Noncovalent Interaction of Graphene with Heterocyclic Compounds: Benzene, Imidazole, Tetracene, and Imidazophenazines Eugene Zarudnev,[a] Stepan Stepanian,[a] Ludwik Adamowicz,[b] and Victor Karachevtsev*[a] Noncovalent functionalization of graphene with organic molecules offers a direct route to multifunctional modification of this nanomaterial, leading to its various possible practical applications. In this work, the structures of hybrids formed by linear heterocyclic compounds such as imidazophenazine (F1) and its derivatives (F2-F4) with graphene and the corresponding interaction energies are studied by using the DFT method. Special attention is paid to the hybrids where the attached molecule is located along the graphene zigzag (GZZ) and armchair (GAC) directions. The interaction energies corresponding to the graphene hybrids of the F1-F4 compounds for the two
directions are found to be distinct, while tetracene (being a symmetrical molecule) shows a small difference between these binding energies. It is found that the back-side CH3 and CF3 groups have an important influence on the arrangements of F1 derivatives on graphene and on their binding energies. The contribution of the CF3 group to the total binding energy of the F3 molecule with graphene is the largest (3.4 kcal mol¢1) (the GZZ direction) while the CH3 group increases this energy of F2 only by 2.0 kcal mol¢1 (the GAC direction). It is shown that replacing the carbons with other atoms or adding a back-side group enables one to vary the polarizability of graphene.
1. Introduction Graphene possesses exceptional mechanical, thermal, optical, and electrical properties, which have attracted great scientific interest among researchers involved in both fundamental investigations and application studies. Some of these properties are already being exploited in technological applications in the areas of nanoelectronics, nanophotonics, biosensors,[4–7] and nanocomposites. To realize the full potential of these applications, efficient approaches and procedures for studying the use of graphene in the areas of materials science and nanotechnology need to be developed. Functionalization of graphene with organic molecules or polymers is one of such approaches. It offers a direct route to multifunctional modification of this nanomaterial which may lead to various possible graphene applications. Among the many research projects aimed at functionalization of graphene, the noncovalent functionalization is preferred because this type of interaction, unlike covalent functionalization, does not disrupt the extended p-conjugation of graphene. In particular, the noncovalent interaction of aromatic rings with graphene is often employed in these systems. Some reviews devoted to the analysis of non[a] Dr. E. Zarudnev, Dr. S. Stepanian, Dr. V. Karachevtsev B.I. Verkin Institute for Low Temperature Physics and Engineering National Academy of Sciences of Ukraine 47 Lenin Avenue, 61103 Kharkov (Ukraine) E-mail: [email protected]
[b] L. Adamowicz Department of Chemistry University of Arizona Tucson, AZ 85721 (USA) Supporting Information for this article can be found under http:// dx.doi.org/10.1002/cphc.201500839.
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covalent interactions between aromatic compounds and graphene have been recently published.[9–14] Several theoretical studies have focused on the interactions between graphene and different heterocyclic aromatic hydrocarbons, such as benzene,[15–25] naphthalene,[18, 21, 24–26] anthracene, pentacene, pyrene,[24, 27–31] coronene,[22, 24, 32] and ovalene.[22, 24] It was established that these flat-structure molecules bind to graphene sheets in the planar stack orientation with the interaction energy which increases with the increasing intermolecular contact area. It has been also shown that there is no significant charge transfer between the noncovalently attached molecules and graphene, and that the electronic structure of graphene is only weakly perturbed by these molecules. The studies also have demonstrated that the dispersion forces are the dominant contributions to the intermolecular interaction while the electrostatic interactions contribute much less to the total binding energy. The dispersion forces can be described by both ab initio and density functional theory (DFT) calculations. Wang and co-workers determined that in the adsorption of benzene on graphene, the dispersion forces represent about 71 % of the total attractive forces, whereas the electrostatic forces contribute only about 25 % to the overall attraction interaction. In contrast, the induction forces add only 4 % to the binding energy in the benzene–graphene complex. In the analysis of the noncovalent p–p interactions between graphene and benzene and hexafluorobenzene it was established that the aromatic fluorine substitution in the benzene molecules results in an increase of the binding energy by about 3 kcal mol¢1.[25, 29] The structural alteration of the benzene molecule in some carbon atoms are replaced by nitrogen atoms
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Articles leads to an increase of the binding energy. However, this increase is not very significant, while adding amino-groups in back sites enhances this energy more significantly. Note that the adsorption of such benzene derivatives as nitrogen compounds (HNCs) on graphene has also been studied.[33–36] The interaction energy between aromatic hydrocarbons and graphene increases upon substitution with both electron-donating and -withdrawing groups, as identified by DFT calculations.[25, 27, 28] It was shown that -CN and -OH groups added to anthracene and pyrene molecules are effective substituents for enhancing binding to graphene. It was determined that the binding energy is sensitive to the detailed atomic alignment of the substituent groups over the graphene sheet. Two backside amino groups added to naphthalene enhance its interaction energy with graphene by 5.2 kcal mol¢1. Note that for a flat configuration of molecules adsorbed on graphene, an increased number of atoms (and electrons) of both the main molecule and substituted groups come in contact with the graphene surface leading to stronger van der Waals interactions. In the present study, we compare the interaction of the following chromophores: imidazo-[4,5-d]-phenazine (F1) and its derivatives (2-methylimidazo-[4,5-d]-phenazine (F2), 2-trifluoromethylimidazo-[4,5-d]-phenazine (F3), and 1,2,3-triazole-[4,5-d]phenazine (F4) (Figure 1) with graphene. Note that these compounds are very perspective in DNA structure studies,[37–40] and the fluorescence study of these dyes shows pH sensitivity of their spectral properties. Pre-resonance Raman and IR absorption spectroscopy techniques were applied to study the influence of substitutes in the imidazole ring of F1 on its vibrational structure.[42, 43] In this work, by comparing the binding of tetracene (TET) (Figure 1) and the above-mentioned compounds with graphene along two different directions of the graphene hexagons, we analyze the influence of the asymmetry of these
Figure 1. Structure of the studied adsorbent molecules: imidazo-[4,5-d]phenazine (F1), 2-methylimidazo-[4,5-d]-phenazine (F2), 2-trifluoromethylimidazo-[4,5-d]-phenazine (F3), 1,2,3-triazole-[4,5-d]-phenazine (F4) and tetracene (TET).
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linear systems on the binding energy. The investigation starts with studying the adsorption of benzene and imidazole which are these systems’ building blocks. We also consider a question how the adding the back-side CH3 (F2) or CF3 (F3) groups to F1 compound influences on the arrangement of the F2 and F3 derivatives along the GAC and GZZ directions and on their binding energies with graphene.
2. Results and Discussion Imidazophenazine and its derivatives (F1-F4, Figure 1) studied here contain four rings, three of them are six-atom rings and one is a five-atom ring. The interaction of graphene with molecules of these four compounds is compared with the graphene interaction of TET which also is a four-ring hydrocarbon. The main difference in the structures of the TET and F1-F4 molecules is the appearance of the imidazole ring in the latter systems and the appearance of the CH3 and CF3 side groups in F2 and F3, respectively. To understand better the contribution of each ring to the total interaction energy of F1-F4 and TET with graphene we first performed DFT calculations of the hybrids formed by benzene and imidazole molecules with graphene. In these calculations the binding energies between the components of these hybrids in selected four characteristic positions of each molecule relative to the graphene surface are determined. 2.1. Binding Benzene and Imidazole with Graphene: Structures and Interaction Energies Benzene and imidazole rings, which are fragments of the studied molecules, may adsorb in several possible configurations on the graphene surface. Among these configurations, only four can be considered as the main configurations, with the remaining ones being intermediate configurations. The geometry for each main configuration is first fully optimized and then the interaction energy is determined. The main configurations of the benzene molecule at the graphene surface (see Figure 2) are: the configuration with the center of the benzene ring positioned directly above a carbon atom of graphene (B1), the configuration with the benzene ring position over “the bridge” connecting two carbon atoms of graphene (B2), the configuration with the benzene ring located over a graphene hexagon (B3), and the configuration with the center of the benzene ring placed over the carbon atom of graphene with some displacement (B4). The calculations show that structures B1 and B2 are the most energetically favorable (the interaction energies being 8.4 and 8.3 kcal mol¢1, respectively) and structure B4 also showing a strong interaction energy (8.0 kcal mol¢1) but less favorable than structures B1 and B2. The symmetrical position of the benzene molecule over the graphene hexagon (B3) is the least favorable and it has the smallest binding energy of only 5.9 kcal mol¢1. This least favorable interaction can be explained by the maxima of the electron densities of benzene and hexagon positioned directly in top of each other (in configuration B3) and repelling.
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Figure 2. Four different locations of a benzene molecule on graphene, in which the benzene ring is situated over: the carbon atom of graphene (B1), two carbon atoms of graphene (B2), the hexagon of graphene (B3), the hexagon of graphene with some displacement (B4).
The equilibrium distances between all the carbon atoms of benzene and the graphene sheet are determined in the calculations. It turns out that all the carbon atoms of benzene are located practically at the same distance from graphene (ca. 3.3 æ), indicating that benzene is adsorbed in a virtually parallel orientation (see Table S1 in the Supporting Information). Note that the present interaction energies for benzene adsorbed on graphene are somewhat smaller than those determined earlier using DFT with empirical dispersion corrections.[15–25] This is consistent with our earlier determination that the latter method overestimates the binding energy of p– p stacked molecules of carbon nanostructures. The same procedure is applied to study structures of the complex formed between graphene and the imidazole ring, and to calculate the corresponding interaction energies (see Figure 3). Similarly as for the benzene molecule, the following four main configurations are selected to search for the equilibrium structures: the configuration with the center of the imidazole ring located over a carbon atom of graphene (Im1), the configuration with the imidazole ring placed over a carbon atom of graphene with some displacement (Im2), the configuration with the imidazole ring located over “the bridge” linking two carbon atoms of graphene (Im3), and the configuration with the imidazole ring situated directly over a graphene hexagon (Im4). It is found that (as in the case of benzene) the most energetically favorable configuration is Im1. Configuration Im2 is less stable than Im1 but more stable than Im3 and Im4. The binding energy of imidazole to graphene in Im1 is ¢7.9 kcal mol¢1. It should be noted that in this configuration the imidazole molecule is slightly tilted relative to graphene. The tilt is 6.4o and causes the N3 atom (see FigChemPhysChem 2016, 17, 1204 – 1212
Figure 3. Four different locations of an imidazole molecule on graphene, in which the imidazole ring is situated over: a carbon atom of graphene (Im1), a carbon atom of graphene with some displacement (Im2), two carbon atoms of graphene (Im3), and a hexagon of graphene (Im4). The interaction energies of the complexes Im1 - Im4 are ¢7.9, ¢6.8, ¢6.3 and-5.0 kcal mol¢1, respectively.
ure S1) to be located the closest to graphene (at distance 3.13 æ) and the C5 atom to be located the farthest from graphene (at distance 3.36 æ). These structural features suggest the existence of a significant attractive interaction between the N3 atom and graphene, which is sufficient to disturb the parallel relative orientation of the two systems. The attractive interaction is due to the positive charge located on the hydrogen atom bonded to the nitrogen atom (N3) being larger (+ 0.26e) (Table S2) than the positive charges of the hydrogens bonded to carbons. Note that for the hydrogen bound with C5 atom the charge is only + 0.12e explaining its more distant position relative to graphene. 2.2. Hybrids Formed by F1, F2, F3, F4, and TET with Graphene As the structures of all the studied adsorbent molecules are elongated in one direction, an analysis is performed to determine how this direction coincides with the two non-equivalent main directions of the graphene surface. The two main directions in graphene are the zigzag (GZZ) direction and the armchair (GAC) direction (see Figure 4). The two directions are important not only for graphene but especially for single-walled carbon nanotubes. The orientation of adsorbent organic molecules along the zigzag and armchair directions of these systems is an important feature, as it corresponds to the two limit values of the chirality angle (08 and 308). Before analyzing
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Figure 4. Optimized structures of TET with graphene along the zigzag (left) and armchair (right) directions.
of the structures of the hybrids formed by F1-F4 with graphene, the location of the symmetrical TET molecule relative the two main directions on the graphene surface is first determined (see Figure 4). A comparison of the interaction energies for two optimized structures of TET along the main directions of graphene shows that the hybrid with the geometry along GAC has somewhat higher value (by 0.2 kcal mol¢1) than that for the GZZ direction (Table 1). This difference in the energy can be explained by the position of TET along GAC being more energetically favorable due to a higher overlap of the tetracene rings with the graphene hexagons (B1) than for the position with TET along GZZ (B4).
Table 1. Interaction energies (Eint, kcal mol¢1) for structures formed by heterocyclic compounds with graphene along the GZZ and GAC directions. D [kcal mol¢1] is the difference between the energies corresponding to the two directions.
Eint along GZZ
Eint along GAC
TET F1 F2 F3 F4
¢23.2 ¢20.3 ¢21.5 ¢22.6 ¢19.2
¢23.4 ¢21.2 ¢23.0 ¢22.3 ¢20.5
¢0.2 ¢0.9 ¢1.5 0.3 ¢1.3
The plane of the TET molecule is bent along the long molecular axis for both positions of the molecule along the two directions of graphene (see Table S3 in the Supporting Information). This causes the carbon atoms in the central rings to be somewhat more distant from graphene than the carbons of the peripheral rings. The largest difference in the distances relative to the graphene plane for the carbon atoms of the outer and central rings is 0.11 æ. The closer location of the carbon atoms of the peripheral rings than of the central rings to graphene is caused by the stronger interaction of the former with the graphene surface due to a larger number of hydrogens in these rings. Note that the delocalized p-electrons of TET make this system more rigid and reduce its deviation from planarity. In the next step, we determine the equilibrium structures of the hybrids formed by F1-F4 with graphene (Figure 5) and calculate the interaction energies between the components of the hybrids (Table 1). These calculations reveal that the binding energy of the F4 molecule with graphene is the smallest ChemPhysChem 2016, 17, 1204 – 1212
Figure 5. Optimized structures of the F1-F4 molecules located along the zigzag (Gzz) and armchair (GAC) directions of graphene.
(19.2 kcal mol¢1), whereas the binding energy of the F2 molecule is the largest (23.0 kcal mol¢1). But even this latter value is smaller than the one obtained for TET on graphene. This can be attributed to the total number of atoms in TET molecule of 30 being larger than in F4 (24 atoms) and in F2 and F3 (28 atoms). A comparison of the interaction energies of F1, F2, F3 and F4 with graphene (see Table 1) reveals that the F1, F2 and F4 molecules have stronger binding energies with graphene along the GAC direction than along the GZZ direction. However, adding a CF3 group to the imidazophenazine structure (F3) makes Gzz the most preferred direction. Note that large differences in the binding energy for the GZZ and GAC directions are
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Articles observed for the F4 (1.3 kcal mol¢1) and F2 (1.5 kcal mol¢1) molecules, while the difference is smaller for the F3 molecule. As the adsorbent molecules (especially F2 and F3) studied here are relatively large, we carry out additional calculations for a complex of a F3 molecule with the larger fragment of the graphene surface (the C150H30 fragment, Figure S2). It is found that adding an extra row of carbon atoms to the graphene sheet does not significantly affect the interaction energy (the difference does not exceed 0.3 kcal mol¢1). Thus, we conclude that the C96H24 fragment of the graphene surface used in the present calculations is sufficiently large to model the interactions between the studied molecules and graphene. Comparing the optimized structures of the graphene complexes with the F1 and F4 molecules reveals that the positions on these systems on the graphene surface along the zigzag direction are practically the same. The larger binding energy observed for the F1 molecule in comparison with the F4 molecule (1.1 kcal mol¢1) can be explained by additional H atoms in the structure of the F1 molecule and by the replacement of a carbon atom with a nitrogen atom in the imidazole ring. Shorter distances between graphene and the atoms of the pentagons of the F1 and F4 molecules in comparison with the corresponding distances of the F2 and F3 molecules are observed. For the F1 molecule, atom C16 (see Figure 1) is located the closest to graphene among the C and N atoms for both graphene directions (3.25 and 3.18 æ for the zigzag and armchair directions, respectively, see Table S3). The N7 atom is situated the furthest from graphene (3.35 and 3.31 æ in the GZZ and GAC directions, respectively). A similar situation is observed for the F4 molecule. Atom N16 is located the closest to the graphene surface for both directions (3.26 and 3.20 æ for the zigzag and armchair directions, respectively). Note that N16 is replaced by C16 in the F1 molecule. The N7 atom (F1) is the farthest from graphene in the GZZ direction (3.36 æ). This distance decreases to 3.33 æ for the GAC direction. For these two molecules (F1 and F4), the largest binding energy in the GAC direction is explained by the energetically favorable position of three hexagons of each molecule with respect to graphene, namely the B1 position for F1 and the B2 position for F4. Note that in these positions the benzene molecule has also the strongest binding energy with graphene. 2.3. Influence of the Side Groups on the Structures of the Hybrids Formed by F2 or F3 with Graphene and Corresponding Interaction Energies One of the aims of this study is to determine the influence of side groups such as CH3 and CF3 on the structures of the hybrids formed by F2 or F3 with graphene, and on the corresponding interaction energies. To understand the difference in the binding energies of F2 and F3 molecules along two different graphene directions we analyze the location of the rings of these molecules relative to the graphene surface along the GAC and GZZ directions. For the GZZ direction, two rings of the F2 molecule arrange over graphene in the B4 position and other two ones in the B2 and Im3 positions, respectively. For the GAC ChemPhysChem 2016, 17, 1204 – 1212
direction, three rings are arranged in the B1 position (with a small displacement) and the imidazole ring arranges in the Im2 position. Preliminary (visual) estimation of the interaction of F2 with graphene based only on the analysis of the arrangement of the rings over the graphene surface suggests a stronger interaction for the GAC direction than for the GZZ direction. The analysis of the arrangement of the F3 molecule over graphene in the GAC direction shows that three rings of this molecule are of the B1 position and the forth is in the Im3 position with a small displacement from the perfect alignment. In the GZZ direction the F3 molecule arranges over the graphene surface with one ring occupying the B1 position, two rings the B2 position, and one ring in the Im3 position (with some displacement). The comparison of the two locations of the F3 molecule over graphene shows that in the GAC direction the contribution of the rings to the binding energy is larger than when this molecule arranges along the GZZ direction. Note that this estimation of the binding energy should be considered as preliminary because it does not include the contribution from side groups. To estimate the contribution of the CH3 and CF3 groups to the total binding energy of the F2 and F3 molecules with graphene, we first calculate this energy for molecules without these groups, but with the same complex structure. Each group is replaced by a hydrogen atom. The obtained energy values for the two directions of graphene are shown in Table 2.
Table 2. Binding energy (Eint, kcal mol¢1) of the F2 and F3 molecules with graphene with and without CH3 and CF3 groups. After removing the groups, they are replaced with hydrogens. Addition of the groups causes an increase (shown as D, kcal mol¢1) of the binding energy.
Eint without group
Eint with group
CH3, GZZ CH3, GAC CF3, GZZ CF3, GAC
¢20.1 ¢21.0 ¢19.2 ¢21.0
¢21.5 ¢23.0 ¢22.6 ¢22.3
¢1.4 ¢2.0 ¢3.4 ¢1.3
The results show that the binding energy increases after the addition of either of the two groups (see D in the table). The contribution of the CF3 group to the total binding energy of the F3 molecule with graphene along the GZZ direction is the largest (3.4 kcal mol¢1). The addition of the CH3 group along the GAC direction increases the binding energy of F2 by 2.0 kcal mol¢1. The possible reason of the large enhancement of the binding energy due to the addition of the CF3 group is the placement of two fluorine atoms over the center of two graphene hexagons. Note that the contribution of the CH3 group to the total interaction energy is almost equal for the two graphene directions, while the contribution of the CF3 group in the GAC direction is significantly lower (equal to 1.3 kcal mol¢1) than in the GZZ direction. Thus we can conclude that the increase of the interaction energy due to the addition of backside groups can be significant and depends on the direction of graphene along which the molecule is placed.
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Articles A comparison of distances between the two molecules and graphene shows that for the F2 molecule positioned along the GZZ direction, a small distortion from the perfect parallel orientation of the planes of the molecule and graphene appears. In this configuration, the distance from the N15 atom to the graphene plane is the largest (3.39 æ) among the ring atoms and the distance for the C5 atom is the smallest (3.25 æ) (Table S4). It should be noted that the carbon atom in the side group (C25) is located in the plane of the molecule (3.32 æ away from graphene). No off-plane distortion of the F2 molecule positioned along the GAC direction of graphene is observed. In this configuration, the distance between the C25 atom and the graphene plane is the largest (3.32 æ) and the C5 atom is situated at the nearest distance to graphene (3.27 æ) among the ring atoms (Table S4). Thus, for the atoms of F2, the largest difference between their distances from graphene for the GZZ direction reaches 0.14 æ, while for the GAC direction, the difference does not exceed 0.05 æ. For the F3 molecule, a different behavior is observed. Here, the center atom of the side group (C24) for both GZZ and GAC directions is situated the farthest from the graphene surface (3.59 and 3.55 æ for the GZZ and GAC directions, respectively, see Table S4). The C4 (3.27 æ) atom is the closest to the graphene surface for the molecule positioned along the GZZ direction of graphene and the C5 (3.20 æ) atom is the closest to the surface when the molecule is positioned along the GAC direction. The difference between the largest and the smallest distances from the graphene surface for the F3 atoms are 0.32 and 0.35 æ for the GZZ and GAC directions, respectively. The analysis of the distances shows that the C24 atom moves away from the plane of the molecule when F3 adsorbs to graphene. This off-plane deformation can be explained by the considerably larger size of the two fluorine (in comparison with hydrogen) directed and attached to the C24 atom. These atoms prevent C24 to closer approach the graphene surface (Figure S3). This is the most important difference in the structures of the graphene hybrids with the F2 and F3 molecules. The increase of the distance between the C24 atom and the graphene sheet lowers their interaction but this decrease is compensated by the strong interaction of graphene with the two fluorine atoms (F26 and F27).
2.4. Electrostatic Potential Distribution for Hybrids of the Studied Molecules and Graphene To analyze the noncovalent interactions between graphene and the studied molecules in more detail, we use the electrostatic potential surface. The surface is calculated as a superposition of the electrostatic potentials generated by the partial charges located on the atoms of the studied system in points being away by a fixed distance from the atom centers (in the present calculations this distance is 2 æ). The electrostatic potential surfaces are also determined for graphene modified by the presence of the studied molecules. Such a surface is obtained by subtracting the potential of the studied molecule from the potential of their hybrids. ChemPhysChem 2016, 17, 1204 – 1212
Figure 6. Surfaces of the electrostatic potential of: benzene, imidazole and tetracene (central vertical raw), and hybrids of these molecules with graphene in the GAC direction (left vertical raw). The graphene differential potential induced by the adsorbed molecule is also shown (right vertical raw). The potential surface of a hybrid is obtained by the summation of the electrostatic potentials of the two molecules forming the hybrid. The potential is calculated for the fixed distance of 2 æ from the atoms.
It should be noted that for molecules such as benzene or tetracene (Figure 6), the surface of the molecular electrostatic potential is uniform. This happens because of the high symmetry of these molecules and because they consist only of carbon and hydrogen atoms forming hexagons and with hydrogen atoms on periphery. On the whole, TET and benzene molecules, and graphene are neutral. In such situation the positive charges located on hydrogen atoms are compensated by the negative charges of the carbon atoms. As the negative charges on the carbon atoms of benzene are equal, they create a small negative potential on the framework of the molecule while on the periphery the hydrogen atoms create a ring of a small positive potential. In TET, the charges localized on the carbon atoms are not even and the charge of a particular atom depends on its location in the molecule. The carbon atoms connecting the rings (C1, C2, C8, C9, C12, and C13; see Figure 1) have small positive charges while other carbons have small negative charges. However, the difference of the charges has a very small effect on the electrostatic potential at 2 æ distance from the atoms. The peripheral hydrogen atoms of TET form a chain of small positive potential around the framework of the molecule.
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Articles Graphene is a large system with a uniform distribution of the potential. In contrast to benzene or TET, the negative potential on the carbon atoms of graphene is smaller. This is explained by a smaller hydrogen/carbon atom ratio for C96H24 (0.25) than for TET (0.5) or for benzene (1.0). As mentioned before, for a neutral molecule, the positive charges located on hydrogens are compensated by the negative charges located on the carbon atoms. Therefore, the negative potential in the central part of benzene or TET is larger than for graphene. The hydrogen atoms of these molecules induce a small negative net charge on graphene (Figure 6, right raw). When comparing the distribution of the potential of the hybrids of benzene and imidazole with graphene (Figure 6), asymmetry of the potential distribution created by the imidazole molecule can be noted. This is due to the two nitrogen atoms in the structure of this molecule, which possess small negative partial charges. Nitrogen N1, not bonded to any hydrogens, has a much larger negative partial charge (¢0.51e) than nitrogen N3 (¢0.14e) bound to hydrogen H7. As a result, the electrostatic potential of the hybrid is negative around the N1 and N3 atoms. This region of the negative potential of imidazole causes that a zone of a small positive potential appears on the graphene surface located close to the N1 and N3 atoms of imidazole and a zone of a negative potential close to the hydrogen atoms (Figure 6). The electrostatic potential surfaces of the hybrids of F1-F4 with graphene are calculated for these molecules positioned along the GZZ (Figure 7) and GAC (Figure S4) directions of graphene. For all four molecules, the surfaces of the electrostatic potential show the presence of partial charges located on the nitrogen and hydrogen atoms. Note that the distribution of the electrostatic potential on the F1-F4 molecules is asymmetric in comparison with TET, where it is symmetric. In these molecules, nitrogen atoms N15 and N17 (which correspond to N1 and N3 atoms of imidazole) and also atoms N7 and N10 generate negative potential in some local places of these molecules. Note that atoms N7 and N10 have negative partial charges ranging from ¢0.57e to ¢0.61e depending on the molecule. Thus, the nitrogen atoms of F1-F4 form a zone of negative potential (Figure 7, left raw) which induces a surface of positive potential on graphene (Figure 7, right raw). Note that the areas of negative potential induced by the F1 and F2 molecules on graphene are larger than by the F3 and F4 molecules. The presence of the backside groups in F2 and F3 introduces additional asymmetry in the electrostatic potential distribution on graphene. Comparing the influence of these groups on the distribution of the electrostatic potential on graphene shows that the CH3 group of F2 enhances the positive potential on the periphery of the molecule due to the positive net charges of the hydrogen atoms while the CF3 group of F3 molecule enhances the negative potential on the periphery due to the negative net charges on the fluorine atoms. These negative partial charges also cause a decrease of the negative potential near other rings of the F3 molecule. A similar situation is observed in the potential distribution of graphene induced by the F3 molecule. The zone of the induced negative potential on graphene deChemPhysChem 2016, 17, 1204 – 1212
Figure 7. Surfaces of the electrostatic potential of: F1-F4 (positioned along the GZZ direction) (central vertical raw) and hybrids of these molecules with graphene (left vertical raw). The graphene differential potentials induced by the adsorbed molecules are also shown (right vertical raw).
creases in comparison with F2 because partially negatively charged fluorine atoms compensate the positive partial charges of the hydrogens of the imidazole ring (Figure 7, right arrow). Thus, the positive partial charges of the hydrogens in the imidazole ring in F1 and their combination with the CH3 group of F2 induce stronger polarize graphene than F3 and F4. Thus, by replacing carbons with other atoms or by adding back-side groups (with partial positive or negative charges) the polarization of graphene and its optical properties can be modified. Analysis of dipole moments of graphene complexes with imidazophenazine derivatives and tetracene (Table S5) showed that addition of non-polar tetracene molecule to graphene changes only Z-component of the dipole moment which is perpendicular to the graphene sheet, while X and Y components are almost zeroes. At the same time addition of polar imidazophenazine derivatives resulted in significant changes of all components of the dipole moment. It should be noted that dipole moments and especially some their components essentially depend on orientation of the molecules on graphene. Quadrupole moments of the complexes are present-
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Articles ed in Table S6. From this Table follows that they decreased in absolute values with respect to the quadrupole moment of graphene itself and also depend on orientation of the molecules on graphene. Our research demonstrates that the presence of functional groups can significantly increase the p–p interactions of the adsorbed molecules with graphene along the selected direction. This observation indicates that certain linear heterocyclic compounds can form ordered 2D supramolecular assembly on the graphene sheet. Thus, graphene is potentially useful as a new substrate for the controlled synthesis of practical 2D molecular structures that may be used in new extended applications. In this context, the ordered adsorption of molecules with a local dipole in 2D assembly is regarded as a potential route to create a charge density wave in graphene.
3. Conclusions Both benzene and imidazole molecules strongly interact with graphene when the centers of the rings of the molecules are located over a carbon atom of graphene. It is revealed that the imidazole in the hybrid with graphene has a slightly tilted parallel configuration. The tilt is explained by the somewhat more positive partial charge located on the hydrogen atom bound with the nitrogen N3 atom than the charges on other imidazole hydrogens. The high symmetry of the tetracene molecule causes that the most energetically favorable location of this molecule on the graphene sheet is along the armchair direction, in which the center of each of its four rings is located over a carbon atom of graphene. In the zigzag direction the tetracene molecule has a somewhat smaller binding energy (by 0.2 kcal mol¢1). The calculations show that for asymmetrical linear molecules such as imidazophenazines, there is a difference in the binding energies with graphene along the zigzag and armchair directions. It is shown that this difference is larger for the F2 and F4 molecules than for the F1 and F3 molecules. It is also found that for the F1, F2 and F4 molecules, the binding energy along the armchair direction of graphene is larger than that for the zigzag one. The opposite is observed for the F3 molecule, which is explained by a larger contribution of the CF3 group to the total binding energy in the zigzag direction than in the armchair direction. This conclusion is confirmed by the calculation of the binding energy of the F3 molecule with graphene with and without CF3 group. The calculations also show that in the binding of linear cyclic hydrocarbons and their derivatives with graphene back-side groups can noticeably contribute to the total interaction energy. This energy can be different for the different directions of the graphene surface. Symmetrical molecules such as benzene and tetracene give rise to a uniform distribution of the electrostatic potential on graphene. On the contrary, an asymmetrical potential distribution is generated by the imidazole molecule. The asymmetry is caused by two nitrogen atoms in this molecule which possess small negative partial charges. As a result, the surface of the electrostatic potential of the hybrid of imidazole with graChemPhysChem 2016, 17, 1204 – 1212
phene has negative values around these nitrogen atoms. This region of the negative potential affects the electrostatic potential of graphene; a local zone of small positive potential appears on this surface close to the nitrogens and a zone of negative potential appears close to the hydrogen atoms. The electrostatic potentials on the surfaces of the F1-F4 molecules, as well as of their hybrids with graphene, have different signs that are mainly caused by the presence of nitrogen and hydrogen atoms in their structure. The electrostatic potentials of the F1-F4 molecules are asymmetric, unlike the electrostatic potential of TET, which is symmetric. The nitrogen atoms of F1-F4, as well as of their hybrids with graphene, due to their partial negative charges, induce a positive electrostatic potential on graphene. Also, the positive partial charges of hydrogens of the imidazole ring in F1 and these charges in combination with the positive charges on the hydrogens of the CH3 group in F2 stronger polarize graphene than F3 and F4. Replacing the carbons with other atoms or adding a back-side group (which has a partial positive or negative charge) enables to vary the polarizability of graphene. The obtained results on the modification of graphene by linear hydrocarbon derivatives can be applied to green chemistry applications such as the remediation of the environment from toxic aromatic compounds. On the other hand, the acquired knowledge on the hybrid structures and the binding energy values can be exploited for drug delivery in cells using graphene oxide as extended scaffold. Noncovalent functionalization of 2D graphene with organic heterocyclic compounds facilitates the development of new 3D graphene nanostructures, which is already showing promise in capacitors, fuel cells and water remediation. The adsorption of organic heterocyclic compounds can also be used to modify the band structure in graphene, thereby opening a small band gap. Thus, noncovalent functionalization of graphene with different organic molecules allows the creation of well-defined interfaces relevant for field-effect transistors. Note that the control of the band-gap opening of graphene is the main problem that restrains the broad application of this nanomaterial in the electronic devices industry.
Computational Methods The geometries of the complexes formed by a graphene sheet with tetracene, imidazophenazine, and its derivatives (Figure 1) were optimized at the DFT level of theory. The M05-2X functional was used. As shown before, the M05-2X functional is capable of predicting the structures and the interaction energies of noncovalent complexes formed by carbon nanotubes, in close agreement with the MP2 results.[44, 46, 47] In this work, we also used the SLDB (same level different basis) approach to decrease the total number of basis functions in the calculations. For the graphene carbon atoms and all the atoms of the studied adsorbent molecules, the standard 6-31G(d) and 6-31 + + G(d,p) basis sets were used, respectively. For the terminal hydrogen atoms of the carbon surface, the standard STO-3G basis set was used. In the calculations, the graphene surface is represented by a graphene sheet containing 96 carbons and 24 terminal hydrogens. As it was shown earlier,[44, 46] such a fragment is large enough to ade-
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Articles quately model the interaction of graphene with small- and medium-size molecules of organic heterocyclic compounds. To further confirm this assumption, calculations are performed for several complexes involving a larger C150H30 graphite sheet. The studied adsorbent molecules in the starting configurations are placed on graphene along the non-equivalent zigzag and armchair directions. All quantum chemical calculations were performed using the Gaussian 09 program package. The molecular orbitals, electrostatic potential, and electron density were generated with the “cubegen” utility of the Gaussian 09 package. The ChemCraft software was used for visualization of the results.
Acknowledgements This work has been partially supported by NAS of Ukraine (Grant N 15/15-H within the program “Fundamental Problems of the creation of new Nanomaterials and Nanotechnology” and Grant N 0114U001070). An allocation of computer time from the Computational Center at Institute for Low Temperature Physics and Engineering and from UA Research High Performance Computing (HPC) and High Throughput Computing (HTC) at the University of Arizona is gratefully acknowledged. Keywords: DFT · graphene · interaction nanostructures · phenazine derivatives
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Manuscript received: September 25, 2015 Accepted Article published: November 19, 2015 Final Article published: February 16, 2016
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