Ab Initio Study of the Vibrational Signatures for the Covalent ...Ab Initio Study of the Vibrational Signatures for the Covalent Functionalization of Graphene Ahmed M. Abuelela,†,‡

Ab Initio Study of the Vibrational Signatures for the CovalentFunctionalization of GrapheneAhmed M. Abuelela,†,‡ Rabei S. Farag,† Tarek A. Mohamed,† and Oleg V. Prezhdo*,‡

†Department of Chemistry, Faculty of Science, Al-Azhar University, Nasr City, Cairo 11884, Egypt‡Department of Chemistry, University of Rochester, Rochester, New York 14642, United States

*S Supporting Information

ABSTRACT: The present work reports a theoretical study of the infrared (IR) andRaman spectra of chemical structures that are useful for the description of thesurface chemistry of carbon materials. There has been a recent demand in materialsscience and surface functionalization to couple organic entities with sp2 carbonnanostructures. A slab model of single-layer graphene with its edges terminated byhydrogen atoms containing 82 atoms per unit cell was used in our study. Theorganic coupling agent, perfluorophenylazide (PFPA), was used according to arecent experiment [Liu, L.-H.; et al.et al. Nano Lett. 2010, 10, 3754]. Two ab initioDFT functionals, B3LYP and ωB97XD, were adopted to calculate the IR andRaman spectra. The computational approach was tested by comparing thecalculated IR spectra to those obtained experimentally for various referencecompounds. The vibrational features were probed before and after the reaction, andthe changes, arising in both PFPA and graphene spectra as a result of the coupling,were identified. B3LYP gave better agreement with the experimental results than ωB97XD for frequency calculations. The stretchmodes of the azide group, as well as the fingerprint feature of the CF2 axial stretching vibrations, were used to probe the reaction,and the results were in good agreement with the experimental observations. Special attention was paid to the elucidation of theorigins of the G-, D-, and D′-bands in the Raman spectra of graphene. Finally, the predicted assignments were employed tointerpret the IR and Raman spectra obtained experimentally for functionalized graphenes.

1. INTRODUCTION

Graphene, one of the allotropes of elemental carbon (otherexamples include carbon nanotubes, fullerene, and diamond), isa planar monolayer of carbon atoms arranged into a two-dimensional (2D) honeycomb lattice. It has been the subject ofnumerous studies since its discovery in 2004,1 and there areseemingly limitless applications of this form of carbon.2−4

Graphene is a highly stable5 material with unique electronic6,7

and mechanical8,9 properties. Its derivatives have potentialapplications in many areas: electrochemistry and biosen-sors,10,11 energy applications (fuel cells, Li-ion batteries,supercapacitors),12,13 solar cells,14 transparent electrodes,8,10

electronics,10,15 among others. In addition, a distinct band gapcan be generated as the dimension of graphene is reduced intonarrow ribbons with a width of 1−2 nm, producingsemiconductive graphene having potential applications intransistors.16,17 Graphene has clearly risen as an importantand high value material for scientists searching for newmaterials in potential electronic and composite industryapplications.The chemical modification of graphene by covalently

functionalizing its surface potentially allows a wider flexibilityby engineering its electronic structure. Numerous methodshave been developed to functionalize graphene covalently withother molecular species.18,19 Among these, perfluorophenyla-zide (PFPA) covalent functionalization of graphene is well

established. Functionalization of graphene by PFPA perturbs π-conjugation and opens its band gap, thereby changing itselectronic properties from metallic to semiconducting.20 Uponphotochemical or thermal activation, PFPA is converted to thehighly reactive singlet perfluorophenylnitrene (PFPN) bylosing an N2 molecule.

21 This highly reactive cation cansubsequently undergo CC addition reactions with neighbor-ing molecules.22 Graphene, having a network of sp2 C atoms,could in principle undergo an addition reaction with nitrene toform an aziridine adduct. In fact, PFPAs have been successfullyused to functionalize C60,

23 carbon nanotubes,24,24 andgraphene.21

Obtaining information at the molecular level for surfacechemistry on carbon materials is difficult;25 consequently,techniques that can provide direct information about surfacefunctionalization are of primary importance in predicting thestate and applications of carbon materials. In particular,vibrational spectroscopy has been widely used over the pastfour decades to characterize pyrolytic graphite, carbon fibers,glassy carbon, pitch-based graphitic foams,26 nanographiteribbons,27 fullerenes,28 carbon nanotubes,29,30 and graphene.31

However, the vibrational spectra of carbon materials are

Received: June 12, 2013Revised: August 28, 2013Published: August 29, 2013

Article

pubs.acs.org/JPCC

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difficult to obtain because of issues in sample preparation, poortransmission, uneven light scattering related to large particlesize, etc. Moreover, the electronic structure of carbon materialsresults in a complete absorption band through the visible regionto the infrared. Fortunately, some of these problems can beovercome by improving the sample preparation (e.g., carbonfilms) and by using more recently developed IR and Ramantechniques, such as diffuse reflectance Fourier transform IRspectroscopy and surface enhanced Raman spectroscopy.32

Aside from the technical difficulties in obtaining the vibrationalspectra of carbon materials, their interpretation is oftenproblematic because not all of the observed absorption bandscan be assigned unequivocally to specific molecular motions offunctional groups, most likely because of the overlap of severalbands, as well as fundamental coupling. In some cases, it is notuncommon that some band assignments differ substantiallyamong the recent vibrational studies on carbon materials.The current work reports an ab initio analysis of the infrared

and Raman spectra of a graphene sheet functionalized withPFPA in the 4000−200 cm−1 range. The calculation of thevibrational spectra is much more time-consuming thanelectronic and geometric structural optimization,33 since itrequires normal-mode analysis involving second derivatives ofenergy with respect to nuclear displacements. Density func-tional theory (DFT) calculations are widely used to simulatethe vibrational spectra for molecules of relatively moderatesize.34,35 The calculations are greatly facilitated by theavailability of analytical second derivative techniques,36 whichreduce the computational cost, making the vibrationalfrequency calculations of larger molecules possible.37 Inaddition, semiempirical dispersion-corrected functionals(DFT-D) have recently been developed to treat the dispersioneffects, which have been demonstrated to be a useful andaffordable method for studies involving large polynucleararomatic molecules and molecules on metal surfaces.38 In thiswork, we test the well-known (DFT) hybrid functional B3LYPagainst the (DFT-D) dispersion corrected functional ωB97XDin the context of vibrational spectra calculations.

2. METHODSThe structural optimization of large functionalized-graphenesystems presents significant computational challenges, sincesubtle changes in the initial guess and the subsequent drift innuclear positions during optimization can lead to saddle pointsand local energy minima. Imaginary vibrational frequenciesassist in identifying saddle points while obstructing the normal-mode analysis of the global minima. Trapping in local minimacan misrepresent the structure as well as the vibrational signals.Moreover, locating the global energy minimum generallyrequires a high computational cost. The difficulties of geometryoptimization originate from two factors: PFPA is relatively highin flexibility and mobility with respect to the graphene surface,and there is a large conformational space of long PFPAmolecules to sample.The initial geometry of the slab model was used for the

graphene sheet with an optimized C−C bond length (1.435 Å,Figure 1). We will use the abbreviation PFPA for the couplingagent before it binds to the graphene and the abbreviationPFPN after it binds to the graphene. The geometry wasoptimized using plane-wave DFT, implemented using theVienna ab initio simulation package (VASP).39 Then onemolecule of PFPN (after eliminating N2) was added to theoptimized graphene sheet, and the geometries of the combined

graphene−PFPN systems were optimized. We added oneadditional PFPN molecule to account for the stability of thecoverage ratio on the graphene sheet. Depending on thecoverage, the number of atoms in the unit cell fell in the rangefrom 82 (bare graphene) to 120 (graphene with two PFPNspecies). The VASP simulations were carried out in a cubic cellthat was periodically replicated in three dimensions. To preventspurious interactions between the system’s periodic images, thecell was constructed to have at least 10 Å of vacuum spacebetween the replicas. All atoms in the unit cell were allowed torelax, and the force tolerance was set at 0.0157 eV/Å. ThePerdew, Burke, and Ernzerhof (PBE) DFT functional40 and aconverged plane-wave basis were used. The core electrons weretreated using the projector-augmented wave (PAW) ap-proach.41

The geometries obtained in VASP were optimized furtherusing the hybrid B3LYP functional42 with atomic Gaussianbasis sets 6-31g(d,p) for the PFPN−graphene systems usingthe Gaussian 09 software package.43 To evaluate its perform-ance in the context of simulating the vibrational spectra,ωB97XD57 was also used. The electrons of the elementsforming the graphene core were treated via effective corepotentials (ECPs), which include relativistic effects that areimportant in these systems. The energy minima with respect tothe nuclear coordinates were obtained by simultaneousrelaxation of all geometric parameters using the gradientmethod of Pulay.44 Full convergence was achieved with themaximum component of the force below 0.000 45 mdyne andthe maximum displacement below 0.0018 Ǻ. The optimizedstructures are shown in (Figure 1).By use of the optimized minima, the theoretical Raman and

infrared frequencies were predicted using B3LYP and ωB97XDmethods. The calculated Raman spectra were simulated fromDFT predicted frequencies and Raman scattering activities. TheRaman scattering cross sections (∂σj)/(∂Ω), which areproportional to the Raman intensities, can be calculated fromthe scattering activities and the predicted frequencies for eachnormal mode.45 To obtain the polarized Raman scattering crosssections, the polarizabilities are incorporated into Sj by [Sj(1 −ρj)/(1 + ρj)], where ρj is the depolarization ratio of the jthnormal mode. Sj can be expressed as

α β= +S g (45 7 )j j j j2 2

where gj is the degeneracy of the vibrational mode, j and αj arethe derivatives of the isotropic polarizability, and βj is that ofthe anisotropic polarizability. The Raman scattering crosssections and calculated frequencies were used together with aLorentzian function to obtain the calculated spectrum.Infrared intensities were calculated based on the dipole

moment derivatives with respect to the Cartesian coordinates.

Figure 1. Optimized geometries of (A) 1.14 nm wide graphenenanoribbon with the edges terminated by hydrogen atoms, (B)functionalized graphene with one PFPN at the center, and (C)functionalized graphene with two PFPN, one at the center and one atthe edge.

The Journal of Physical Chemistry C Article

dx.doi.org/10.1021/jp405819b | J. Phys. Chem. C 2013, 117, 19489−1949819490

The derivatives were taken from the DFT calculationtransformed to the normal coordinates using

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3. RESULTS AND DISCUSSIONOne advantage of the covalent functionalization of graphenewith polymers is that the addition of long polymer chains canfacilitate the solubility of graphene in a wide range of solvents,even at a low degree of functionalization.21 The resultingsoluble graphene can further undergo in situ polymerizationswith immobilized functional groups. Although it is importantfor solubility, the side chains of PFPA are not crucial to thevibrational properties of this nanocomposite. As such, wereplaced the side chains of PFPA with methyl (−CH3) groupsin order to simplify the vibrational spectra calculations.3.1. Stability and Geometric Structures of the

Graphene−PFPN Systems. The adsorption energy of thefunctionalized graphene has been calculated for the sheet with aPFPN in the center (Figure 1B) and for the sheet with twoPFPN species, one in the center and one at the edge (Figure1C). The adsorption energy for the graphene−one-PFPNsystem was calculated according to the equation

= − −

E

E E E

(sheet/PFPN)

(sheet/PFPN) (sheet) (PFPN)ads

The values obtained using the B3LYP and ωB97XD functionalswere 1.48 and −19.64 kcal/mol, respectively. After the additionof the second PFPN to the edge site of the sheet, theadsorption energy was calculated according to the equation

= − −

E

E E E

(sheet/(2 PFPN))

(sheet/(2 PFPN)) (sheet) (2 PFPN)ads

The B3LYP and ωB97XD functionals gave −26.92 and −72.16kcal/mol, respectively. The adsorption energy decreased by25.4/52.5 kcal/mol (B3LYP/ωB97XD) after the addition ofthe second PFPN. This indicates that the second addition iseasier, and the system stability is raised by increasing thecoverage of the graphene surface. The first attack is much moredifficult because the graphene sheet is intact. After this firstattack, the geometry of the graphene sheet is distorted, and thesheet is no longer fully planar. The created defects facilitate thesecond attack. Here, ωB97XD gives qualitatively better resultsthan B3LYP. B3LYP predicts that ligand adsorption onto thegraphene sheet is energetically unstable, in contradiction withthe experimental data. On the contrary, ωB97XD favorsadsorption. Although ωB97XD was originally proposed toinclude atom−atom dispersion corrections for noncovalentinteractions, it performs noticeably well for covalent systems aswell.46

The structural parameters for PFPA before and after it iscovalently bonded to the graphene sheet are listed in (Table 1).

The PFPA undergoes a CC addition reaction; two singlebonds are generated between it and the sheet, owing to theconversion of a conjugated CC bond of graphene to a singlebond. According to the calculated structural parameters, thebond length between the C atom of graphene and the N atomof the adduct is approximately 1.43 Å, typical of a single C−Nbond, indicating covalent bond formation. The C atom and itsnearest neighbors in graphene is approximately 1.591 Å,notably larger than the C−C bond length of 1.47 Å of graphenewith sp2 hybridization, which indicates bond breaking. The C−C bond lengths in graphene beyond its nearest neighbors arefound to be negligibly affected by the functionalization. On theother hand, the plane of the sheet is largely affected afterbinding to PFPA. For example, the τ(C−C−C−C) of thebenzene ring was ∼0.001−0.002° (Table 1); however, itbecomes 13.39° after binding, showing that the binding causesa curvature in the plane of benzene ring. For the secondaddition, this value shifts to −14.4° for the central PFPN, whilethe one at the edge causes a change of only −9.24°.

3.2. Vibrational Assignment. The vibrational spectrumcan be studied from two different perspectives, and we willtherefore divide this part into two sections.

3.2.1. Probing Changes Relative to the PFPA Spectrum.The vibrational spectra of organic azides have been investigatedpreviously, both experimentally and computationally.47,48

However, a brief discussion of the vibrational assignments isrequired for the sake of comparison of the PFPA spectra before

Table 1. Geometrical Parameters of PFPA and PFPNObtained with B3LYP and ωB97XD Using 6-31G(d,p)a

B3LYP ωB97XD

bond length/angle PFPA PFPN PFPA PFPN

Methylaminocarbonylr(C7−C14) 1.516 1.512 1.513 1.510r(C14−N16) 1.363 1.366 1.357 1.359r(C14O15) 1.223 1.224 1.217 1.218r(N16−C17) 1.454 1.452 1.449 1.447r(N16−H18) 1.008 1.008 1.006 1.006r(C17−H21) 1.090 1.090 1.090 1.090∠(C7−C14−N16) 115.5 115.5 115.4 115.1∠(C7−C14−O15) 120.7 121.1 121.0 121.2∠(C14−N16−C17) 121.5 121.7 120.7 121.5τ(C−C−N−C) 176.8 −176.9 176.1 −176.1τ(C−C−O−N) 178.3 −178.4 178.1 −178.3

Benzene Ringr(CC) 1.388 1.387 1.385 1.385r(C−F) 1.338 1.354 1.341 1.343∠(C5−C−C9) 117.0 116.0 117.2 116.7∠(C4−C5−F) 119.7 119.8 119.7 120.0

Azide Groupr(N1N2) 1.137 1.129r(N2N3) 1.245 1.241∠(N−NN) 10.79 10.27τ(C−NNN) 179.8 179.6

Graphene Sheetr(C−C) 1.435 1.591 1.577τ(C−C−C−C) 0.001 13.39 0.002 14.69

aThe bond lengths and angles are in Ǻ and degrees, respectively. Theatom numbers are defined in Figure 4.



and after binding to the graphene sheet in order to probe theeffects of the attachment. Figures 2 and 3 represent the

simulated infrared and Raman spectra of PFPA before and afterbinding in the spectral range of 4000−200 cm−1. The normalmodes for perfluorophenylazide can be distributed betweenthree sets of fundamental vibrations, those arising from themethylcarbamoyl group, from the fluoro-substituted ring, and

from the azide group (see Figure 4 for a few selected vibrationalmodes).It is worth mentioning that vibrational frequencies obtained

by quantum chemical calculations are typically larger than theirexperimental counterparts, and thus, empirical scaling factorsare often used to match the experimental data.49 It isemphasized that the theoretical data reported herein were notscaled, since the current work focuses on the changes in thePFPA spectra induced by binding to the graphene sheet ratherthan on the absolute values of the frequencies.

3.2.1.1. Assignment of Methylcarbamoyl (Methylamino-carbonyl). The methylcarbamoyl group could be in either cis ortrans configuration, depending on the orientation of thehydrogen and oxygen atoms with respect to each other,which in turn affects the frequencies positions. We adopted themost stable trans configuration (see Figure 4).The hydrogen-bonded NH stretch appears strong and fairly

broad, in the region of 3315 ± 45 cm−1.50 The calculatedspectra (Figures 2 and 3) of the B3LYP functional show a weakband at 3663 cm−1, which was predicted at 3706 cm−1 using theωB97XD functional. This calculated absorbance is assigned tothe free NH stretching vibration, which is relatively higher thanthe observed absorbance because of the absence of hydrogenbonding interactions, since our calculation is for an isolatedmolecule, presumably in the gas phase.The antisymmetric methyl stretching vibrations, often

observed in the region of 2995−2900 cm−1,50,51 are in goodagreement with those predicted at 3175/3198 cm−1 and 3107/3154 cm−1 using the B3LYP and ωB97XD functionals (Table2), while the symmetric stretch is observed in the region of2870 ± 45 cm−1, clearly separated from the antisymmetriccounterpart.52 The high frequencies usually corresponds to thetrans-RC(O)NHMe rather than to the cis configuration,which explains the good agreement with the recorded value of2915 cm−1 52 and our calculated values of 3040/3067 cm−1

using B3LYP/ωB97XD functionals, which favor the transconfiguration (Table 2).The CO stretching vibration gives rise to a strong band in

the region of 1680 ± 60 cm−1.50 The frequencies tend to be the

Figure 2. Calculated infrared spectra (4000−200 cm−1) of PFPA usingB3LYP functional (green line) and ωB97XD functional (blue line).

Figure 3. Calculated Raman spectra (4000−200 cm−1) of PFPA usingB3LYP functional (green line) and ωB97XD functional (blue line).

Figure 4. Atom numbering and selected normal modes of the PFPA: (A) atom numbering of the optimized structure at B3LYP/6-31g(d,p); (B)CO stretch; (C) ring stretch; (D) azide stretch. The normal mode displacement vectors are shown in blue, and the dipole-derivative unit vectorsare shown in orange.



same when using both the infrared and Raman techniques,although the intensities differ. In the infrared spectra, νCOtends to be among the strongest bands present, while its band isconsiderably weaker in the Raman spectra.51 The calculatedspectrum shows good agreement in both the expected positionand intensity of the CO stretch, at 1782/1834 cm−1(B3LYP/ωB97XD), in both the infrared and Raman spectra(Figures 2 and 3), with a higher intensity in the IR than in theRaman spectrum (Table 2).The CO in-plane deformation is observed with a moderate

to strong intensity in the region of 695 ± 75 cm−1. The COout-of-plane deformation, γCO/NH or γNH/CO, absorbsmoderately in the region 600 ± 70 cm−1. With this vibration,the O and H atoms move simultaneously out of the plane inopposite directions.52 The band calculated at 764/776 and746/758 cm−1 (B3LYP/ωB97XD) could be assigned to the in-plane and the out-of-plane deformations, respectively (Table2).The NH in-plane deformation is coupled to the C−N stretch

(δNH/νC−N), which absorbs only in the range 1550 ± 50cm−1 for the trans configuration,50 although for most of thesecondary amides the δNH makes a larger contribution.52 Thecalculated B3LYP/ωB97XD absorbance at 1582/1597 cm−1 ischaracteristic for a noncyclic monosubstituted amide; therefore,it can be assigned to the above-mentioned mixed mode.

Similarly, the mixed νC−N/δNH vibration usually appears inthe region of 1270 ± 55 cm−1 with moderate to strong infraredintensities, although the C−N stretch is dominant in secondaryamides.51,53 Therefore, the calculated absorbance at 1315/1348cm−1 (B3LYP/ωB97XD) is assigned for this mixed mode.The γNH/CO or ωNH/CO wagging mode is

moderately but broadly observed in the infrared region of735 ± 60 cm−1, in which the O and H atoms movesimultaneously out of the plane in the same direction.54 It isyet unknown whether the γNH or the γCO groupscontribute to a great extent to this vibration; this deformationcould be compared to that of ωNH2/CO in primaryamines.52 Therefore, the calculated B3LYP/ωB97XD frequencyat 815/831 cm−1 could be attributed to this mode.Methyl antisymmetric deformations are usually observed

between 1480 and 1410 cm−1.50,53 The calculated spectra(Figures 2 and 3) show a band at 1520/1529 cm−1 (B3LYP/ωB97XD), which could be assigned to the antisymmetric (in-plane) deformation of the methyl group. The symmetric methyldeformation appears between 1425 and 1375 cm−1,54 whichwas calculated at 1445/1470 cm−1 (B3LYP/ωB97XD) (Table2) and is assigned to the umbrella mode of the methyl group(Figures 2 and 3). The methyl rocks and twists are coupled toN−CMe stretches, and they absorb weakly rather thanmoderately in the IR region. The rock occurs at 1155 ± 30

Table 2. Selected Vibrational Frequencies (cm−1) of PFPA and PFPN

B3LYP ωB97XD

assignment exptl50−52 PFPA PFPN PFPA PFPN IR intensityc Raman activityc

MethylaminocarbonylνNH 3360 3663 3664 3706 3718 5.96/6.06 9.40/0.00νaMe 2995 3175 3175 3198 3197 0.33/38.8 8.59/41.0νaMe 2900 3107 3097 3154 3142 3.78/9.28 20.5/0.84νsMe 2915 3040 3036 3067 3064 9.40/15.9 50.4/0.99νCO 1740 1782 1777 1834 1832 45.8/31.3 11.3/0.22δNH/νCNa 1550 ± 50 1582 1581 1597 1607 30.2/65.4 5.89/19.9δaMe 1480 1520 1523 1529 1527 45.8/60.0 42.8/46.0δsMe (umbrella) 1425−1375 1445 1449 1470 1468 3.81/12.3 50.9/10.0νC−N/δNHa 1270 ± 55 1315 1290 1348 1356 59.3/60.8 35.4/81.7ρMe (rock) 1155 ± 30 1182 1179 1199 1198 4.92/28.5 1.53/4.65ρMe (twist) 1100 ± 65 1150 1152 1162 1156 3.09/8.86 2.10/0.87νN−C 1015 1103 1106 1128 1132 1.83/7.42 4.92/0.93γNH/COa 735 ± 60 815 812 831 839 0.84/7.42 0.99/1.08δCO 695 ± 75 764 763 776 774 3.81/12.6 2.52/1.65γCO 600 ± 70 746 742 758 754 1.98/14.5 0.84/1.26δ−C(O)−N 450 ± 100 428 436 436 444 1.14/7.33 1.26/0.87δ−C−N−C 315 ± 55 282 277 293 300 0.57/1.11 0.96/0.48

Benzene RingνaC−F 1195 ± 90 1171 1158 1199 1189 2.94/8.14 1.50/1.26νsC−F 1195 ± 90 1023 995 1039 1042 19.1/4.23 0.39/1.65ring stretch 1600 1678 1677 1719 1721 12.5/32.7 99.3/4.38

1580 1631 1626 1677 1672 3.51/12.4 2.61/28.61490 1533 1523 1569 1562 24.8/70.3 23.1/43.11440 1441 1436 1482 1476 3.66/12.8 52.9/7.901315 ± 65 1340 1359 1348 1336 4.35/16.7 13.2/11.01000 1020 1023 1038 1042 19.2/14.0 0.51/0.48

Azide Group2169−2080b 2283 2339 99.8 17.41343−1177b 1377 1403 3.51 4.14

aThe first fundamental has a major contribution that is coupled to a small extent to the second fundamental. bInfrared bands only, taken from ref 51.cNormalized infrared intensity and Raman activity multiplied by 102. We have chosen B3LYP to account for the intensities before and after binding,as ωB97XD would be relatively similar by comparison.



cm−1, and the twist is more extensive at 1100 ± 65 cm−1.51−53

Moreover, these modes are very sensitive to the immediateenvironments, so the frequencies and intensities varyconsiderably.51 The calculated spectra show identical agree-ment at 1182/1199 and 1150/1162 cm−1 (B3LYP/ωB97XD)for the rock and twist modes, respectively (Table 2).The N−CMe stretch, essentially, the symmetric counterpart

of the amide vibration, can be found in the region of 1015 ± 95cm−1. The intensity fluctuates between weak and moderate inthe infrared spectrum. Disregarding the high values around1106 cm−1, which is coincident with the methyl rock, themajority of the investigated molecules display the νC−Naround 1050 ± 45 cm−1.50,52 Nevertheless, the calculated bandat 1103/1128 cm−1 (B3LYP/ωB97XD) could be assigned tothis mode, taking into consideration that it is in goodagreement with a higher value recorded around 1106 cm−1.The external −C(O)−N skeletal deformation appears to

have weak to moderate intensities within a wide range of 450 ±100 cm−1, similar to the skeletal C−N−CH3 deformation in theregion of 315 ± 55 cm−1.52 Thus, the bands calculated at 428/436 and 334/340 cm−1 (B3LYP/ωB97XD) can be assigned tothe δ−C(O)−N and γC−N−CH3 modes, respectively(Table 2).3.2.1.2. Assignment of the Fluoro-Substituted Ring.

Benzene, belonging to the point group D6h, has 20 normalmodes of vibrations, of which four are infrared active. Aftersubstitution of an H atom by an F atom, the symmetry islowered from D6h to either C2v or Cs. The stretching andbending fundamentals of the substituent bond not only give riseto phenyl−CF stretching vibrations and a Ph−CF in-plane anda Ph−CF out-of-plane deformation but also influence the ringstretches in-plane and out-of-plane ring deformations. In fact,there is no pure C−F stretching vibrational motion influorobenzene; it is primarily accompanied by some vibrationalmotion of the benzene ring. These coupled ring/Ph−CFvibrations make it difficult to determine which wavenumber canbe attributed to either the Ph−CF stretch or ring vibrations(bending and stretching).52,55 According to Varsańyi andSzöke,56 absorption in the region of 1195 ± 90 and 1090 ±30 cm−1 is primarily due to a C−X stretch in substitutedbenzenes with atomic masses of X < 25 (light atom) and X > 25(heavy atom), respectively. In addition, benzenes with multiplesubstituents were found to absorb at lower wavenumbers.52

Therefore, calculated bands at 1171/1199 and 1023/1039 cm−1

(B3LYP/ωB97XD) could be assigned to the C−F symmetricand antisymmetric vibrations, respectively (Table 2).The benzene ring possesses six ring stretches; the four with

the highest wavenumbers occur near 1600, 1580, 1490, and1440 cm−1.51,52 With heavy atom substituents, these bands tendto shift to somewhat lower wavenumbers. A larger number ofsubstituents on the ring results in broader observed bands. TheB3LYP/ωB97XD calculated bands at 1678/1719, 1631/1677,1533/1569, and 1441/1482 cm−1 could be assigned to the ringgroup vibrations (Figures 2 and 3). The fifth ring stretchingvibration (Kekule ́ vibration) is active near 1315 ± 65 cm−1,51,52which agrees well with the calculated band at 1340/1348 cm−1

(B3LYP/ωB97XD). The sixth ring stretch (ring breathing) issubstituent-sensitive; it appears as a weak infrared band near1000 cm−1 in mono-, 1,3-di-, and 1,3,5-trisubstitutedbenzenes.54 The calculated wavenumber at 1020/1038 cm−1

(B3LYP/ωB97XD) could be assigned to this mode. On theother hand, three or more ring deformations are substituent-sensitive and their utility for identification purposes is very

limited for the organic functionalities attached to graphene. Thering deformations are strongly coupled to the (Ph)−CFstretching vibration, and an interchange with the stretch cannotbe excluded. The ring twist deformation occurring near 695cm−1, on the contrary, is a beneficial group vibration.

3.2.1.3. Assignment of Azide Group. The group frequenciesof organic azides have been studied extensively by Lieber etal.57 The asymmetric NNN group’s stretch falls in theregion of 2169−2080 cm−1 (IR, vs), and the correspondingsymmetric mode appears in the region of 1343−1177 cm−1 (IR,w). Typically, other bands with weaker infrared intensities near2400 and 2200 cm−1 are observed in the case of an unsaturatedmoiety (e.g., Ph, CC, CO) adjacent to the azide group.58The observed splitting of the NNN asymmetric bands isattributed to the Fermi resonance of the NNNasymmetric stretch with the combination tones of NNNand C−N stretches, along with other low-lying frequencies.However, because of the four highly electronegative fluorineatoms in the aryl ring, the splitting disappears in theperfluorophenylazide spectra (Figure 2). We calculated a verystrong IR band at 2283/2339 cm−1 and a weak band at 1377/1403 cm−1 (B3LYP/ωB97XD), which could be assigned toasymmetric and symmetric stretching vibrations, respectively.The asymmetric NNN stretching mode exhibits mediumto strong Raman intensity. Not only is the symmetric modemuch weaker, but it also appears to be more variable in positionthan the asymmetric mode. Accordingly, it appears to be ofnegligible analytical use in the current study.

3.2.1.4. Assignment of the PFPA Fundamentals afterFunctionalization. By comparison of the vibrational spectrumof the PFPA before and after binding, a vibrational signaturethat confirms an attachment can be obtained. Liu et al.21

compared a graphene infrared spectrum before and afterbinding to PFPAs bearing a perfluoroalkyl group. Some of thePFPA vibrational frequencies, which were absent in the IRspectrum of the pristine graphene, appeared in the spectrumafter binding. Intense absorption bands at 1340 and 1140−1200 cm−1 were assigned to CF2(axial) symmetric andasymmetric stretches, respectively. These fingerprints wereused by Liu to confirm the functionalization. However, thosevibrations should be observed for the PFPA whether it hasbound to the sheet or not. A more powerful confirmationwould be the absence of the azide group stretching vibrationfrom the PFPA spectrum after binding to graphene, owing tothe liberation of an N2 molecule. The very strong IR band ofthe azide asymmetric stretch at 2283/2339 cm−1 (B3LYP/ωB97XD) disappeared after binding with graphene (Figures 5and 6 for comparison). A similar result was observed for theweak (IR) band of symmetric stretching at 1377/1403 cm−1

(B3LYP/ωB97XD).The region of 1600−600 cm−1 is referred to as the

fingerprint region, where many vibrational modes are notlocalized, making it useful for molecular characterization beforeand after binding. Thus, we can refer to the hypotheticallocalized motions as being coupled; the delocalized vibrationalmotion involves more atoms in the investigated molecule. Themost relevant region to examine the effect of graphenevibrations on PFPA vibrations is the region between 200 and2000 cm−1 where both graphene and PFPA vibrations stronglyoverlap. It is noted that hydrogen vibrations strongly mix withthe motion of the carbon skeleton, and because of their“artificial presence” in our models, these spectra can onlyprovide a qualitative picture of the effects of functionalization.



Because of the complex nature of these vibrations, it is verydifficult to assign a one-to-one correspondence of modes forpristine and functionalized graphene. Accordingly, we haveselected major vibrational features for the PFPA and itscorresponding modes after binding for comparison (see Table2). A further change that is notable is the increase in theinfrared intensities and Raman activities. Figures 5 and 6 clearlyshow that the IR intensities and the Raman activities increaseafter functionalization by a factor of approximately 1.5−45.5(km/mol) and 1.26−46.3 (Å4/amu), respectively.Another notable difference in frequency is the red-shift of the

fingerprint C−F vibrations (Table 2) by 13 and 28 cm−1 forsymmetric and antisymmetric modes, respectively. These shiftscan be explained by changes in the charge distribution upon thegraphene−PFPN binding. Interaction with graphene decreasesthe polarization of the C−F atoms. The Mullikan charges onthe C11−F16/C13−F18 bonds are (0.302 to −0.262)/(0.310 to−0.277) before binding and (0.285 to −0.274)/(0.278 to−0.273) after binding. As a result, the electrostatic interactionthat contributes to bond strength decreases and νC−Fundergoes red frequency shifts, in good agreement withexperimental data.21 Other than the absence of the azidefundamentals, C−F bond shift, and the increase in intensities,the location of the rest of the bands does not change by morethan 10 wavenumbers.When the orbital coefficients are examined, the most

important factor is their relative magnitudes with respect toone another within that orbital, regardless of sign. Themolecular orbitals correspond essentially to the atoms withthe highest magnitudes. In Figure S1 in SupportingInformation, it is evident that the highest magnitudes comefrom the carbon atoms, even after functionalization. Low

contributions arise from the PFPA atoms, implying that theHOMO and LUMO are localized on the graphene sheet ratherthan the PFPA molecule. This result can also be determinedfrom charge density calculations for the HOMO and LUMO(Figure 7). The sheet has 82 atoms, while the functionalized

sheet has 101 atoms. In the sheet, both the HOMO andLUMO are formed primarily from pz orbitals from the carbonatoms (Figure S1). The carbons lie in the XY-plane, so the pzorbitals lie above and below the CC bonds. In both the HOMOand LUMO, the orbitals have opposite signs. However, in theHOMO, a few opposite signs are not equal, indicating that theHOMO has a bonding character, unlike the LUMO. Theorbitals suggest no significant differences in the frequencies forthe two systems, which would explain the similarity betweenthe experimental spectra of the sheet and the sheet + PFPN.21

3.2.2. Probing the Changes Relative to the GrapheneSpectrum. For sp2 nanocarbons such as graphene and carbonnanotubes, Raman spectroscopy can give additional informa-tion such as crystallite size, clustering of the sp2 phase, thepresence of sp2−sp3 hybridization, as well as the presence ofchemical impurities, the magnitude of the mass density, theoptical energy gap, elastic constants, doping, defects and othercrystal disorders, edge structure, strain, number of graphenelayers, nanotube diameter, chirality, curvature, and metallic vssemiconducting behavior. In this article, we consider threeaspects of calculated Raman spectra, which are sensitive enoughto provide unique information about the changes in graphenestructure.The first spectral feature is called the G-band, and it arises

because of the E2g vibrational mode of sp2 bonded carbon in

graphitic materials, which is common to all sp2 carbon systems.When the bond lengths and angles of graphene are modified bystrain caused by the interaction with a substrate or othergraphene layers (external perturbations), the hexagonalsymmetry of graphene is broken.59 The G-band is thereforehighly sensitive to strain effects in sp2 nanocarbons and can beused to probe any modification to the flat geometric structureof graphene, such as the strain induced by external forces.Usually, a single Raman peak is observed for a 2D graphenesheet at 1582 cm−1. In order to locate the calculated frequencyassociated with the G-band, we analyzed the normal modeswith respect to the nuclei displacement over the range from1595.8 to 1621.6 cm−1 (Figure S2). The vibrations arising fromboth C−C and C−H bonds are highly mixed in this region, sothis procedure is important for resolving these vibrations. Thedisplacement of the normal modes takes place in the XY-plane.In the standard orientation, the Z coordinates for all atoms arezero. When normal modes are interpreted, the signs andrelative values of the displacements of the different atoms havemore relevance to the interpretation than their exact

Figure 5. Calculated infrared spectra (4000−200 cm−1) of PFPA(green line) and graphene−PFPN system (blue line) using B3LYP/6-31g(d,p).

Figure 6. Calculated Raman spectra (4000−200 cm−1) of PFPA(green line) and graphene−PFPN system (blue line) using B3LYP/6-31g(d,p).

Figure 7. Isosurface plot of charge densities of (A) highest occupiedmolecular orbital (HOMO) and (B) lowest unoccupied molecularorbital (LUMO).



magnitudes. Figure S2 shows that the C−C bonds contribute tothe vast majority of the vibration at 1595.8 cm−1. It has thelowest oscillation for hydrogen atoms at the equilibriumpositions, while the C−C bonds oscillate correspondingly andmost effectively among the other vibrations in both positive andnegative directions. In our treatment, we illustrate the motionby showing the paths of the nuclei in both directions; therefore,this vibration could be assigned to the G-band signature (Figure8). This is in reasonable agreement with the experimental value.

The presence of disorder in sp2-hybridized carbon systemsleads to rich and intriguing phenomena in their resonanceRaman spectra. Because of this and the fact that Ramanspectroscopy is one of the most sensitive and informativetechniques to characterize disorder in sp2 carbon materials, ithas become an instrumental tool and is widely used to identifydisorder in the sp2 network of different carbon structures, suchas diamond-like carbon, amorphous carbon, and nanostruc-tured carbon.60 When graphene is attacked, point defects areformed and the Raman spectra of the disordered grapheneexhibits two new sharp features appearing at 1345 and 1626cm−1 (see the inset in Figure 8, taken from ref 61). These twofeatures have been termed the D- and D′-bands, respectively, todenote disorder. Quantifying disorder in a graphene monolayeris usually determined by analyzing the ID/IG intensity ratiobetween the disorder-induced D-band and the Raman-allowedG-band. The D-band is ring breathing (A1g mode) and becomesRaman active after neighboring sp2 carbons are converted to sp3

hybridization in graphitic materials. In order to assign the D-band in the spectrum of graphene attached to the PFPN, weanalyzed the normal modes in the range between 1363 and1392.6 cm−1 (Figure S3). We found that the calculatedfrequency at 1392.6 cm−1 has the lowest contribution from thehydrogen atoms around the equilibrium position rather thanthe carbon atoms of the graphene; therefore, this vibration isattributed to the D-band.Using the same procedure for the analysis of normal modes

(Figure S4), we assigned the calculated band at 1652.7 cm−1 tothe D′-band (Figure 8). It is notable to find that the frequency1677 cm−1 has no contribution to the graphene sheet, as it isattributed to the ring of PFPN, in agreement with PFPN-modesinterpretations after binding (see Table 2 for this particularassignment). We excluded the PFPN atoms to facilitate thenormal-mode analysis; otherwise, the contribution wouldfluctuate strongly around equilibrium in the PFPN atomsregion.

A blue-shift in the G-band also takes place afterfunctionalization, from 1595.8 to 1621 cm−1 (25 cm−1) (Figure8), which agrees fairly well with experimental functionalizationusing nitrophenyl.62 In these experimental results, a blue shiftwas found from 1580 to 1585 cm−1 to the exfoliated grapheneand a red shift from 1586 to 1564 cm−1 to the epitaxialgraphene. It is worth noting that the shift direction (blue orred) of the G-band is difficult to discern when modelinggraphene. Kudin et al.63 investigated this issue intensively fordifferent models of graphene. Computationally, among all ofthe structures that they have considered, only the alternatingpattern of single−double carbon bonds within the sp2 carbonribbons, as well as the Stone−Wales (SW) defects and thedouble vacancy (C2) defects, which is composed of twopentagonal rings and one octagonal ring (5−8−5), yieldsRaman bands of high enough intensity that are blue-shiftedcompared to the G-band of graphite. Also, to obtain single−double bond alternation within extended sp2 carbon areas, it isnecessary to have sp3 carbons on the edges of the carbonribbon. Termination of the edges with hydrogen atoms leads tothe same result and sufficiently mimics the experimental resultsthat we have adopted.The product of the perfluorophenylazide functionalization on

graphene indicates that the introduction of the azide groupsleads to saturated sites in the graphene lattice that may beviewed as internal edges to the conjugated regions, taking1392.6 cm−1 for the D-band as the frequency of a structuraldefect in pristine graphene and graphitic materials with long-range crystalline order and 1652.7 cm−1 for the D′ band, alongwith the blue shift in the G-band.

4. CONCLUSIONS

We performed density functional (both DFT and DFT-D)geometry optimization and frequency calculations on a modelof single layer graphene and its functionalized form to gaininsight into the changes that take place in geometries andvibrational spectra upon graphene functionalization. Weadopted a slab model of 82 atoms for the graphene, terminatedby hydrogen atoms and functionalized by one (G-PFPN) andtwo (G-2PFPN) perfluorophenylazide units. G-2PFPN wasfound to be much more stable than G-PFPN. This finding canbe explained by structure defects and symmetry breaking in theintact graphene plane, as reflected in the geometricalparameters. Introducing sp3 centers in the ring causes a sharpkink in the local structure, which makes the second attack mucheasier. Significant spectral changes are observed uponfunctionalization: the azide fundamental of the PFPA at 2283and 1377 cm−1 disappears and the C−F antisymmetric andsymmetric stretches undergo a red-shift in the fingerprintregion (13 and 28 cm−1). The B97XD functional tends toproduce higher vibrational frequencies than B3LYP, over-estimating the values relative to the experimental frequencies.Bending defects introduced in graphene by chemicalfunctionalization reveal themselves in the Raman spectrum ofgraphene as a blue-shift in the G-band accompanied byappearance of the D- and D′-bands. The normal-mode analysisprovides detailed information regarding the modes involved inthe IR and Raman signals, characterizing the specific types ofnuclear motions generating the spectroscopic data. Accordingto current model calculations, chemical functionalization ofgraphene introduces sp3-type defects, leading to significantchanges in the nanostructure.

Figure 8. Calculated Raman spectra (4000−200 cm−1) of graphene−PFPN system (upper panel) and graphene sheet (lower panel) usingB3LYP/6-31g(d,p). Inset is the experimental spectra61 of (A) defectedgraphene and (B) bare graphene.



■ ASSOCIATED CONTENT*S Supporting InformationMolecular orbital coefficients and normal mode analysis. Thismaterial is available free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*Phone: 585-276-5664. Fax: 585-276-0205. E-mail: [email protected].

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSFinancial support of the U.S. National Science Foundation,Grant CHE-1300118, is gratefully acknowledged.

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Ab Initio Study of the Vibrational Signatures for the Covalent ...Ab Initio Study of the Vibrational Signatures for the Covalent Functionalization of Graphene Ahmed M. Abuelela,†,‡