Computational investigation of the effects of perfluorination on the charge-transport properties of polyaromatic hydrocarbons

Accepted Manuscript Computational investigation of the effects of perfluorination on the chargetransport properties of polyaromatic hydrocarbons R. Cardia, G. Malloci, A. Bosin, G. Serra, G. Cappellini PII: DOI: Reference:

S0301-0104(16)30213-0 http://dx.doi.org/10.1016/j.chemphys.2016.06.015 CHEMPH 9589

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Chemical Physics

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11 March 2016

Please cite this article as: R. Cardia, G. Malloci, A. Bosin, G. Serra, G. Cappellini, Computational investigation of the effects of perfluorination on the charge-transport properties of polyaromatic hydrocarbons, Chemical Physics (2016), doi: http://dx.doi.org/10.1016/j.chemphys.2016.06.015

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Computational investigation of the effects of perfluorination on the charge-transport properties of polyaromatic hydrocarbons R. Cardiaa,b , G. Mallocia,∗, A. Bosina , G. Serraa , G. Cappellinia,b,∗ a

Universit` a degli studi di Cagliari, Dipartimento di Fisica, Cittadella Universitaria, I-09042 Monserrato (Cagliari), Italy b Istituto Officina dei Materiali (CNR - IOM), UOS di Cagliari, Cittadella Universitaria, I-09042 Monserrato, Cagliari, Italy

Abstract We present a systematic computational study of the effects of perfluorination on the charge-transport properties of three homologous classes of polyaromatic hydrocarbons of interest for molecular electronics: acenes, pyrenes, and circumacenes. By means of Density Functional Theory calculations we first obtained the key molecular properties for transport of both holes and electrons. We then used these parameters in the framework of Marcus theory to compare charge-transfer rates in the high temperatures regime for both unsubstituted and perfluorinated molecules. We additionally estimated the relative charge-mobility of each unsubstituted (perfluorinated) molecule with respect to unsubstituted (perfluorinated) pentacene. We found in all cases that perfluorination reduces the charge-transfer rate in absolute terms. This is largely due to the higher values of the molecular reorganization energies ∗

Corresponding Authors: Email addresses: [email protected] (G. Malloci), [email protected] (G. Cappellini)

Preprint submitted to Chemical Physics

July 8, 2016

predicted for perfluorinated compounds. Interestingly, however, the chargetransfer rates for both holes and electrons of perfluorinated species are remarkably similar, especially for the larger species. In addition, in the case of the larger circumacenes the charge-mobility values relative to pentacene values are found to increase upon perfluorination. 1. Introduction Efficient charge transport in organic materials is of paramount importance for their use as active elements in electronic devices. Carrier mobilities can be finely tailored by chemical modification of the molecular building blocks composing the material. Alteration with strong electronegative substituents, for example, is an effective approach for converting p-type organic semiconductors to n-type [1,2] . To obtain bipolar transistors, in fact, it would be important to have both n-type and p-type organic semiconductors with similar physical and electrical properties [3,4] . Polyaromatic hydrocarbons (PAHs) in their crystalline state are widely used for different applications in molecular electronics. For these compounds, however, it has turned out to be more difficult to achieve n-type transport; e.g., pentacene based organic field-effect transistors exhibit hole mobilities one order of magnitude larger than the electron ones [3] . Typically, n-type materials based on PAHs are produced by attaching to the conjugate core strong electron-withdrawing groups such as CN [5] or by replacing the peripheral hydrogens with halogen atoms (e.g., fluorine and clorine) [4,6] . Fluorine atoms, in particular, may confer unique qualities: halogen atoms are known to lower both the highest-occupied and lowest-unoccupied molec2

ular orbital energy levels. As a consequence, the electron injection is made easier, the materials display greater resistance against the degradative oxidation processes and organic n-type or ambipolar semiconducting materials may result. Moreover, Carbon-Hydrogen-Fluorine (C-H-F) interactions play a key role in the solid state supramolecular organization, giving rise to a typical π-stack arrangement which enhances charge carrier mobility [7,8] . Theoretical calculations of the building blocks of organic seminconductors can contribute to the knowledge of their properties and provide guidelines for dedicated applicative research [9,10,11,12] . A widely adopted framework to compute the charge-transport properties of organic-based semiconductors is the semi-classical Marcus theory [13,14] . This theory describes charge-transfer as a self-exchange hole(electron)-transfer chemical reaction between adjacent molecules. Marcus theory has been applied extensively in conjuction with quantum-chemical calculations to evaluate charge-transport properties of organic semiconductors (see e.g. Ref.[ 15,9,10,11,12]). In this work we followed the same approach adopted in previous investigations [15,16,17,18] to quantify the effects of perfluorination (complete substitution of the peripheral hydrogens by fluorine atoms) on the charge-transport properties of three homologous classes of PAHs, namely acenes (C4n+2 H2n+4 ), pyrenes (C6n−2 H2n+4 ), and circumacenes (C8n+8 H2n+8 ). The molecules considered, corresponding to n=3,4,5, are sketched in Fig. 1; they cover an ample range of different possible PAHs morphologies from linear to compact, to ultracompact ones. Circumacenes, in particular, characterized by large conjugated cores, have been previously proposed as promising candidates for future technological applications [19] .

3

We first computed the intrinsic molecular properties for charge-transport of both holes and electrons by means of well established Density Functional Theory calculations. In particular, for the calculation of the electron couplings we considered in all cases the simplified approximation of facially stacked structures. It is well known that molecular parameters of charge transport depend on the packing of the monomers in the crystal. Supramolecular issues have been therefore extensively addressed in the literature from both the experimental and theoretical points of views, especially for nonfunctionalized and functionalized linear acenes [20,21,22,23,24] . In particular, the formation of package structures with a high degree of π-overlap is believed to facilitate charge migration [25] . The face-to-face π-stacking motif is thus more efficient for charge transport than the edge-to-face herringbone-packing structures typical of organic semiconductors such as pentacene, rubrene etc. [25,26] . Several studies have shown that the face-to-face π stacking is more common with molecules possessing a two-dimensional extended aromatic system and is rarely observed for linear molecules such as oligoacenes [27] . For PAHs with large conjugated cores, in particular, self-assembly via strong π-π interactions has been demonstated to result in the formation of one-dimensional nanostructures [28,29] . Based on the above considerations, since our sample includes molecules expected to pack in very different ways, for comparative purposes we decided to adopt the simplified approximation of treating on the same footing all of the linear, compact, and ultracompact species investigated. We subsequently used the above parameters in the framework of the semiclassical Marcus theory to compare charge-transfer rates in the high temperatures regime for both unsubstituted and perfluorinated molecules. To ease

4

the comparison between molecules we additionally estimated the relative charge-mobility of each unsubstituted (perfluorinated) molecule with respect to unsubstituted (perfluorinated) pentacene, which is a benchmark in the field of organic semiconductors (in particular as hole transporter).

Figure 1: Skematic depiction of the different families of PAHs investigated. Acenes (top): anthracene, tetracene, pentacene (C4n+2 H2n+4 , n=3,4,5); Pyrenes (middle): pyrene, anthanthrene, peri-naphthacenonaphthacene (C6n−2 H2n+4 , n=3,4,5); Circumacenes (bottom): ovalene, circumanthracene, circumtetracene (C8n+8 H2n+8 , n=3,4,5).

2. Computational details In the framework of Marcus theory [13,14] the charge-transfer rate KCT in the weak-coupling regime is described as a self-exchange hole(electron)transfer chemical reaction between adjacent molecules. KCT is expressed by

5

the following equation: [30,31,32]   √ π t2 λ √ KCT = exp − ~ λkB T 4kB T

(1)

in which kB is Boltzmann’s constant and T is the absolute temperature. As shown by the above equation, the charge-transfer rate KCT depends critically on two parameters: the intramolecular coupling, or reorganization energy (λ), and the electronic coupling between adjacent molecules, or transfer integral (t). Since λ enters in the argument of an exponential, it has a stronger influence in the hopping rate and, as a consequence, on the mobility of the charge carriers. We computed both quantities t and λ at the Density Functional Theory level by using the hybrid exchange-correlation functional B3LYP [33] in conjunction with the Gaussian basis-set 6-31G? . The combination B3LYP/6-31G? is widely adopted for the calculation of a vast range of very different compounds, from organic antibiotics [34] to inorganic nanocrystals [35] . All quantum chemical calculations have been performed with the NWChem 6.5 package [36] starting from the geometry available in Ref. 37 for each molecule reported in Fig.1. The use of the B3LYP functional is rather standard and some limitations are well documented, such as the system-size-dependent errors found for the lowest short-polarized electronic transitions of oligoacenes [38] . In the specific case of PAHs, we have checked in previous works [39,40,18] both the sensitivity of our calculations to different DFT functionals, and their reliability in comparison with available experimental data. Our benchmark investigations included long-range corrected functionals such as CAMB3LYP [41] , which has been devised to handle the wrong asymptotic behaviour of B3LYP which decays faster than 1/R for large distances R from the nuclei. 6

With only a few exceptions we found that the hybrid B3LYP functional yields the overall best performance by considering electronic, optical, and transport properties. Note that, while the performances of the B3LYP functional for evaluating key transport properties in conjugated materials can be improved by precisely calibrated DFT functionals [42] , its use in the present work is justified since it is expected to describe reasonably well the differences arising upon perfluorination in the different families considered. The molecular reorganization energy λ is composed by two terms, the inner and external terms. The latter, in particular, is associated to the reorganization energy of the surrounding medium [19,43] and has found to be of negligible importance for oligoacenes [44] . Following previous works, e.g. Ref. 19, we therefore neglected this term and computed the inner contribution to λ by using the so-called four-point method [45,46] . This method requires the separate geometry optimization of the neutral (En ) and charged molecules (Ec ) and the single-point energy calculations of the neutral molecule at the (c)

charged geometry (En ) and of the charged molecule at the neutral geometry (n)

(Ec ): λ = λ1 + λ2 = (En(c) − En ) + (Ec(n) − Ec ).

(2)

Concerning the calculation of the charge transfer integral t (or electronic coupling), it is possible to use the so-called energy splitting in dimer method [47,48,49,50] . The application of the method for holes(electrons) assumes the knowledge of the HOMO(LUMO+1) and HOMO-1(LUMO) energies of the closed-shell configuration of the nuetral state of the dimer, as well as the site energies of each isolated molecule in the dimer. In the simplified case of

7

symmetrically arranged molecules: th[e] =

εHOMO[LUMO+1] − εHOMO−1[LUMO] 2

(3)

In particular, by moving the monomers along the vertical axis with respect to each other, we evaluated the above equation at the distance at which the interaction energy between two facially stacked molecules is at its minimum. To this aim we used the same B3LYP/6-31G? method employed for monomers calculations with the additional inclusion of an empirical longrange contribution [51] to account for van der Waals interactions (B3LYP-D). Interaction energies are corrected for the basis-set superposition error using the counterpoise method [52] . The computational procedure adopted to estimate the transfer integral t is described in detail in the Appendix A. Using Marcus theory it is also possible to obtain the relative chargemobilities, which are key physical quantities for charge-transport. In the zero-field limit, absolute values of mobility can be estimated through Einstein equation µ = eD/kB T , where D is the charge-diffusion coefficient. For a one dimensional charge transport D = 1/2 l2 KCT , l being the distance between the molecules in the dimer involved in the hopping process [53] . From Eq.1, the ratio of the charge carriers mobility of a given compound (MOL) with respect to a reference one (REF) can be thus expressed as: r  2  2 λ  µM OL KCT,M OL dM OL t2M OL λREF dM OL REF − λM OL = = 2 exp µREF KCT,REF dREF tREF λM OL dREF 4kB T (4) where dM OL and dREF are the interplanar distances for the given and reference compounds, respectively. Note that, the explicit dependence of the relative mobility on the intermolecular distance in the packing is usually ne8

glected by assuming that the best intermolecular distance is the same for both the system of interest and the reference compound. Equations 1 and 4 have been evaluated in the temperature range 150400K chosen to match at best the domain of validity of Marcus theory [54] and including the high-temperature region particularly important for technological applications [55] . 3. Results and discussion 3.1. Reorganization energies and transfer integrals

Figure 2: Molecular reorganization energies (λh continuous line, λe dotted line) of unsubstituted (left) and perfluorinated (right) acenes (red diamonds), pyrenes (blue squares), and circumacenes (green circles), as a function of the inverse of the total number of carbon atoms.

Table 1 reports the reorganization energies λ and transfer integrals t as computed at the B3LYP/6-31G? level using Eqs.2 and 3 for both unsub9

Unsubstituted

Perfluorinated

n λh

λe

th

te

λh

λe

th

te

Acenes (C4n+2 H2n+4 ) 3

138

200

205

214

309

364

251

275

4

112

160

210

222

257

281

276

305

5

94

132

213

229

221

225

255

287

Pyrenes (C6n−2 H2n+4 ) 3

155

212

223

219

327

342

261

265

4

117

154

245

240

252

258

266

268

5

90

116

254

251

204

200

269

273

Circumacenes (C8n+8 H2n+8 ) 3

97

123

267

262

195

203

274

248

4

75

93

266

263

161

158

276

281

5

58

69

288

284

134

123

277

282

Table 1: Comparison between reorganization energies for holes and electrons (λh and λe ), and transfer integrals (th and te ) as computed at the B3LYP/6-31G? level using Eqs.2 and 3 for both unsubstituted and perfluorinated molecules. All values are given in meV.

stituted and perfluorinated molecules. The reorganization energies are displayed in Fig.2 as a function of the inverse of the total number of carbon atoms NC . The picture shows clear trends in all cases. More specifically, for unsubstituted molecules the reorganization energies for electrons are always found to be higher than the corresponding quantities for holes. The scatters between λh and λe decrease at increasing molecular size. The slopes appear to increase when going from acenes to pyrenes, to circumacenes. These re-

10

sults agree with previous findings [19,40] , and confirm that circumacenes are indeed good candidates for new emerging technologies. The effect of perfluoration on λ is twofold. As compared to their corresponding unsubstituted counterparts, perfluorinated species present very close values for λh and λe . In addition, perfluorinated species show more pronounced slopes for both λh and λe for each family considered. On the contrary, we could not find clear trends for the computed transfer integrals which, on average, increase for each series as a consequence of perfluorination. 3.2. Charge-transfer rates and relative mobilities Figure 3 compares the charge-transfer rate KCT computed through Eq.1 (values from Table 1) for the plain and perfluorinated molecules considered. Along each unsubstituted and perfluorinated family the charge-transfer rates for both holes and electrons follow similar trends as a function of temperature and increase at increasing n. For all unsubstituted molecules the chargetransfer rate KCT for holes is always higher than the corresponding quantity for electrons. This is especially true for pyrenes and, to a lesser extent, for acenes. For each family the difference between the two quantities decreases slightly at increasing molecular size. Interestingly, the curves corresponding to the larger molecules of the three families (n=5, orange lines) appear to have the same behaviour although they are shifted upward going from acenes to pyrenes to circumacenes. Perfluorination gives rise to sensible changes of the charge-transfer rates in all cases. First, the curves for the perfluorinated species are qualitatively different from those of the corresponding plain molecules and display a steeper increase of KCT with increasing temperature. In addition, from a quantitative point of view, the values of KCT for both 11

Figure 3: Charge transfer rate KCT (holes continuous line, electrons dotted line) for unsubstituted (left) and perfluorinated (right) acenes (bottom), pyrenes (middle), and circumacenes (top), as a function of the absolute temperature (see Eq.1). In each molecular family the brown, violet, and orange curves correspond to n=3,4,5, respectively.

holes and electrons appear to be greatly reduced in the whole temperature range considered. This reflects the higher molecular reorganization energies of the perfluorinated compounds. For example, at the fixed temperature

12

T=300K, the rate decreases by 70-80% for holes and 50-60% for electrons following perfluorination. Interestingly, however, the charge-transfer rates for both holes and electrons of perfluorinated species are remarkably similar, especially for the larger species considered. Again, this reflects the very close values of λh and λe for perfluorinated species. In addition, at variance with unsubstituted molecules, for perfluorinated species the rates for electron-transfer tend to overcome that for holes as n increases along the series. Similar to Fig. 3, Fig. 4 compares the relative mobility µrel computed through Eq.4 for the unsubstitued and perfluorinated molecules. To ease the comparison in the whole sample considered, for both pure and functionalized molecules the hole and electron mobilities values have been expressed in terms of the corresponding values for pure and functionalized pentacene. Like for KCT in Fig. 3, the relative mobilities µrel for both holes and electrons follow similar trends as a function of temperature. In particular, the left panel of Fig. 4 confirms once again the promising transport properties of circumacenes [19,40] , that appear to outperform pentacene in all cases. Notably, with the only exception of electron transfer in ovalene (dotted curve, n=3), perfluorination appears to further improve the charge mobility in comparison to that of perfluorated pentacene. 4. Conclusions Summing up, we have performed a systematic computational investigation on the effects of perfluorination on the charge-transport properties of three homologous classes of polyaromatic hydrocarbons of interest for molec13

Figure 4: Charge mobility relative to pentacene µrel (holes continuous line, electrons dotted line) for unsubstituted (left) and perfluorinated (right) acenes (bottom), pyrenes (middle), and circumacenes (top), as a function of the absolute temperature (see Eq.4). In each molecular family the brown, violet, and orange curves correspond to n=3,4,5, respectively.

ular electronics: acenes, pyrenes, and circumacenes. We have first performed standard Density Functional Theory calculations to compute the intrinsic transport properties (reorganization energies and transfer integrals) of both 14

holes and electrons. We have then employed the above key transport parameters in the framework of semi-classical Marcus theory for charge-transport to compare charge-transfer rates in the high temperatures regime for both unsubstituted and perfluorinated molecules. We have additionally estimated the charge-mobility of each molecule with respect to pentacene. We found that, in absolute terms, perfluorination reduces the charge-transfer rate in all cases considered. The above results trace back to the higher values of the molecular reorganization energies predicted for perfluorinated compounds. Interestingly, however, the charge-transfer rates for both holes and electrons of perfluorinated species are remarkably similar, especially for the larger species considered. In addition, in the case of the larger circumacenes, the charge-mobility values for both holes and electrons relative to pentacene values, are found to increase upon perfluorination. Perfluorinated circumacenes molecules are therefore found to display ambipolar transport capabilities, thus confirming the potential of this class for technological applications. 5. Acknowledgements R.C. gratefully acknowledges Sardinia Regional Government for the financial support of his Ph.D. scolarship (P.O.R. Sardegna F.S.E. Operational Programme of the Autonomous Region of Sardegna, European Social Fund 2007.2013 - Axis IV Human Resources, Objective I.3, Line of Activity I.3.1.). G.C. acknowledges financial support from Project RAS - L. R. 07/08/2007 n 7, cod. CRP - 26666. The authors acknowledge computational support by CRS4. G.C. acknowledges financial support from IDEA-AISBL-Brussells.

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Appendix A. Calculation of the tranfer integrals

Figure A.5: Binding energy of the anthanthrene dimer as a function of intermolecular distance. The computed data are represented by squares while the continuous line is the result of a quadratic fit. The inset reports the entire curve showing the correct behaviour when the monomers are far apart.

To compute the transfer integral t we evaluated Eq. 3 at the distance at which the interaction energy between two facially stacked molecules is at its minimum. To this aim we first duplicated and cofacially stacked into a dimeric structure the optimized geometry of the monomer. Keeping frozen each monomer we then performed single-point energy calculations for a grid of intramolecular distances spaced by 0.05 ˚ A around 3.7 ˚ A (unsubstituted) and 3.5 ˚ A (perfluorinated). We determined the distance for which the energy is at its minimum, take the three distances immediately lower and higher, 16

and with the seven couples of values energy/distance we then performed a quadratic fit to determine the approximate optimal value for the minimum distance between monomers. An additional single-point energy calculation has been performed at the fitted distance: if the corresponding energy is not the lowest, we simply retained the previously determined optimal distance. In this way we avoid using a finer grid which is computationally more demanding, with an error in the distance of the order of 0.02 ˚ A which is comparable with the error intrinsic to the DFT (and other) approximations for this observable. As an example, Fig.A.5 illustrates the above procedure for the specific case of the anthanthrene dimer where the fit gives the optimal distance of 3.73 ˚ A. The equilibrium distances obtained for all the dimers considered (with F substitutions, dFeq , and without, deq ) are summarized in Table A.2. As clearly shown by the Table, perfluorination makes the dimers more compact with very similar equilibrium distances (3.45 ˚ A with the only exception of 3.40 ˚ A for perfluorinated tetracene). Acenes

Pyrenes

Circumacenes

deq (˚ A)

3.85

3.82

3.80

3.80

3.73

3.70

3.65

3.65

3.60

dFeq (˚ A)

3.45

3.40

3.45

3.45

3.45

3.45

3.45

3.45

3.45

Table A.2: Equilibrium distances (expressed in ˚ A) for all of the molecules considered (see Fig.1).

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