge length nz is above 30.46-48 This feature also differs from that of phosphorene nanoribbons with bare edges, which suggests that phosphorene nanoribbons with bare zigzag edges are metallic and those with bare armchair edges are semiconductive.49 Furthermore, the ground state electronic structures of black-PQDs are always closed-shell singlets, irrespective of the sizes of na or nz. In contrast, those of GQDs turn from closed-shell singlets to open-shell singlets as na and especially nz increase.24 The continuous decrease of energy gap of GQD with increasing its size agrees with that the graphene with an infinite size has a zero band gap.50 The preservation of a sizeable energy gap with increasing the size of black-PQD suggests that the two dimensional black-P with an infinite size will have a finite bandgap, in agreement with that a single-layer black-P has a band gap of about 2.0 eV.51 The edge lengths na and nz influence not only the kinetic stability (H-L energy gap) but also the thermodynamic stability of the black-PQDs. According to the definition of black-PQDS in Figure 1, black-PQDs [m, n] and [n, m] are structural isomers with exactly the same chemical constituents. Our calculation suggests that black-PQD [m, n] is lower in energy than its isomer [n, m] when m < n, which means that black-PQDs with more zigzag edges and fewer armchair edges are more thermodynamically stable than their structural isomers with fewer zigzag edges and more armchair edges. The energy difference (Ediff) between black-PQDs [m, n] and [n, m] increases with the increase of the n − m value. For example, black-PQD [2, 3] is energetically lower than [3, 2] by only 6 kcal mol−1. However, black-PQD [2, 9] is energetically lower than black-PQDs [9, 2] by over 20 kcal mol−1 (Figure 2d). This is again opposite to that found for GQDs, for which the armchair edges are beneficial to the thermodynamic stabilities.24 The destabilizing effects of the zigzag edges on the kinetic and thermodynamic stabilities of GQDs have been ascribed to their specific unpaired electrons located at the outmost carbon atoms along the zigzag edges.24, 26-34

To understand the peculiar destabilizing effects of the armchair edges on the kinetic and thermodynamic stabilities of black-PQDs, we analyzed the ELPs that are ubiquitous on the surfaces of black-PQDs. All P atoms in black-PQDs are sp3 hybridized and each sp3 P has an ELP.51 The existence of an

ELP at each P atom of black-PQDs can be verified by inspecting their molecular orbitals. DFT calculations suggested that for black-PQDs with N(P) P-atoms, their N(P) highest occupied molecular orbitals are all distributed at P atoms with their shape like the ELPs of the sp3 P atoms. The N(P) values for rectangular-shaped black-PQDs [na, nz] passivated by hydrogen atoms can be calculated through N(P) = 2(nanz + na + nz) (1) where na and nz are the lengths of the armchair and zigzag edges defined in Figure 1. For example, Figure 2e shows the HOMO and HOMO – 29 of black-PQD [3, 3] with 30 P atoms. Obviously, HOMO and HOMO – 29 are the linear combinations of the ELPs of P atoms. In Figures 1a and 1b, the ELPs of some of the P atoms are drawn. We report that the ELPs are responsible for the peculiar edge effects of black-PQDs. As shown in Figure 1a, the two ELPs of the P atoms labelled with 1 and 4 (P1 and P4) are closely aligned in a head-to-head manner (see Figure S1 of the SI for the orbital diagrams from DFT calculations). These two ELPs have a remarkable Coulomb repulsion and thus can be termed as an electron pair repulsion (EPR). Likewise, there is another EPR between P4 and P7 in Figure 1a. Generally, any two P atoms of the Black-P layer that are 1,4-adjacent and located on the same sub-plane have an EPR. Because the Coulomb repulsion associated with an EPR increases the total energy and decreases the H-L gap of the system, we infer that the number of EPRs (NEPR) contained in the black-PQD can be used as the descriptor for both kinetic and thermodynamic stabilities: the black-PQD isomer with a smaller NEPR have a larger H-L gap and lower relative energy. Indeed, the total energy difference between the two black-PQDs [m, n] and [n, m] is approximately linearly correlated with the corresponding difference in their NEPR’s. Specifically, we found Ediff = 2.8Ndiff + 3.2 (2) where Ediff is the total energy difference of black-PQDs [m, n] and [n, m], and Ndiff is the difference of NEPR of the two black-PQDs (Figure 2d). From Eq. 1, the energy increase associated with one EPR is about 2.8 kcal mol−1. Such a linear relationship between the total energy and the NEPR means that the peculiar destabilizing effect of the armchair edges of black-PQDs presumably originates from the EPRs present in the armchair edges.



(b)

(a)

(c)

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(e)

(d)

Ediff = 2.8Ndiff + 3.2

Figure 2. Three dimensional bar graphs plotting the H-L energy gaps of black-PQDs (a) and blue-PQDs (b). (c) H-L gaps of narrow blackand blue-PQDs. (d) Total energy difference between black-PQD isomers [m, n] and [n, m] and that between blue-PQD isomers [m, n] and [n, m]. (e) The diagrams for the HOMO and HOMO − 29 of black-PQD [3, 3]. In (d), the equation fitted for the total energy difference (Ediff) and the difference of the numbers of EPRs (Ndiff) of black-PQDs is given.

We thus further examine the relationship between the NEPR and edge structures for black-PQDs. The NEPR in a black-P unit cell consisting of N(P) P atoms is N(P). For a black-PQD with edges, the NEPR is reduced because of the creation of edge P atoms. As shown in Figure 1a, there are two types of edge P atoms in the black-PQD system: zigzag and armchair P atoms, which we will call Pzig and Parm, respectively. Each edge P atom forms only two P−P covalent bonds with its two neighboring P atoms, distinguishing it from the inner P-atoms each of which forms three P−P bonds. For example, P1, P2, P8, and P9 of Figure 1a are edge P atoms, and P3, P4, P5, P6, and P7 are inner P atoms. Here, we exactly define Pzig and Parm of black-PQDs of this study: Pzig is the P atom whose two neighboring P atoms are located in the same sub-plane; Pzig is the P atom whose two neighboring P atoms are in different sub-planes. For example, P8 of Figure 1a belongs to Pzig because its two neighbors P1 and P7 are both in sub-plane A; P1 belongs to Parm because its two neighbors P2 and P8 are in different sub-planes. Similarly, P9 and P2 belong to Pzig and Parm, respectively. The difference between Pzig and Parm is that the introduction of one Pzig into the black-PQD system reduces its NEPR by two but the introduction of one Parm reduces the NEPR by only one half. Therefore, we have NEPR = N(P) − 2N(Pzig) – 0.5N(Parm) (3) where N(Pzig), and N(Parm) are the numbers of Pzig and Parm, respectively, and N(P) is the total number of P-atoms of the

black-PQD. For the rectangular-shaped black-PQDs [na, nz] defined in Figure 1a, the NEPR can be simply calculated from na and nz as NEPR = (2nz + 1)(na − 1) (4) So, the destabilizing effect of the armchair edges of black-PQDs compared with the zigzag edges can be ascribed to that the creation of armchair edges in Black-PQDs is less effective in reducing the Coulomb repulsion between the ELPs of the system. As illustrated in Figure 1a, the armchair edge still contains EPRs, e.g., that between P1 and P4. In contrast, the zigzag edge is free from EPRs. This straightforwardly accounts for the enhanced stability of the zigzag edge compared to that of the armchair edge of black-PQDs. Unlike black-PQDs with the edge-dependent thermodynamic and kinetic stabilities, blue-PQDs have a weaker dependence of both stabilities on their edge structures and lengths. As shown in Figure 2b, the decrease of H-L gaps of blue-PQDs caused by edge types and the increase of edge sizes is much slower than that found for black-PQDs. Figure 2c shows the H-L gaps of blue-PQDs [1, n] and [n, 1], whose difference are within 0.6 eV when n > 15. The total energies of blue-PQDs [m, n] and [n, m] are almost equal as well. For example, the energy difference between blue-PQDs [9, 2] and [2, 9] is only about 2.5 kcal mol−1 (Figure 2d). Such a weak edge-dependent H-L gaps and total energies of blue-PQDs can


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The Journal of Physical Chemistry Letters be ascribed to their electronic structures. As shown in Figure 1b, the ELPs of all P atoms in blue-PQDs are parallel to each other. Furthermore, in blue-PQDs, the P atoms of the same sub-planes are almost evenly spaced along both the zigzag and armchair directions. For example, the distance between P1 and P3 and that between P1 and P2 are nearly identical, which are 3.337 and 3.313 Å, respectively. Namely, the Coulomb repulsion between the ELPs in blue-PQDs is negligible and isotropic, independent of the zigzag or armchair direction. This accounts for the weak dependence of kinetic and thermodynamic stabilities on their edge structures and lengths. As discussed above, EPRs critically destabilize black-PQDs by decreasing their H-L gaps and increasing their total

energies. Therefore, surface derivatizations utilizing vacant orbitals to accommodate the ELPs of black-Ps will effectively enhance their stabilities. Indeed, Zhao et al. have used titanium sulfonate as the ligand to functionalize black-Ps, in which the P atoms make coordination bonds with the transition-metal cores of the ligands, and the titanium sulfonate modified black-Ps have exhibited robust stability in air and water.41 Here, we computationally explore the coordination reactions using boron species as the ligands to functionalize black-Ps. This strategy does not involve transition metals and thus may be more environmentally friendly and better suited for application as electronics.

Figure 3. The proposed surface derivatization reactions for black-PQD, which cause no damage to the pristine bond connectivity of the phosphorus materials. In the structures 3, the P atoms of the phosphorous substrates make donor-acceptor bonds with the boron-containing ligands. The inserts illustrate the donor-acceptor bonds, along with the corresponding HOMO and LUMO diagrams supporting the formation of the donor-acceptor bonds

We constructed structure 3 and studied its stability to examine the possibility of making stable donor-acceptor bonds between black-Ps and boron-containing ligands. Structure 3 can be regarded as the coordination complex consisting of black-PQD [4, 2] (1) and the dimethyldiborene ligand (Figure 3). Reportedly, each boron atom in the dimethyldiborene ligand has a vacant p orbital,52 which will accept the donation of the ELP from the phosphorene sheet to form the P→B coordination bond (see the insert of Figure 3). The calculated bond dissociation energy (BDE) of the two P→B bonds in 3 is 35.40 kcal mol−1 on average. Such a large bond energy suggests the considerably strong coordination interaction between the phosphorene sheet and the organic boron ligand.53 To explore the possibility of realizing the surface coordination of black-P with the dimethyldiborene ligands, we investigated the thermodynamics of the reaction of Figure 3, in which 1 was used as the model of black-P. The changes in Gibbs free energy at 298.15 K (Gr, 298.15 K) and total energy (Er) of this reaction are -1.75 and 13.42 kcal mol−1, respectively. Because this reaction is entropically favorable (∆S = 0.05 cal mol−1 K−1), a high temperature will be favored. The change in Gibbs free energy becomes -4.19 kcal mol−1 at 353 K (Gr, 353 K = −4.19 kcal mol−1), indicating the thermodynamically spontaneous coordination reaction between 1 and 2 to yield 3 at 298.15 K and higher temperatures. Interestingly, the Gr, 353 K calculated at singlet and triplet excited states are much more negative, which are -56.22 and −23.44 kcal mol−1, respectively. Therefore, the reaction of Figure 3 will be more thermodynamically favored under light. When two dimethyldiborene ligands 2 are added to the different surfaces of 1, the total Gr, 353 K = −7.12 kcal mol−1, which almost linearly scales with the number of ligands. Note that dimethyldiborene compounds like 2 are already experimentally available.52 We thus expect that the surface

coordination reaction like that of Figure 3 could be realized in the future. Compared with the usual covalent functionalization,38 one of the main merits of the above coordination functionalization is that the latter keeps the pristine structures of black-P nearly intact. Figure 3 shows the structures of black-PQD [4, 2] before and after the coordination of the dimethyldiborene ligand. The changes in the P−P−P angle and P−P length before and after the coordination are less than 0.6° and 0.04 Å, respectively. In contrast, Wang and coworkers have shown by computation that the formation of a covalent bond between black-P and nitrobenzene unavoidably breaks the P−P bond of black-P, severely changing its structure and electronic properties.39 Such a difference is obviously due to the different nature of coordination and covalent interactions. The former involves the donation of the ELP from black-P to the vacant orbital of the boron ligand, which does not resort to the breaking of the pristine bonds in black-P. But the latter requires the sharing of unpaired electrons, for which P−P bonds of black-P must be cleaved to afford the unpaired electrons. Because the coordination of dimethyldiborene little changes the structures of black-P, we expect that the electronic structures near the Fermi levels of black-PQDs and black-P will be also little changed by the coordination. Shown in Figure 4a are the HOMO and LUMO of black-PQD [4, 2] (1) before and after the coordination of the dimethyldiborene ligand. Indeed, the LUMOs of 1 and 3 are almost identical in shape and distribution, and the HOMO of 1 turns to the HOMO − 1 of 3. The HOMO of 3 is new, which obviously originated from the π bonding orbital of the dimethyldiborene ligand. Therefore, when the B=B double bond of 3 is saturated by the addition of H to form structure 7 (Figure S2), both HOMO and LUMO of 7 are nearly identical to those of 1. Shown in Figures 4b and 4c are the electronic band structures of black-P near the Fermi level before and after the



coordination of the dimethyldiborene ligand. The main difference between the band structures of Figures 4b and 4c is the defect state of Figure 4c, which corresponds to the π bonding orbital of the B=B double bond of the dimethyldiborene ligand. Another difference is the increase of band gap from about 0.5 eV for black-P (Figure 4b) to about 1.0 eV for black-P with the dimethylborene ligand (Figure 4c). Such a band gap increase is consistent with the H-L gap increase of Figure 4a, which can be explained by the relief of

Coulomb repulsion associated with the addition of the dimethylborene ligand. As in Figure 4d, the defect state can be completely removed by the hydrogenation of the B=B double bond of the dimethyldiborene ligand. Therefore, the coordination functionalization proposed here induces no damages to the pristine structures and electronic properties of black-P, which may serve as an ideal surface derivation for the protection of black-P from the erosion by water and air.

Figure 4. (a) Diagrams of HOMO and LUMO of black-PQD [4, 2] (a). Band structures near the Fermi level for black-P (b), dimethyldiborene coordinated black-P (c, d). In (d), the B=B double bond of the dimethyldiborene ligand is saturated by the addition of two hydrogen atoms. In summary, the ELPs of black-P have severe Coulomb set(B3LYP/6-31G(d,p)//B3LYP/3-21G(d)). All calculations repulsion, which are responsible for the peculiar edge effects were performed by using Gaussian 09 package.55 of H-passivated black-PQDs. The outermost P atoms of the The average BDE of the two P → B bonds in 3 was zigzag edges of black-PQDs are free from the Coulomb calculated with the method similar to that previously used by repulsion, but those of the armchair edges experience the Frenking and workers.53 Namely, repulsion. This difference accounts for the sensitive decrease of energy gaps of black-PQDs with extension of their armchair, BDE = (EA-B − EA – EB) / n (4) rather than zigzag, edges. The relative energies of structural In Equation 4, EA-B, EA, and EB are the total energies of the isomers of black-PQDs are quantitatively correlated with the product structure (i.e., 3), the black-P fragment, and boron numbers of Coulomb repulsion pairs contained in the isomers. ligand fragment, respectively, and n is the number of chemical The relief of the Coulomb repulsion can be a chemical driving bonds between the two fragments (i.e., two for 3). The EA-B force to make electron-donor-acceptor bonds with chemical was calculated by geometry optimization of the product groups bearing vacant orbitals. This driving force can be used structure 3 with the B3LYP/6-31G(d,p) method, and the total to design surface functionalization reactions for black-P that energies of the fragments were calculated by single-point cause no damages to the pristine bond connectivity and energy calculations with the same method based on the electronic properties. The results provide insights into the fragment geometries of 3. To calculate the changes in total mechanism responsible for the peculiar edge effects of black-P energies and Gibbs free energies for the reaction of Figure 3, and highlight the opportunity to use the ELPs of black-P for all the species involved in the reaction were geometrically their damage-free surface functionalization. optimized with the B3LYP/6-31G(d,p) method followed by frequency calculations at the same level of theory. ■ COMPUTATIONAL METHODS The calculation of black-P and its derivatives was The black-PQDs and blue-PQDs models were optimized by performed with the Vienna ab initio Simulation Package using the spin-restricted Kohn-Sham method along with the (VASP).56-57 The 3 × 6 unit cell was used as the slab model of hybrid B3LYP54 exchange and correlation functionals black-P. The vacuum space between two adjacent sheets was combined with the 3-21G(d) basis set. Based on these set at least 15 Å to eliminate the interactive effect on each optimized structures, the HOMO-LUMO gap were computed other. The generalized gradient approximation (GGA) with the using the hybrid B3LYP exchange and correlation functionals functional described by Perdew−Burke−Ernzerhof (PBE) combined with 6-31G(d,p) basis


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The Journal of Physical Chemistry Letters functional was used for geometry optimizations and band structure descriptions.58 The projector-augmented wave (PAW) method59-60 was applied to describe the wave functions in the core regions, while the valence wave functions were expanded as linear combination of plane-waves with a cutoff energy of 500 eV. Because of the large supercells we used, the Brillouin zones were sampled with Monkhorst-Pack61 mesh kpoint grids of 3 × 3 for both geometry optimizations and band structure calculations. In the geometry optimizations, the total energy was converged to 10−5 eV, and the Hellmann−Feynman force on each relaxed atom was less than 1 meV/Å. PBE and B3LYP functionals have been used in this work for the 2D sheets and clusters, respectively. To examine the different performance of both methods, we selected some black-PQDs and calculated their H-L gaps and relative energies using both methods. The PBE systemically underestimates the gaps by about 2 eV (Figure S3) and energies associated with one EPR by about 1.1 kcal mol−1 (2.8 vs. 1.7 kcal mol−1, see Figure S4) as comparted with the B3LYP. However, the variation tendency of the gaps and relative energies predicted by both methods, which are more important for the present work, are the same. Therefore, the conclusion made based on the results by these two different methods is valid.

■ ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: xx.xxxx/acs.jpclett.5b02457. Figures S1−S4, Table S1, and full citation of Ref. 55 (PDF)

■ AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] (X. G.); [email protected] (J. J.)

Notes The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS This work was supported by the NSFC Project (21773095). This paper was also supported by the Brain Pool Project of the MEST (Ministry of Education, Science and Technology) and by the National Research Foundation of Korea Grant funded by the Korean Government (no. NRF-2015R1A2A2A01004208).

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