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Article: Jones, L orcid.org/0000-0001-6657-2632 and Lin, L orcid.org/0000-0001-9123-5208 (2017) An In Silico Study on the Isomers of Pentacene: the Case for Air-Stable and Alternative C22H14 Acenes for Organic Electronics. Journal of Physical Chemistry A, 121 (14). pp. 2804-2813. ISSN 1089-5639 https://doi.org/10.1021/acs.jpca.6b11770
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1 2 3 4 5 6 7 An In Silico Study on the Isomers of Pentacene: 8 9 10 11 the Case for Air Stable and Alternative C22H14 12 13 14 15 Acenes for Organic Electronics 16 17 18 19 20 Leighton Jones and Long Lin* 21 22 23 Centre for Industrial Collaboration, School of Chemistry, University of Leeds, Woodhouse 24 25 Lane, Leeds, West Yorkshire, UK, LS2 9JT 26 27 28 29 Abstract: Pentacene is one of the most investigated candidates for organic thin film transistor 30 31 (OTFT) applications over the last few decades even though it unstable in air (Eg = 1.80 eV), 32 33 owing in part to its planar nature and high charge transfer mobilities as both a single crystal 34 35 (35 cm2 V 1 s 1) and as a thin film (3.0 cm2 V 1 s 1). Until now, picene is the only isomer of 36 37 38 pentacene to be investigated for organic electronic applications, due to its greater stability
39 2 1 1 40 (Eg = 4.21 eV) and high charge transfer mobility (3.0 cm V s ); even benefitting from 41 42 oxygen doping. In the present study, a total of twelve fused ring isomers (including 43 44 pentacene, picene and ten other structures) of the formula C22H14 were analyzed and 45 46 investigated for their electronic and optical properties for worth in OTFT applications. We 47 48 49 screened several pure and hybrid DFT functionals against the experimental frontier molecular 50 51 orbitals (FMOs) of pentacene, then deployed Marcus Theory, Koopmans’ Theorem and 52 53 Green’s function with the P3 electron propagator variant, for the internal hole reorganization 54 55 energy, the hole transfer integral (via the ‘splitting in dimer method’ at d=3.0, 3.5 and 4.0 Å), 56 57 58 1 59 60 ACS Paragon Plus Environment The Journal of Physical Chemistry Page 2 of 36
1 2 3 the charge transfer rate constant and vertical ionization energies. Using these as a basis, we 4 5 studied pentacene’s isomers and found that the four non planar structures, namely 6 7 benzo[g]chrysene (3), naphtho[c]phenanthrene (7), benzo[c]chrysene (11) and 8 9 10 dibenzo[c,c’]phenthrene (12), are (I) more stable than pentacene, by up to 2 eV, and (II) have 11 12 relatively similar ionization energies (7.5 7.6 eV) to those of picene’s experimental value 13 14 (7.51 eV). The largest charge transfer rates at 3.5 Å dimer separations were given by the 15 16 isomers benzo[b]chrysene 4, naphtha[c]phenanthrene 7, dibenzo[a,c]anthracene 8 and 17 18 14 1 19 benzo[a]tetracene 10 and found to be 2.92, 1.72, 1.30 and 3.09×10 s respectively. In
20 14 1 21 comparison to that of pentacene (KCT = 3.97×10 s ), these unusual isomers are thus 22 23 promising air stable and alternative candidates for organic electronic applications. 24 25 26 27 28 29 I. INTRODUCTION 30 31 32 There has been great progress in the fields of materials chemistry and engineering in the 33 34 last few decades for high performing small molecule charge transfer materials1 4, as the 35 36 active component in opto electronic devices which include light emitting diodes, 37 38 5 9 39 photovoltaics and flexible display screens . Charge transfer materials need to overcome a 40 41 number of diverse issues and further satisfy the increasing demand of greater performance, 42 43 driven both by commercial growth and scientific inquest. Such macroscopic issues include 44 45 industrial scale device fabrication, the ease of processing each individual component layer, 46 47 and overall device performance. While these are highly important, there are a number of 48 49 50 microscopic issues at the molecular level which have yet to be addressed, and include air 51 52 stability for ambient condition processing and efficient charge transfer across the active layer. 53 54 Thus, suitable molecular structures are needed to bring together all the above concepts and 55 56 provide the next generation of candidates for high performing properties and device outputs. 57 58 2 59 60 ACS Paragon Plus Environment Page 3 of 36 The Journal of Physical Chemistry
1 2 3 Polycyclic aromatic hydrocarbons (PAHs) have been extensively investigated as organic 4 5 semiconductors (OSCs) for the active layer in organic electronic devices. These are found to 6 7 satisfy a large number of the above issues, yet there are few which have both air stability and 8 9 10 high charge transfer properties. One line of inquiry is the investigation of the charge transfer 11 11 12 12 mechanisms for the improvement of organic based devices. These investigations tend to 13 14 focus on single crystal OSC devices, where charge transfer mobility can reach as high as 15 16 35 cm2 V 1 s 1 with a PAH molecule called pentacene13 17. Pentacene (1, Figure 1) is 17 18 19 comprised of five fused benzene rings in a linear array of only carbon and hydrogen atoms. 20 21 22 23 24 25 26 27 28 Figure 1. Structures of pentacene (1) and picene (2). 29 30 31 32 33 Single crystals of OSCs are commonly used because of their close packing continuum of 34 35 the organic molecules in the solid phase. On the other hand, the OSCs applied to organic 36 37 electronics are in a thin film state and do not necessarily obey the same charge transport 38 39 conduction mechanisms18, even though they can still reach high transport mobilities, such as 40 41 2 1 1 15,19 42 3.0 cm V s with a thin film transistor of pentacene . For this reason, more fundamental 43 44 investigations, based solely on their molecular structures and not on the device architecture, 45 46 are needed. 47 48 It was found that pentacene gave different values for the same charge transfer and 49 50 51 optoelectronic properties, depending on the applied experimental conditions. It was soon 52 4 53 evident that pentacene is unstable in air due to its small HOMO LUMO gap (Eg = 1.8 eV), 54 55 so is easily oxidised and difficult to operate under ambient conditions. Picene, an isomer of 56 57 58 3 59 60 ACS Paragon Plus Environment The Journal of Physical Chemistry Page 4 of 36
1 2 3 pentacene (2, Figure 1), is surprising in the sense that its charge transport benefits from 4 5 oxygen doping20 22, which is a well known p type doping phenomenon23 25 with other OSCs. 6 7 This suggests that picene with E = 4.21 eV has a superior stability over pentacene, imparted 8 g 9 10 only from its molecular structure. Although this was further explored through both 11 22,26 12 experimental observations and theoretical calculations , the studies, however, focused on 13 14 the charge transfer properties of just these two isomers alone. There are twelve known 15 16 27 29 isomers of (and including) pentacene , which have the formula C22H14. It is thus 17 18 19 reasonable to continue this long line of investigation and probe the properties of the other 20 21 isomers. 22 23 So far, their structures have only been explored with regards to their size27 and aromatic 24 25 nature28,29. To date, there are no known studies on the fundamental electronic and optical 26 27 properties of the isomers of pentacene, even though there are reports of some being 28 29 30,31 30 successfully synthesized, but not subjected to charge transfer investigations . The 31 32 identification and characterization of these isomeric structures is paramount to develop this 33 34 set of C22H14 PAHs and more importantly, determine which isomers are best suited for 35 36 acene based small molecule technology. 37 38 39 This can be investigated with computational chemistry, where electronic and optical 40 41 properties can be adequately modelled using a combination of molecular and quantum 42 43 mechanics. Generally, a range of theories are tested and compared with experimental 44 45 observations where possible or other theoretical calculations in the literature, then one is 46 47 selected and applied to a wider range of structures. This approach has huge merit for 48 49 50 materials chemistry and particularly small molecule organic electronic devices, as large 51 52 numbers of structures can be effectively screened for the active layer prior to any synthetic 53 54 work undertaken and subsequently minimizes both the resources and the time used in 55 56 57 58 4 59 60 ACS Paragon Plus Environment Page 5 of 36 The Journal of Physical Chemistry
1 2 3 synthetic endeavors, as structures predicted to have high performing properties can be 4 5 specifically targeted out of a pool of potential candidates. 6 7 Herein, this present work deploys different theories which include density functional theory 8 9 10 (DFT), Koopman’s Theorem and Green’s Function to calculate the physical properties of 11 12 these isomers and identify suitable isomers as alternative candidates for the improvement of 13 14 (1) their stability relative to pentacene, and (2) high charge transfer properties for organic 15 16 electronics. We start by investigating their stability by predicting the HOMO LUMO gaps 17 18 19 and ionization energies of the twelve isomers and then probe their charge transfer properties 20 21 through the Marcus Theory, which involves the calculation of their internal reorganization 22 23 energies and using the ‘splitting in dimer’ method to calculate the transfer integrals across 24 25 three intermolecular separations (d = 3.0, 3.5 and 4.0 Å); these parameters enable the rates of 26 27 charge transfer to be determined and thus a deep understanding of the suitability of the 28 29 30 isomers for organic electronic applications in comparison to pentacene. This study presents 31 32 evidence that suggests the theoretical assessment of a leading target’s isomers is a worthy 33 34 pursuit prior to synthetic investigations to uncover new candidates for high performing 35 36 structures and highlight those which may have improved properties. 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 5 59 60 ACS Paragon Plus Environment The Journal of Physical Chemistry Page 6 of 36
1 2 3 II. THEORETICAL AND COMPUTATIONAL METHODS 4 5 6 All structures were drawn and visualized in Avogadro (version 1.1.1)32. The ground states 7 8 of the molecular structures were first optimized in Avogadro with the molecular mechanics 9 10 universal force field (UFF), then optimized with quantum mechanics at the given theoretical 11 12 13 level using density functional theory (DFT), or time dependent density functional theory 14 33 15 (TD DFT) for the excited state calculations, in Gaussian 09 (version D.01) ; all subsequent 16 17 single point DFT calculations for the charge transfer properties were performed in Gaussian 18 19 09 starting with the optimized structure at the same level of theory. 20 21 22 For the benchmarking section, a molecule of pentacene was individually optimized with 23 24 each functional, and found to be a minimum with frequency calculations, i.e. no imaginary 25 26 frequencies were observed – see ESI† for the infrared spectra calculated with each functional, 27 28 and the spectra for all isomers investigated later in this study; the vibrational frequencies of 29 30 34,35 31 pentacene correlate well with the literature . 32 33 Several DFT functionals were screened against the experimental values of pentacene and 34 35 probed some charge transfer interactions, as shown in Tables 1 and 2; these functionals 36 37 include pure (BLYP, PBE) and hybrid (B3LYP, wB97XD, PBE0, B3P86, BHandH, 38 39 BHandHLYP) with long range corrections (LC and CAM) and Grimme’s dispersion (D3). 40 41 42 The properties include the HOMO, LUMO, Eg, first vertical ionization energy (IEV), 43 44 reorganization energy, transfer integral and rate of charge transfer. Both pure and hybrid 45 46 functionals were included, along with long range correction (LC/CAM) and Grimme’s third 47 48 order dispersion (D3) factor. The ionization energy was probed with Koopmans’ Theorem50 49 50 52 53 55 51 (KT), outer valence Green’s function (OVGF), and a variant, the third order electron 52 56 59 53 propagator (P3). 54 55 56 57 58 6 59 60 ACS Paragon Plus Environment Page 7 of 36 The Journal of Physical Chemistry
1 2 3 Although the 6 31G(d) and 6 31+G(d) basis sets have been found to give satisfactory 4 5 values to experimental observations36 39, more complete basis sets such as of 6 311G to 6 7 6 311++G(d,p) are also prevalent throughout the literature40 43 for higher accuracy where 8 9 10 needed. We also deploy the 6 311++G(d,p) basis set, owing to the unknown structures and 11 12 charge transfer properties of the isomers of pentacene, particularly with regards to the dimer 13 14 separations of the non planar isomers, which do not have experimental observations for 15 16 comparison with this work. 17 18 44 19 Marcus Theory (Equation 1), was used to describe the charge transfer, which is as a 20 21 self exchange between a neutral and a charged molecule. Two key parameters, the internal 22 45 23 hole reorganization energy (λh) , which is intrinsic only to the extent of relaxation between 24 25 the neutral and cationic surfaces and upon which, the electron delocalization of a molecular 26 27 geometry plays a key part, and the hole transfer integral (t ), which is the electronic coupling 28 h 29 30 between the molecules in relation to the intermolecular separations between them. KB is 31 32 Boltzmann’s constant, T is temperature (298.15 K used here) and ћ is the reduced Planck’s 33 34 constant. Ideally, internal reorganization energies should be very small 46, ca. 0.1 eV. 35 36 37 38 ± ⁄ (1) 39 = 40 ћ ± 41 42 43 A vertically ionized or reduced state is the immediate nature of a molecule which has 44 45 gained or lost an electron and an adiabatic state is where the vertical state has subsequently 46 47 relaxed to a minima on its potential energy surface. The energy processes of electron 48 49 50 exchange, excitation and relaxation are illustrated in Figure 2. 51 52 53 54 55 56 57 58 7 59 60 ACS Paragon Plus Environment The Journal of Physical Chemistry Page 8 of 36
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
17 18 Figure 2. The ionization energy (IE) and electron affinity (EA) pathways between the neutral 19 20 (black) and cation (green) potential energy surfaces for the calculation of the hole 21 22 23 reorganization energy λh. 24 25 λ 26 The internal hole reorganization energy ( h) is comprised of two relaxation terms, the 27 28 energy of the cationic (λ1) and neutral (λ2) surfaces, as defined in Equation 2. 29 30 (2) 31 = + 32 The cationic reorganization energy λ is determined from the difference between the 33 1 34 35 vertical and adiabatic ionization energies calculated via the vertical, single point geometry of 36 + + 37 the cation (M SP) and the optimized cation structure (M OPT), (Equation 3). 38 39 (3) 40 = ( ) − 41 Addition of an electron to the minimized cationic structure returns the molecule back to its 42 43 44 neutral potential energy surface and is performed with a vertical electron affinity of the 45 + 46 cation, EAv ; the difference between this state and the minimum of the neutral molecule is λ2 47 48 (Equation 4). 49 50 (4) 51 = ( )− ( ) 52 The hole transfer integral th is an important component in Marcus Theory and can be 53 54 36,42,47,48 55 estimated from the ‘splitting in dimer’ method (Equation 5), comprising of two 56 57 cofacial molecules separated by a distance d (Å) and determined from calculating half the 58 8 59 60 ACS Paragon Plus Environment Page 9 of 36 The Journal of Physical Chemistry
1 2 3 energy difference between the HOMO and HOMO 1 levels of the dimer. The transfer integral 4 5 decreases with increasing d, so a range of separations are appropriate to determine the extent 6 7 of the electronic coupling interaction. Although a separation between d=3.3 3.8 Å was found 8 9 48 36 43 10 to be suitable for OSCs such as pentacene , circum(oligo)acenes , and substituted acenes , 11 12 it is reasonable to assume that not all of the other isomers in this study, some being 13 14 non planar, will have an identical packing arrangement, and thus three integrals were 15 16 calculated at 3.0, 3.5 and 4.0 Å. 17 18 (5) 19 = (Φ − Φ ) 20 21 Substituting values for λh and th into Equation 1, enables KCT to be determined at any 22 23 24 given separation d. 25 26 27 28 II.I FUNCTIONAL SELECTION 29 30 Different DFT functionals were screened against pentacene’s FMO experimental properties, 31 32 with other theories such as KT, OVGF and P3 deployed for comparison of the vertical 33 34 ionization energy. The charge transfer properties, such as the internal reorganization energy, 35 36 transfer integral and rate of charge transfer, were then calculated and compared to 37 38 39 experimental and theoretical literature values. Table 1 shows the hybrid functionals B3LYP 40 41 and PBE0, which gave the closest HOMO, LUMO and Eg energies in comparison to the 42 43 experimental energies60,61 of 5.00 eV, 3.20 eV and 1.80 eV respectively, although the 44 45 B3P86, BHandH and BHandHLYP functionals were off by more than 0.5 eV. While the pure 46 47 functionals BLYP and PBEPBE proved exceptionally poor, the worst performing functionals 48 49 50 were those of the long range corrected or range separated hybrids, namely LC BLYP, 51 52 LC ωPBE, CAM B3LYP and ωB97XD, with differences to experiment between 1 2 eV. 53 54 In stark contrast, the long range corrected functionals gave some of the closest values to the 55 56 experimental first vertical ionization energy62 of 6.59 eV, with LC BLYP and LC ωPBE 57 58 9 59 60 ACS Paragon Plus Environment The Journal of Physical Chemistry Page 10 of 36
1 2 3 proving the most accurate, except for CAM B3LYP which has a difference of 0.76 eV. 4 5 Interestingly, the ωB97XD gave a close under estimation of 6.42 eV, while the hybrid B3P86 6 7 over estimates at 6.84 eV. The widely used Koopmans’ Theorem underperformed by 8 9 10 0.53 eV, similar to the BLYP functional. The outer valence Green’s function gave relatively 11 12 similar values to the hybrid functionals B3LYP and PBE0, while the third order electron 13 14 propagator, P3, was the most accurate, slightly beating LC BLYP, at 6.51 eV. 15 16 Table 2 shows the calculated internal hole reorganization energies (λh), hole transfer 17 18 19 integral (th) and the rate of charge transfer (KCT) for each functional; Grimme’s third order 20 21 dispersion (D3) term were added for comparison of the intermolecular interactions. The 22 23 lowest reorganization energy were found with BLYP and PBEPBE (61 meV), followed 24 25 closely by B3P86 (94 meV) and B3LYP (97 meV), which correlate well with both the 26 27 experimental value62 of 59 meV and theoretical calculations39,48,63. PBE0 gave a similar 28 29 30 energy, 106 meV, while other hybrid functionals such as ωB97XD, BHandH and 31 32 BHandHLYP are relatively higher at 171, 159 and 176 meV respectively. The largest 33 34 reorganization energies for pentacene were obtained with the long range corrected 35 36 ω 37 functionals, including LC BLYP (291 meV), CAM B3LYP (189 meV) and LC PBE 38 39 (265 meV). 40 41 The spacing of d = 3.3 3.8 Å are reported in the literature36,48,64 to be suitable for the 42 43 transfer integrals of OSCs such as pentacene, although here we calculate d for 3.0, 3.5 and 44 45 4.0 Å to determine how the functionals affect the electronic coupling over a range of 46 47 48 intermolecular separations. The first trend is the depreciation of both the transfer integral and 49 50 the rate constant with increasing dimer spacings, across the range of functionals used, in 51 52 agreement with the literature48. This is natural, as the intermolecular distances increase, i.e. 53 54 the molecules in the dimer become further separated, their electronic coupling decreases and 55 56 57 58 10 59 60 ACS Paragon Plus Environment Page 11 of 36 The Journal of Physical Chemistry
1 2 3 thus charge transfer would diminish. With each 0.5 Å increment, the hole transfer integrals 4 5 decrease exponentially48 6 7 8 9 10 11 12 Table 1. HOMO, LUMO, Eg and Vertical Ionization Potential IEv of 13 Pentacene, in Electron Volts (eV) with Various Functionalsa 14 15 Functional HOMO LUMO Eg IEv 16 17 BLYP -4.26 -3.12 1.15 5.99 18 19 LC-BLYP -7.16 -0.75 6.41 6.65 20 21 B3LYP -4.94 -2.75 2.19 6.23 22 23 CAM-B3LYP -6.04 -1.70 4.33 5.83 24 25 LC-ωPBE -7.12 -0.89 6.23 6.65 26 27 PBEPBE -4.45 -3.31 1.15 6.18 28 29 PBE0 -5.09 -2.64 2.45 6.27 30 31 ωB97XD -6.57 -1.14 5.43 6.42 32 33 B3P86 -5.55 -3.36 2.19 6.84 34 35 BHandH -5.57 -1.77 3.80 6.17 36 37 BHandHLYP -5.59 -1.75 3.84 6.16 38 39 KT 6.06 40 41 OVGF 6.25 42 43 P3 6.51 44 45 Experimental 5.00 3.20 1.80 6.59 46 a 47 Basis set 6 311++G(d,p) 48 49 50 51 for the BLYP functionals, from 416 meV at 3.0 Å through 315 meV at 3.5 Å to 144 meV at 52 53 4.0 Å. Interestingly, there is little interaction of the Grimme’s third order dispersion across 54 55 the dimer separations d = 3.0 4.0. The wB97XD, B3P86, BHandH and BHandHLYP 56 57 58 11 59 60 ACS Paragon Plus Environment The Journal of Physical Chemistry Page 12 of 36
1 2 3 functionals have exceedingly high hole transfer integrals for d = 3.0 Å at 804, 633, 764 and 4 5 745 meV respectively, similar to the long range functionals such as LC BLYP (826 meV), 6 7 CAM B3LYP (790 meV) and LC ωPBE (806 meV). The majority of the hybrid functionals 8 9 10 give relatively lower hole transfer integrals around 345 350 Å. Moreover, the integrals at 11 12 4.0 Å range between 140 and 190 meV for the uncorrected pure and hybrid functionals; 13 14 interestingly that of B3LYP has excellent correlation with thin film studies65. 15 16 The charge transfer rate constants are of the order 0.014 1.963×1015 s 1 for the dimer 17 18 36,48 19 distances d = 3.0 4.0 Å and functionals investigated in agreement with the literature . The 20 21 rates calculated at the 3.0 Å spacing were found to be relatively lower with long range 22 15 1 23 corrected functionals such as LC BLYP (KCT = 0.199×10 s ) and CAM B3LYP 24 25 15 1 15 1 (KCT = 0.610×10 s ) than uncorrected pure BLYP (KCT = 1.04×10 s ) and hybrid B3LYP 26 27 (K = 1.30×1015 s 1) respectively; this trend is reproducible with increasing d. The transfer 28 CT 29 30 integrals for long range functionals approximately halve with each 0.5 Å angstrom 31 32 increment, inferring a linear dependency, but the uncorrected pure and hybrid functionals 33 34 show exponential decreases in accordance with the literature48. Having screened pentacene’s 35 36 properties with various functionals, it is apparent that neither dispersion nor long range 37 38 39 functionals are appropriate for further investigations but rather the best performing one was 40 36,48,64 41 B3LYP in correlation with the literature and therefore selected for the calculation of the 42 43 electronic and optical properties of the remaining isomers. 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 12 59 60 ACS Paragon Plus Environment Page 13 of 36 The Journal of Physical Chemistry
1 2
3 Table 2. Internal Hole Reorganization Energy (λλλh / meV), Hole Transfer Integral 15 -1 4 (th / meV) and the Rate of Charge Transfer (KCT ×10 / s ) for Each Functional 5 at d=3.0, 3.5 and 4.0 Å Dimer Spacings for Pentacene 6 7 d=3.0 Å d=3.5 Å d=4.0 Å 8 Functional λ t K t K t K 9 h h CT h CT h CT 10 BLYP 61 416 1.04 315 0.595 144 0.124 11 12 BLYP-D3 61 418 1.04 315 0.594 144 0.124 13 14 LC-BLYP 291 826 0.199 419 0.051 200 0.012 15 16 B3LYP 97 624 1.30 345 0.397 159 0.084 17 B3LYP-D3 97 625 1.30 345 0.397 159 0.084 18 19 CAM-B3LYP 189 790 0.610 381 0.142 180 0.032 20 21 CAM-B3LYP-D3 169 791 0.786 381 0.183 180 0.041 22 23 LC-ωPBE 265 806 0.256 399 0.063 185 0.014 24 25 LC-ωPBE-D3 265 806 0.256 399 0.063 185 0.014 26 27 PBEPBE 61 413 1.02 315 0.592 142 0.120 28 29 PBEPBE-D3 61 414 1.03 315 0.592 141 0.120 30 31 PBE0 106 654 1.25 351 0.362 160 0.075 32 33 PBE0-D3 106 655 1.25 351 0.362 160 0.075 34 35 ωB97XD 171 804 0.791 383 0.179 181 0.040 36 37 B3P86 94 633 1.40 345 0.416 156 0.085 38 39 BHandH 159 764 0.832 404 0.233 190 0.051 40 41 BHandHLYP 176 745 0.638 176 0.176 183 0.039 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 13 59 60 ACS Paragon Plus Environment The Journal of Physical Chemistry Page 14 of 36
1 2 3 III. RESULTS AND DISCUSSION 4 5 6 The twelve known isomers of pentacene are illustrated in Figure 3, with selected bond 7 8 lengths and angles. Their shapes vary from linear (pentacene, isomer 1) to phenacene like 9 10 (picene, isomer 2). Isomers benzo[g]chrysene 3 and dibenzo[a,c]anthracene 8 have a 11 12 13 phenacene like backbone with a phenyl ring appended in a sec and tert arrangement, 14 15 respectively. The remaining isomers 4 7 and 9 12 have an end on end linear array of phenyl 16 17 rings, which includes the nonplanar structures benzo[c]chrysene 11 and 18 19 dibenzo[c,c’]phenanthrene 12. Isomer 12 is unusual, as it is a primitive or a ‘half’ helicene, 20 21 22 making it a distinctive non planar structure; there are four nonplanar structures in total, 23 24 namely isomers 3, 7, 11 and 12, as illustrated in Figure 4. 3 has a saddle horse type structure, 25 26 7 and 11 have out of plane phenyl rings and 12 is half helical. 27 28 It is important to note the arrangements of the phenyl rings and the separation between the 29 30 adjacent C H units49. For example, pentacene has a zig zag motif imparted by a 1,3 C H 31 32 33 arrangement, whereas picene has a chair motif from a 1,4 C H arrangement. Structures which 34 35 have 1,5 (3, 11) or 1,6 (12) arrangements are found, as expected, to be non planar, due to 36 37 steric hindrance. 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 14 59 60 ACS Paragon Plus Environment Page 15 of 36 The Journal of Physical Chemistry
1 2 3 4 5 6 7 8 9 10 11 Pentacene Picene Benzo[g]chrysene 12 13 1 2 3 14 15 16 17 18 19 20 21 22 Benzo[b]chrysene Dibenzo[a,h]anthracene Dibenzo[d,d’]phenanthrene 23 24 4 5 6 25 26 27 28 29 30 31 32 33 34 Naphtho[c]phenanthrene Dibenzo[a,c]anthracene Dibenzo[a,f]anthracene 35 36 7 8 9 37 38 39 40 41 42 43 44 45 Benzo[a]tetracene Benzo[c]chrysene Dibenzo[c,c’]phenanthrene 46 47 10 11 12 48 49 Figure 3. Structures of the 12 isomers investigated in this work with selected angles (°) and 50 bond lengths (Å). 51 52 53 54 55 56 57 58 15 59 60 ACS Paragon Plus Environment The Journal of Physical Chemistry Page 16 of 36
1 2 3 4 5 6 7 8
9 10 Benzo[g]chrysene 11 Naphtho[c]phenanthrene 12 3 13 7 14 15 16 17 18 19 20 21 22 23 Benzo[c]chrysene Dibenzo[c,c’]phenanthrene 24 25 11 12 26 27 Figure 4. Structures of the four non planar isomers. 28 29 30 31 The HOMO energy of pentacene ( 4.94 eV) is the highest out of all the isomers studied 32 33 (Table 3); the relatively high HOMO energy is a known issue, which is considered to 34 35 contribute to its instability22,26. By rearranging just one of the terminal rings, isomer 10 shows 36 37 38 a relatively similar HOMO energy at 5.29 eV but significant improvement in stability, as 39 40 evidenced by an increase in both the Eg and the optical gap energies, by more than 0.6 and 41 42 0.69 eV respectively; however 10 is the second least stable after pentacene out of all the 43 44 isomers. 45 46 Other than picene, the remaining planar isomers 4 6 and 8 and 9 also have significantly 47 48 49 improved stability and deeper HOMO levels than pentacene. Isomer 9 is one of the most 50 51 stable planar structures (Eg = 3.89 eV) excluding picene; followed closely by isomers 5 and 8, 52 53 which have the same gap (Eg = 3.85 eV). 54 55 56 57 58 16 59 60 ACS Paragon Plus Environment Page 17 of 36 The Journal of Physical Chemistry
1 2 3 The FMO energies of the non planar 3, 11 and 12 isomers are relatively similar to those of 4 5 picene (2), with their deep HOMO levels centered at 5.85 eV, the LUMO at 1.70 eV and the 6 7 Table 3. HOMO, LUMO, E , Optical Gap (S -S ) with the 8 g 0 1 Oscillator Strength in Parenthesis of the Optimized Isomers at the 9 10 B3LYP/6-311++G(d,p) level, in electron volts eV 11 12 Isomer H 1 H L L+1 Eg S0 S1 13 1 -6.22 -4.94 -2.75 -1.33 2.19 1.90 (0.04) 14 15 2 -6.12 -5.85 -1.64 -1.59 4.21 3.55 (0.006) 16 17 3 -6.21 -5.80 -1.75 -1.38 4.05 3.60 (0.02) 18 19 4 -6.32 -5.55 -2.07 -1.32 3.48 3.10 (0.07) 20 21 5 -6.12 -5.72 -1.87 -1.56 3.85 3.36 (0.02) 22 23 6 -5.82 -5.66 -1.92 -1.90 3.75 3.11 (0.002) 24 25 7 -6.17 -5.52 -2.10 -1.36 3.42 3.02 (0.04) 26 27 8 -6.25 -5.76 -1.91 -1.32 3.85 3.43 (0.02) 28 29 9 -6.04 -5.76 -1.87 -1.56 3.89 3.38 (0.0004) 30 31 10 -6.28 -5.29 -2.37 -1.32 2.92 2.59 (0.04) 32 33 11 -5.95 -5.88 -1.67 -1.67 4.21 3.43 (0.002) 34 35 12 -5.97 -5.84 -1.72 -1.69 4.12 3.35 (0.001) 36 37 38 39 Eg at 4.2 eV; 7 is the exception with values 5.52, 2.10 and 3.42 eV respectively, but not 40 41 far from ideal. The HOMO 1 states for isomers 1 to 5 and 7 to 10 are relatively similar, 42 43 focusing around 6.20 eV, suggesting this is a common and stable lower FMO energy; 44 45 although no distinct trend is observed with the LUMO+1 states. The FMO levels are 46 47 48 illustrated in Figure 5 and clearly shows the trends in stability between the planar and non 49 50 planar isomers. The molecular orbital plots are presented in Table S78 in the ESI† showing 51 52 the differences between the pentacene and phenacene like structures, which correlate well 53 54 with the literature66 69. 55 56 57 58 17 59 60 ACS Paragon Plus Environment The Journal of Physical Chemistry Page 18 of 36
1 2 3 These trends are reflected in the optical gap (S0 S1 / eV), determined from TD DFT 4 5 calculations. The excitation wavelengths of 5, 8, 11 and 12 are nearly doubled in comparison 6 7 to pentacene (3.35 3.43 eV). 4 and 6 have moderate stability (3.10 3.11 eV), while the lowest 8 9 10 is with isomer 10 at 2.59 eV. Interestingly, the non planar isomer 3 is the most stable, more 11 12 than picene by 0.05 eV. 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 Figure 5. FMO energy diagram of HOMO (H), LUMO (L) and Eg (H L separation drawn as 42 43 bars) for all isomers with energies in electron volts (eV). 44 45 46 47 So far, we have probed the twelve isomers and their various optical properties, leading to 48 49 trends in stabilities. Now, their ionization energies are investigated with three different types 50 51 52 of theories (two DFT, KT and Green’s function with the P3 variant). We learnt from the data 53 54 in Table 1, that long range functionals such as LC BLYP overestimates, while pure BLYP 55 56 underestimates, B3LYP is moderate and similar to that of OVGF, KT is poor and P3 is the 57 58 18 59 60 ACS Paragon Plus Environment Page 19 of 36 The Journal of Physical Chemistry
1 2 3 most accurate with respect to the experimental value. With this in mind, we now apply these 4 5 to focus on calculating the vertical ionization energies that are expected to bracket the 6 7 experimental values. 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 19 59 60 ACS Paragon Plus Environment The Journal of Physical Chemistry Page 20 of 36
1 2 3 Table 4 shows the vertical ionization energy of the twelve isomers, and lists the pole 4 5 strengths in parenthesis for OVGF and P3. All of the isomers 2 to 12 show relatively higher 6 7 vertical ionization energies than pentacene, with values reaching 7.24 eV with 11, a 8 9 10 difference of 1.11 eV. All reproduce the trend that pentacene has the lowest ionization 11 12 energy, followed closely by isomers 10 and then 4. Except for pentacene, KT and OVGF give 13 14 similar values for each isomer, which are on average 0.15 eV greater than the B3LYP 15 16 functional; the LC BLYP functional consistently gives the largest IEvs, and has a difference 17 18 19 to B3LYP between 0.4 and 0.6 eV. The variation between the theories and the isomers are 20 21 illustrated in Figure 6. 22 23 24 25 st Table 4. 1 Vertical Ionization Energy (IEV) in electron volts (eV), 26 Calculated with B3LYP, LC-BLYP, Koopmans‘ Theorem (KT), Outer 27 Valence Green‘s Function (OVGF) and Third Order Electron 28 29 Propagator (P3) with their Associated Pole Strengths (PS) 30 Isomer B3LYP LC BLYP KT OVGF P3 31 32 1 6.23 6.65 6.06 6.25 (0.87) 6.51 (0.85) 33 34 2 7.20 7.82 7.42 7.37 (0.88) 7.58 (0.86) 35 36 3 7.16 7.67 7.31 7.28 (0.88) 7.54 (0.87) 37 38 4 6.88 7.44 6.98 7.01 (0.88) 7.24 (0.86) 39 40 5 7.07 7.65 7.24 7.20 (0.88) 7.42 (0.86) 41 42 6 6.99 7.57 7.16 7.14 (0.87) 7.35 (0.86) 43 44 7 6.87 7.40 7.03 6.98 (0.88) 7.29 (0.86) 45 46 8 7.12 7.71 7.29 7.25 (0.88) 7.48 (0.86) 47 48 9 7.10 7.71 7.28 7.23 (0.88) 7.46 (0.86) 49 50 10 6.62 7.11 6.64 6.71 (0.87) 6.94 (0.86) 51 52 11 7.24 7.85 7.43 7.39 (0.88) 7.62 (0.86) 53 54 12 7.21 7.79 7.38 7.35 (0.88) 7.59 (0.87) 55 56 57 58 20 59 60 ACS Paragon Plus Environment Page 21 of 36 The Journal of Physical Chemistry
1 2 3 In general, the P3 functional gives values that are 0.2 eV greater than the commonly 4 5 used OVGF functional. The IEv for picene with P3 is 7.58 eV, which is in excellent 6 7 agreement with the experimental value at 7.51 eV and suggests that P3 should be given more 8 9 10 attention in future studies, particularly due to its level of accuracy over OVGF. The P3 values 11 12 for isomers 3 (7.54 eV) and 12 (7.59 eV) are remarkably similar to that of picene, while those 13 14 of 5, 8 and 9 are similar to each other at 7.44 eV. Both isomers 4 and 6 have relatively low 15 16 ionization energies (P3) with 7.24 eV and 7.3 eV respectively. Isomer 11 has the greatest IEv, 17 18 65 19 only slightly larger than picene’s theoretical value by 0.06 eV, but significantly greater than 20 21 pentacene with a difference of 1.11 eV. Isomer 10 is the second lowest at 6.94 eV, after 22 23 pentacene, but the difference between them is a stabilizing 0.43 eV. 24 25 26 27 28 29 30 8.0 31 32 7.8 33 7.6 34 35 7.4 ) / eV ) / 36 v 37 IE 7.2 38 39 7.0 40 41 6.8 42 6.6 43 44 6.4 45 Vertical Ionization Energy ( Energy Ionization Vertical 46 6.2 47 48 6.0 LC-BLYP B3LYP KT OVGF P3 49 50 1 2 3 4 5 6 7 8 9 101112 51 Isomer 52 53 54 Figure 6. Vertical ionization energies (IE ) in electron volts (eV) calculated using different 55 V 56 57 theories (LC BLYP, B3LYP, KT, OVGF, P3) for all isomers. 58 21 59 60 ACS Paragon Plus Environment The Journal of Physical Chemistry Page 22 of 36
1 2 3 4 5 Now we consider (1) the structural relaxation ability of the isomers by calculating their 6 7 internal hole reorganization energies, (2) their electronic coupling transfer integrals and (3) 8 9 10 their rates of charge transfer, for each dimer separation d = 3.0, 3.5 and 4.0 Å, as illustrated in 11 12 Table 5. The internal hole reorganization energies are overall relatively low, with isomers 4 13 14 and 7 to 11 being exceptional between 115 and 143 meV (Figure 7). Relatively high values 15 16 are observed with 3 (188 meV), 5 (171 meV) and 6 (181 meV), which are similar to that of 17 18 19 picene (188 meV); isomer 12 has the highest hole reorganization energy with 212 meV. 20 21 22 23 λλλ 24 Table 5. Hole Reorganization Energy ( h / meV) for Each Isomer and the t 25 Hole Transfer Integral ( h / meV) with the Rate of Charge Transfer 14 -1 26 (KCT ×10 / s ) for each Intermolecular Separation of d = 3.0, 3.5 and 27 4.0 Å 28 29 d = 3.0 Å d = 3.5 Å d = 4.0 Å 30 Isomer λh th KCT th KCT th KCT 31 1 97 624 13.022 345 3.968 159 0.841 32 33 2 188 147 0.213 144 0.206 141 0.197 34 35 3 188 194 0.373 201 0.400 120 0.142 36 37 4 122 383 3.433 353 2.918 164 0.632 38 39 5 171 205 0.516 205 0.513 162 0.323 40 41 6 181 83 0.075 82 0.072 80 0.070 42 43 7 133 284 1.627 292 1.715 127 0.326 44 45 8 127 242 1.277 244 1.296 159 0.552 46 47 9 133 139 0.386 139 0.390 140 0.392 48 49 10 115 486 6.082 346 3.087 159 0.653 50 51 11 143 20 0.007 18 0.006 23 0.009 52 53 12 212 159 0.212 40 0.012 3 0.000 54 55 56 57 58 22 59 60 ACS Paragon Plus Environment Page 23 of 36 The Journal of Physical Chemistry
1 2 3 4 220 5 6 200 / meV / h λ
7 8 180 9 10 160 11 12 140 13 14 120 15 16 100
17 energy Reorganization Hole Internal 18 80 19 1 2 3 4 5 6 7 8 9 101112 20 Isomer 21 22 Figure 7. Internal hole reorganization energy (λh) in millielectron volts (meV) for each 23 isomer. 24 25 26 27 Except for pentacene, the hole transfer integrals of the remaining isomers are largely 28 29 unchanged between the d = 3.0 and 3.5 Å separation. The greatest difference is between the 30 31 d = 3.5 and 4.0 Å separation, where the hole transfer integrals are approximately halved. At 32 33 d = 3.0 Å, pentacene has the largest transfer integral at 624 meV, with relatively high values 34 35 for isomers 4 (383 meV), 7 (284 meV), 8 (242meV) and 10 (486 meV). At d = 3.5 Å, these 36 37 38 values for the same isomers remain largely unchanged with differences of < 20 meV. At 39 40 d = 4.0 Å, the integral for 7 has decreased by 165 meV, although remarkably, those of 41 42 isomers 8 and 10 are the same as pentacene at 159 meV, with those of isomers 4 and 5 being 43 44 even greater at 164 and 162 meV respectively. The relatively strong electronic coupling at 45 46 47 this separation may be due to the isomers 4, 5, 8 and 10 being both planar and have linear 48 49 anthracene segments in their structures, with the exceptions being 6 and 9. 50 51 52 The rates of charge transfer at d = 3.0 Å for 4, 7, 8 and 10 are exceptional with KCT = 3.43, 53 54 1.63, 1.28 and 6.08×1014 s 1 respectively, in comparison to that of pentacene’s (13.0×1014 s 1); 55 56 at d = 3.5 Å, their rates are of the same order of magnitude at KCT = 2.92, 1.72, 1.30 and 57 58 23 59 60 ACS Paragon Plus Environment The Journal of Physical Chemistry Page 24 of 36
1 2 3 3.09×1014 s 1 respectively; those for d = 4.0 Å are significantly lower. It is clear these isomers 4 5 out perform all other isomers, except for pentacene, with increasing dimer separation. The 6 7 non planar isomer 3 has a transfer integral and rate constant of 301 meV and 0.400×1014 s 1 8 9 10 respectively, which is unexpected given its distorted structure. Those of the other two 11 12 non planar isomers 11 and 12 are much less so, with rates up to three orders of magnitude 13 14 less. The alternative contenders with regards to rates of charge transfer are easily identified 15 16 from Figure 8, which shows the high performing values of pentacene at each dimer 17 18 19 separation (decreasing from 4.0 to 3.0 Å with increasing th) and those of isomers 4, 7, 8 and 20 21 10 being of the same order of magnitude. 22 23 24 25 26
27 1 28 2 12 3 29 4 30 5 6 31 -1 7 10 8 32 / s )
14 9 33 10
þ10 11
34 CT 8 12 35 K 36 37 6 38 39 4 40 41 42 2 Rate of Charge Transfer ( Transfer Charge of Rate 43 44 45 0 46 0 100 200 300 400 500 600 Hole Transfer Integral (t ) / meV 47 h 48 49 Figure 8. The rate of charge transfer (KCT) versus the hole transfer integral (th) in electron 50 51 volts (meV) for each intermolecular separation (d = 3.0, 3.5, 4.0 Å, decreasing separation 52 53 with increasing transfer integral) for all isomers. 54 55 56 57 58 24 59 60 ACS Paragon Plus Environment Page 25 of 36 The Journal of Physical Chemistry
1 2 3 IV. CONCLUSION 4 5 6 This study is the first of its kind to probe the fundamental electronic and optical properties 7 8 of pentacene’s isomers, for both stability and charge transfer in organic electronic 9 10 applications. Several pure and hybrid functionals were screened for pentacene’s FMOs and 11 12 13 charge transfer properties, and the common B3LYP was found to perform the best in 14 15 comparison to experimental values. Subsequently, the non planar isomers 3, 11 and 12 were 16 17 found to have a relatively similar HOMO to that of picene, while their air stability is nearly 18 19 two fold to that of pentacene. 20 21 22 The third order electron propagator (P3) functional gives the most accurate first vertical 23 24 ionization energy, in comparison to the experimental values of pentacene and picene, and 25 26 should be used over all other theories for excellent estimates of similar acenes. The isomer 11 27 28 was found to have the greatest increase in vertical ionization in comparison to pentacene 29 30 using P3, by 1.11 eV. 31 32 33 The internal hole reorganization energies of picene and isomer 3 are identical at 0.188 eV, 34 35 with those of isomers 4, 7, 8, and 10 are less than 0.133 eV. The hole transfer integrals and 36 37 the rates of charge transfer at three intermolecular separations were evaluated for all isomers 38 39 and it is no surprise that 4, 7, 8, and 10 have the same order of magnitude as those of 40 41 42 pentacene at 3.5 Å, suggesting strong interactions in the solid phase for these molecules. The 43 44 rates of charge transfer are also exceptional for isomers 4, 7, 8 and 10. Combining these 45 46 observations with their air stabilities, isomer 8 is the best all round alternative candidate to 47 48 pentacene, followed closely by the other three depending on the specific property of interest. 49 50 Overall, this study shows that the isomers of pentacene deserve attention as potential 51 52 53 air stable and high performing alternative candidates for organic electronic applications. 54 55 56 57 58 25 59 60 ACS Paragon Plus Environment The Journal of Physical Chemistry Page 26 of 36
1 2 3 AUTHOR INFORMATION 4 5 Corresponding Author 6 7 8 E mail: [email protected] 9 10 11 12 13 14 Author Contributions 15 16 The manuscript was written through contributions of all authors. All authors have given 17 18 approval to the final version of the manuscript. L Jones and L Lin contributed equally. 19 20 21 22 The authors declare no competing financial interest. 23 24 25 26 27 SUPPORTING INFORMATION 28 Cartesian coordinates of all optimized and vertical (i.e. ionized or electron affinity) structures 29 30 31 for the calculation of the internal hole reorganization energy according to Marcus Theory, 32 33 frequency calculations and electronic transitions are available in the Supporting Information. 34 35 36 37 ACKNOWLEDGEMENTS 38 39 We are grateful to the Gunnell and Matthews Scholarship for funding and the use of the 40 41 University of Leeds HPC advanced research computing (ARC2) facilities. 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 26 59 60 ACS Paragon Plus Environment Page 27 of 36 The Journal of Physical Chemistry
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1 2 3 Table of Contents Graphic (TOC) 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 36 59 60 ACS Paragon Plus Environment