Band Gap Opening in Dual-Doped Monolayer Graphene - American

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Band Gap Opening in Dual Doped Monolayer Graphene. Pablo A. Denis, Claudia Mercedes Pereyra Huelmo, and Adriano Souza Martins J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b11709 • Publication Date (Web): 07 Mar 2016 Downloaded from http://pubs.acs.org on March 14, 2016

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The Journal of Physical Chemistry

Band Gap Opening in Dual Doped Monolayer Graphene. Pablo A. Denisa,*, C. Pereyra Huelmoa and A.S. Martinsb a- Computational Nanotechnology, DETEMA, Facultad de Química, UDELAR, CC 1157, 11800 Montevideo, Uruguay b-Departamento de Fisica, ICEx, Polo Universitario de Volta Redonda, Universidade Federal Fluminense, Brazil * e-mail: [email protected] Tel: +59899714280, Fax: +589229241906

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Abstract 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

By means of periodic density functional calculations we studied the effect of dual doping on the stability and electronic structure of graphene. To this end, we have substituted two carbon atoms with one 2p element (B, N or O), and one 3p element (Al, Si, P or S). We have determined that in all cases the dual doping is much easier to attain than the introduction of only one dopant in the graphene framework. We demonstrate that this conclusion does not depend on the chemical species used to compute the formation energies. Moreover, we show which condition must satisfy the dopants in order to prefer dual doping instead of the monodoping. As regards the electronic properties, we found that in most cases the gaps computed at the HSE level for the dual doped graphenes are smaller than those estimated for monodoped graphenes, despite the lower concentration of dopant present in the latter. In effect, for some dual doped graphenes the structures of the Dirac cones are preserved and gaps as small as 0.02 eV were computed. Keywords: carbon nanomaterials, defects, graphene, density functional calculations, doping


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1. Introduction 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Heteroatom doped graphene is established as one of the preferred approaches to expand the family of two dimensional materials.1-4 It has been proven that Boron doped graphene (p-type semiconducting nanostructure) can be scalable produced. Its doping level can be used as an attractive way to alter its electrochemical properties, such as electrocatalysis toward reduction of oxygen and its capacitance.5 In addition to this, the presence of B atoms increases the affinity between with carboxyl groups and graphene.6 Also, the optical absorption of B-doped graphene spectra was found to vary dramatically with dopant concentration.7 When B-doped graphene is produced via thermal exfoliation of graphene oxide, in BF3 atmosphere, it was shown that the electronic properties of B-doped graphene are clearly different than those observed for Nitrogen doped graphene, as the electron donating atom turns graphene more conductive than B.8 Probably, for this reason, Nitrogen, is likely to be one of the most studied dopants of graphene for which more information is available,7-14 and the influence of precursors and conditions on the synthesis is well established.9 A large amount of evidence supports the catalytic properties of N-doped graphene, for example as basic catalyst in the dehydrogenation of ethanol10 or in the oxygen reduction reaction.11 The applications of N-doped graphene are not limited to catalysis, but also include: the design of better lithium batteries12 sensing,13 and the modulation of the electric properties of graphene.14 If we move one row below in the periodic table we find that, although not yet synthetized, Al-doped graphene has been predicted to have unique catalytic properties.15-18 On the contrary, silicon doped graphene19-24 was observed experimentally and the embedding of Si atoms in the graphene lattice is supported by atomically resolved electron energy-loss spectroscopy on a scanning transmission electron microscope.21 As regards phosphorus doped graphene,19-20,25-32 the synthetic procedures to incorporate P are well established25-27 and interesting properties like good energy storage,25 NH3 sensing,26 tunable band gap32 have been reported. Among the 3p elements, sulfur is the dopant which induces the most interesting properties in graphene,32-41 such as: tunable conductivity,39 distinct optoelectronic properties40 and metal-free electrocatalysis for an oxygen reduction reaction.41 The list of monodoped graphenes include more atoms than the 2p and 3p elements. In effect, Se,42-43 ACS Paragon Plus Environment

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Ni, 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

44-45

Fe,

45-47

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Co, Mn, and even large atoms like U and Th were used to dope graphene, as shown

by Sofer et al.48 Notwithstanding the fact that single doping of graphene, as well as its chemical functionalization49-52 have been very useful to improve the properties of graphene, it is necessary to obtain a better degree of control on the modifications performed. Thus, in order to expand the range of applicability of graphene, the simultaneous introduction of two dopants may pave the way towards new two dimensional materials with unique properties. In this line, P and N dual doped graphene53-55 as well as sulfur and nitrogen dual doped graphene56-65 have been synthetized in large quantities. In particular, PN dual doped graphene, which was firstly studied theoretically by Cruz-Silva et al.,53 is a high performance anode material for Li batteries54 and an outstanding catalyst for hydrogen evolution.55 Similar properties were reported for SN dual doped graphene.56-65 Although it was observed in small amounts, Si and N dual doped graphene was studied by Zhou et al. in 2012.21 Following our long term characterization of doped graphenes, by means of ab initio calculations, we recently studied the catalytic properties of the 12 dual doped graphenes that can be assembled when B, N and O are combined with Al, Si, P and S.64 In the latter work, we found that in all cases except one, the dopants adopt a disposition in which they are bonded, i.e. they replace a CC bond. The sole exception was SiB doped graphene for which the Si and B atoms favored the para arrangement of the heteroatoms. In general, the dual doping significantly increases the reactivity of graphene, being the most promising combinations: AlO, SN, PO and SiB. The latter proven to be more reactive than pristine graphene and monodoped graphenes. Nevertheless, little is known about the energetic cost required two introduce two dopants and the electronic properties of dual doped graphenes. Among the 12 2p/3p dual doped graphenes, only the electronic properties of SN dual doped graphene were studied by us,65 while Ervasti et al.,66 investigated the reactivity of SiO and SiN dual doped graphene and the electronic properties of the latter. Considering the importance of doped graphenes, we decided to perform a systematic study of the electronic properties of the 12 possible 2p/3p systems that can be constructed. Although one is tempted to expect that, given the larger dopant concentration, a larger gap would be opened, we will show that ACS Paragon Plus Environment

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this is not always the case. In addition to this, we demonstrate that regardless of the references used to 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

compute the formation energies of the doped graphenes, the dual doping of graphene is energetically favored over the monodoped graphenes. We outline which rule must satisfy a dual doped graphene to meet this requirement. It is our aim that this work can trigger new experimental investigations which pursue the synthesis of dual doped graphenes.

2. Methods We studied the electronic properties of dual doped monolayer graphene with the aid of the Van der Waals density functional (VDW-DF),67 the Minessotta class functional M06-L68-69 and the HatreeFock screened functional, Heyd, Scuseria and Ernzerhof (HSEH1PBE)70-71 density functionals. Gaussian 0972 was used to carry out the M06-L and HSEH1PBE calculations. The ultrafine grid and the 6-31G*73 basis set was selected. Unit cells were sampled using 3000 k−points. For the calculations performed with VDW-DF method the SIESTA code was employed.74-75 We selected the double−zeta basis set with polarization functions (DZP) and fixed the orbital confining cut−off to 0.01 Ry. The split norm used was 0.15. The interaction between ionic cores and valence electrons was described by the Troullier−Martins norm conserving pseudopotentials.76 The Mesh cut−off was fixed to 200 Ry, which gave converged binding energies within 0.02 eV. We optimized the lattice parameters along the a and b directions but the c axis was maintained frozen at 20 Å. Unit cells were sampled using a Monkhorst−Pack k−point sampling scheme of 40×40×1 k points, which yielded converged results in all calculations.

Band

structures

in

the

first

Brillouin

zone

were

calculated

along

the

Γ−Μ−Κ−Γ−Μ’−Κ’−Γ−Μ’’−Κ’’−Γ path, recently employed by Ervasti et al.66. Geometry optimizations were pursued using the conjugate gradient algorithm until all residual forces were smaller than 0.01 eV/Å. For the calculations involving monolayer graphene we utilized N×N unit cells, N=5, 7, 8. Based on the results obtained in our previous investigation on the catalytic properties of dual doped graphenes, we selected the ortho disposition of the dopants, except in the case of SiB, for which we found that the para disposition is energetically favored,64 both structures are shown in Figures 1a and 1b for ortho and para configurations, respectively. ACS Paragon Plus Environment

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3. Results and Discussion 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

3.1 Formation Energies: Analysis of the formation energies (FE) is interesting to gauge which of these dual doped graphenes (DDG) are more stable and thus more appealing to be synthetized. The FE are presented in Table 1. We used the atomic forms of all dopants as chemical potentials while the chemical potential of carbon was calculated as the cohesive energy per atom of graphene. We note most of the findings of this section are independent of the chemical species used to calculate the FE, as we demonstrate below. The DDG which presents the lowest formation energy is PB dual-doped monolayer graphene with a FE of -6.40 eV, for a 8×8 unit cell. The second most stable doped graphene studied is para SiB DDG, displaying a FE which is only 0.17 eV larger that than of PB DDG. In contraposition, AlO DDG displays the largest FE, -2.15 eV, more than 4 eV above PB DDG. The average FE of the 12 DDG assayed is -4.32 eV, a value which is lower than all of the FE of the monodoped graphenes, except B-doped graphene. To the best of our knowledge, all monodoped graphenes listed in Table 1 have been prepared, except Al-doped graphene. This fact is in nice agreement with the FE calculated, given that Al-doped graphene exhibits the largest formation energy, i.e. 2.58 eV. Interestingly, we found that all FE of AlX DDG (X= B,N,O) are lower than the one computed for Al-doped G. The same statement is valid for SiX, PX and SX DDG, X= B,N,O as their FE are lower than those corresponding to Si, P and S-doped graphene, respectively. Therefore, it is easier to introduce two dopants (2p and 3p) in the graphene framework, than to dope graphene with only one 3p dopant. In table 2, we compare the FE of the DDG vs. the sum of the FE of dopants X and Y. For all DDG the sum of the FE of the monodoped graphenes is larger than that corresponding to the DDG. The cases in which the difference is more noticeable are those in which oxygen participates, AlO, SiO, PO and SO. The question that obviously arises is whether the results obtained in the previous paragraph depend on the references used to calculate the chemical potentials of the dopants and carbon. In a first approach, we used the atomic form of carbon as chemical potential for C. The conclusions remained unchanged. A closer inspection of the equations used to compute the FE reveals that the stability of the DDG related to that of the monodoped graphenes is independent of the chemical potential employed: ACS Paragon Plus Environment

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FE(XY-dual-doped-graphene) = Energy(XY-dual-doped-graphene) + 2µC – µX –µy – Energy(graphene) (1) FE(X-doped graphene) = Energy(X-doped-graphene) + µC – µX – Energy(graphene)

(2)

FE(Y-doped graphene) = Energy(Y-doped-graphene) + µC – µY – Energy(graphene)

(3)

If we subtract equations 2 and 3 from 1 we obtain:

FE(XY-dual-doped-graphene) – FE(X-doped graphene) – FE(Y-doped graphene) = Energy(XY-dual-doped-graphene) – Energy(X-dopedgraphene)

– Energy(Y-doped-graphene) + Energy(graphene)

(4)

Equation 4 reveals that the difference between the FE of a DDG and the sum of the FE of the monodoped graphenes depends only on the absolute energy of the doped graphenes. Bearing in mind that sulfur doped graphene has been prepared, as originally predicted by theoretical calculations,31,34 and considering that the FE of S-doped graphene is 1.39 eV we conclude that the 12 DDG studied can be prepared, even those which include the Al dopant, since the presence of a 2p dopant dramatically decreases the energy required to introduce one Al atom in the carbon framework. Although the absolute values of the FE depend on the compounds used to compute the chemical potentials, the larger stability of the dual doped graphenes with respect to the monodoped ones holds true. There are different methods which can be used to prepare the DDG. For example those which include oxygen may be prepared when graphene is obtained from thermal exfoliation of graphite oxide, as Wang et al.5 reported to obtain Bdoped graphene by the use of a BF3 atmosphere. A different approach is the use of heterocyclic compounds which contain the desired dopants and then metal surfaces area used to catalyze the dehydrogenation which conducts to the formation of graphene islands as attained by Cloke et al.70 to prepare B-doped graphene nanoribbons. Finally, vacancies can be created using high energy ions and then the corresponding atoms are introduced as Robertson et al.46 reported for the preparation and characterization of Fe doped graphene. ACS Paragon Plus Environment

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3.2 Electronic properties: Before discussing the electronic properties of the DDG studied, it is 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

mandatory to analyze their magnetic moments, which are presented in Table 3 for 8×8 DDG. They were calculated employing a spin polarized wavefunction in all cases. Among the 12 DDG we can appreciate that there are six systems in which the sum of the electrons is even and the magnetic moment is zero, at the VDW-DF/DZP level. However, in those systems where the sum of electrons of the unit cell is odd we can face two situations: a) the magnetic moment is 1.0 µB, for AlO, PO and SiN, b) the magnetic moment is 0 µB for para-SiB and SB, and 0.69 µB for SN. The latter case (b) is somewhat unexpected for chemists because for molecules, an odd count of electrons indicates that we are in the presence of a singly occupied alpha molecular orbital and an associated unoccupied beta molecular orbital. However, for periodic systems it is possible to allow the variation of the magnetic moments and a zero magnetic moment can be obtained even though the calculation was run as polarized. In our previous work about SN DDG we showed that different electronic properties can be obtained depending on the value of the magnetic moment. In first place, we discuss the graphenes in which the magnetic moments need a deep analysis, and then we focus our attention in those which did not have methodological problems. In the case of paraSiB and SB DDG, we faced the situation when the magnetic moment is zero. Thus, we ran the VDWDF calculations with fixed magnetic moment of 1.0 µB. Interestingly, we found that the magnetic solutions are 0.077 and 0.028 eV below the energy obtained when it is 0.0 µB. We note that this situation persists even when larger supercells are employed. In these cases, the band structures shown in Figures 2a-2b, 3a-3b for para-SiB and SB DDG, respectively, indicated that they are metals for both spin channels. The band structure of SN DDG is shown in Figures 4a-4b. For para-SiB DDG the shape of the Dirac cones at the K points are preserved, but the Fermi level moved below the valence band of graphene. On the contrary, the presence of the S and B dopants significantly altered the structure of the valence and conduction bands of graphene. When the magnetic moment was fixed we found that paraSiB and SB DDG are small gap semiconductors, at the VDW-DF/DZP level. This finding is supported by M06-L/6-31G* and HSEH1PBE/6-31G* calculations performed with Gaussian 2009 and fixing the ACS Paragon Plus Environment

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magnetic moment to 1.0 µB. The band gaps are gathered in Table 4. The values are 0.19/0.25 and 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0.19/0.19 eV for 8×8 para-SiB and SB DDG, respectively (up/down notation), at the HSEH1PBE/631G* level of theory. As we have shown before, decreasing the size of the unit cell up to 5×5 increases the band gap, except in the case of the 6×6 unit cell, which has been shown to be special case because the position of the K and Γ points. If we compare the band gap obtained for SB DDG with that computed for S doped graphene, we found that a slightly larger gap is obtained for the latter, a fact that was unexpected because for SB DDG the dopant concentration is higher. On the contrary, the gap computed for B doped graphene is lower than that determined for SB DDG. Therefore, the gap of SB DDG is bracketed by those of B and S doped graphene. In the case of para-SiB DDG the gap is larger than those of Si and B monodoped graphenes. We note that Silicon is not very effective in opening a gap in graphene because of the similar electronic structure between Si and C. In summary, depending on the magnetic moment obtained for para-SiB and SB DDG, they can be considered metals or small gap semiconductors, but we cannot forget that both solutions are almost degenerated. We note that a similar scenario was found for Al, B and N doped graphene. They behave exactly as para-SiB and SB DDG. The magnetic moment obtained is zero and the systems are metals, even though the calculation was run as spin polarized. For the three cases there is a solution with magnetic moment equal to 1.0 µB, which is less than 0.14 eV above in energy and the fixation of the magnetic moment turn the systems into small gap semiconductors, as can be seen in the values listed in Table 4 at the HSEH1PBE/6-31G* level. The band structures of the three magnetic systems SiN, AlO and PO DDG are presented in Figures 5a-5b, 6a-6b, and 7a-7b respectively, while the gaps computed at the M06-L and HSEH1PBE levels can be found in Table 4. For SiN DDG our results are similar to those reported by Ervasti et al.66, the system is a small gap semiconductor with a gap that is 0.23 eV for the spin up channel and 0.04 eV for the spin down one, at the HSEH1PBE/6-31G* level. The latter gaps are larger than those computed for N and Si monodoped graphene, in line with the results obtained for SB DDG. The difference between the gaps computed for both channels increases as the unit cell is reduced, being almost ten times larger the spin ACS Paragon Plus Environment

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up gap for the 5×5 unit cell. Thus, SiN DDG may be useful to develop spin filters as earlier suggested 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

by Ervasti et al.66 here we highlight the importance of: a) dopant concentration, in order to increase the difference in the gap computed for both spins b) the fact that there is a strong preference for the Si and N dopants to be joined.64 In the case of AlO DDG, we found that the behavior is completely different than that observed for SiN DDG. Although the system is polarized the band gap calculated for both spins are rather similar and thus no filtering is expected. Therefore, the most interesting application of AlO DDG may be in catalysis due to the enhanced reactivity recently highlighted by us.64 Finally, for PO DDG we have found that it is an intermediate case between SiN and AlO DDG, given that the spin down band gap is 50% larger than the spin up gap for all unit cells (except 6×6), at the HSEH1PBE/631G* level. This difference is larger than that observed for AlO DDG, but smaller than the one determined for SiN DDG. In the case of AlB, AlN, SiO, PB, PN, and SO DDG the spin polarized calculations pointed to a non magnetic ground state, even though in the case of SiO and SO DDG the dopants prefer to replace a CC bond, but are not joined.64 The band structures are shown in Figures 8, 9, 10, 11, 12 and 13, for AlB, AlN, SiO, PB, PN, and SO, respectively. Three systems present band gaps below 0.10 eV for 8×8 unit cells: SiO, AlN and SO DDG. For SiO DDG the Dirac cone is only slightly modified at the K´´ point and the band gap is 0.02 eV at the HSEH1PBE level. Larger gaps are predicted for AlN and SO DDG. The widest openings at the K points are observed for the systems which involve P, 0.17 and 0.13 eV for PN and PB, respectively. This finding maybe related to the fact that P is very effective in opening a gap in monodoped monolayer graphene.32 However, it is important to stress that for PN and PB DDG the gaps are significantly lower than that computed for P doped monolayer graphene. In effect, for an 8×8 monolayer graphene the gap is 0.49/0.41 eV when only P is present, while it is below 0.2 eV for PB and PN DDG. Therefore, as mentioned above, the dual doping does not guarantee a larger gap despite the larger concentration of dopant present in DDG. In the same line, we found the gap of SO DDG is smaller than that computed for S doped graphene.


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To gain deeper insight into the peculiar variation of the band gaps computed for the DDG, we have listed in Table 5 the differences between the band gaps computed for the DDG and the monodoped graphenes. On the one hand we have the difference GapXY-GapX, while on the other hand we calculated the GapXY-GapY difference. When we compare the GapXY vs. GapX we found that in nine cases the gaps of the DDG are lower than those determined for X (X= Al, Si, P, S) monodoped graphenes. The three exceptions are SiBpara, SiN and SN DDG. The cases which involve Silicon can be understood if we consider that Si doped graphene presents the lowest band gap among the monodoped graphenes. In effect, for the 8×8 unit cells the gap is only 0.03 eV at the HSEH1PBE/6-31G* level. Furthermore, even though there is a reduction of the gap computed for SiO DDG, the lowering is as small as 0.01 eV. Thus, even when other dopants are present, Silicon is able to minimally alter the electronic structure of graphene and in the particular case of SiO DDG, quenches the effect of the oxygen dopant maintaining the degeneracy of the π and π* bands at the K’’ point (see Figure 10). The largest reductions are observed for the PY DDG graphenes. Irrespective of the characteristics of the Y dopant, i.e acceptor (B) or donor (N), the gaps are reduced significantly with respect to P doped graphene, almost 0.4 eV! Why are we observing the largest reductions for the PY DDG? We attribute this behavior to the fact that P doped graphene displays the largest band gaps among the monodoped sheets. Therefore, in a context where the dual doping tends to decrease the band gaps for most systems, it is reasonable to expect the largest lowering for PY DDG and the lowest ones for the SiY DDG. When we turn to the analysis of the GapXY-GapY difference we found that in six cases there are reductions with respect to the monodoped systems, while in four they are increased. Although for oxygen we always observe reductions, B and N present an erratic behavior which could not be correlated with the nature of the 3p dopants. Although the absolute values of the gap may change if more advanced techniques are used, the lower gaps observed at the HSEH1PBE for most of the DDG and monodoped graphenes are expected to hold true given that the systems are rather similar.


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4. Conclusions 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

We have employed the VDW-DF, M06-L and HSEH1PBE density functionals to study the stability and electronic structure of dual doped monolayer graphene. Two dopants were simultaneously introduced in the carbon sp2 framework: one 2p element (B, N or O), and one 3p element (Al, Si, P or S). Analysis of the formation energies revealed that in all cases the dual doping is less expensive from a thermodynamical stand point that the monodoping of graphene. This finding does not depend on the chemical species used to compute the formation energies. By combining the equations used to compute the formation energies we explain which condition must satisfy the dopants in order to prefer dual doping instead of the monodoping. In contrast with our previous findings for monodoped graphene we found that in several cases the gaps computed at the HSE level for the dual doped graphenes are smaller than those computed for monodoped graphenes. This behavior was not expected because of the larger concentration of dopants in dual doped monolayer graphene. Acknowledgments The authors thank PEDECIBA−Quimica for financial support and ANII for project FSE6160. The authors declare no competing financial interest. References 1) Wang, X.; Sun, G.; Routh, P.; Kim, D.H.; Huang, W. Heteroatom-doped Graphene Materials: Syntheses, Properties and Applications. Chem. Soc. Rev. 2014, 43, 7067-7098. 2) Terrones, H.; Lv, R.; Terrones, M.; Dresselhaus, M. S. The Role of Defects and Doping in 2D Graphene Sheets and 1D Nanoribbons. Rep. Prog. Phys. 2012, 75, 062501. 3) Paraknowitsch, J.P.; Thomas, A. Doping Carbons Beyond Nitrogen: an Overview of Advanced Heteroatom Doped Carbons with Boron, Sulphur and Phosphorus for Energy. Energy Environ. Sci. 2013, 6, 2839-2855. 4) Qu, L.; Chen, N.; Huang, X. Heteroatom Substituted and Decorated Graphene: Preparation and Applications. Phys. Chem. Chem. Phys. 2015, 17, 32077-32098.


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5) Wang, L.; Sofer, Z.; Simek, P.; Tomandl, I.; Pumera, M. Boron-Doped Graphene: Scalable and 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Tunable p-Type Carrier Concentration Doping. J. Phys. Chem. C 2013, 117, 23251-23257. 6) Al-Aqtash, N.; Vasiliev, I. Ab Initio Study of Boron- and Nitrogen-Doped Graphene and Carbon Nanotubes Functionalized with Carboxyl Groups. J. Phys. Chem. C 2011, 115, 18500-18510. 7) Laref, A.; Ahmed, A.; Binomran, S.; Luo, S.J. First-principle Analysis of the Electronic and Optical Properties of Boron and Nitrogen Doped Carbon Monolayer Graphenes. Carbon 2015, 81, 179-192. 8) Poh, H.L.; Simek, P.; Sofer, Z.; Tomandl, I.; Pumera, M. Boron and Nitrogen Doping of Graphene via Thermal Exfoliation of Graphite Oxide in a BF3 or NH3 Atmosphere: Contrasting Properties. J. Mater. Chem. A, 2013,1, 13146-13153 9) Wang, L.; Sofer, Z.; Luxa, J.; Pumera, M. Nitrogen Doped Graphene: Influence of Precursors and Conditions of the Synthesis. J. Mater. Chem. C, 2014, 2, 2887-2893. 10) Asedegbega-Nieto, E.; Perez-Cadenas, M.; Morales, M.V.; Bachiller-Baezab, B.; GallegosSuarez, E.; Rodriguez-Ramos, I.; Guerrero-Ruiz, High Nitrogen Doped Graphenes and Their Applicability as Basic Catalysts. A. Diamond Relat. Mater. 2014, 44, 26-32. 11) Zhang, L.; Xia, Z. Mechanisms of Oxygen Reduction Reaction on Nitrogen-Doped Graphene for Fuel Cells. J. Phys. Chem. C 2011, 115, 11170-11176. 12) Reedy, A.L.M.; Srivastava, A.; Gowda, S.R.; Gullapalli, H.; Dubey,

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15) Fukushima, A., Sawairi, A., Doi, K., Senami, M., Chen, L., Cheng, H., Tachibana, A. Role of an 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Aluminum Atom on Graphene for Hydrogen Adsorption. J. Phys. Soc. Jpn. 2011, 80, 074705. 16) Ao, Z.M.; Yang, J.; Li, S.; Jiang, Q. Enhancement of CO Detection in Al Doped Graphene. Chem. Phys. Lett. 2008, 461, 276-279. 17) Ao, Z.M.; Yang, J.; Li, S.; Jiang, Q. Thermal stability of Interaction Between the CO Molecules and the Al Doped Graphene. Phys. Chem. Chem. Phys. 2009, 11, 1683-1687. 18) J. Dai; Yuan, J.; Giannozzi, P. Gas Adsorption on Graphene Doped with B, N, Al, and S: A Theoretical Study. Appl. Phys. Lett. 2009, 95, 232105. 19) Denis, P.A. Band Gap Opening of Monolayer and Bilayer Graphene Doped with Aluminium, Silicon, Phosphorus, and Sulfur. Chem. Phys. Lett. 2010, 492, 251-257. 20) Denis, P.A. When Noncovalent Interactions are Stronger than Covalent Bonds: Bilayer Graphene Doped with Second Row Atoms, Aluminum, Silicon, Phosphorus and Sulfur. Chem. Phys. Lett. 2011, 508, 95-101. 21) Zhou, W.; Kapetanakis, M.D.; Prange, M.P.; Pantelides, S.T.; Pennycook, S.J.; Idrobo, J.-C. Direct Determination of the Chemical Bonding of Individual Impurities in Graphene. Phys. Rev. Lett. 2012, 109, 206803. 22) Ramasse, Q.M.; Seabourne, C.R.; Kepaptsoglou, D.-M; Zan, R.; Bangert, U.; Scott, A.J. Probing the Bonding and Electronic Structure of Single Atom Dopants in Graphene with Electron Energy Loss Spectroscopy. Nano Lett. 2013, 13, 4989-4995. 23) Zou, Y.; Li, F.; Zhu, Z.H.; Zhao, M.W.; Xu, X.G.; Su, X.Y. An ab initio study on gas sensing properties of graphene and Si-doped graphene. Eur. Phys. J. B 2011, 81, 475-479. 24) Houmad, M.; Zaari, H.; Benyoussef, A.; El Kenz, A.; Ez-Zahraouy, H. Optical Conductivity Enhancement and Band Gap Opening with Silicon Doped Graphene. Carbon, 2015, 94, 10211027. 25) Poh, H.L.; Sofer, Z.; Novacek, M.; Pumera, M. Concurrent Phosphorus Doping and Reduction of Graphene Oxide. Chem. Eur. J. 2014, 20, 4284-4291. ACS Paragon Plus Environment

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26) Niu, F.; Tao, L.-M.; Deng, Y.-C.; Wang, Q.-H.; Song, W.-G. Phosphorus Doped Graphene 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nanosheets for Room Temperature NH3 Sensing. New J. Chem. 2014, 38, 2269-2272. 27) Gonzalez Larrude, D.; Garcia-Basabe, Y.; Lazaro Freire, F. Jr.; Rocco, M.L.M. Electronic Structure and Ultrafast Charge Transfer Dynamics of Phosphorous Doped Graphene Layers on a Copper Substrate: a Combined Spectroscopic Study RSC Adv. 2015, 5, 74189-74197 28) Denis, P.A. Tuning the Electronic Properties of Doped Bilayer Graphene with Small Structural Changes. Comp. Theor Chem. 2011, 974, 21-25. 29) Dai, J.; Yuan, J. Modulating the Electronic and Magnetic Structures of P-doped Graphene by Molecule Doping. J. Phys.: Condens. Matter 2010, 22, 225501. 30) Gueorguiev, G.K.; Furlan, A.; Czigany, Z.; Stafstrom, S.; Hultman, L. Intercalation of P atoms in Fullerene-like CPx. Chem. Phys. Lett. 2011, 501, 400-403. 31) Zhang, C., Mahmood, N., Yin, H., Liu, F., Hou, Y. Synthesis of Phosphorus-Doped Graphene and its Multifunctional Applications for Oxygen Reduction Reaction and Lithium Ion Batteries. Adv. Mater. 2013, 25, 4932-4937. 32) Denis, P.A. Concentration Dependence of the Band Gaps of Phosphorus and Sulfur Doped Graphene. Comput. Mater. Sci. 2013, 67, 203-206. 33) Denis, P.A.; Faccio, R.; Mombru, A.W. Is It Possible to Dope Single-Walled Carbon Nanotubes and Graphene with Sulfur? ChemPhysChem 2009, 10, 715-722. 34) Denis, P.A. Density Functional Investigation of Thioepoxidated and Thiolated Graphene. J. Phys.Chem. C 2009, 113, 5612-5619. 35) Zhang, J.; Li, J.; Wang, Z.; Wang, X.; Feng, W.; Zheng, W.; Cao, W.; Hu, P. Low-Temperature Growth of Large-Area Heteroatom-Doped Graphene Film. Chem. Mater. 2014, 26, 2460-2466. 36) Garcia, A.L.E.; Baltazar, S.E.; Romero, A.H.; Perez Robles, J.F.; Rubio, A. Influence of S and P Doping in a Graphene Sheet. J. Comput. Theor. Nanosci. 2008, 5, 1-9. 37) Goyenola, C.; Stafstrom, S.; Hultman, L.; Gueorguiev, G.K.; Structural Patterns Arising during Synthetic Growth of Fullerene-Like Sulfocarbide. J. Phys. Chem. C 2012, 116, 21124-21131. ACS Paragon Plus Environment

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38) Yang, S.; Zhi, L.; Tang, K.; Feng, X.; Maier, J.; Müllen K. Efficient Synthesis of Heteroatom (N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

or S)-Doped Graphene Based on Ultrathin Graphene Oxide-Porous Silica Sheets for Oxygen Reduction Reactions. Adv. Funct. Mater. 2012, 22, 3634-3640. 39) Rao, A.; Quan, W.; Vajtai, R.; Ajayan, P.M. Synthesis of S-doped graphene by liquid precursor. Nanotechnology 2012, 23, 275605. 40) Wang, Z.; Li, P.; Chen, Y.; He, J.; Zhang, W.; Schmidt, O.G.; Li, Y. Pure Thiophene–sulfur Doped Reduced Graphene Oxide: Synthesis, Structure, and Electrical Properties. Nanoscale 2014, 6, 7281-7287. 41) Poh, H. L.; Šimek, P.; Sofer, Z.; Pumera, M. Sulfur-Doped Graphene via Thermal Exfoliation of Graphite Oxide in H2S, SO2, or CS2 Gas. ACSNANO, 2013, 7, 5262–5272. 42) Jin, Z.; Nie, H.; Yang, Z.; Zhang, J.; Liu, Z.; Xu, X.; Huang, S. Metal-free Selenium Doped Carbon Nanotube/Graphene Networks as a Synergistically Improved Cathode Catalyst for Oxygen Reduction Reaction. Nanoscale 2012, 4, 6455-6460. 43) Denis. P.A. Chemical Reactivity and Band-gap Opening of Graphene Doped with Gallium, Germanium, Arsenic, and Selenium Atoms. ChemPhysChem, 2014, 15, 3994-4000. 44) Santons, E.J.G.; Ayuela, A.; Sanchez-Portal, D. Strain-Tunable Spin Moment in Ni-Doped Graphene. J. Phys. Chem. C 2012, 116, 1174–1178. 45) Toh, R.J.; Poh, H.L.; Sofer, Z.; Pumera, M. Transition Metal (Mn, Fe, Co, Ni)-Doped Graphene Hybrids for Electrocatalysis. Chem. Asian J. 2013, 8, 1295-1300. 46) Robertson, A.W.; Montanari, B.; He, K.; Kim, J.; Allen, C.S.; Wu, Y.A.; Olivier, J.; Neethling, J.; Harrison, N.; Kirkland, A.I.; Warner, J.H. Dynamics of Single Fe Atoms in Graphene Vacancies. Nano Lett. 2013, 13, 1468−1475. 47) Zhao, J.; Deng, Q.; Bachmatiuk, A.; Sandeep, G.; Popov, A.; Eckert, J.; Rümmeli, M. H. FreeStanding Single-Atom-Thick Iron Membranes Suspended in Graphene Pores. Science 2014, 343, 1228-1232.


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48) Sofer, Z.; Jankovsky, O.; Simek, P.; Klimova, K.; Mackova, A.; Pumera, M. Uranium- and 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Thorium-Doped Graphene for Efficient Oxygen and Hydrogen Peroxide Reduction. ACSNANO 2014, 8, 7106-7114. 49) Jankovský, O.; Simek, P.; Sedmidubský, D.; Matějková, S.; Janousek, Z.; Sembera, F.; Pumera, M.; Sofer, Z. Water-soluble Highly Fluorinated Graphite Oxide. RSC Adv., 2014, 4, 1378-1387. 50) Sofer, Z.; Jankovský, O.; Simek, P.; Soferova, L.; Sedmidubsky, D.; Pumera, M. Highly Hydrogenated Graphene via Active Hydrogen Reduction of Graphene Oxide in the Aqueous Phase at Room Temperature. Nanoscale, 2014, 6, 2153-2160. 51) Denis, P.A. Organic Chemistry of Graphene: The Diels–Alder Reaction. Chem. Eur. J. 2013, 19, 15719–15725. 52) Denis, P.A. On the Addition of Aryl Radicals to Graphene: the Importance of Nonbonded Interactions. ChemPhysChem 2013, 14, 3271 – 3277. 53) Cruz-Silva, E.; López-Urías, F.; Muñoz-Sandoval, E.; Sumpter, B.G.; Terrones, H.; Charlier J.C.; Meunier, V.; Terrones, M. Electronic Transport and Mechanical Properties of Phosphorusand Phosphorus−Nitrogen-Doped Carbon Nanotubes. ACSNANO 2009, 3,1913–1921. 54) Ma, X.; Ning, G.; Xu, C.; Gao, J. Phosphorus and Nitrogen Dual-doped Few-layered Porous Graphene: a High Performance Anode Material for Lithium Ion Batteries. ACS Appl. Mater Interfaces 2014, 6, 14415-14422. 55) Zheng, Y.; Jiao, Y.; Li L.H.; Xing, T.; Chen, Y.; Jaroniec, M.; Qiao, S.Z. Toward Design of Synergistically Active Carbon-Based Catalysts for Electrocatalytic Hydrogen Evolution. ACSNANO 2014, 8, 5290-5296. 56) Paraknowitsch, J.P.; Wienert, B.; Zhang, Y.; Thomas, A. Intrinsically Sulfur- and Nitrogen-Codoped Carbons from Thiazolium Salts. Chem. Eur. J. 2012, 18, 15416-15423. 57) Liang, L.; Jiao, Y.; Jaroniec, M.; Qiao, S.Z. Sulfur and Nitrogen Dual-Doped Mesoporous Graphene Electrocatalyst for Oxygen Reduction with Synergistically Enhanced Performance. Angew. Chem. Int. Ed. 2012, 51, 11496-11500. ACS Paragon Plus Environment

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58) Xu, J.; Dong, G.; Jin, C.; Huan, M.; Guan, L. Sulfur and Nitrogen Co-Doped, Few-Layered 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Graphene Oxide as a Highly Efficient Electrocatalyst for the Oxygen-Reduction Reaction. ChemSusChem 2013, 6, 493-499. 59) Wohlgemuth, S.-A.; Vilela, F.; Titirici, M.-M.; Antonietti, M. A One-pot Hydrothermal Synthesis of Tunable Dual Heteroatom-doped Carbon Microspheres. Green. Chem. 2012, 14, 741-749. 60) Wohlgemuth, S.-A.; White, R.J.; Willinger, M.-G.; Titirici, M.-M.; Antonietti, M. A One-pot Hydrothermal Synthesis of Sulfur and Nitrogen Doped Carbon Aerogels with Enhanced Electrocatalytic Activity in the Oxygen Reduction Reaction. Green. Chem. 2012, 14, 1515-1523. 61) Feng, B.; Xie, J.; Dong, C.; Zhang, S.; Cao G.; Zhao, X. From Graphite Oxide to Nitrogen and Sulfur Co-doped Few-layered Graphene by a Green Reduction Route via Chinese Medicinal Herbs RSC Adv. 2014, 4, 17902-17907. 62) Ma, X; Ning, G.; Sun, Y.; Pu Y.; Gao, J. High Ccapacity Li Storage in Sulfur and Nitrogen Dual-doped Graphene Networks. Carbon 2014, 79, 310-320. 63) You, J.M.; Ahmed, M.S.; Han, H.S.; Choe, J.; Ustundag, Z.; Jeon, S. New Approach of Nitrogen and Sulfur-doped Graphene Synthesis Using Dipyrrolemethane and Their Electrocatalytic Activity for Oxygen Reduction in Alkaline Media. J. Power Sources 2015, 275, 73-79. 64) Denis, P.A.; Pereyra, C.P. Structural Characterization and Chemical Reactivity of Dual Doped Graphene. Carbon 2015, 87, 106-115. 65) Denis, P.A.; Pereyra Huelmo, C.; Iribarne, F. Theoretical Characterization of Sulfur and Nitrogen Dual-doped Graphene. Comp. Theor Chem. 2014, 1049, 13-19. 66) Ervasti, M. M.; Fan, Z.; Uppstu, A.; Krasheninnikov, A.; Harju, A. Silicon and Silicon-nitrogen Impurities in Graphene: Structure, Energetics and Effects on Electronic Transport. Phys. Rev. B 2015, 92, 235412. 67) Dion, M.; Rydberg, H.; Schroder, E.; Langreth, D.C.; Lundqvist B.I. Van der Waals density functional for general geometries. Phys. Rev. Lett. 2004, 92, 246401. ACS Paragon Plus Environment

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68) Zhao, Y.; Truhlar, D. G. A New Local Density Functional for Main-group Thermochemistry, 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Transition Metal Bonding, Thermochemical Kinetics, and Noncovalent Interactions J. Chem. Phys. 2006, 125, 194101. 69) Zhao, Y.; Truhlar, D.G. Density Functionals with Broad Applicability in Chemistry. Theor. Chem. Account. 2008, 120, 215-241. 70) Heyd J.; Scuseria, G. E. Assessment and Validation of a Screened Coulomb Hybrid Density Functional. J. Chem. Phys., 2004, 120, 7274-7280. 71) Barone V.; Scuseria, G. E. Theoretical Study of the Electronic Properties of Narrow Singlewalled Carbon Nanotubes: Beyond the Local Density Approximation. J. Chem. Phys. 2004, 121, 10376-10379. 72) Gaussian 09, Revision D, Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian, Inc., Wallingford CT, 2009. 73) Hehre, W.; Radom, L.; Schleyer, P. v. R.; Pople J. A. Ab initio Molecular Orbital Theory, Wiley, New Work (1986). 74) Soler, J. M.; Artacho, E.; Gale, J. D.; Garcia, A.; Junquera, J.; Ordejon, P.; Sanchez-Portal, D. The SIESTA Method for Ab Initio Order-N Materials Simulation. J. Phys.: Condens. Matter, 2002, 14, 2745-2779. 75) Ordejon, P.; Artacho, E.; Soler, J. M. Self-consistent order-N Density-functional Calculations for Very Large Systems. Phys. Rev. B 1996, 53, R10441-R10444. 76) Troullier, N.; Martins, J.L. Efficient Pseudopotentials for Plane-Wave Calculations. Phys. Rev. B 1991, 43, 1993-2006. 77) Cloke, R. R.; Marangoni, T.; Nguyen, G. D.; Joshi, T.; Rizzo, D. J.; Bronner, C.; Cao, T.; Louie, S. G.; Crommie, M. F.; Fischer, F. R. Site-Specific Substitutional Boron Doping of Semiconducting Armchair Graphene Nanoribbons. J. Am. Chem. Soc. 2015, 137, 8872−8875.


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Table 1. Formation energies (eV) computed for monodoped and dual doped monolayer graphene, at the VDW-DF/DZP and M06-L/6-31G* levels. Formation Energy AlB AlN AlO PB PN PO SB SN SO SiBpara SiN SiO B N O Al Si P S

5×5

7×7

8×8

5×5

6 ×6

7×7

8×8

VDW-DF -3.80 -4.55 -2.77 -6.33 -5.51 -3.45 -5.57 -4.07 -3.88 -6.39 -6.28 -4.45

VDW-DF -3.96 -4.65 -2.84 -6.41 -5.57 -3.49 -5.61 -4.16 -3.91 -6.53 -6.35 -4.51

VDW-DF -3.94 -4.63 -2.78 -6.37 -5.52 -3.42 -5.57 -4.11 -3.85 -6.40 -6.30 -4.45

M06-L -3.55 -3.97 -2.14 -6.37 -5.01 -2.85 -5.38 -3.42 -3.30 -6.11 -5.72 -3.85 -5.05 -3.50 0.46 2.58 -0.55 -0.09 1.39

M06-L -3.43 -4.00 -2.15 -6.37 -5.00 -2.81 -5.36 -3.43 -3.29 -6.11 -5.71 -3.86

M06-L -3.50 -4.02 -2.14 -6.39 -4.99 -2.81 -5.39 -3.47 -3.28 -6.17 -5.72 -3.84

M06-L -3.50 -4.04 -2.15 -6.40 -4.99 -2.80 -5.40 -3.50 -3.27 -6.23 -5.73 -3.84


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2. Difference between the formation energies (eV) computed for 5×5 dual doped graphenes and the sum of the formation energies of 5×5 monodoped graphene, at the M06-L/6-31G* level. 5×5 EformXY Σ(EformX+EformY) AlB -3.55 -2.47 AlN -3.97 -0.92 AlO -2.14 3.04 PB -6.37 -5.14 PN -5.01 -3.59 PO -2.85 0.37 SB -5.38 -3.66 SN -3.42 -2.11 SO -3.30 1.85 SiB -6.11 -5.60 SiN -5.72 -4.05 SiO -3.85 -0.09 a ∆ = EformXY - Σ(EformX+EformY)

∆a -1.08 -3.05 -5.18 -1.23 -1.42 -3.22 -1.72 -1.31 -5.15 -0.51 -1.67 -3.76


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Table 3. Magnetic moments (µB) computed at the VDW-DF/DZP level of theory for monodoped and dual doped 8×8 monolayer graphene. System AlB AlN AlO SiB SiN SiO PB PN PO SB SN SO B N Al Si P S a

µ 0.00 0.00 1.00 0.00 0.95 0.00 0.00 0.00 1.0 0.06 0.69 0.0 0.00 0.00 0.00 0.00 1.00 0.00

∆E(eV)a

0.07

0.028 0.006 0.131 0.116 0.096

Energy difference between the calculation with fixed spin (µB =1) and the energy obtained when the

magnetic moment was allowed to vary. The calculation with variable magnetic moment is always lower in energy.


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 4. Band gaps (eV) determined for monolayer graphene doped with one 2p element (B, N, O) and one 3p element (Al, Si, P and S). M06-L 5×5 6×6 AlB 0.19 0.03 AlN 0.13 0.09 AlO 0.12/0.19 0.18/0.14 SiBpara 0.31/0.33 0.04/Ma SiN 0.38/0.05 0.06/0.03 SiO 0.05 0.14 PB 0.30 0.06 PN 0.37 0.08 0.17/0.12 PO 0.22/0.53 SB 0.37/0.40 0.02/0.05 0.17/M SN 0.58/0.54 SO 0.17 0.13 B 0.23/0.26 0.03/M N 0.31/0.24 M/0.04 O 0.60 M Al 0.19/0.34 0.05/M Si 0.10 0.02 0.15/0.15 P 0.71/0.61 S 0.52 0.02 a M denotes Metal character.

7×7 0.11 0.08 0.10/0.09 0.17/M 0.22/0.05 0.02 0.16 0.08 0.13/0.29 0.23/0.23 0.34/0.34 0.09 0.12/M M/0.13 0.37 0.13/0.05 0.06 0.44/0.37 0.29

8×8 0.10 0.07 0.08/0.06 0.13/0.13 0.18/0.08 0.02 0.13 0.17 0.11/0.24 0.19/0.19 0.28/0.30 0.08 0.11/0.03 0.06/0.11 0.35 0.11/0.16 0.05 0.39/0.31 0.24

5×5 0.25 0.20 0.26/0.31 0.44/0.51 0.50/0.06 0.03 0.36 0.45 0.37/0.73 0.54/0.59 0.84/0.80 0.22 0.37/0.48 0.53/0.37 0.78 0.38/0.70 0.06 0.94/0.82 0.61


HSEH1PBE 6×6 7×7 0.03 0.15 0.12 0.12 0.28/0.21 0.17/0.14 0.13/M 0.25/0.11 0.12/0.03 0.28/0.03 0.22 0.03 0.10 0.19 0.13 0.24 0.24/0.19 0.21/0.40 0.06/0.18 0.33/0.34 0.37/0.18 0.50/0.50 0.19 0.19 0.10/M 0.20/M M/0.12 M/0.21 M 0.51 0.20/M 0.25/0.27 0.02 0.04 0.35/0.36 0.57/0.51 0.05 0.36

8×8 0.10 0.07 0.12/0.11 0.19/0.25 0.23/0.04 0.02 0.13 0.17 0.11/0.24 0.19/0.19 0.44/0.44 0.08 0.17/0.12 0.15/0.17 0.46 0.21/0.36 0.03 0.49/0.41 0.28

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Table 5. Difference between the band gaps (eV) determined for 8×8 dual doped monolayer graphene doped and monodoped graphene, at the HSEH1PBE/6-31G* level. System XY GapXY AlB 0.10 AlN 0.07 AlO 0.12/0.11 SiBpara 0.19/0.25 SiN 0.23/0.04 SiO 0.02 PB 0.13 PN 0.17 PO 0.11/0.24 SB 0.19/0.19 SN 0.44/0.44 SO 0.08 B 0.17/0.12 N 0.15/0.17 O 0.47 Al 0.21/0.36 Si 0.03 P 0.49/0.41 S 0.28 aA negative value indicates that the band gap

GapXY-GapXa -0.11/-0.26 -0.14/-0.29 -0.09/-0.25 0.16/0.22 0.20/0.01 -0.01 -0.36/-0.28 -0.32/-0.24 -0.38/-0.17 -0.09/-0.09 0.16/0.16 -0.20

GapXY-GapYb -0.07/-0.02 -0.08/-0.10 -0.35/-0.36 0.02/0.13 0.08/-0.13 -0.45 -0.04/0.01 0.02/0.0 -0.46/-0.23 0.02/0.07 0.29/0.27 -0.39

of XY dual doped graphene is lower than that computed

for X doped graphene. b-

A negative value indicates that the band gap of XY dual doped graphene is lower than that computed

for Y doped graphene.


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Figure 1. 5×5 unit cells employed for ortho (a) and para (b) XY dual doped graphene.


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Figure 2. Band structure determined for SiB dual doped 8×8 monolayer graphene, at the VDW-DF/DZP level. a) SiB spin up, b) SiB spin down.


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Figure 3. Band structures determined for SB dual doped 8×8 monolayer graphene, at the VDW-DF/DZP level. a) SB spin up, b) SB spin down.


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Figure 4. Band structure determined for SN dual doped 8×8 monolayer graphene, at the VDW-DF/DZP level. a) SN spin up, b) SN spin down.


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Figure 5. Band structure determined for SiN dual doped 8×8 monolayer graphene, at the VDW-DF/DZP level. a) SiN spin up, b) SiN spin down.


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Figure 6. Band structures determined for AlO dual doped 8×8 monolayer graphene, at the VDWDF/DZP level. a) AlO spin up, b) AlO spin down.


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Figure 7. Band structures determined for PO dual doped 8×8 monolayer graphene, at the VDWDF/DZP level. a) PO spin up, b) PO spin down.


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Figure 8. Band structures determined for AlB dual doped 8×8 monolayer graphene, at the VDWDF/DZP level.


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Figure 9. Band structures determined for AlN dual doped 8×8 monolayer graphene, at the VDWDF/DZP level.


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Figure 10. Band structures determined for SiO dual doped 8×8 monolayer graphene, at the VDWDF/DZP level.


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Figure 11. Band structures determined for PB dual doped 8×8 monolayer graphene, at the VDWDF/DZP level.


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Figure 12. Band structures determined for PN dual doped 8×8 monolayer graphene, at the VDWDF/DZP level.


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Figure 13. Band structures determined for SiO dual doped 8×8 monolayer graphene, at the VDWDF/DZP level.


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Graphical


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Band Gap Opening in Dual-Doped Monolayer Graphene - American

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