Interaction of Graphene with Out-of-Plane Aromatic Hydrocarbons

Subscriber access provided by Nottingham Trent University

C: Surfaces, Interfaces, Porous Materials, and Catalysis

Interaction of Graphene with Out-of-Plane Aromatic Hydrocarbons Stefan K. Kolev, Hristiyan A. Aleksandrov, Victor A. Atanasov, Valentin N. Popov, and Teodor Ivanov Milenov J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b03550 • Publication Date (Web): 12 Aug 2019 Downloaded from pubs.acs.org on August 13, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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

The Journal of Physical Chemistry

Interaction of Graphene with Out-of-Plane Aromatic Hydrocarbons S. K. Kolev1,*, H. А. Aleksandrov2, V. A. Atanasov3,V. N. Popov3 and T. I. Milenov1 1”E.

Djakov” Institute of Electronics- Bulgarian Academy of Sciences, 72 Tzarigradsko Chausee Blvd., 1784 Sofia, Bulgaria 2Faculty of Chemistry and Pharmacy, Sofia University, 1 J. Bourchier Blvd., Sofia 1164, Bulgaria 3Faculty of Physics, Sofia University, 5 J. Bourchier Blvd., Sofia 1164, Bulgaria * corresponding author e-mail: [email protected]

Abstract In the present article, graphene complexes with out-of-plane organic substances triphenylmethyl radical, anion and cation are studied. Comparison is made with the similar closed-shell molecule (cyclohexa-2,5-dien-1-ylidenemethylene)dibenzene. The nearest contact in the complexes is realized between a hydrogen atom of the organic molecule and a carbon atom of graphene. The geometry of the organic molecules does not change significantly, but changes in graphene’s electronic density of states make possible the identification of the formed π-π complex. This effect represents an extension of the idea that graphene is capable of single molecule detection to graphene being capable of adsorption complex detection and more importantly – identification.

1. Introduction

The study of graphene has attracted much attention because it is a promising new material for a variety of applications in the electronics industry, durable low resistant coatings and medical applications.1 For example, it is demonstrated that sensors of pristine graphene can achieve a detection limit beyond the ppm (parts-per-million) range for gas molecules of NO, NO2, NH3, N2O, O2, SO2, CO2 and H2O at room temperature: 0.16, 2.06, 33.02, 103,38.8, 67.4, 136 and 103 parts-per-trillion (ppt), respectively.2 The capability of detecting an event such as a single gas molecule attaching or detaching from its surface is related to the changes in the local carrier concentration in graphene caused by immobilizing of one electron at a time by the adsorbed molecule which leads to step-like changes in resistance.3 This is reminiscent of the field effect in semiconductor physics. In effect, graphene is recognized as a single molecule

1 ACS Paragon Plus Environment

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

Page 2 of 22

detector. Also, a lot of efforts are concentrated on the possible functionalization of graphene in order to refine the detector’s response: it is established experimentally that the sensitivity of the sensors can be enhanced by functionalization of the graphene surface by a self-assembled single stranded deoxyribonucleic acid (DNA) layer,4 moreover it is observed that the sensitivity depends on the DNA sequences. Later on, it is reported that covalent functionalization of graphene, for example with 4-nitrophenyl groups,5 can lead to a bandgap opening. This is caused by transition of carbon atoms from sp2 to sp3 hybridization and subtraction of p electron density from the graphene sheet. Graphene, possessing a bandgap, can be used directly in the semiconductor industry or as a sensor material with very low quiescent current. Graphene, modified with anthraquinone has also been proposed for use in electronic components.6 With this material, the energy storage (per weight) of a battery/supercapacitor can be increased more than 2 times. In general, the functionalizing species (different organic molecules/ amino-acids/ peptides/ proteins/ enzimes etc.) can interact with the graphene surface covalently or noncovalently (π-π or electrostatic interaction, hydrogen bonding) thus diversifying the behavior of graphene as an active detector’s media. It is clear that carefully driven ab initio simulations of such interactions can significantly facilitate the correct choice of functionalization species by predicting geometry, stability and electronic structure of the formed complexes. Various small molecules and polymers can bind to graphene with different affinity. The interaction of the latter with aromatic molecules (benzene, anthracene, pyrene, tetracene) has been studied computationally using DFT with PBE or B3LYP functional as well as with the semi-empirical method DFTB.7,8 The binding energy of benzene on graphene/Ru(0001), 52.9 kJ/mol, is experimentally obtained from thermal desorption spectroscopy (TDS) peak positions.9 Desorption activation energies of the graphite interaction with benzene, naphthalene, coronene, and ovalene: 48.2 kJ/mol, 82.0 kJ/mol, 135.1 kJ/mol, and 202.6 kJ/mol, respectively, are also obtained with TDS.10 These values were compared with vdW-DF calculations.11 Theoretical values compare well, when experimental errors and the influence of the graphite layers are taken into account.10,11 As a result, the binding energy of the adsorbed aromatic molecule to graphene increases with increasing the number of condensed aromatic rings. The equilibrium separation between the molecules and graphene is about 320-350 pm in all cases. The maximum adhesion force also increases with the increase in the number of aromatic rings. The energy gap of benzene in gas phase and adsorbed to graphite is compared, using GW method.12 It is concluded that the gap decreases with 3.2 eV following the adsorption.


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


The interaction of benzoic acid with graphene sheet has been investigated using DFT at the LDA level.13 It should be noted that at this level, the theory does not cover non-local electron correlation effects and thus cannot describe the intermolecular interactions quantitatively. Qualitative analysis, however, reveals that the presence of substituents significantly alters the π-π interactions between the adsorbates and the graphene surface. The calculated adsorption energy for benzene is twice lower than for benzoic acid. The absorption energy does not increase linearly with the number of COOH groups in the molecule. The interaction of graphene with chlorinated and nitrated benzene derivatives has also been studied theoretically.13 Experimental STM study shows that 1,3,5-Benzenetribenzoic acid can absorb to graphene and assemble in a porous network. Without annealing, both ordered and disordered structures can be detected. If the sample is subjected to annealing, domains with long range order can be fabricated.14 Amino acids are important for the biocompatibility of a material. Their interactions with graphene have been studied with theoretical methods.15-17 As a rule of thumb, charged groups, like the organic ammonium ion (-NH3+), interact more strongly with the graphene sheet than electrically neutral groups as, for example, the amino group (-NH2). In this regard, atomistic ab initio molecular dynamics simulations have demonstrated that pristine graphene has very low reactivity toward ammonia NH3 in comparison with molecules that can accept electrons from the graphene π-electron cloud.18 Nevertheless, the presence of defects in the carbon sheet significantly enhances the graphene/ammonia interactions, thus leading to relatively facile NH3 dissociation at moderately low temperatures.19 Rajesh et. al.20 studied the interaction of phenylalanine (Phe), histidine (His), tyrosine (Tyr), and tryptophan (Trp), with attention to the π–π interactions between the aromatic rings and the surface. As one can expect, the covalent bonds between graphene and various organic molecules are found to be more stable than the various non-covalent interactions.21 The interaction of graphene with different polymers, used to form composites, has also been studied.22 Non-covalent interactions of graphene with polymers rely on the van der Waals interaction, electrostatic interaction or π-π stacking. Such interactions are observed between graphene and polymers that have charged or aromatic/conjugated groups in their macromolecules like PFVSO3 or PEG-OPE. In order to functionalize graphene or graphene oxide with PMMA, polyurethane or their derivatives covalent bonding with the surface is preferred. However, residual PMMA left on graphene after the fabrication process affects its electrical and thermal properties.23



Page 4 of 22

Since dyes are mostly aromatic molecules, they can engage in π-π interactions with graphene. Rhodamine 6G – graphene (and defective graphene) interactions have been studied theoretically employing DFT with PBE functional as well as using DFTB+.24 Covalent bonding is employed as a method for graphene functionalization. Bonding between epoxy/hydroxyl group (if present on the surface) and the dye amine groups is observed. Additionally, experimental characterization of the dye interactions with graphene materials are investigated using SPR spectroscopy. Non-covalent adsorption of perylene bisimide derivative, has also been reported.25 The resulting film, characterized by Raman spectroscopy and XPS, exhibits high stability. Dye molecules (such as tetracyanoquinodimethane (TCQN) – a good electron acceptor) have been proposed to enhance the electronic properties of pristine and doped graphene.26 Literature lacks theoretical works, dedicated to the interaction of out-of-plane aromatic molecules with graphene. This lack of specific knowledge inspired the present study, as computational chemistry offers useful tools to shed light on the hybrid systems, composed of 2D solid body (graphene) and the adsorbed out-of-plane molecules. Triphenylmethyl radical, cation and anion were chosen as they can present the interactions in purest form, without substituents in the hydrocarbon part. In the present article, the interaction between graphene and out-of-plane aromatic substances triphenylmethyl radical, cation and anion is studied theoretically for the first time, to the best of our knowledge. Because the electronic delocalization along the three benzene rings stabilizes the radical, cation and anion,27-29 these structures are observed experimentally and can be used in practice to alter the properties of graphene or other carbon based materials, similarly to the functionalization examples already discussed. The basic properties of the complexes such as binding energy, geometry structure and electronic configuration are investigated and synthetic approaches are discussed. A comparison is made with the (cyclohexa-2,5-dien-1ylidenemethylene)dibenzene complex of graphene. The former molecule is similar in structure to triphenylmethyl particles, but represents a neutral closed shell system. The present investigation sheds light on the interactions of graphene with out-of-plane aromatic hydrocarbons, including an open shell structure (radical) and closed shell cation and anion. We have studied the subtle changes in the density of states of the graphene sheet in the cases of triphenylmethyl radical, anion and cation complexes. The observed unique changes in the DOS, caused by the π-π interactions with the aromatic molecules, can be used not only to detect adsorption/desorption of molecules but also to identify the type of molecular complex formed with graphene. Effectively, we extend the idea of graphene, being a single molecule


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


detector, to graphene, being capable of detection of π-π complexes by their unique DOS features. Such detection can be achieved in any scheme utilizing the shape of the DOS of a graphene channel (field effect transistor or other).

2. Computational details All geometry optimizations necessary to calculate the binding energies of the complexes and the energies of reactions are performed using the CP2K/Quickstep package.30,31 The DFT is applied within the generalized gradient approximation (GGA), using Perdew-Burke-Ernzerhof (PBE) functional.32 Double-zeta basis set DZVP-MOLOPT-SR-GTH, optimized for calculating molecular properties in gas and condensed phase, is applied for all atoms in the studied systems.33 For reducing the computational cost, Gaussian and Plane-Wave (GPW) expansion sets are used for expanding the electronic wavefunctions.34,35. Only the valence electrons are explicitly considered. Their interaction with the remaining ions is described using the pseudopotentials of Goedecker-Teter-Hutter (GTH).36,37 The charge density cutoff of the finest grid level is equal to 400 Ry. The number of used multigrids is 5. All systems with odd number of electrons (containing radicals) are studied employing the unrestricted Kohn-Sham formalism. The convergence of the SCF procedure is usually difficult to achieve in systems with small bandgap as metals and semi-metals. This difficulty arises from having to integrate discontinuous functions that drop to zero when a band crosses the Fermi energy.38 The difficulty in converging the SCF procedure increases with increasing the complexity of the system. The electronic structure of graphene complexes in ground state with triphenylmethane radical, cation and anion could not be optimized correctly employing the Orbital Transformation (OT) or the standard diagonalization methods. In order to improve the convergence with respect to Brillouin zone sampling in our systems with small bandgap, electronic temperature is introduced, using the Fermi distribution function.38 All CP2K calculations are performed at T = 300 K and, for the case of complexes, 100 additional unoccupied orbitals are added. The smearing of the occupation numbers of the molecular orbitals led to partial occupation of orbitals close to the Fermi energy. This method allowed for achieving convergence in all cases. For the radical species, difference of 1 between the numbers of electrons having spin up and spin down, is shifted with the smearing procedure. Dispersion interactions (for the PBE functional) are taken into account for all studied complexes. DFT + D approach, with D3 set, recommended for use with electro neutral and charged complexes is used.39 5 ACS Paragon Plus Environment


Page 6 of 22

Geometry optimization of the complexes is performed from starting with different initial separation of the organic molecule of 200-250 pm and 350–450 pm from graphene. Trust (maximum) radius of the optimization step was initially set to 5 pm, but in some cases oscillation of geometry and energy occurred. In these cases the trust radius is reduced to 1 pm in order to achieve convergence. The binding energies of the complexes, ∆E, are calculated according to equation 1 ∆E = (Eg + Em) - Ec (1) where Ec is the electronic energy of the complex, Eg is the electronic energy of the periodic graphene sheet and Em is the electronic energy of the molecule (radical or ion), which interacts with the graphene sheet. Positive ∆E values indicate exothermic interactions. Energies of the reactions are calculated as the difference between energies of the starting materials and products. The DOS are calculated with VASP software,40,41 employing PBE functional with D3 dispersion. DOS are recalculated with the optPBE-vdW functional from the PBE+D3 geometry in order to take into account the non-local electron correlations, important for the description of the graphene-adsorbates interactions.42 For the calculations with PBE+D3, k-point sampling with 5×5×1 grid is used for all systems, with one exception. For the complex of graphene and triphenylmethyl radical, 3×3×1 grid is used. For all calculations with optPBE-vdW, 3×3×1 grid is used, because of the very high computational cost. We employed double-zeta basis set in our calculations with CP2K, while the kinetic energy cut-off is 415 eV in VASP calculations. The band gap values are calculated directly from the electronic structure of the systems as a HOMOLUMO energy difference. It is checked that both CP2K and VASP give identical optimized geometries of the studied complexes. M06-2X calculations are performed only on the triphenylmethyl radical in gas phase, using Gaussian09 software, with 6-311+G* basis set.43,44 A hybrid functional is used in order to test if the self-interaction error, occurring with the GGA functional PBE, will have effect on the spatial localization of the unpaired electron in the triphenylmethyl radical.

3. Results and discussion 3.1. Geometry and stability of the complexes. 3.1.1 Geometry of the complexes.

The studied complexes represent a single graphene sheet, interacting with an organic substance (molecule, radical or ion). The unit cell of graphene consists of two carbon atoms with


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


lattice parameters a and b of 246 pm. In order to avoid errors associated with small systems (too high adsorbate loading, incorect geometry of the substrate), the supercell used for the simulations contains 288 carbon atoms in a hexagonal cell with lattice parameters A=12×a and B=12×b.45 The C- edge, i.e., the vacuum space between the graphene sheets, is fixed to 2000 pm. The dimension of the C- edge of the supercell is assumed to be long enough to eliminate the interaction between the periodic images. The angles between the A, B and C edges of the supercell: α- between B and C, β- between A and C, and γ- between A and B, have values of 900, 900 and 600, respectively. Triphenylmethyl radical, anion and cation are chosen to form complexes with graphene, which are denoted as RadicalGr, AnionGr and CationGr. Their geometry is represented in Fig 1 a, b. A graphene complex with a closed shell (singlet) molecule with a similar structure is also studied. The chosen molecule, cyclohexa-2,5-dien-1-ylidenemethylene)dibenzene (denoted as Yl), is presented in Fig 1 c, d. The complex is denoted as YlGr.

Figure 1. Geometry of the organic substances: a) and b) top and side view of triphenylmethyl cation, anion and radical; c) and d) top and side view of cyclohexa-2,5-dien-1ylidenemethylene)dibenzene. Selected atoms are denoted by numbers. Carbon atoms are presented as gray spheres, and hydrogen atoms, as light blue spheres.

Geometry optimization is performed in order to study the spatial characteristics and stability of the formed complexes. The initial positions of the organic molecules and graphene were as follows; a) initial distance of 350-450 pm, in order to study the π-π interactions, and b) the central carbon atom C1 of the organic molecule covalently bonded to the graphene layer. The 7 ACS Paragon Plus Environment


Page 8 of 22

second, covalently bonded type of interaction was found to be unstable and thus, it is not discussed further. Two initial structures are used with respect to the stacking between the organic molecule and the graphene sheet, AB stacking Fig 2 a and AA stacking Fig 2 b. Initial AB and AA stacking produced AB and AA optimized complexes, respectively.

Figure 2. Geometry of the graphene complexes: a) AB configuration, b) AA configuration, c) side view of the graphene complexes with triphenylmethyl cation, anion and radical, and d) side view of the graphene complex with cyclohexa-2,5-dien-1-ylidenemethylene)dibenzene.

The nearest distance between a hydrogen atom from the Yl molecule and carbon atom from graphene (Cg…Hh), Table 1, is 277 pm for AB configuration and 266 pm for AA configuration, Fig 2. For the RadicalGr, AnionGr and CationGr complexes, these distances are in the range of 282-287 pm, which is about 5-10 pm larger than for the YlGr complex in AB configuration. The similar Cg…Hh distances can be explained with the similar geometries of the RadicalGr, AnionGr and CationGr complexes. The nearest distance between a carbon atom from the Yl molecule, triphenylmethyl radical, anion and cation (Cg...Ch), and a carbon atom from graphene is in the range of 324-336 pm. The distance between the central carbon atom of the organic molecule (Cg...C1) and the nearest carbon atom from graphene is in the range of 397-419 pm.


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


It should be noted that, when graphene interacts with non-planar aromatic hydrocarbons, the distance between the organic molecule and graphene is closer than in the complexes of graphene with planar aromatic molecule. For example, the Cg…Hh distance in the studied complexes of non-planar molecules is in the range of 270-290 pm, while the optimized distance in the case of planar aromatic hydrocarbons is in the range of 340-350 pm (calculated with PBED3.8 The reason for this is the small atomic radius of the hydrogen atoms that come into contact with the graphene sheet compared to the carbon atoms in the complexes of the non-planar molecules, see Fig 2 c and d.

Table 1. Geometric and energy characteristics of the complexes. Cg – nearest carbon atom from graphene; Hh – nearest hydrogen atom from the organic molecule; Ch – nearest carbon atom from the organic molecule; C1 – the central carbon atom of the organic molecule; ∆E - the binding energies of the complexes Complex/Configuration Cg…Hh [pm]

Cg…Ch [pm]

Cg…C1 [pm]

∆E [kJ/mol]

YlGr / AB

277

324

416

87

YlGr / AA

266

331

403

82

RadicalGr / AB

282

329

417

82

RadicalGr / AA

283

335

397

82

AnionGr / AB

285

328

418

128

AnionGr / AA

287

332

397

127

CationGr / AB

285

330

419

301

CationGr / AA

284

336

397

300

The geometry of the organic molecules in gas phase and adsorbed in the complex with graphene is studied. The bond lengths between the central carbon atom and the covalent bonded carbon atom from the benzene rings (partially aromatic ring in Yl) are compared (for notation of the atoms, see Fig 1). The dihedral angles are also studied, Table 2. For the Yl molecule, the C-C bond distances (C1-C2, C1-C3, C1-C4) are 139 pm, 148 and 148 pm, respectively. The double bond is the shortest one of 139 pm. In the complex, these bond lengths do not change significantly. In the AB configuration, one of the bonds is elongated by 1 pm from 148 pm to 149 pm. All C-C distances in the gas phase radical and anion are 146 pm and do not change in



Page 10 of 22

the complex (see Table 2). The C-C bond lengths in the cation are 145 pm. One of the bonds is longer by 1 pm in the AB and AA configurations. Dihedral angles, that define the planarity of the molecules, are also studied (see, Fig 1 and Table 2). In the case of the Yl molecule, the dihedral angles C4C1C2C5 and C3C1C2C6, containing atoms of the partially conjugated ring, have small values of 13.3o. The double bond at the partially conjugated ring is responsible for this effect. In the complexes with graphene, these values generally decrease (Yl becoming more planar), with one exception at the AA configuration. Triphenylmethyl radical, anion and cation have C3v group of symmetry. By this reason, C1-C2, C1-C3, C1-C4 bonds are equal in length and dihedral angles have similar values. The dihedrals angles are equal to 33.5 – 33.8o for the radical, 30.3 – 30.6o for the anion, and 33.4 – 33.6o for the cation (Table 2). The geometry of the organic molecules does not change significantly in the complexes. When the complexes are formed, the organic molecules generally become slightly more planar. Dihedral angles’ values decrease; for YlGr complexes with 1-6o, for the RadicalGr with 2-3o and for CationGr with 1-3o. Exceptions are AnionGr complexes, where dihedral angles either do not change, or increase with up to 1o.

Table 2. Bond lengths and dihedrals of the organic molecules in vacuum and in the adsorption complexes with graphene. Bond lengths [pm] and dihedrals [o]

Radical

Yl

Anion

Cation

Molecules

C1-C2

146

139

146

145

in vacuum

C1-C3

146

148

146

145

C1-C4

146

148

146

145

C4C1C2C5; C3C1C2C6

33.7; 33.8 13.3; 13.3 30.5; 30.6 33.6; 33.6

C2C1C4C10; C3C1C4C9

33.7; 33.6 47.5; 45.0 30.4; 30.5 33.5; 33.6

C8C3C1C4; C7C3C1C2

33.7; 33.5 44.7; 47.3 30.4; 30.3 33.5; 33.4

AB configuration

C1-C2

146

139

146

146

of the complexes

C1-C3

146

148

146

145

C1-C4

146

149

146

145

C4C1C2C5; C3C1C2C6

31.0; 30.9 11.6; 11.4 30.5; 30.4 32.4; 32.1

C2C1C4C10; C3C1C4C9

31.7; 31.7 47.0; 44.2 30.4; 30.4 29.9; 29.9

C8C3C1C4; C7C3C1C2

30.1; 30.2 39.0; 40.9 31.4; 31.5 31.2; 31.3


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


AA configuration

C1-C2

146

139

146

146

of the complexes

C1-C3

146

148

146

145

C1-C4

146

148

146

145

C4C1C2C5; C3C1C2C6

31.6; 31.5 13.4; 12.8 31.0; 31.2 31.8; 31.7

C2C1C4C10; C3C1C4C9

30.9; 30.9 46.0; 43.2 31.6; 31.4 30.6; 30.6

C8C3C1C4; C7C3C1C2

30.4; 30.4 38.1; 40.8 30.3; 30.2 31.1; 31.1

3.1.2 Stability of the complexes.

The binding energies, accounting for the stability of the complexes are calculated. Organic cation and anion produce more stable complexes, with the most stable being the complexes with triplenylmethyl cation, ∆E = 301 kJ/mol for AB and 300 kJ/mol for AA configuration, Table 1. Second most stable are the complexes of triplenylmethyl anion with ∆E = 128 kJ/mol for AB configuration and 127 kJ/mol for AA. The radical and the closed shell molecule (Yl) have similar binding energies (in the range of 82-87 kJ/mol). In the case of YlGr complex, the AB configuration is more stable than the AA one with 5 kJ/mol. For the other complexes, the AB and AA configurations have similar stability. Other theoretical works suggest that AB is the preferred way of stacking in the complexes of graphene and planar aromatic molecules.8,46 It should be noted that both Cg…Hh, Cg...Ch and Cg...C1 distances do not correlate with the binding energy between the organic molecule and the graphene sheet. No correlation is observed between the binding energy and the C1-C2, C1-C3, C1-C4 bonds as well as the dihedral angles. The binding energies of graphene complexes with planar aromatic hydrocarbons, having 18-20 C atoms, are calculated to be in the range of 105-115 kJ/mol (PBED3).8 These values differ by only 20 kJ/mol from the binding energies of YlGr, RadicalGr and AnionGr complexes. In order to get insight into the cation complex high stability, adiabatic ionization potential (IP) for the triphenylmethyl radical in vacuum and in graphene complex is calculated. IP is calculated as the energy difference between cation and radical. Results show that IP is higher in the case of the radical in vacuum (482 kJ/mol) than in the complex RadicalGr (263 kJ/mol), with other words, ionization is less energetically demanding for the complex. It can be concluded that the cation is stabilized, due to the interaction with the electron rich π system of graphene. This stabilization is the reason for the high energy of formation (binding energy) for the CationGr complex. Adiabatic electron affinity (EA) for the triphenylmethyl radical in vacuum and in 11 ACS Paragon Plus Environment


Page 12 of 22

complex is also calculated. EA is relatively higher in the case of the radical in complex RadicalGr (238 kJ/mol) than in vacuum (192 kJ/mol). Hence, it is more energetically favorable for the complex to receive electron. Possible routes for the synthesis of the studied complexes are considered, via vacuum deposition technology, to avoid interference with atmospheric gasses. Starting materials are chosen for their relative stability, see equations 2-8. YlGr complex can be synthesized from the Yl molecule and graphene (Gr), equation 2. As it is already discussed, the reaction is exothermic, with energy of 87 kJ/mol. Also, there is no activation energy for the π-π complex formation (equation 2), as the process does not involve chemical bonds scission or overcoming of other potential barriers. The possibility of RadicalGr complex formation by the reaction of equation 3 is also studied. The reaction is also exothermic, with energy of 66 kJ/mol. However, the first elementary step of reaction in equation 3 includes C-H bond cleavage which typically requires more than 400 kJ/mol (416 kJ/mol in cyclohexane),47 hence this process could be energetically hindered. Thus, we recommend that the direct synthesis of the YlGr complex is carried out at low temperature, to avoid side processes. AnionGr and CationGr complexes can be synthesized utilizing elimination reactions, equations 4 and 5, where (Ph3C)Na is triphenylmethylsodium48 and (Ph3C)Cl is trityl chloride (CAS Number: 76-83-5). It is expected that the good leaving groups (Na+ and Cl-) will favor the progress of reactions. Calculations show that the first reaction is endothermic, with energy of -159 kJ/mol, and the second, with -57 kJ/mol. Regardless the endothermic nature of the reactions, electric fields can be used in vacuum to draw Na+ and Clleaving groups away from the reaction products, thus accelerating the processes and making them irreversible. The formation of CationGr and AnionGr complexes by the reactions of equations 6 and 7, having H- and H+ as leaving groups, is highly disfavored, by -1200 and -1144 kJ/mol respectively. And finally, RadicalGr complex can be synthesized from chlorinated graphene (GrCl) and triphenylmethylsodium (Ph3C)Na, yielding NaCl in gas phase. This reaction is exothermic, with energy of 317 kJ/mol, equation 8.

Yl + Gr → YlGr +87 kJ/mol (2) Yl + Gr → RadicalGr + ½ H2 +66 kJ/mol (3) (Ph3C)Na + Gr → AnionGr + Na+ -159 kJ/mol (4) (Ph3C)Cl + Gr → CationGr + Cl- -57 kJ/mol (5) Yl + Gr → CationGr + H- -1200 kJ/mol (6) Yl + Gr → AnionGr + H+ -1144 kJ/mol (7) 12 ACS Paragon Plus Environment

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


(Ph3C)Na + GrCl → RadicalGr + NaCl +317 kJ/mol (8)

3.2 Electronic structure of molecules and complexes. First, the electronic structure of pristine graphene is simulated, in order to compare to that of the complexes. A supercell containing 288 carbon atoms is used,45 corresponding to that for the complexes. After geometry optimization, the C-C interatomic distance is mainly 142 pm, which is the mean value reached after 1 ps of dynamical simulation.45 The DOS of the system is calculated, and as expected, there are continuous valence and conduction bands, with DOS approaching zero at the Dirac point (see Supporting Information, Fig. S1). The energy gap (difference between the highest occupied orbital (HOMO) and the lowest unoccupied orbital (LUMO)) is < 1 meV. Such value is negligible, having in mind that Density Functional Theory, PBE functional, usually has errors (mean absolute deviation compared to thermochemical experimental data) > 0.1 eV.49

Table 3. Energy gaps (in eV) of the complexes (in AB and AA configurations), the organic molecules (abv. as Mol.) in gas phase (vacuum), and the organic molecules in the complexes, calculated with PBE and optPBE-vdW functionals. Radical

Yl

Anion

Cation

AB, PBE+D3, optPBE-vdW

< 1×10-3 < 1×10-3 < 1×10-3 < 1×10-3

AA, PBE+D3, optPBE-vdW

< 1×10-3 < 1×10-3 < 1×10-3 < 1×10-3

Mol. in gas, PBE, optPBE-vdW

2.6

2.5

2.0

2.2

Mol. in AB, PBE+D3

2.6

2.4

2.2

2.4

Mol. in AB, optPBE-vdW

2.5

2.4

2.2

2.4

The energy gaps of the organic molecules in vacuum and participating in the complexes are calculated with PBE and optPBE-vdW functionals (Table 3). The values vary from 2.0 eV (for the anion) to 2.6 eV (for the radical) and do not change significantly during the complexes formation. These values are typical for aromatic organic molecules, including dyes. It should be noted that the energy gaps of the complexes and adsorbates in vacuum are directly derived from HOMO – LUMO differences for the corresponding systems. The energy gaps for the adsorbates



Page 14 of 22

in the complexes are calculated from the decomposed DOS (Fig 3), as the energy differences from peak to peak, around the Fermi level. The energy gaps of the radical (in vacuum and complex) are obtained as differences between the SOMO orbital and the next state, higher than the singly unoccupied orbital. The geometry and electronic structure of the adsorbates in vacuum are not affected by dispersion interactions as they are determined by covalent bonding, thus PBE and optPBE-vdW functionals give the same values for their energy gaps. The DOS for the graphene complexes and the individual adsorbates in the complexes are presented in Fig 3. When the corresponding out-of-plane hydrocarbons are adsorbed at graphene, the electronic structure is not changed significantly and the whole systems remain conducting with zero band gap, because of the graphene part. The values of the HOMO-LUMO gaps for all complexes are very close to zero, in all cases < 1 meV. The notable change in the DOS, when adsorbates are added, is the appearance of additional states near the Fermi level, seen as small peaks, for both PBE and optPBE-vdW functionals. The decomposition of DOS proves that these small peaks are exactly caused by the adsorbates, Fig 3. The graphics of the DOS for the complexes and the adsorbates in complexes, for both used functionals, practically coincide at ± 2 eV from the Fermi level. As expected, DOS graphics, calculated with 3×3×1 k-points grid, have lower resolution (curved line) than those, calculated with 5×5×1 grid, see Section 2. The conductivity σ(ε), known as the transport distribution function, is given by: σ(ε) = D(ε) f(ε) eμ(ε) = n(ε) eμ(e), (9) Equation 9, where D(ε) is the energy dependent DOS, f(ε) is the Fermi distribution function, and μ(ε) is the charge carrier mobility. n(ε) = D(ε) f(ε) is the carrier concentration. Effectively, the conductivity of a graphene field effect transistor channel depends on the DOS of the material. However, the DOS is determined by the formed π-π complex (see Fig 3) and therefore a graphene channel in a field effect transistor can “sense” the different chemical complexes formed with hydrocarbons. Finally, the localization of the singly occupied molecular orbital (SOMO) of the triphenylmethyl radical and its complex with graphene is investigated. The SOMO orbital of the radical is presented in Fig 4 a. The hybrid functional M06-2X with 54% Hartree–Fock exchange is chosen for the wave function optimization in order to avoid electron self-interaction, associated with GGA functionals. As expected, the electron density is localized mainly around the central carbon atom of the molecules (C1). It should be noted that the PBE functional gives the same orbital localization and therefore self-interaction should be neglected for the


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


corresponding system. The single electron, visualized as spin density of the complex RadicalGr, is presented in Fig 4 b. The same localization as in the radical in vacuum is observed. Hence, the formation of a complex with graphene does not change the localization of the single electron.

Figure 3. DOS of the studied complexes in AB configuration, calculated with PBE and optPBEvdW functionals (black and blue lines, respectively); local DOS of the adsorbates in the complexes, calculated with PBE and optPBE-vdW functionals (red and green lines, respectively): a) YlGr; b) RadicalGr; c) AnionGr, and d) CationGr. The calculated Fermi energies, with respect to the vacuum level, for the complexes with Yl and the triplenylmethyl radical, anion and cation are: -2.65, -2.63, -2.07, -3.06 eV for PBE and -2.75, -2.72, -2.17, -3.16 eV for optPBE-vdW functional, respectively. They are scaled to 0 eV.



Page 16 of 22

Figure 4. a) The SOMO orbital of the radical in vacuum, calculated with the hybrid functional

M06-2X. Dark red color represents the positive phase of the wave function, and green – the negative phase; b) Position of the single (unpaired) electron in the complex RadicalGr, calculated with the GGA functional PBE. Its spin density is visualized with red color. 4. Conclusions

Graphene complexes with out-of-plane organic substances: triphenylmethyl radical, anion and cation, as well as cyclohexa-2,5-dien-1-ylidenemethylene)dibenzene are studied in their AA and AB configurations. In these complexes, the nearest contact is between a hydrogen atom from the organic molecule and a carbon atom from graphene. This distance is in the range of 270-290 pm and is about 65 pm smaller than the nearest C-C contact in the complexes of graphene with planar aromatic molecules. The geometry of the organic molecules does not change significantly, but when the complexes are formed, the organic part generally becomes more planar. Organic cation and anion produce more stable complexes than the radical or the closed shell molecule (Yl) with the same structure. The stability of the studied complexes decreases in the following order: triplenylmethyl cation > anion > closed shell (Yl) ~ radical. High stability of the cation complexes can be attributed to the stabilizing interaction with the electron rich π system of graphene. In all cases, the AB stacked configurations have higher stability than the AA ones. No correlation is observed between the geometry parameters and stability of the optimized complexes. Possible routes for the synthesis of the complexes are considered, and nature of the leaving groups is found to play a major role for the energetic feasibility of the processes. When the corresponding out-of-plane hydrocarbons form a complex with graphene, the electronic structure is not significantly changed and the systems remain conductors with a zero band gap. The density of states near the Fermi level, however, is altered by the interaction with 16 ACS Paragon Plus Environment

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


the adsorbates. The single electron in the triphenylmethyl radical is localized mainly around the central carbon atom, both in vacuum and in the complex with graphene. We report the changes in DOS of the graphene sheet when various organic molecules are adsorbed due to the formation of π-π complexes. The observed changes in DOS can be used to identify the type of molecular complex formed with graphene, and as a result, we predict graphene being capable of detection of adsorption complexes.

Acknowledgements S. K. Kolev, V. A. Atanasov, V. N. Popov and T. I. Milenov gratefully acknowledge financial support from the National Science Fund of Bulgaria under grant DN18/9-11.12.2017. H. A. Aleksandrov acknowledges financial support by the European Regional Development Fund and the Operational Program “Science and Education for Smart Growth” under contract UNITe No. BG05M2OP001-1.001-0004-C01.

References

(1)

Ferrari, A.; Bonaccorso, F.; Fal'ko, V.; Novoselov, K.; Roche, S.; Bøggild, P.; Borini, S.; Koppens, F.; Palermo, V.; Pugno, N. et al. Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems. Nanoscale 2015, 7, 4598-5062.

(2)

Chen, G.; Paronyan, T.; Harutyunyan, A.; Sub-ppt gas detection with pristine graphene. Appl. Phys. Lett. 2012, 101, 053119.

(3)

Schedin, F.; Geim, A.; Morozov, S.; Hill, E.; Blake, P.; Katsnelson, M.; Novoselov, K. Detection of individual gas molecules adsorbed on graphene. Nat. Mater. 2007, 6, 652655.

(4)

Lu, Y.; Goldsmith, B.; Kybert, N.; Johnson, A. DNA-decorated graphene chemical sensors. Appl. Phys. Lett. 2010, 97, 083107.

(5)

Niyogi, S.; Bekyarova, E.; Itkis, M.; Zhang, H.; Shepperd, K.; Hicks, J.; Sprinkle, M.; Berger, C.; Ning Lau, C.; de Heer, W.; Conrad, E.; Haddon, R. Spectroscopy of covalently functionalized graphene. Nano Lett. 2010, 10, 4061- 4066.

(6)

Campbell, P.; Merrill, M.; Wood, B.; Montalvo, E.; Worsley, M.; Baumann, T.; Biener, J. Battery/supercapacitor hybrid via non-covalent functionalization of graphene macroassemblies. J. Mater. Chem. A 2014, 2, 17764−17770. 17 ACS Paragon Plus Environment


Page 18 of 22

(7)

Lechner, C.; Sax, A. Adhesive forces between aromatic molecules and graphene. J. Phys. Chem. C, 2014, 118, 20970−20981.

(8)

Li, B.; Ou, P.; Wei, Y.; Zhang, X.; Song, J. Polycyclic aromatic hydrocarbons adsorption onto graphene: A DFT and AIMD study. Materials, 2018, 11, 726.

(9)

A. Chakradhar, K. Trettel and U. Burghaus, U. Benzene adsorption on Ru(0 0 0 1) and graphene/Ru(0 0 0 1)-How to synthesize epitaxial graphene without STM or LEED? Chem. Phys. Lett. 2013, 590, 146-152.

(10) Zacharia, R.; Ulbricht, H.; Hertel, T. Interlayer cohesive energy of graphite from thermal desorption of polyaromatic hydrocarbons. Phys. Rev. B 2004, 69,155406. (11) Chakarova-Käck, S.; Schröder, E.; Lundqvist, B.; Langreth, D.; Application of van der Waals density functional to an extended system: adsorption of benzene and naphthalene on graphite. Phys. Rev. Lett. 2006, 96, 146107. (12) Neaton, J.; Hybertsen, M.; Louie, S. Renormalization of molecular electronic levels at metal-molecule interfaces. Phys. Rev. Lett. 2006, 97, 216405 (13) Rochefort, A.; Wuest, J. Interaction of substituted aromatic compounds with graphene Langmuir, 2009, 25, 210-215. (14) Li, J.; Gottardi, S.; Solianyk, L.; Moreno-López, J.; Stöhr, M. 1,3,5-Benzenetribenzoic acid on Cu(111) and graphene/Cu(111): a comparative STM study. J. Phys. Chem. C 2016, 120, 18093-18098 (15) Wang, Q.; Wang, H.; Wang, F.; Liu, Y.; Zhang, P.; Lu, X.; Zhang, D. Computer simulation of biomolecule–biomaterial interactions at surfaces and interfaces. Biomed Mater. 2015, 10, 032001. (16) Cazorla, C. Ab initio study of the binding of collagen amino acids to graphene and Adoped (A=H, Ca) graphene. Thin Solid Films, 2010, 518, 6951–6961. (17) Luo, H.; Li, H.; Fu, Q.; Chu, Y.; Cao, X.; Sun, C.; Yuan, X.; Liu, L. Density functional theory study on the interactions of L-cysteine with graphene: adsorption stability and magnetism. Nanotechnology, 2013, 24, 495702. (18) Sangiovanni, D.; Gueorguiev, G.; Kakanakova-Georgieva, A. Ab initio molecular dynamics of atomic-scale surface reactions: insights into metal organic chemical vapor deposition of AlN on graphene. Physical Chemistry Chemical Physics, 2018, 20, 17751. (19) Li, X.; Lian, K.; Liu, L.; Wu, Y.; Qiu, Q.; Jiang, J.; Deng, M.; Luo, Y. Unraveling the formation mechanism of graphitic nitrogen-doping in thermally treated graphene with ammonia. Scientific Reports 2016, 6, 23495.


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


(20) Rajesh, C.; Majumder, C.; Mizuseki, H.; Kawazoe, Y. A theoretical study on the interaction of aromatic amino acids with graphene and single walled carbon nanotube. J. Chem. Phys. 2009, 130, 124911. (21) Li, D.; Zhang, W.; Yu, X.; Wang, Z.; Su, Z.; Wei, G. When biomolecules meet graphene: from molecule-level interactions to material design and applications. Nanoscale 2016, 47, 19491-19509. (22) INTECH Nanotechnology and Nanomaterials, New progress on graphene research, Edited by Gong, J. 2013, Chapter 8 Surface functionalization of graphene with polymers for enhanced properties, By Zheng, W.; Shen, B.; Zhai, W. (23) Suk, J.; Lee, W.; Lee, J.; Chou, H.; Piner, R.; Hao, Y.; Akinwande, D.; Ruoff, R. Enhancement of the electrical properties of graphene grown by chemical vapor deposition via controlling the effects of polymer residue. Nano Lett., 2013, 13, 1462–1467. (24) Zhang, K.; Yu, S.; Jv, B.; Zheng, W. Interaction of Rhodamine 6G molecules with graphene: a combined computational – experimental study. Phys. Chem. Chem. Phys, 2016, 18, 28418-28427. (25) Winters, S.; Berner, N.; Mishra, R.; DuЁmbgen, K.; Backes, C.; Hegner, M.; Hirschd, A.; Duesberg, G. On-surface derivatisation of aromatic molecules on graphene: the importance of packing density. Chem. Commun. 2015, 51, 16778- 16781. (26) Kong, L.; Enders, A.; Rahman, T.; Dowben, P. Molecular adsorption on graphene. J. Phys.: Condens. Matter. 2014, 26, 443001. (27) Gomberg, M.; An instance of trivalent carbon: triphenylmethyl. J. Am. Chem. Soc., 1900, 22, 757–771. (28) Urch, C. Triphenylmethyl hexafluorophosphate, Encyclopedia of reagents for organic synthesis. 2001, John Wiley & Sons Ltd. (29) Olmstead, M.; Power, P. The isolation and X-ray structures of lithium crownether salts of the free phenyl carbanions [CHPh2]-and [CPh3]-. J. Am. Chem. Soc. 1985, 107, 21742175. (30) The CP2K developers group, http://www.cp2k.org/ (2012). (31) VandeVondele, J.; Krack, M.; Mohamed, F.; Parrinello, M.; Chassaing, T.; Hutter, J. Fast and accurate Density Functional calculations using a mixed Gaussian and plane waves approach. Comput. Phys. Commun. 2005, 167, 103-128. (32) Perdew, P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple Phys. Rev. Lett., 1996, 77, 3865-3868. (33) VandeVondele, J.; Hutter, J. Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases. J. Chem. Phys. 2007, 127, 114105.



Page 20 of 22

(34) Lippert, G.; Hutter, J.; Parrinello, M. A hybrid Gaussian and plane wave Density Functional scheme. Molec. Phys. 1997, 92, 477-487. (35) Lippert, G.; Hutter, J.; Parrinello, M. The Gaussian and augmented-plane-wave Density Functional method for Ab Initio molecular dynamics simulations. Theor. Chem. Acc., 1999, 103, 124-140. (36) Goedecker, S.; Teter, M.; Hutter, J. Separable dual-space Gaussian pseudopotentials. Phys. Rev. B 2006, 54, 1703-1710. (37) Hartwigsen, C.; Goedecker, S.; Hutter, J. Relativistic separable dual-space Gaussian pseudopotentials from H to Rn. Phys. Rev. B 1998, 58, 3641-3662. (38) Lee, J.; Computational Materials Science: An Introduction. CRC Press, 2016. (39) Sure, R.; Antony, J.; Grimme, S. Blind prediction of binding affinities for charged supramolecular host–guest systems: achievements and shortcomings of DFT-D3. J. Phys. Chem. B. 2014, 118, 3431–3440. (40) Kresse, G.; Hafner, J. Ab initio molecular-dynamics simulation of the liquid-metal– amorphous-semiconductor transition in germanium. Phys. Rev. B 1994, 49, 14251–14269. (41) Kresse, G.; Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. J. Comput. Mater. Sci. 1996, 6, 15–50. (42) Lazar, P.; Karlický, F.; Jurečka, P.; Kocman, M.; Otyepková, E.; Šafářová, K.; Otyepka, M. Adsorption of small organic molecules on grapheme. J. Am. Chem. Soc. 2013, 135, 6372−6377 (43) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A.; Jr., Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.;Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.;Farkas, O.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, Revision A.02, 2009, Gaussian, Inc.: Wallingford, CT (44) Zhao, Y.; Truhlar, D. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states and


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


transition elements: two new functionals and systematic testing of four M06-Class functionals and 12 other functionals. Theor. Chem. Acc. 2006, 120, 215–241. (45) Kolev, S.; Balchev, I.; Cvetkov, K.; Tinchev, S.; Milenov, T. Ab-Initio molecular dynamics simulation of graphene sheet. J. Phys.: Conf. Ser. 2017, 780, 012014. (46) Bailey, S.; Visontai, D.; Lambert, C.; Bryce, M.; Frampton, H.; Chappell, D. A study of planar anchor groups for graphene-based single-molecule electronics. J. Chem. Phys. 2014, 140, 054708 (47) Luo, R., Comprehensive handbook of chemical bond energies. CRC Press, Boca Raton, FL., 2007 (48) Renfrow Jr, W.; Hauser, C. Triphenylmethylsodium. Org. Synth. 1939, 19, 83 (49) Xu X.; Goddard, W. The extended Perdew-Burke-Ernzerhof functional with improved accuracy for thermodynamic and electronic properties of molecular systems. J. Chem. Phys. 2004, 121, 4068- 4082.



Page 22 of 22

TOC Graphic


Interaction of Graphene with Out-of-Plane Aromatic Hydrocarbons

Recommend Documents