Perhalogenation and Percyanation of Coronene for Characterization of the New Ecient Organic Semiconductors for Charge Transport

We have investigated the structures, electronic properties, hole and electron mobilities of perﬂuorinated, perchlorinated and percyanated coronene molecules, using the density functional theory (DFT) at the B3LYP-D3/6-311++G(d,p) and ω B97XD/6-311++G(d,p) levels and Markus-Hush charge transfer theory. The calculated geometric parameters for coronene and perchlorocoronene are in good agreement with the experimental data. Our theoretical investigations have shown B3LYP-D3 functional is suitable to well deﬁne vibrational assignments for studied molecules. We have shown that the per-halogenation and per-cyanation of coronene increases the adiabatic electron aﬃnities (AEAs) and reduces the LUMO levels and the hole mobilities thus indicating an ambipolar behavior and air-stable material. We have shown that the percyanation of coronene is a promising pathway for the design of new materials useful in optoelectronics. perchlorocoronene and percyanocoronene respectively. The close values of the magnitude bond-length change during reduction and oxidation processes indicate a balanced charge transfer and the potentially close values of hole and electron reorganisation energies.

2 Theoretical and computational models 2.1 Theoretical models

Electronic properties
The vertical electron affinity and ionization potential (VEA and VIP, respectively), adiabatic electron affinity and ionization potential (AEA and AIP, respectively), 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 [21,22,23,24,25] : and 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.

Charge transport properties
There are several theoretical models to describe the transport properties in organic materials. The model used in this work to perform the charge transfer rate is the Marcus-Hush theory [26,27] and so called the hopping model. The Marcus-Hush approach was used for two main reasons. First, it describes the charge transfer through the intermolecular interactions between adjacent molecules of a crystal system by the hopping mecanism. Second, it correctly describes the anisotropic mobilities for organic molecular compounds [4]. The charge transfer rate K, according to the electronic hopping mechanism is given as follow [26,27] V ef f is the effective intermolecular coupling energy between two adjacent dimers of the crystal, K B is the Boltzmann constant, T is the temperature (in our case, it was set at 298.15 K). The drift mobility of the charge carriers is calculated according to a random hopping model, known as the Einstein relation [28] and is given by Where, e is the elementary charge and R, the distance between the considered monomers. The effective charge transfer integral V ef f is performed according to Eq. 9. It principally depends on transfer integral V 12 , on overlap integral S 12 between the fragments considered and on site energies ε 1 and ε 2 of the two molecular orbitals where charges are localized [2]: With, In these equations, ψ H/L 1 and ψ H/L 2 represent the highest occupied molecular orbitals (HOMO) / lowest unoccupied molecular orbital (LUMO) of the two monomers considered andĤ ks is the Kohn-Sham Hamiltonian of the dimer system used for the calculation of charge transfer.
Perhalogenation and percyanation of coronene for characterization of the new efficient organic semiconductors for charge transport. 3

Computational details
The geometry optimization and electronic properties of studied molecules was carried out using the dispersion-corrected functionals B3LYP-D3 [29,30] and the long-range dispersion corrected hybrid exchange and correlation functional ωB97XD [31] using the 6-311++G(d,p) basis set. The intermolecular coupling energies between the dimers have been calculated at the same levels. The choice of DFT is justified by the fact that: -It offers an excellent compromise between computation time and electronic correlation [32]; -It is well known that the B3LYP hybrid fuctional offers the good description of geometric stucture in charge transfer mechanism [33,34,35,36]. And it is often used in the literature to easily predict the reorganization energies of aromatic π-conjugated organic molecules [37,38].
All calculations in this document are made using Gaussian 16 software package [39]. The coupling energies, V ef f (see Eq. 9) were calculated with the aid of calc J package [40] which uses the direct calculation method (see refs [41,42] for more details).

Geometric and electronic structure
The geometries of experimental single coronene and perchlorocoronene molecules were extracted from their crystalline structure and presented as follow: a=16.119Å, b=4.702Å, c=10.102Å, α=90 • , β=110.9 • , γ=90 • , space group P21/a for coronene [10] and a=22.217Å, b=8.214Å c=12.921Å, α=90 • , β=90 • , γ=90 • , space group Cmca for perchlorocoronene [43]. The crystallographic information file (CIF) of these two crystalline structures were taken from Cambridge structural database (CSD) (N • 1129883 and N • 1181564, respectively). The molecules of perfluorocoronene and percyanocoronene have not been synthetised yet and were constructed intituively starting from the molecular geometry of coronene molecule. Fig. 1 shows the optimized ground state structure of studied molecules. It is important to specify that the figures optimized at the B3LYP-D3 and ωB97XD levels are nearly identical and do not present any major differences with bond lengths differing more than 0.012, 0.011, 0.012 and 0.012Å for coronene, perfluorocoronene, perchlorocoronene and percyanocoronene, respectively (see Tables S1-S4). As presented, the substitution of the hydrogen by chlorine atoms or cyano group induces a distrosion of the initial geometry, which is not the case for the substitution by fluorine atoms. According to Erkoç et al. [44], these effects can be attribuated to the size of the different atoms used. Tables S1-S4 also collect the neutral, anionic and cationic bond lengths of studied molecules, using the B3LYP-D3 and ωB97XD functionals. In order to well define the effect of B3LYP-D3 and ωB97XD functioanls on optimized bond lenghts of coronene and perchlorocoronene molecules, we calculated the average deviation ∆R throught the Eq 14 as: R i and R exp i represent the calculated and experimental ith bond lengths for considered studied molecule. The computed ∆R B3LY P and ∆R ωB97XD are respectively 0.014 and 0.014Å for coronene and for perchlorocoronene it is 0.025 and 0.024 A. By comparision, the bond lengths are slightly different than the experimental values for the two functionals used, showing that B3LYP-D3 and ωB97XD well define the geometry of coronene and perchlorocoronene molecules. In addition for the coronene molecule, the deviation between the calculated bond lengths of ground state and the experimental data range from 0 to 0.038Å for B3LYP-D3 and from 0 to 0.036Å for ωB97XD. For the perchlorocoronene molecule we show that the deviation between the calculated bond lengths of ground state and the experimental data range from 0.006 to 0.043Å for B3LYP-D3 and from 0.005 to 0.052Å for ωB97XD. This shows that the functionals used are suitable for study the titled molecules. The bond length variations between neutral and anionic/cationic geometries for studied molecules have been plotted with the values given in Tables S1-S4 and shown in Fig. 2. The oxidation/reduction curves correspond to the difference between the bond length of the neutral state and its corresponding in the cationic/anionic state. As presented, the variations in bond length appear on almost all of the entire molecules. This is certainly due to the presence of the extended π-system [45]. To quantitatively elaborate the geometric distortions during charge transfer, we have calculated the magnitude of
The computed IR spectra at the DFT/B3LYP-D3/6-311++G(d,p) and DFT/ωB97XD/6-311++G(d,p) levels are plotted and presented in Fig. 4. No imaginary frequency was observed; we can conclude that the molecular structures are stable and that a minimum position of the potential energy surface is obtained for each studied geometry [47]. A Comparison with calculated (unscaled) and experimental IR frequencies for coronene shows closer agreement at the B3LYP-D3 level than that obtained with ωB97XD (see Table 1). Thus, a more reliable assignment of IR modes of vibration can be carried out at the B3LYP-D3/6-311++G(d,p) level for coronene and related molecules.
The calculated frequencies, as well as the potential energy distributions (PEDs) as implemented in VEDA 4 program [48] of some specific vibrational modes for studied molecules are listed in Table 1 and discussed in this section. We noted a maximal absorption in the coronene molecule, strongly affected by a streching of the C-H bond (with PED contribution of 93%), centered at 3173.12 cm −1 and which coincides well with the experimental observation (3199.3 cm −1 ). The perfunctionalization of the coronene with heteroatoms of fluorine, chlorine or with the cyano group induces a shift of the maximum peak towards frequencies respectively centered at 1390.6, 1321.25 and 1470.06 cm −1 and for which the vibrational assignments and PED contributions are collected in Table 1. We have also found the highest PED contributions for the respective cases of coronene, perfluorocoronene, and perchlorocoronene molecules of 93, 21 and −16 %, centered at 3173.1, 1678.3 and 719.10 and whose assignments are collected in the same table 1. Thus showing the effect of the perfunctionalization of the coronene molecule by the fluorine and chlorine heteroatoms on the intensity of the stretching effects of the peripheral C-X (X = F, Cl) bonds.

Frontier molecular orbitals (FMO).
In this section, we explain the charge carrier properties of studied molecules throught the spatial distribution of frontier molecular orbitbals [50]. The HOMO/LUMO orbitals as well as their corresponding energies were determined to study the efficiency of charge transfer, and also to study the major charge carriers. In order to compare our result with the experimental data, we have choosen to compute the HOMO-LUMO gap energies using three main DFT functionals, as B3LYP-D3, ωB97XD, HSE using the same basis set 6-311++G(d,p). We emphasis the performance of HSE functional in prediction of gap energy of molecular systems [51]. The calculated HOMO-LUMO gap of studied molecule are collected in Table 2 and discussed in this section. As seen, the gap energy of coronene shows a close agreement between B3LYP-D3, HSE methods, 4.00 and 3.63eV respectively and experimental data, 3.37 eV. While the ωB97XD functional overestimates the gap energies, it was shown that the B3LYP-D3 presents a good agreement with the experimental value. Thus, more realistic diagrams of molecular orbitals can be done at the DFT/B3LYP-D3/ 6-311++G(d,p) level.
As presented in Fig. 5, the spatial distribution of both molecular orbitals (HOMO and LUMO) are uniform in all the molecular geometry of studied compounds. Explaining that the charge carriers are uniformly distributed over the entire surface of the geometry. In addition, the studied compounds exhibit the π-type frontier molecular orbitals and mainly dominated by the p z orbitals of the carbon atoms. From the same figure, it was noted that the gap energies and the LUMO level decrease during halogenation and cyanation. But it is not the case for the HOMO level. The calculated gap energies for coronene, perfluorinated and perchlorinated coronene are slightly higher than those performed by Sancho-García and Pérez-Jiménez [21] at the B Λ LYP/def2-TZVP level (4.30, 4.10 and 3.54 eV, respectively). We emphasis in the fact that, the HOMO -LUMO gap energies were evaluated to study the nature of the compounds studied. 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 ) [52]. In other words, the threshold wavelength of the photon which must ensure the electron to jump from HOMO to LUMO level is given by: where the numerator 1240 eV nm representes the product of Planck's constant(h, in eV s) by the celerity of light(c, in m/s) and E gap is the HOMO -LUMO gap. Our B3LYP-D3 calculated absorption wavelength for coronene (λ = 310nm) agree well with those obtained experimentally (λ = 377nm) by the ultraviolet photoelectron spectroscopy (UPS) measurments [53]. Compared to coronene, we expected that percyanation of coronene causes a shift of this wavelength from the ultraviolet to visilble region. This is effectively the case for this compound for which λ is equal to 393 nm.

Electron affinity and ionization potential
We have reported in Table 2 the properties derived from the calculation of the electronic energies. Electron affinities, ionization potentials and 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) [54,1]. As presented from this table, the close values of adiabatic and vertical energies at the two theoretical levels show that geometric relaxations during charge injection are small [55]. Electron affinities increase after substitution of the different groups, which is not really suppressing with regard to the similar behavior for the energies of the LUMO level commented in the section 3.3. Our estimated vertical electron affinity/ionization potential of coronene are respectively 0.45/7.13 eV at the B3LYP-D3 and 0.24/7.26 eV at the ωB97XD levels, showing close agreement in comparison to the available experimental data (0.47/7.29 eV) from photoionisation threshold [53,56]. It is well known that, n-type organic semiconductors are characterized by high electron affinity [57,50]. In opposition to coronene, for which majority charge carriers are the holes [2], percyanocoronene are promising materials for charge transport by electrons (ambipolar materials). In addition, Chao et al. [58] 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 percyanocoronene at the two levels of theory B3LYP-D3 and ωB97XD are 4.66 and 4.52 eV, respectively. This indicates an air-stable material.

Partial conclusion
In this section, we have shown the important effect of perfluorination, perchlorination and percyanation of the coronene molecule on the geometric and electronic properties. We have emphasized the fact that the proposed percyanocoronene molecule has good electronic properties through its gap energy and that the latter is stable in air. The B3LYP-D3 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-D3/6-311++G(d,p) method and its reliability in our results.

Reorganization energies
As presented in Eqs. 5 and 6, and according to Marcus-Hush charge transfer theory, we have calculated and reported in Table 2, the reorganization energies of charge carrier for all studied molecules. We need to mention that the calculated reorganization energies of coronene and related molecules do not take into account the external reorganisation energy due to the polarization effect. The reason is that, the calculation of this energy is very dificult due to the presence of the other molecules of crystal in the solid state [59,60,61,62]. The reorganisation energies for all the studied molecules show that λ e is higher than λ h . Thus, the creation of holes is more favorable in these materials than the introduction of electrons, which leads to a mobility by the holes (µ h ). We emphasise in the case of coronene that our estimates of the electron and hole reorganisation energies at the B3LYP-D3/6-311++G(d,p) level (λ e =170 meV, and λ h =128 meV are slightly lower than previous estimates at the B3LYP/6-311++G(d,p) level (λ e = 172 meV, λ h = 129 meV) [2]. This difference represents the energy of the 3rd order Grimme correction (D3 term) [63] which was used in our results to obtain more refined energy values. However, in comparison with the functional B3LYP-D3, the estimated values of the reorganization energies at the ωB97XD/6-311++G(d,p) level are very high, thus showing an overestimation of these energies. We also noted that the reorganization energies of the holes are very close to those of the electrons regardless of the method used. This result, therefore, confirms that: i the charge transport are balanced between the holes and the electrons (see section 3.1); ii the geometric distortions during the electron transfer (from neutral state to anionic state) are identical to the geometric distortion during the hole transfer (from neutral state to cationic state).

Calculations in dimers systems
We summarized in Table 3, all properties related to the charge transport of the optimized dimers obtained by halogenation and cyanation of coronene (see Fig. 3). The coupling energies (V ij and V ef f ) were calculated using two different levels of theory in order to show a close dependence on the method used, and the important contribution of the energy of dispersion interactions in π-stacked dimers. We noted for the case of the coronene dimer that our results obtained at the B3LYP-D3/6-311++G(d, p) level of theory shows a close agreement with the theoretical previous estimates at the PBEPBE/TZ2P level [2]. Thus showing the performance of calc J package in the prediction of charge transfer properties. The equilibrium interaction distances, R eq (between the centroids of each monomer) were calculated and compared to those obtained from theoretical predictions. Our results obtained at the B3LYP-D3 and ωB97XD levels for the coronene dimer are respectively 3.733 and 3.684Å thus showing a close agreement with the results obtained by Sancho-García and Pérez-Jiménez [21], R eq = 3.74Å (at the B Λ LYP-D3/def2-TZVP level), but slightly higher than those obtained by Sanyal et al. [2], R eq = 3.45 A (at the ωB97XD/6-311++G(d,p) level). As can be seen in the same Table 3, the equilibrium interaction distances for perchlorocoronene and percyanoronene dimers show high parallel shifts, thus indicating low charge transfer rates in these dimeric systems. We find that the calculated V ef f of hole at the B3LYP-D3 level is significantly larger than that of electron one for all the dimeric system studied, indicating a transport by holes. We noticed a significant increase in the adiabatic electron affinity (AEA), a decrease in the energy of the LUMO level (See Table 2), and a considerable decrease in the mobility of the holes, due to the full substitution of the hydrogen atoms by the fluorine, chlorine, and cyanide electron-donor groups: thus indicating ambipolar behavior. In addition, it is important to note that lowering the LUMO level also reduces the hole injection barrier and promotes the development of n-type materials. Thus it is obvious that the cyanation of coronene appears to be a very promising path for the development of organic semiconductors (OSC).

Conclusion
In summary, we have theoretically investigated structures, electronic parameters and charge transport properties of perhalogenated and percyanated coronene. The DTF method was coupled to Marcus-Hush hopping charge transport model to describe the hole and electron mobilities. The geometric analysis indicates that the bond lengths are in good agreement with experimental data for coronene and perchlorocoronene. The calculated results reveal that, the introduction of halogens or cyanide groups (-CN) significally reduces the bang gap energy of coronene, stabilizes the frontier molecular orbital and enhance the air-stable materials. The obtained high mobility of electrons for percyanated coronene indicates that percyanocoronene is the promoted ambipolar material. In the present theoretical protocol, it was question for us to study for the first time the important effect of the electron-donor substituents of cyanide groups on the charge transport properties of coronene. Our results will thus allow to promote pathway towards the new ambipolar materials derived from coronene and potentially useful in the field of optoelectronic.       Table 3: Estimates of hole (h) and electron (e) effective electronic couplings (V ef f , in meV), the center-of-mass distance ( R inÅ) and the drift electrons/hole mobilities (µ e/h , in cm 2 V −1 s −1 ) for studied molecules.