Effet of edge fluorination and chlorination on structures, stability, electronic and charge transport properties of benzo[o]bistriphenyleno[2,1,12,11-efghi:2',1',12',11'-uvabc]ovalene molecule : DFT study.


 We have investigated the structures, electronic properties, hole and electron mobilities of ﬂuorinated and chlorinated nanographene of benzo[o]bistriphenyleno[2,1,12,11-efghi:2',1',12',11'-uvabc]ovalene (TCHG) molecules, us- ing the density functional theory (DFT) and Markus-Hush charge transfer theory. The calculated geometric parameters and the IR spectrum for chlorinated TCHG are in good agreement with the experimental data. Our theoretical investigations have shown that ﬂuorination and chlorination signiﬁcantly reduce the bandgap energy of TCHG. The obtained adiabatic electron aﬃnities (AEAs) values are 2.76 and 2.93 eV respectively, indicating the air-stable materials. The calculation of charge carriers mobilities in chlorinated dimer shows that the mobility of the electrons is ten times that of the holes, suggesting an n-type behavior. We have shown that the ﬂuorination and chlorination of TCHG are promising pathways for the design of new materials useful in optoelectronics


Introduction
Polycyclic aromatic hydrocarbons (PAHs) have found an important and primordial place in scientific research since the work by Alan, MacDiarmid, and Shirakawa [1,2] on polyacetylene and the recent work of Andre Geim and his collaborators on graphene [3]. It is now possible to characterize organic chemical compounds in order to use them as substitutes for certain inorganic materials which are generally toxic, difficult to extract, and very expensive. This new way of thinking has led to a lot of researches in the field of science which has given birth to new sectors such as the field of synthetic metals [1] and organic electronic [4]. Graphene is a bidimensional crystal, extracted from a single layer of graphite. This crystal compound has attracted much attention [3]. The electrons in graphene move as if they have no mass, and thus are similar to the neutrinos of high energy physics, but the only difference that they carry an electric charge. Despite all the prowess attributable to graphene, the latter is limited in its applications in optoelectronics due to its zero-gap energy [5].
It is well known that the chemical functionalization of graphene can modify its chemical and physical properties and create a bandgap. Then these properties vary considerably depending on the shape and size of the functionalized graphene structure, and also the group of atoms used for the functionalization.
We report, a DFT study of the functionalization effects of the edges of a triangular structure of nanographene named benzo [o]bistriphenyleno [2,1,12,11-efghi:2',1',12',11'-uvabc]ovalene and so-called the tetracosahydro-C60graphene (C 60 H 24 ), by fluorine (tetracosafluoro-C60graphene) and by chlorine (tetracosachloro-C60graphene) atoms as presented in Fig  1. The tetracosahydro-C60graphene molecule have been already synthesized by Feng et al. [6], and recently functionalized by Yuan et al. [7] through the cyclodehydrogenation of dendritic polyphenylene precursors to produce the tetracosachloro-C60graphene (C 60 Cl 24 ) molecule. Here, we propose for the first time the structure of fluorinated tetracosahydro-C60graphene (C 60 F 24 ). Additionally, we have studied the optical, electronic, and charge transport properties of all the molecules cited in order to classify them as potential materials useful as nanomaterial devices.

Electronic properties
The vertical (electron affinity/ionization potential) EA v /IP v , adiabatic (electron affinity/ionization potential) EA a /IP a , reorganization energy for electron Λ e and reorganization energy for hole Λ h are calculated from the electronic energies and described respectively by the following equations [8,9,10,11,12] : Where : -E n (Q n ) is the total energy of the neutral molecule. Calculated from the optimized structure of the neutral molecule; -E a (Q a ) and E c (Q c ) are the total energies of the molecule in the anion and cation states. Calculated from the optimized structure of the geometry in the anion and cation state, respectively; -E n (Q a ) and E n (Q c ) are the total energies of the neutral molecule. Calculated from the optimized structure of the molecule in the anion and cation state, respectively; -E a (Q n ) and E c (Q n ) are the total energies of the anion and cation, respectively. Calculated from the optimized structure of the molecule taken in the neutral state. The TDOS, PDOS, and OPDOS were calculated using the normalized Gaussian function defined by: with a = F W HM 2 √ 2ln2 . For this work, the adjustable parameter FWHM (full width at half maximum) has been taken equal to 1.36 eV.

NLO property calculations
The average values of polarizability and first order hyperpolarizability are described by equations 5 and 6 derived from refs [13,14,15].

Charge transport properties
The theoretical model used to describe the transport properties in our organic materials is the Marcus-hush theory [16,17] and so-called the hopping model. According to the electronic hopping mechanism, the charge transfer rate K CT , is given by: V ef f is the effective electron coupling energy between the considered dimers, K B is the Boltzmann constant, T is the temperature (in our case, it was set at 298.15 K). The charge transfer mobility, µ is calculated with the aid of Einstein relation [18]: Where, e is the elementary charge, and R is the distance between the monomers. The effective coupling energies, V ef f (see Eq.9) were calculated with the aid of calc J package [19] which uses the direct calculation method.
V 12 is the charge transfer integral, S 12 denotes the overlap integral between the fragments of dimer considered, ε 1 and ε 2 are the energies of molecular orbitals where charges are localized (Eqs 10 to 13) [20].
In these equations, ψ H/L 1 and ψ H/L 2 represent the HOMO/LUMO of the isolated molecules 1 and 2, respectively and H ks is the Kohn-Sham Hamiltonian of the dimer system used for the calculation of charge transfer.

Computational details
The studied geometries were fully optimized at the B3LYP-D3 [21,22] and MN15 [23] levels with the aid of pople's type basis set 6-31+G(d,p) [24,25]. Frequencies calculation were performed at the same level of theory to ensure the nonexistence of imaginary frequencies [26]. The Coulomb-attenuating method (CAM-B3LYP) [27] have been employed to perform polarizability (α) and first hyperpolarizability (β) at the 6-31+G(d,p) basis set. Optimization of the dimers was done using the long-range corrected hybrid functional (ωB97X-D), including empirical atom-atom dispersion corrections [28], with the aid of 6-31g(d) basis set to account for the dispersion interactions between the considered dimers. According to Jeng et al. [28], the ωB97X-D functional is significantly superior to the B3LYP for the description of the non-bounded interactions. The intermolecular coupling energies have been calculated using the PW91PW91/6-31+g(d) method. Because according to Huang et al. [29] and Guo et al. [30], PW91PW91 functional is suitable for the prediction of transfer integrals of organic solids and it provides the reasonable result at the DFT level. Note that the choice of DFT is justified by the fact that it offers an excellent compromise between computation time and electronic correlation [31]. And its B3LYP functional is often used in the literature to easily predict the reorganization energies of aromatic π-conjugated organic molecules [32,33].
All DFT calculations in this document are made using Gaussian 16 software package [34]. Multiwfn 3.7 software [35] was used to plot the total, partial, and overlap density-of-states curves map (TDOS, PDOS, and OPDOS).

Results and discussion
3.1 Geometric, electronic structure and vibrational analysis

Geometric and electronic structure
The molecules C 60 H 24 and C 60 Cl 24 were already synthesized and their geometries derive from refs [6,7]. The geometry of triangular C 60 F 24 molecule was constructed by replacing the hydrogen atoms of C 60 H 24 molecule by fluorine atoms. To simplify, we have chosen to use the acronyms of TCHG to designate the tetracosahydro-C60graphene, TCFG to designate the tetracosafluoro-C60graphene, and TCCG to mention the tetracosafluoro-C60graphene molecule. Fig 1 shows the optimized ground state structure of studied molecules at the B3LYP-D3/6-31+G(d,p) level. As presented, the substitution of hydrogen by fluorine and chlorine atoms significantly act on geometry and induces a distortion of the initial geometry. According to Erkoç et al. [36], these effects can be attributed to the size of the different atoms used. As presented in the same figure, the geometric distortion is more pronounced for chlorine than fluorine. This can be explained by the difference in mass between these two atoms. Tables 1, 2 and 3 collect bond lengths of studied molecules. As presented, the deviation between the calculated bond lengths of the ground state and the crystal data for TCCG range from 0.005 to 0.103Å. Then, optimized bond lengths of TCCG molecule are in good agreement with the reported experimental crystal structure [7]. This suggests that the method B3LYP-D3/6-31+G(d,p) used is reliable for predicting the geometric structure of the studied molecules. By comparison, the calculated averages C-C bonds for the TCHG, TCFG and TCCG molecules are 1.420, 1.421 and 1.422Å, respectively and for C-X (X=H, F, Cl) bonds they are 1.083, 1.340 and 1.743Å, respectively. This suggests that edge functionalization of nanographene TCHG by fluorine (-F) and chlorine (-Cl) atoms does not affect C-C bonds but acts significantly on peripherical ones. Introducing the electron-withdrawing atoms of fluorine and chlorine into the TCHG molecule prolongs the peripherical bonds by 23 and 61%, respectively. This crucial result allows us to emphasize the effects of fluorination and chlorination of TCHG on the obtained geometries. To quantitatively study the different geometric distortions during charge transfer, we have plotted and consigned in Fig 2, the bond length variations between neutral, anionic, and cationic geometries of studied molecules. The oxidation/reduction curve corresponds to the difference between the bond length of the neutral state and its corresponding in the cationic/anionic state. As seen, the geometry relaxation appears to be balanced during the oxidation and reduction processes for all the geometries. However, further analysis show that the calculated |∆(A−G)| and |∆(C −G)| are 0.410/0.375, 0.606/0.511 and 0.592/0.509Å for TCHG, TCFG and TCCG respectively. Suggesting that for all studied molecules, the electrons reorganization energy is larger than the hole ones [9].

Vibrational analysis
Each studied molecule contains 84 atoms, leading to 246 normal modes made up of 83 stretchings, 82 bendings and 81 torsions (out-of-plane).
-The stretching is a movement of two bonded atoms A 1 -A 2 in opposite directions along the bond.
-By bending we understand the movement of three bonded atoms A 1 -A 2 -A 3 changing the A 1 A 2 A 3 angle.
-The torsion movement is defined for four bonded atoms A 1 -A 2 -A 3 -A 4 as either a change of angle between two planes (  The computed IR spectra at the DFT/B3LYP-D3/6-31+G(d,p) level is plotted and presented in Fig 3. No imaginary frequency was observed; we can conclude that the molecular structures are stable and that a minimum energy geometry is obtained [37]. A Comparison of computed and experimental IR spectra of TCCG shows good agreement [7]. Thus, a more reliable assignment of IR modes of vibration can be carried out.
The calculated frequencies, as well as the potential energy distributions (PEDs) as implemented in VEDA 4 program [38] of some specific vibrational modes for TCHG, TCFG, and TCCG are listed in Table 4 and discussed in this section.
The calculated IR spectrum of the TCHG molecule exhibits: 3 main stretching bands characterized by C-H (2 bands) and C-C (1 band) bonds and centered at 3245, 3200 and 1511 cm −1 respectively, 1 bending (H-C-C bond) centered at 1301 cm −1 and 2 torsions (H-C-C-C bond) at 818 and 767 cm −1 . We observed two prominent peaks: a peak at 3245 cm −1 which is due to a symmetric and asymmetric stretching of C-H bond with PED contributions of 10 and 77 % and with good agreements to reported experimental range [39]. A second peak is observed at 767 cm −1 and attribuated to bonded H-C-C-C torsion with PED distribution of 49%. For TCFG molecule, the IR spectrum shows 5 peaks located at 1638, 1523, 1475, 1128 and 1006 cm −1 and only affected to stretching of C-C and C-F bonds. We observed a peak with a strong intensity corresponding to an asymmetric stretch of the C-C bond with PED distribution of 21% and asymmetric stretch of C-F bond with PED distribution of 12% all located at 1523 cm −1 . The calculated IR spectrum of the TCCG molecule presents a peak with strong intensity located at 1311 cm −1 related to stretching of C-C bond associated to a PED contribution of 21%.

Density of state (DOS) and frontier molecular orbital (FMO).
The density-of-states (DOS) is a concept in solid physics that allows analyzing the electronic structure and the orbital contribution of the fragments on the compound to the electronic energy. In Fig 4, Partial (PDOS) , overlap (OPDOS) and total (TDOS) curves of studied molecules have been plotted. For TCHG ( Fig 4 (a)), only the atomic orbitals of carbon atoms contribute to the molecular orbitals in the occupied region (from −21.77 to −5.41 eV). In comparison, it is noticed that for TCFG and TCCG, it is not typically the case. As presented , the atomic orbitals of carbon atoms for TCFG ( Fig 4 (b)) contribute from −21.77 to −17.84 and from −9.34 to −6.49, the fluorine atoms contribute from −17.84 to −9.34. For TCCG (Fig 4 (c)), the carbon atoms contribute from −21.77 to −12.77 and the chlorine atoms contribute from −12.77 to −6.31. To explain the charge carrier properties, we have also plotted the spatial distribution of frontier molecular orbitals (FMO) [40]. The HOMO/LUMO orbitals as well as their corresponding energies were determined to study the efficiency of charge transfer in the studied molecules, and also the major charge carriers. As presented, the spatial distribution of both molecular orbitals (HOMO and LUMO) is uniform in all the molecular geometry of studied molecules. This explains that the charge carriers are uniformly distributed over the entire surface of the geometry. In addition, the studied molecules exhibit the π-type frontier molecular orbitals and mainly dominated by the p z orbitals of the carbon atoms.

Linear and nonlinear optical properties
In this section, we present the computation of polarizability tensors α and the first-order static hyperpolarizability tensors β for all the nanographene studied, using the method by derivation of the dipole moment as implemented in the Gaussian 16 package. We Notice that the dipole moment is an important descriptor of the charge distribution in a molecule [15]. The values of the tensors and the averages of the polarizability α 0 and the first static hyperpolarizability β 0 of the studied molecules are reported in Table 5. In this table, the first static hyperpolarizability of TCHG, TCFG and TCCG are 0.93, 215.41 and 462.57 au, respectively. As reported, the substitution of hydrogens by Fluorine and chlorine atoms increases the polarizability and first-order hyperpolarizability. To ensure the reliability of our calculations, we have compared our DFT results on the linear and nonlinear optical properties of para-nitroaniline (p-NA) with its reported experimental values. It is well known that, the p-NA is a typical example of a push-pull molecule [41], commonly used in nonlinear optics [42]. As reported in Table 5, we find that the obtained results for p-NA are in close agreement with the experimental data [43,44]. Compared to our molecules, the first hyperpolarizability of p-NA is four times higher than those of TCCG. Thus, the studied molecules do not exhibit strong first-order nonlinear behavior. However, we notice that the polarizabilities are 8, 9 and 12 times higher than those of P-NA for TCHG, TCFG, and TCCG, respectively. This shows that these molecules have high polarizability values and can be useful as nonlinear material devices.  a Results from dc electric field induced second-harmonic generation (EFISH) experiments, in acetone [43] b Results from gas-phase EFISH measurements [44] Table 7 presents the parameters deriving from the calculation of the electronic energies. Electron affinities, ionization potentials, and calculated intermolecular reorganization energies have been reported. Transport properties, holes, and electrons injection capabilities of the organic semiconductor material can be explained by the ionization potentials (IPs) and electron affinities (EAs) [45,46]. As presented from the same Table, the close values of adiabatic and vertical energies show that geometric relaxations during charge injection are small [47]. Similar to HOMO and LUMO levels, electron affinities and ionization potentials energies increase after substitution by fluorine and chlorine atoms. It is well known that p-type and n-type semiconductor materials are characterized by the lower values of IP, and the higher values of EA, respectively [48,40]. The higher value of EA in n-type semiconductors guarantees the fact that the electronic energy barrier can be overcome, to permit the injection of electrons into the LUMO energy level. As presented in the same Table, the increasing of AEA/VEA energies after substitution of hydrogens by the electrondonor of fluorine and chlorine atoms indicates the facile possibility of electron injections. In addition, Chao et al. [49] signaled that for the air-stable electron carriers, the calculated adiabatic electron affinity (AEA) must be close to or larger than 2.8 eV. It can be seen that the obtained AEAs values for TCFG and TCCG are 2.76 and 2.93 eV, respectively. Indicating the air-stable materials, thus indicating the promising pathway for n-type materials. By regarding the HOMO-LUMO gap in Table 7, and in comparison with the two functionals used, it is noticed that the MN15 overestimates this energy, thus the B3LYP-D3 presents a close agreement with the experimental band gap [7]. We emphasize the fact that the HOMO -LUMO gap energies were evaluated to study the nature of the studied molecules. It is well known that one of the crucial conditions for a semiconductor is that this latter must have an absorption range in the visible region (wavelength between 380 and 760 nm ) [50]. In other words, the threshold wavelength of the photon which must ensure the electron to jump from HOMO to LUMO level must be given by: E gap is the HOMO -LUMO gap.
As presented in Table 7, our calculated absorption wavelength for TCHG, TCFG and TCCG are 391.48, 429.41 and 2.46 nm, respectively. In comparison with TCHG for which the wavelength is near the UV region, it is noticed that the fluorination and chlorination of TCHG create a shift toward the IR region: the fluorination of TCHG is also a good procedure to create the new material for nanotechnology. As presented in Eqs. 3, and according to Marcus-Hush charge transfer theory, we have calculated and listed at the end of Table 7, the reorganization energies of charge carrier for all studied molecules. The reported Λ h /Λ e at the B3LYP-D3/6-31+G(d,p) level indicates that the electron reorganization energy is larger than the hole ones. As presented in Eqs. 3, and according to Marcus-Hush charge transfer theory, we have calculated and listed at the end of Table 7, the reorganization energies of charge carrier for all studied molecules. The reported Λ h /Λ e at the B3LYP-D3/6-31+G(d,p) level indicates that the electron reorganization energy is larger than the hole ones thus, this result is in good agreement with those obtained in section see section 3.1.

Partial conclusion
In the sections developed previously, we have shown the important effect of fluorination and chlorination of the edges of the TCFG molecule on the geometric and electronic properties. We emphasized the fact that the proposed TCFG molecule has good electronic properties through its gap energy and that the latter was stable in air. the B3LYP functional used for the calculation of bond length and IR spectra offers an excellent agreement with the experiment, thus showing the performance of the B3LYP-D3/6-31+G(d,p) method and its reliability in our results. In the following sections, it will be a question of studying the charge transfer properties between the dimers of studied molecules by using the charge transfer theory of Marcus-Hush [16,17].

Stabilization energy and Frontiers molecular orbitals
In Fig 5, we summarized the geometries of the TCHG, TCFG, and TCCG dimers as optimized at the ωB97XD/6-31G(d) level of theory. As seen, the TCHG dimer adopts a planar configuration while the TCFG and TCCG dimers are distorted. We emphasize here the crucial role of the Long-Range corrected hybrid functional in the prediction of geometric structures of non-bonded interactions. To analyze the stability of our dimers, we have calculated and consigned in Table 6 the binding energies (with and without the contribution of basis set superposition error (BSSE) corrections [51,52]), using the formula E b = E dimer (∆d) − 2 × E monomers , with E dimer (∆d) the total energy at the optimized distance ∆d (as implemented in Mercury program [53]) between the center of mass of the monomers. Thus in further analysis, we have noticed that : (i) the calculated intermolecular distances (∆d) for TCHG, TCFH and TCCG are 3.677, 3.638 and 6.920Å, respectively. Thus showing a strong intermolecular repulsion in the dimeric system of the TCCG molecule. (ii) the BSSE corrections are found to be small and slightly increase the binding energy. According to Sanyal et al. [20], the higher the modulus of the binding energy value, the lower is the stability. Thus, the TCFG nanographene appears more stable than TCHG and TCCG.We conclude that the process of formation of the nanographene TCFG is more energetically favorable than that of TCHG and TCCG molecules.  Fig 6 do not exhibit the π − π overlap orbitals because it is well known that the systems with this type of overlap generally have high electronic mobilities [20].

Estimating hole and electron mobilities
Although we already have a qualitative idea about the properties of charge carriers through the energies of electronic reorganization and charge transfer energies, it is important to investigate the charge carrier's mobilities for the dimeric structures considered. As presented in Table 8, our results show that the mobilities of the hole carriers for the TCHG and TCFG dimers are significantly greater, almost 3 and 5 times, than electronic mobility, respectively. However, for the case of the TCCG molecule, the opposite effect is noted, the mobility of electron carriers is almost 10 times greater than that of holes. For the specific case of TCCG, it is obvious that the major charge carriers are electrons (µ e /µ h ≈ 10): indicating a promising pathway to an ambipolar material.   7: Estimates at B3LYP-D3/6-31+G(d,p) level of reorganisation energies (Λ e ) and (Λ h ) for electrons and holes (in meV), adiabatic (A), vertical (V) ionization potential (IP, in eV) and electron affinity (EA, in eV), HOMO energy level (E H , in eV), LUMO energy level (E L , in eV), HOMO-LUMO gap energy (E gap , in eV) and the threshold wavelength of the HOMO -LUMO transition (λ, in nm) for studied molecules. The values in parenthesis are the experimental bandgap energies for the TCHG and TCCG molecules [7] .  Table 8: Estimates at PW91PW91/cc-pVTZ level of hole (h) and electron (e) effective electronic couplings (V ef f , in meV), corresponding charge transfer rates (K CT × 10 13 , in s −1 ) and hole/electron mobilities ( µ h/e , in cm 2 V −1 s −1 ) for all studied dimers.

conclusion
In summary, we have theoretically investigated structures, electronic parameters and charge transport properties of fluorinated and chlorinated nanographene of benzo[o]bistriphenyleno[2,1,12,11-efghi:2',1',12',11'-uvabc]ovalene and so-called tetracosahydro-C60graphene (TCHG) molecule. The DTF method was coupled to Marcus-Hush hopping charge transport model to describe the hole and electron mobilities. The geometric analysis made by B3LYP-D3/6-311++G(d,p) level of theory indicates that the bond lengths and IR spectrum are in good agreement with experimental data for the chlorinated TCHG. The calculated results reveal that the introduction of withdrawing substituents of fluorine (-F) and chlorine (-Cl) atoms significantly reduces the bandgap energy of TCHG, stabilizes the frontier molecular orbital, and enhances the air-stable materials. The obtained high mobility of electrons for chlorinated molecules indicates the promoted ambipolar material. In the present theoretical protocol, it was a question for us to study for the first time the effect of the withdrawing substituents of fluorine and chlorine atoms on the charge transport of the TCHG molecule. Our results will thus allow us to promote a pathway towards the new ambipolar materials derived from TCHG and potentially useful in the field of optoelectronic.

Conflict of interest
The authors declare that they have no conflict of interest.