The Role of the Bridging Atom in Stabilizing Odd NumberedGraphene VacanciesAlex W. Robertson,† Gun-Do Lee,*,‡ Kuang He,† Euijoon Yoon,‡ Angus I. Kirkland,†

and Jamie H. Warner*,†

†Department of Materials, University of Oxford, Parks Road, Oxford, OX1 3PH, United Kingdom‡Department of Materials Science and Engineering, Seoul National University, Seoul, Korea

*S Supporting Information

ABSTRACT: Vacancy defects in graphene with an oddnumber of missing atoms, such as the trivacancy, have beenimaged at atomic resolution using aberration correctedtransmission electron microscopy. These defects are not juststabilized by simple bond reconstructions between under-coordinated carbon atoms, as exhibited by even vacancies suchas the divacancy. Instead we have observed reconstructionsconsisting of under-coordinated bridging carbon atomsspanning the vacancy to saturate edge atoms. We reportdetailed studies of the effect of this bridging atom on theconfiguration of the trivacancy and higher order odd numbervacancies, as well as its role in defect stabilization inamorphous systems. Theoretical analysis using density functional theory and tight-binding molecular dynamics calculationsdemonstrate that the bridging atom enables the low energy reconfiguration of these defect structures.

KEYWORDS: Graphene, ACTEM, HRTEM, electron microscopy, defects, TEM

Understanding the behavior and impact of defects inmaterials is a fundamental requirement in the optimiza-

tion of properties and tuning performance for specificapplications. Graphene has properties that can be engineeredthrough defect addition and manipulation, for instance, bydoping to change the conductivity.1 Modification by substitu-tional doping and functionalization of the graphene sheetrequires either the formation of unsaturated edge states forchemical attachment2−6 or vacancy defects for dopants tooccupy.7−10 However, it is also possible to tailor graphene’sproperties purely through structural changes to the graphenelattice. Carbon atom removal plus restructuring bond rotationscan create vacancy structures that act as metallic nanowires11 ormagnetic centers.12−14

This utilization of atomic vacancies to induce localizedferromagnetic behavior could be of use in spintronicapplications.15,16 Irradiation studies have been conducted onthe effect of vacancies on the magnetic properties ofgraphite,17,18 suggesting a clear correlation does exist. However,the relationship between magnetism and vacancies in graphitecould only be inferred. This shortcoming can be overcome byemploying density functional theory (DFT) to model whethera vacancy structure exhibits a magnetic moment. However, thisapproach requires a realistic atomic structure to initialize thecalculations. The optimal atomic structure for the trivacancyand for larger odd-numbered vacancies has not beenunambiguously established. This is due to an odd number ofatoms requiring at least one carbon atom in the sp2 graphene

system to be under-coordinated. As an illustration, Figure 1a−dshows the accepted atomic models for the graphene mono-, di-,tri-, and tetravacancy, respectively. The stabilization of themonovacancy is achieved by a Jahn−Teller bond reconstructionthat eliminates the 3-fold symmetry of the initial vacancy state,forming a bond between two of the under-coordinated carbonsand leaving one carbon with only two bonds.19,20 For thedivacancy, an even vacancy, reconstructions form across thevacancy leaving all four of the initially under-coordinatedcarbons fully bonded.21 The trivacancy, as with themonovacancy, undergoes bond reconstructions that leave oneunder-coordinated carbon atom. The frequently modeledstructure for the tetravacancy has the fourth atom removedto yield a 3-fold symmetric pattern.22

In this work, we describe an investigation of the trivacancyand the wider family of odd numbered vacancies in the sp2

graphene system. This was achieved by imaging defects atatomic resolution in chemical vapor deposition (CVD) growngraphene using low-voltage aberration-corrected transmissionelectron microscopy (ACTEM). The images were capturedusing the Oxford-JEOL 2200 MCO ACTEM with imagingspherical aberration correctors23 at a beam current density of∼105 e− nm−2 s−1 and an accelerating voltage of 80 kV, where

Received: April 9, 2014Revised: May 19, 2014

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any knock-on damage of carbon from the graphene by electronimpact should be negligible.24 Some of the images shown weretaken using a monochromated source (Figures 2, 3, and 8),permitting the clear resolution of the carbon atoms.23 Thegraphene samples were prepared by CVD growth onto a liquidcopper catalyst,25 followed by transfer via a PMMA scaffold to aholey silicon nitride TEM grid. Graphene defects weregenerated in situ by electron beam irradiation at a high currentdensity within a nanoscale region.26 This allowed for the facileand rapid generation of vacancies suitable for immediate studyand without risking damage to the rest of the sample. ACTEMfigures shown in this manuscript have been subjected to variousfiltering regimes in order to assist the resolution of particularfeatures and the overall bonding structure. A comparison of theeffect of these filters with the unprocessed image is available inpreviously published work.27 Smoothed images had a nearestneighbor (3 × 3) smoothing filter applied. Maximized filteredimages were first smoothed and then had the maximum filter inthe ImageJ software package applied, which replaces a pixel

intensity value with the maximum value of its nearest neighbors(within a 4−6 pixel radius).28 DFT calculations were performedwithin the generalized gradient approximation (GGA) using thePerdew−Burke−Ernzerhof (PBE) functional in the Vienna abinitio simulation package (VASP).29−32 Tight-binding molec-ular-dynamics (TBMD) simulations were calculated using amodified environment-dependent tight-binding carbon poten-tial suitable for carbon sp2 networks.31−35 Multislice TEMimage simulations were calculated with the JEMS softwarepackage36 on atomic models created in Discovery StudioVisualizer with microscope parameters corresponding to theJEOL 2200MCO and its alignment conditions during imaging.Figure 2a shows a smoothed ACTEM image of a graphene

trivacancy defect with a corresponding DFT geometryoptimized atomic model shown in Figure 2b. It is clear thatthe imaged structure is in disagreement with the trivacancyshown in Figure 1c. Rather than relying solely on forming bondreconstructions, in common with the various vacancies shownin Figure 1, the imaged trivacancy defect is instead stabilized

Figure 1. Schematic models illustrating the bonding configuration for increasingly large vacancy structures. Highlighted are the atoms removed (top)and bonds that reconstruct (bottom).

Figure 2. (a) Smoothed ACTEM image of a bridging atom stabilized trivacancy with a false color look up table (LUT). Scale bar is 0.5 nm. (b)Atomic model of the DFT geometry optimized b-trivacancy with the under-coordinated, stabilizing bridging atom highlighted. (c) TEM imagesimulation of the DFT optimized structure. (d) Box-averaged intensity line profiles taken from the dashed boxed regions in (a) and (c). Thedirection of positive x-axis is indicated by the arrows adjacent to the box. (e) TBMD simulation summary, showing the steps involved in the mergingof a monovacancy and a divacancy to form the b-trivacancy (see Supporting Information Movie S1). Dashed lines indicate a bond that forms in thefollowing frame, and a cross denotes a bond that is broken.

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with the remaining under-coordinated carbon atom in a centralbridging position. For this work, we will discriminate betweenthe two trivacancy structures by referring to the type shown inFigure 1c as a reconstructed trivacancy (r-trivacancy), and thestructure presented in Figure 2a as a bridging atom stabilizedtrivacancy (b-trivacancy). Figure 2c shows a TEM imagesimulation calculated using the DFT model shown in Figure 2b,which is in excellent agreement with the experimental image.Box-averaged intensity profiles taken from the dotted rectanglesin both the experimental and modeled images are presented inFigure 2d, confirming the close agreement. Bond lengthmeasurements were extracted from these intensity profiles,corresponding to the distance between minima. Measurementsfrom the bulk area around the defect yielded an average C−Cbond length of 0.142 ± 0.004 nm. We assume that the standarderror found for these bulk measurements is a reasonableapproximation of the error for the measurement of the bridgingatom bond lengths, which is 0.145 ± 0.004 nm for the bottombond and 0.147 ± 0.004 nm for the top bond, which areequivalent within the error. Bond lengths extracted from thesimulated image agree with there being no variation betweenthe two bond lengths, although they are found to lie justoutside the error range at 0.150 ± 0.004 nm.The DFT calculated formation energy for the r-trivacancy

structure shown in Figure 1c is 1.55 eV lower than the b-trivacancy. However, we have not imaged this r-trivacancy in asizable data set of images of graphene vacancies, despite thelower formation energy compared to the bridging atomstabilized structure. Interestingly the r-trivacancy has been

recorded by Wang et al. in an ACTEM study of ion irradiatedgraphene.7 We attribute this discrepancy to the differentmethod used for defect creation with the work of Wang et al.using high velocity ions to bombard the graphene sheet, ratherthan creating defects with an electron beam. We hypothesizethat a single sufficiently energetic and massive incident ioncould potentially eject all three adjacent carbon atoms due to itssize, essentially removing the three highlighted atoms in Figure1c together. However, an electron collision is limited tosputtering a single carbon atom, forming a monovacancy, whichin turn can form divacancies under continued irradiation due tothe increased sputtering cross-section of the under-coordinatedcarbon.21 Within this model, higher order vacancies wouldmostly form from mono- and divacancy migration andagglomeration. TBMD calculations, shown in SupportingInformation Movie S1 and summarized in Figure 2e, suggestthat the formation of a b-trivacancy rather than a r-trivacancy ispreferred when a monovacancy merges with a divacancy.Interestingly, through spin-polarized DFT calculations wefound that the b-trivacancy exhibits a magnetic moment of1.92 μB, significantly higher than the 1.02−1.04 μB calculatedfor the r-trivacancy formed through ionic bombardment.37,38

An example of the formation and elimination of a b-trivacancy is shown in Figure 3. Starting from an initialextended armchair hexavacancy (Figure 3a), the defect initiallysplits into a divacancy and a b-trivacancy following theincorporation of an additional carbon adatom (Figure 3b).The b-trivacancy defect is subsequently quenched by a furtheradatom, leading to two adjacent monovacancies (Figure 3c)

Figure 3. (a) Smoothed ACTEM image and accompanying atomic model of an extended armchair six atom vacancy. (b) The addition of an atomcauses the initial defect to split into a divacancy (top left) and a b-trivacancy (bottom right). (c) An atom is incorporated into the b-trivacancy alongthe bridging unit, transforming the b-trivacancy into two adjacent monovacancies. (d) The two monovacancies reconfigure into a divacancy. Timestamps indicate the elapsed time (seconds) from (a). Scale bar is 0.5 nm for all cases. (e,f) Two detailed pathways for the defect reconfigurationconsistent between the data in frames (a) and (b). The red dot indicates the addition of a carbon atom, crosses show bond breakage, dotted linesindicate bond formation, and arrows indicate a SW bond rotation.

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that in turn reconfigure into a divacancy (Figure 3d). Acomparison of intensity profiles across both the b-trivacancybridging atom and the double bridging unit of the two adjacentmonovacancies is presented in Supporting Information FigureS1, showing clearly the addition of a further atom to thebridging bond. This two atom bridging chain is the same as thatproposed by Hashimoto et al. to explain images they obtainfrom early high-resolution TEM studies of graphene.39 Thebonding reconfigurations between Figure 3a,b are shown inmore detail in Figure 3e,f, where the two possible pathways forthe inclusion of an additional carbon atom and the subsequentbonding reconfiguration are highlighted. In Figure 3e, the initialincorporation of a carbon atom forms a structural unitcontaining a stabilizing bridging atom. This bridging atom isable to easily switch bonding with neighboring carbons due tothe low energy barrier of 2.11 eV required for bond switchingthat we calculate from DFT. TBMD simulation studies havefound under-coordinated adatoms in dislocation formationperform a similar bond switching role.34 Figure 3e shows howthis low energy barrier enables the bridging atom to reconfigurethe defect into the structure observed in Figure 3b. Figure 3fpresents an alternate path, where the atom addition isaccompanied by three Stone−Wales (SW) bond rotations togenerate the observed structure. However, the energy barrierfor a SW rotation in defective graphene of 5.2eV is significantlyhigher than the 2.11eV required for bridging atom rebonding.31

Considering these energy barriers, the pathway illustrated inFigure 3e with the bridging atom acting to mediate in the defectreconfiguration is the more plausible.The bridging atom forms in the trivacancy in order to

stabilize a vacancy defect that has an odd number of under-coordinated edge carbons. It follows that bridging atoms shouldalso stabilize higher order odd numbered vacancies, such aspenta- and heptavacancies. In Figure 4, we show observationsof the formation of a pentavacancy stabilized by a singlebridging atom (b-pentavacancy). A single atom is initiallysputtered from a tetravacancy (Figure 4a) to form a b-

pentavacancy. The b-pentavacancy (Figure 4b) resembles anextended armchair vacancy, however, rather than beingextended along a single armchair axis, as with the hexavacancyin Figure 4d,h, the b-pentavacancy is split across two adjacentparallel armchair axes. The bridging atom unit of the b-pentavacancy resembles that found in the b-trivacancy. InFigure 4c, the bottom half of the b-pentavacancy switches to anadjacent lattice plane, likely through two bridging atommediated bond reconfigurations, due to the lower energybarrier for bond reconfigurations involving the bridging atom,as discussed for the formation of a b-trivacancy in Figure 3. Afurther sputtering event leads to the formation of an extendedarmchair hexavacancy (Figure 4d).Odd numbered vacancies extending along the armchair axis

were observed to form an alternate bridging atom stabilizedstructure to that shown in Figure 4. Figure 5a shows a b-heptavacancy extended along the armchair axis and, unlike theextended armchair b-pentavacancy shown in Figure 4, remainsalong the original armchair axis instead of breaking on to anadjacent parallel axis at the bridging atom. Another notabledifference in the atomic structure between the two armchairodd numbered vacancies is the presence of a 5-membered ringon either side of the bridging atom bond in Figure 5a defect.Inspection of the images in Figure 5 shows the bridging atom

exhibits a flex angle (<180°) between the two bridging bonds.The direction of this flex switches between left and right-handed directions in Figure 5a to b, following a SW bondrotation between Figure 5a and b (arrows). A similar set ofobservations is presented in Supporting Information Figure S2with a SW rotation apparently initiating a switch in the bridgingatom flex direction. A geometry optimization of the imaged b-heptavacancy structure by DFT did not replicate the observedbridge bond flex, instead yielding a straight bridging bond asobserved with the b-trivacancy in Figure 2a (see SupportingInformation Figure S3). However, further detailed study of theimaged b-heptavacancy demonstrated that a small contractionoccurs between the armchair lattice planes parallel to the defect

Figure 4. Smoothed ACTEM images showing the formation of a bridging atom reconstruction in an extended armchair vacancy. (a) A 3-foldsymmetric tetravacancy. (b) The removal of an atom leads to the formation of a b-pentavacancy with a single bridging atom. (c) Two bond switchesmediated by the bridging atom cause a shift in the defect configuration. (d) A further atom is sputtered, yielding an extended armchair hexavacancy.(e−h) Atomic models of the corresponding TEM images. Dotted lines indicate bonds that will form, crosses indicate bonds that are broken, and thearrow indicates an atom to be ejected in the following frame. Time stamps indicate the elapsed time (seconds) from (a). Scale bar is 0.5 nm for allcases.

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axis, which is localized to the area around the vacancy (Figure5e). We determined the exact size of this contraction by usingintensity line profiles to measure the distance between thearmchair axes, both around the defect and in the bulk, yieldinga contraction of (91.4 ± 0.7)%. This observation was notrealized in the initial DFT optimization due to the use of afinite crystal unit cell, preventing any compression fromoccurring. To compensate for this we modified the inputstructure for the calculations to include compression with theresulting geometry optimized structures (Figure 5c,d) present-ing a much better agreement with our experimental images.Insets to Figure 5c,d demonstrate that there are significant out-of-plane distortions due to the compression. Importantly, thesestructures both demonstrate the kink in the bridging bond, andalso agree over the strength of the kink with a stronger bendobservable in image Figure 5b.The odd numbered vacancies shown in Figures 4 and 5 were

both examples of larger odd number vacancies extended alongthe armchair axis. It was found that odd numbered vacanciesextended along the zigzag axis employed a different bridge atomstabilized geometry. Figure 6a shows a maximized filtered TEMimage of an extended zigzag hexavacancy defect, whichincorporates an additional carbon atom (red circle in Figure6c) to form a b-pentavacancy (Figure 6b). TBMD calculationsshow agreement with this atom inclusion (see the first 13 s ofSupporting Information Movie S2 and Supporting InformationFigure S5). Direct interpretation of the TEM image suggeststhat the b-pentavacancy structure requires three bridging atomsin series, as illustrated schematically in Figure 6d. Figures 6e-g

show a further example of the formation of a zigzag b-pentavacancy defect, although instead from an armchairhexavacancy. This switching from an armchair to a zigzagorientation is supported by TBMD calculations (SupportingInformation Movie S3 and Supporting Information Figure S6).Direct interpretation of the TEM image shown in Figure 6galso suggests three bridging atom units are present (Figure 6j),as seen for Figure 6b.The direct interpretation of the atomic structures shown in

Figure 6b,g is that there are three bridging atoms spanning theb-pentavacancy. However, such a model seems intuitivelyunlikely, as it does not minimize the number of under-coordinated carbon atoms, especially as there is clearly thepossibility for bond reconstruction in the models shown inFigure 6d,j. This suggests another possible model for the zigzagb-pentavacancy structure in which the bonding resonatesbetween two metastable states at a frequency greater than thetemporal resolution available, and hence the image recorded isactually a superposition of these states. The two metastablestates necessary for the zigzag b-pentavacancy are illustratedschematically in Figure 7a, both of which reduce the number ofunder-coordinated carbon atoms to one. This resonance modelis similar to the mechanism suggested for the stabilization ofthe graphene monovacancy, where a Jahn−Teller reconstruc-tion oscillates between the three under-coordinated edgeatoms.19,20 To confirm this resonance model we performedTEM image simulations based on the two metastable structuresand then averaged the two aligned images to yield an imagerepresentative of an oscillating resonant state (Figure 7b). Wecontrast this to the literally interpreted b-pentavacancystructure of three fixed bridging bonds, as shown in Figure7c. It was not possible to optimize this structure by DFT, as thegeometry relaxed directly to the metastable structures shown inFigure 7a. Instead the manually constructed defect model inFigure 7c was used to generate the TEM image simulation inFigure 7d. While Figure 7b appears to agree well with theexperimentally imaged structure shown in Figure 7e, it isdifficult to categorically discriminate between either Figure 7panel b or panel d with the resolution available. However,TBMD simulations of the zigzag b-pentavacancy structure(Supporting Information Movie S2) show the oscillation ofbonding expected in the bond resonance model. Summaryimages of this are shown in Figure 7f. This, combined with theenergetic favorability of the metastable structures over thethree-bridged structure, supports the resonance mechanism toexplain the observed b-pentavacancy structure. We also notethat a similar mechanism has recently been proposed to explainresults observed by Zettl et al.40

In addition to the imaging of bridging atom stabilizedvacancies, we have also observed the formation of bridgingatom units in studies of graphene that has been partiallytransformed into amorphous carbon (Figure 8). Figure 8ashows a smoothed ACTEM image of localized two-dimensionalamorphous carbon region within an area of graphene, borderedalong the top, left, and right sides by thicker contamination onthe carbon surface. A magnified image of the region indicatedby the dotted box, Figure 8b, shows individual carbon atomsand a clear observation of a stabilizing bridging atom. Thisresult demonstrates the importance of the bridging atom instabilizing graphene defects beyond simply odd numberedvacancies. Two further images are shown in Figure 8d,g thatwere recorded consecutively after Figure 8a, along withaccompanying magnified views and atomic models. Examina-

Figure 5. An armchair axis b-heptavacancy. (a) Smoothed ACTEMimage showing an extended armchair b-heptavacancy with a bridgingatom stabilizing the defect. (b) Smoothed ACTEM image recordedafter (a) with a single SW rotation near the stabilizing bridge. Thebridging atom switches from a left-hand to a right-hand position in thedefect. Scale bar is 0.5 nm for both cases. (c,d) DFT optimizedgeometries of these structures, initialized with a contracted lattice (seemain text). The arrow indicates the bond that undergoes a SWrotation. Insets show side views of the optimized structures. (e) Awider field of view of the same TEM image shown in (a) withannotations demonstrating a contraction between the armchair latticeplanes localized around the vacancy of (91.4 ± 0.7)%.

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Figure 6. Formation of an extended zigzag b-pentavacancy defect. (a) Maximized filtered ACTEM image of an extended zigzag hexavacancy. (b) Anadditional atom is added to the defect, leading to the formation of a b-pentavacancy that appears to consist of three bridging units. (c,d)Corresponding atomic models to (a,b). The red dot indicates the location of the additional incorporated atom. (e) Maximized filtered ACTEMimage of an extended armchair six atom vacancy. (f) After two SW rotations, the right half of the defect splits onto the neighboring armchair axis. (g)The addition of an atom leads to the formation of a b-pentavacancy defect, apparently stabilized by three bridging atom units. (h−j) Atomic modelscorresponding to the images in (e−g), respectively. Time stamps indicate the elapsed time (seconds) from (e). Scale bars are 0.5 nm for all cases.

Figure 7. (a) DFT optimized geometry atomic models of zigzag b-pentavacancies, proposed as a pair of metastable resonant states for the structureobserved in Figure 6g. (b) Combined average multislice image simulations using the atomic models shown in (a). (c) Atomic model of a zigzag b-pentavacancy without the minimization of the number of bridging atoms. (d) Multislice image simulation of the structure shown in (d). (e)Experimental smoothed ACTEM image of the zigzag b-pentavacancy defect. (f) TBMD frames showing the observed switching between the twometastable states (see Supporting Information Movie S3). Dashed lines indicate bond formation and blue crosses bond breakage.

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tion of these images shows a similar bridging atom mediatedrebonding to that observed in the vacancy structures, due to thelow energy of bond reformation. Figure 8j illustrates atomicmodels for the bond creation and breakage required to obtainthe structures in the subsequent images, and in all cases thesebonding changes focused on the more reactive under-coordinated bridging atom.Conclusion. We have presented observations showing the

behavior of the under-coordinated carbon atom in odd numbergraphene vacancy systems and in 2D amorphous carbon. Theseinclude images showing the atomic structure for the graphenetrivacancy that has not been previously observed or proposed,

which we refer to as a bridging atom stabilized trivacancy.Unlike previous reports, our observations show that an under-coordinated carbon atom may occupy bridging positions thatspan a larger aromatic ring in order to stabilize the defect. Thisbridging atom is able to readily rebond with neighboring carbonatoms due to a low net energy for bond reformation andtherefore is often the site of defect reconfiguration, a findingreinforced by TBMD studies. The images and analysisdescribed demonstrate for the first time the existence ofunder-coordinated carbon atoms in defective grapheneconfiguring as a bridging unit and is therefore important for

Figure 8. (a) Smoothed ACTEM image of a small region of amorphous graphene, adjacent to a layer of contamination (top). (b) Magnified view ofthe boxed region in (a) with a false color LUT applied, showing a bridging atom. (c) Atomic model corresponding to (b). The faded area along thetop corresponds to the area obscured by contamination. (d−i) Two subsequent ACTEM images of the same region, accompanied by magnified falsecolor LUT images and atomic models. (j) Atomic models illustrating the changes in bonding configuration between (a), (d), and (g). Dotted linesindicate bond formation and crosses bond breakage. Time stamps indicate the elapsed time (seconds) from (a). All scale bars are 0.5 nm.

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future studies in defect engineering and optimization ofgraphene.

■ ASSOCIATED CONTENT*S Supporting InformationDetails of the experimental and computational methods, furtherTEM images, a more detailed analysis of the oscillating zigzagvacancy structure, and TBMD movies plus summary figures.This material is available free of charge via the Internet athttp://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Authors*E-mail: (J.H.W.)jamie.warner@materials.ox.ac.uk.*E-mail: (G.-D.L.)gdlee@snu.ac.kr.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSJ.H.W. thanks the support from the Royal Society and BalliolCollege, Oxford. A.W.R. has been supported by EPSRC(Platform Grants EP/F048009/1 and EP/K032518/1). Finan-cial support from EPSRC (Grants EP/H001972/1, EP/F028784/1, and EP/F048009/1) is acknowledged. G.-D.L.and E.Y. acknowledge support from the SupercomputingCenter/Korea Institute of Science and Technology Informationwith supercomputing resources (KSC-2013-C3-058), from theBK21 plus program, and from the National ResearchFoundation of Korea (NRF) grant funded by the Koreagovernment (RIAM No. 2010-0012670, MSIP No.2013003535).

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