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Computational Modeling of Isoindigobased Polymers Used in Organic Solar Cells Paolo Salvatori, Edoardo Mosconi, Ergang Wang, Mats R. Andersson, Michele Muccini, and Filippo De Angelis J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp404123x • Publication Date (Web): 08 Aug 2013 Downloaded from http://pubs.acs.org on August 9, 2013

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The Journal of Physical Chemistry

Computational Modeling of Isoindigo-based Polymers Used in Organic Solar Cells Paolo Salvatori,a,b Edoardo Mosconi,a,* Ergang Wang,c Mats Andersson,c Michele Muccini,d Filippo De Angelis a,* a

Computational Laboratory for Hybrid/Organic Photovoltaics (CLHYO), CNR-ISTM, via Elce di Sotto, 8 I-06123, Perugia, Italy. b

c

Department of Chemistry, University of Perugia, Via Elce di Sotto 8, I-06213, Perugia, Italy.

Department of Chemical and Biological Engineering/Polymer Technology, Chalmers University of Technology, SE-412 96 Göteborg, Sweden. d

ISMN-CNR, Via P. Gobetti 101, Bologna, Italy.

CorrespondingAuthors: Dr. Edoardo Mosconi, Dr. Filippo De Angelis E-mail: [email protected]; [email protected] Phone: +39 0755855523

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ABSTRACT: We report a computational modeling investigation, based on DFT and TDDFT calculations, on the structural, electronic and optical properties of three prototypical donor-acceptor polymers based on the isoindigo unit acceptor moiety, namely PTI-1, PBDT-I and PBDT-TIT, in order to calibrate a computational protocol to screen new candidate polymers and to get a better understanding of the properties of the investigated series. Starting from the monomeric units and by using a growing-up approach, we were able to reproduce the experimental electrochemical and optical properties and to estimate the effective conjugation length of these polymers. This study can support the choice of suitable donor and acceptor building blocks and provides the computational framework for an in silico screening of new target photoactive polymeric systems.

Keywords: DFT-TDDFT calculations, Isoindigo, Photovoltaics, Effective Conjugation Length

Donor-Acceptor

Polymers,

Organic


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1. Introduction Low bandgap π-conjugated semiconducting polymers are attracting an increasing interest in a number of materials science fields, including electrochromics, organic transistors and organic photovoltaics.1-7In Bulk-Heterojunction (BHJ) organic solar cells a conjugated polymer, absorbing the sunlight, can generate a bound exciton that rapidly dissociates into an electron and a hole at the interface between the donor polymer and a fullerene acceptor,8-10 typically PC61BM([6,6]-phenylC61-butyric acid methyl ester)11-12 or PC71BM([6,6]-phenyl-C71-butyric acid methyl ester).13-14The electron is then transported to the photoanode by the fullerene, while the hole is collected at the counter-electrode. The solar cell power conversion efficiency (η) is the product of (1): the shortcircuit current density (Jsc),15 the photovoltage under open circuit conditions (Voc)16 and the fill factor (FF),17namely: η = (Jsc x Voc x FF) /PIN where PIN is the incident light power. PC61BM and PC71BM are widely used electron acceptor systems.18From the donor side, a large body of research efforts are concentrated on the search for efficient conjugated polymers. To obtain high photocurrent values, the use of low bandgap conjugated polymers, capable to efficientlyabsorb up to the near IR the solar radiation, is required. Recent design rules have established that the best donor materials should have a bandgap energy in the range of 1.2–1.7 eV.18 Further material-design rules define an energy of the lowest unoccupied molecular orbital (LUMO) of the polymer higher than the LUMO of PCBM, with a minimum offset of ca. 0.3 eV, to guarantee the necessary driving force for efficient electron transfer.19 Accordingly, an energy of the highest occupied molecular orbital (HOMO) of the polymer ranging from -5.2 to -5.7 eV is required, assuming an energy of -4.3 eV for the LUMO of PCBM. Under these conditions, a maximum photovoltage in the range of 0.9-1.4 V, approximated by the difference between the LUMO of PCBM and the HOMO of the polymer, is theoretically obtainable. Along with suitable electronic



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properties, appropriate solubility and processability are also fundamental requisites to optimize the morphology of the active layer, that is the major issue influencing the fill factor.17 An efficient way to develop low band gap polymers is to combine electron-rich (donor) and electron-deficient (acceptor) moieties as repeating units along the polymer backbone, forming internal donor–acceptor (D–A) structures.20 First introduced in macromolecular π-conjugated systems in the 1990s by Havingaet al.,21-22 the D-A approach affords polymer chromophores with narrow band-gaps, red-shifting their absorption spectra toward wavelengths in the 500-800 nm range. This is due to the fact that donor groups raise the HOMO energy and concomitantly the acceptor fragments lower the LUMO level. The proper choice of the donor and acceptor moieties allows a fine tuning of the polymer optical and electrochemical properties. For this purpose, many electron-rich units, such as fluorene,23-24silafluorene,25 2,7-carbazole,26-27 indolo[3,2-b]carbazole,2829

cyclopenta[2,1-b:3,4-b’] dithiophene,30-31dithieno[3,2-b:2’,3’-d]silole,32-33indacenodithiophene,34-

35

thieno[3,4-b]thiophene,36-37 and benzo[1,2-b:4,5-b’]dithiophene (BDT),38-39havebeeninvestigated.

Only a limited number of electron-deficient units, such as, 2,1,3-benzothiadiazole,23, 25

quinoxaline,34-35,

39

diketopyrrolo[3,4-c]-pyrrole-1,4-dione (DPP),40-41 and thieno[3,4-c]pyrrole-

4,6-dione (TPD),34, 42-43have provided good photovoltaic performances. As a strong electron-withdrawing compound, because of its two lactam rings, isoindigo has been used in the dye industry for a long time.44 The application of isoindigo in organic solar cells was first introduced by Reynolds and coworkers in 2010.45 In the last few years, several research groups have presented parallel works about isoindigo-based polymers showing limited efficiencies.46-48 Remarkably, Wang et al. have recently reported a low band gap (1.5eV) polymer based on the isoindigo unit, coded P3TI, which in combination with the PC71BM acceptor exhibits a high photovoltaic efficiency of 6.3%.49 This result demonstrates the high potential of isoindigo as an electron-deficient unit for building D–A polymers toward high efficient solar cells.


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Quantum mechanical simulations can provide a strong support in the detailed understanding of the electrochemical and optical properties of π-conjugated polymers50-52 providing insight into the design rules for new materials and into the processes limiting the efficiency of polymer solar cells.

In the field of hybrid and organic photovoltaics, due to the large dimensions of the

investigated systems, Density Functional Theory (DFT) and Time Dependent Density Functional Theory (TDDFT) methods have demonstrated their accuracy in reproducing the experimental properties of the isolated cells components.53-66 These investigations can give also a predictive support in driving the efforts of synthetic groups, allowing a considerable saving in terms of time, materials and thus human and financial resources. Isoindigo derivatives were previously computationally studied both as isolated molecules and as co-polymers building blocks to get insight on the optical properties,67-69 electrochemical properties70-73 and geometrical topic.74-75 In particular Perpète et al. discussed the difficulties in accurately reproduce the optical signature for isoindigo by using a large panel of functionals,67 due to the significant charge transfer character of the main transition.68In this paper we computationally investigate three experimentally characterized D-A polymers based on the isoindigo building block to gain insight into the structural, electronic and optical properties of these systems along with providing a calibrated computational protocol for the calculation of electrochemical and optical properties of this class of macromolecules, thus enabling the required predictive power. The investigated compounds, coded as PTI-1, (poly[N,N'-bis(2-hexyldecyl)isoindigo-6,6'diyl-alt-thiophene-2,5-diyl]),76

PBDT-I,

(poly{N,N'-bis(2-hexyldecyl)isoindigo-alt-4,8-bis((2-

ethylhexyl)oxy)benzo[1,2-b:4,5-b']dithiophene-2,6-diyl}),

and

PBDT-TIT,(poly{5,5'-[6,6'-

di(thiophen-2-yl)-N,N'-bis(2-hexyldecyl)isoindigo]-alt-4,8-bis((2-ethylhexyl)oxy)benzo[1,2-b:4,5b']dithiophene-2,6-diyl}),77 were synthesized and characterized by Andersson and co-workers. The investigated systems are based on isoindigo as acceptor and, respectively, thiophene, benzo[1,2b:4,5-b’]dithiophene (BDT) and BDT flanked with thiophene as donor moieties (Scheme 1).



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Scheme 1. Molecular structure of (a) PTI-1, (b) PBDT-I and (c) PBDT-TIT polymers.

Our simulations showed a good agreement of the calculated oxidation potentials, HOMO-LUMO and optical band gaps with the available experimental data. We were also able to estimate the effective conjugation length78 of the considered systems, on the basis of the saturation of the calculated properties by increasing the number of the building units. The prediction of this property could be very interesting because it allows to use shorter oligomers, with a better processability and reproducibility, presenting the same properties of a theoretically infinite-chain polymer.

2. Computational and experimental details Geometry optimizations and simulation of the optical absorption spectra were performed by DFT and TDDFT, as implemented in the Gaussian09 program suite.79The ground state geometries were optimized in gas-phase within the B3LYP80 functional, using a 3-21G(d) basis set, (SCF threshold=10-7a.u., and looseas convergence criteria for geometry optimization) that was


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demonstrated to give reliable results for similar D-A polymers.56On the optimized geometries we performed TDDFT calculations employing the B3LYP and MPW1K81functionals and a larger 631G(d) basis set.82 TDDFT excited state calculations were performed both in gas phase and in dichloromethane solution, adopting the non-equilibrium Conductor-like Polarization Model, CPCM83 solvation modelwithin its linear response formulation. To further validate our results, a deeper study was conducted on the PTI-1 polymer to evaluate the effect of a different basis set on the calculated parameters. We tested the larger 6-31+G(d,p) basis set both for the geometry optimization and the TDDFT calculations of the PTI-1 monomer and dimer. Calculations using the CAM-B3LYP84-85functional in solution were also performed for the PTI-1 polymer and its dibromo precursor monomer. The study of the polymers was investigated by a growing up approach, starting from the monomeric units.57 If not otherwise stated, all the data refer to 6-31G(d)/3-21G(d) results. The absorption spectra have been obtained by a convolution of Gaussian functions with

σ=0.17 (FWHM∼0.4 eV), if not otherwise specified in the text. Experimental UV-Vis absorption spectra and determination of the extinction coefficients were carried out with a Perkin Elmer Lambda 900 UV-Vis-NIR absorption spectrometer at 20 °C in chloroform. The path length of the cuvette is 1 cm. 3. Results and discussion 3.1 Methodology Calibration In previous works on organic dye sensitizers54,

86

we found that while B3LYP provides accurate

ground state geometries, while it can have limitations in the correct description of charge transfer excited states.The MPW1K functional, which has an increased percentage of Hartree-Fock exchange, can provide, in cases where strong charge transfer accompanies excitation, transition energies in closer agreement with experimental values. It was also recently reported that the use of long-range corrected functionals87-92 can provide a rather different description of the excited states of D-A polymers.64, 85, 87-100Weused B3LYP, MPW1K and CAM-B3LYP functionals to simulate the 7 ACS Paragon Plus Environment


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optical absorption spectra of the investigated oligomers. As an initial assessment, to gauge the quality of the calculations in reproducing the optical properties of the PTI-1 polymer, we started by simulating the corresponding di-bromo precursor monomer, see Supporting Information, which is experimentally characterized. In Figure 1 we compare the normalized experimental and calculated absorption spectra (B3LYP, MPW1K and CAM-B3LYP in dichloromethane solution) of the PTI-1 di-bromo precursor, while in Table 1 we summarize the calculated vertical transition energies and the theoretically calculated HOMO and LUMO energies and HOMO-LUMO gap.

Figure 1.Comparison between the normalized experimental (black line, i) and calculated absorption spectra in dichloromethane solution by B3LYP (Red line, ii) and MPW1K (Blue line, iii) and CAM-B3LYP (Green line, iv), for the PTI-1 DiBr precursor monomer. Table 1. Summary of calculated (B3LYP and MPW1K and CAM-B3LYP in solution)vertical transition energies, along with their oscillator strength (in brackets), HOMO, LUMO energies and


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band gap of the PTI-1 DiBr precursor monomer. For comparison,the experimental absorption spectral maxima, along with the extinction coefficient (in L*g-1*cm-1)are also reported. All energy values are in eV. B3LYP

MPW1K

CAM-B3LYP

Exp.

Transition 1 (f) 2.31 (0.19)

2.69 (0.33)

2.76 (0.34)

2.47 (3.72)

Transition 2 (f) 3.05 (0.71)

3.53 (0.71)

3.62 (0.68)

3.10 (9.83)

HOMO

-5.88

-6.90

-7.18

----

LUMO

-3.04

-2.65

-1.99

----

Band Gap

2.84

4.25

5.19

----

As it can be noticed, the B3LYP data seem to provide a better description of the entire absorption spectra, although providing a slight red shift of the two main bands of 0.16 eV and 0.05 eV for the low and high energy bands compared to experimental values, respectively. Furthermore, a more balanced description of the relative intensity of the two features is given by B3LYP with respect to both the MPW1K and the CAM-B3LYP, due to the overestimate of the intensity of the visible band provided by the latters. The MPW1K functional, having an elevated percentage of HF exchange, is known to provide larger HOMO-LUMO gaps compared with B3LYP and possibly with respect to the experiment, due to the strong stabilization (destabilization) of the occupied (unoccupied) states. A similar effect is provided also by the CAM-B3LYP functional, providing a clearly overestimated HOMO-LUMO gap. To reduce the computational cost in the demanding excited state calculations, we tested whether the replacement of the polymer alkyl chains with smaller isobutyl groups affected the electronic and optical properties. To evaluate the effect of this simplification on the investigated properties, for the PTI-1dimer, we thus explicitly simulated the system including the real 2-hexyldecyl and model isobutyl side chains, see Figure 2. The results are reported in Table 2, showing that the introduction of the 2-hexyl-decyl side chains in the dimer structure induces a slight opening of 9 ACS Paragon Plus Environment


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the main dihedral angles, with a consequent small increase of the calculated HOMO-LUMO gap (2.32/3.60 vs. 2.27/3.54 eV) and lowest excitation energy (1.94/2.35 vs. 1.91/2.31 eV) compared to the case with isobutyl side chains. Based on these small differences, the reduced model was employed throughout.

Figure 2. Optimized geometries of PTI-1dimer with (a) isobutyl side chains and (b) 2-hexyl-decyl side chains.

Table 2. Dihedral angles (atoms numeration is referred to Figure 2), HOMO, LUMO, Band Gap and excitation energies for the model (isobutyl side chains) and the real (2hexyl-decyl side chains) PTI-1 dimers. Data obtained by the 6-31G(d) basis set in dichloromethane solution on 3-21G(d) geometries optimized in vacuo are reported.

Dihedral

ISO-TIO

angles

C1-C2-C3-S1

PTI-1 dimer

PTI-1 dimer

(isobutyl side chains)

(2 hexyl-decyl side chains)

20.71°

24.9°


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19.88°

27.7°

HOMO

-5.32

-5.34

LUMO

-3.05

-3.02

Band Gap

2.27

2.32

Exc. En.

1.91

1.94

HOMO

-6.24

-6.27

LUMO

-2.70

-2.67

Band Gap

3.54

3.60

Exc. En.

2.31

2.35

TIO-ISO S1-C4-C5-C6 B3LYP

MPW1K

As a further accuracy check, we repeated the DFT/TDDFT calculations for the PTI-I monomer and dimer using the larger 6-31+G(d,p) basis set both in the geometry optimization step and in the TDDFT calculations. The results are reported in Table 3.

Table 3. Comparison between calculated HOMO, LUMO electrochemical and optical band gaps of PTI-1 monomer and dimer by means of different basis sets and exchange-correlation functionals. Values calculated in solution are reported in bracket. All the values are in eV. Monomer basis set opt. basis set TD HOMO LUMO Egap Exc. En. Dimer HOMO

3-21G(d)

B3LYP 6-31+G(d,p)

3-21G(d)

MPW1K 6-31+G(d,p)

6-31G(d) -5.41 (-5.57) -2.71 (-2.89) 2.70 (2.68) 2.29 (2.22)

6-31G(d) -5.37 (-5.54) -2.70 (-2.90) 2.67 (2.64) 2.29 (2.20)

6-31+G(d,p) -5.66 (-5.79) -3.02 (-3.18) 2.64 (2.61) 2.25 (2.16)

6-31G(d) -6.34 (-6.54) -2.28 (-2.50) 4.06 (4.04) 2.67 (2.58)

6-31G(d) -6.29 (-6.51) -2.27 (-2.51) 4.02 (4.00) 2.64 (2.55)

6-31+G(d,p) -6.48 (-6.66) -2.50 (-2.71) 3.98 (3.95) 2.60 (2.50)

-5.17 (-5.32)

---

-5.42 (-5.54)

-6.05 (-6.24)

---

-6.19 (-6.36) 11

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LUMO Egap. Exc. En.

-2.89 (-3.05) 2.28 (2.27) 1.98 (1.91)

-------

-3.19 (-3.34) 2.23 (2.20) --(1.84)

-2.50 (-2.70) 3.55 (3.54) 2.39 (2.31)

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-------

-2.72 (-2.91) 3.47 (3.45) 2.32 (2.23)

When the B3LYP functional is used in combination with the 6-31+G(d,p) basis set both for the optimization and the TDDFT calculations, we can notice a stabilization of the calculated HOMO and LUMO values of about 0.2-0.3 eV, both for the monomer and the dimer, compared to 321G(d)/6-31G(d) results. In the MPW1K calculations the stabilization of HOMO and LUMO values is less marked, of the order of 0.1-0.2 eV. The global effect is a slight reduction of the calculated band gap of the two systems, which amounts to less than 0.1 eV. When the larger 631+G(d,p) basis set is used only in the geometry optimization step, only minimal differences were found in the calculated parameters. This observation underlines the adequacy of the 3-21G(d) basis set in the geometry optimization of these structures. The use of reduced basis sets is very important for the description of the extended oligomeric systems, whereby a large number of atoms need to be considered and thus a large associated computational overhead. 3.2 Polymers: structural properties We now move to the simulation of the three polymers of interest. We initially considered two different dimer structures, that differ by the orientation of the interacting monomeric units. We coded these structures as “A”, when the two monomeric units are oriented in the same way, and “B”, when the second unit is rotated by 180 degrees with respect to the previous one, see Figures 35. To evaluate the relative stability, including a full description of steric effects, in this stage we also included the alkyl side chains in our model. To better describe the weak interaction between the alkyl chains, we include the calculation of the intramolecular dispersion by using the DFT-D3


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method,101-104 on the B3LYP optimized geometries. In Table 4 the relative energies between the A and B structures for each dimer are reported.

Table 4.Relative energies for the PTI-1, PBDT-I and PBDT-TIT dimers in conformations A and B, see also Figures 3-5. conformation PTI-1 dimer PBDT-I dimer PBDT-TIT dimer

A B A B A B

B3LYP (kcal/mole) +0.61 0.00 0.00 +0.64 +0.56 0.00

D3-B3LYP (kcal/mole) +4.98 0.00 0.00 +2.16 0.00 +0.66

With the B3LYP calculations we observe quite small energy differences for all the polymers. For PTI-1 and PBDT-I these differences are emphasized by using the D3 method, favoring respectively the A and the B conformer. For the PBDT-TIT dimer we observe a different trend, having opposite results by using the two methods, although the differences were not marked. In all the cases we used the conformations obtained by the DFT-D3 methods and extended this conformationto the simulation of the larger oligomers (Figures 3, 4 and 5 and Supporting Information), for which we did not consider the alkyl chains in the simulation. In Figure 3 we report the optimized geometries of the calculated A and B dimers and of pentamer of the PTI-1 polymer. The structures of all the optimized oligomers is reported in the Supporting Information.



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Figure 3: Optimized geometries of PTI-1 A and B dimers, see text for discussion, and of the pentamer. For the dimers, the more stable structure is highlighted.

Upon increasing the oligomer chain length, the PTI-1 polymer tends to curl on itself. This trend was already noted in the optimization of the dimer, see Table 2, in which the dihedral angles between isoindigo and thiophene moieties are reported. The main contribution to the twisting of the polymer backbone is given by the thiophene moieties that are not coplanar with the rest of the structure. The strong steric hindrance due to the presence of the long side alkyl chains induces a further offset of about 5-7° with respect to the model structure. As seen in Table 2, the structural distortion from planarity induced by the alkyl chains caused a slight increase (0.03-0.06 eV) of the calculated


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HOMO-LUMO gap and lowest excitation energy at all levels of theory, reflecting the decreased conjugation along the polymer backbone.105 A partial rolling of the structure by increasing the chain length was observed also in the case of the PBDT-I polymer, see Figure 4, showing a dihedral angle of about 25° between the planar benzodithiophene and the isoindigo groups.

Figure 4. Optimized geometries of PBDT-I A and B dimers, see text for discussion, and of the pentamer. For the dimers, the more stable structure is highlighted.

A different behavior is shown by the PBDT-TIT system, for which the polymer chain remains almost planar, with only slight distortions after the introduction of the thiophene rings, see Figure 5.



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Figure 5. Optimized geometries of PBDT-TIT A and B dimers, see text for discussion, and of the pentamer. For the dimers, the more stable structure is highlighted.

To further check the effect of the alkyl side chains, we optimized the geometry of the PBDT-TIT dimer by using both the experimentally employed alkyl side chains on the N isoindigo atom and on the benzodithiophene moieties, to see if a twist of the polymer backbone could take place, see Supporting Information. We found almost no differences in the optimized geometries. A local minimum structure characterized by slightly larger dihedral angles was found to be slightly less stable (+0.6 kcal/mol) with respect to the planar conformation for the PBDT-TIT dimer. The effect of the side alkyl chains on the calculated electrochemical and optical parameters is quite small, similar to what found for the PTI-I system, with an expected slight increase of the band gap and excitation energies in the case of the more twisted geometry,105 see Supporting Information. As recently reported by Ma et al.,77 the high planarity of the backbones in the PBDT-TIT system could be beneficial to maximize the π–π stacking interactions occurring among the polymer


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backbones in the solid state, which in turn may enhance the charge mobility, consistent with the higher photovoltaic performance of PBDT-TIT based solar cells. Koet al.,105 however, demonstrated for the P3HT polymer and its derivates, that the side alkyl chains induced a twisting of the polymer backbones which stabilizes the HOMO level, and thus enhances the devices Voc. This observation is confirmed also in this case, by the experimental results in polymer-PCBM61 heterojunction devices, showing an open-circuit voltage of 0.84 vs. 0.79 V for the more twisted PBDT-I system against the almost planar PBDT-TIT, reflecting the differences in the HOMO level of the two polymers (-5.82 eV for the PBDT-I and -5.78 eV for the PBDT-TIT).77

3.3 Electrochemical properties Two standard ways to computationally estimate oxidation/reduction potentials are: (i) a vertical approximation (i.e. Koopmans theorem), by taking the negative of the HOMO and LUMO single particle eigenvalues, and (ii) by calculating the real oxidation and reduction Gibbs free energy differences, which are effectively corresponding to the measured oxidation and reduction potentials, involving geometrical relaxation of the oxidized and reduced species.54 Both approaches have their merits, with Koopmans theorem offering a simple but approximate computational procedure, requiring only a calculations on the neutral species. The calculation of Gibbs free energies, on the other hand, is accurate but computationally very intensive, requiring calculation of geometries and vibrational frequencies in vacuo and geometries in solution, for both the neutral, oxidized and reduced species. In this work we evaluated the oxidation and reduction potentials by taking the negative of the HOMO and LUMO single particle eigenvalues, within Koopmans theorem, which was previously shown to be a good approximation to Gibbs free energy differences for related conductive polymers.43, 56-57 We thus calculated HOMO and LUMO values, electrochemical band gaps and excitation energies for the first five oligomers of the three polymers. Then, as reported in the literature,55, 58-59,



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65

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using a linear fit and plotting the calculated values against 1/n we can extrapolate the properties

of the infinite polymers as the intercept with the ordinate axes. It has to be noticed, however, that previous reports suggested that such linear extrapolation could be misleading in cases of effective conjugation length limited to few monomeric units.50. In Table 5, we list the values of HOMO and LUMO energies, HOMO-LUMO gaps and lowest excitation energies, along with their oscillator strength (ƒ), calculated using B3LYP and MPW1K functionals, in vacuo and in dichloromethane solution, for the PTI1, PBDT-I and PBDT-TIT monomers and pentamers. Moreover a comparison of the calculated linear fitted HOMO and LUMO energies and HOMO-LUMO gap with the experimental values is reported in Figure 6. For the PTI-1 polymer the results obtained with the CAM-B3LYP functionalare also reported. A detailed list of calculated parameters for all the considered systems (from monomer to pentamer) is reported in the Supporting Information.

Table 5. Comparison between calculated and experimental HOMO-LUMO energies, energy gaps and lowest excitation energies, along with their oscillator strength (ƒ), for the PTI-1, PBDT-I and PBDT-TIT polymers. Values calculated in solution are reported in bracket. All the energy values are in eV. The first transition corresponds in all cases to the most intense one. (PTI.1)n B3LYP HOMO

n=5

Fit

Exp

LUMO

MPW1K H-L

Exc

gap

En/

HOMO

LUMO

ƒ

CAM-B3LYP

H-L

Exc

gap

En/

HOMO

LUMO

H-L gap

ƒ

Exc En/

ƒ

-5.08

-3.01

2.07

1.75/4

-5.95

-2.64

3.31

2.19/

---

---

---

---

(-5.22)

(-3.15)

(2.07)

.57

(-6.12)

(-2.82)

(3.30)

5.70

(-6.39)

(-2.17)

(4.22)

(2.31/

-5.82

-2.74

3.08

(2.15/ 5.67) 2.06

---

---

---

---

-4.97

-3.09

1.89

(1.71/ 4.67) 1.61

5.35)

(-5.11)

(-3.22)

(1.89)

(1.57)

(-5.99)

(-2.91)

(3.07)

(2.02)

(-6.25)

(-2.26)

(3.99)

(2.21)

-5.85

-3.88

1.97

1.78

-5.85

-3.88

1.97

1.78

-5.85

-3.88

1.97

1.78

(PBDT-I)n


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n=5

Fit

Exp

-4.99

-2.96

2.03

1.73/

-5.86

-2.60

3.26

2.22/

(-5.17)

(-3.14)

(2.03)

5.33

(-6.07)

(-2.82)

(3.25)

7.22

-4.95

-3.01

1.94

(1.71/ 5.37) 1.64

-5.81

-2.67

3.14

(2.19/ 6.97) 2.12

(-5.13)

(-3.19)

(1.94)

(1.62)

(-6.01)

(-2.88)

(3.13)

(2.10)

-5.82

-3.88

1.94

1.81

-5.82

-3.88

1.94

1.81

2.18/

(PBDT-TIT)n n=5

Fit

Exp

-4.89

-2.93

1.96

1.68/7

-5.74

-2.57

3.17

(-5.02)

(-3.07)

(1.95)

.53

(-5.91)

(-2.75)

(3.16)

10.69

-5.67

-2.61

3.06

(2.14/ 10.06) 2.10

-4.83

-2.96

1.87

(1.65/ 7.40) 1.59

(-4.96)

(-3.10)

(1.86)

(1.57)

(-5.84)

(-2.78)

(3.05)

(2.08)

-5.78

-3.91

1.87

1.88

-5.78

-3.91

1.87

1.88

By increasing the number of units, due to the increase of the charge delocalization along the polymer backbone, we note a gradual increment of the calculated HOMO energy while the LUMO energy decreases, leading the HOMO-LUMO gaps to converge toward the experimental values (Figure 6). The B3LYP calculated HOMO and LUMO energy values are however both overestimated by 0.7-0.8 eV compared to experimental values, as already found in previous works.56-57, 59, 66 This overestimation is reduced by 0.2-0.3 eV when using the larger 6-31+G(d,p) basis set (see data for the dimer in Table 3). It has to be noticed that the absolute HOMO and LUMO values, when compared to experimental data, should be referred to the same vacuum level; rewardingly, the calculated levels are rigidly shifted compared to the electrochemically measured ones, which makes us confident of the applied methodology. It can be noticed that the rigid upshift of both HOMO and LUMO values, obtained by B3LYP calculations, provides essentially the same electrochemical band gap as experimentally found. The discrepancy is less than 0.15 eV, if the pentamer values are considered, or below 0.1 eV when the “infinite polymer” values are extrapolated by the linear fit for all the considered polymers. It has to be noted that if we consider the pentamer, that give a good approximation of the polymer electrochemical properties, see Conjugation Effective Length paragraph, we are able to reproduce the experimental trend in the 19 ACS Paragon Plus Environment


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HOMO position of the considered polymers, PTI-1 < PBDT-I < PBDT-TIT. This is an interesting finding, being the HOMO position of the donor polymer strictly related to the photovoltage of the devices. Furthermore the Voc results to be almost independent on the fabrication conditions, as the polymer-PCBM ratio, use of additives, and also to the variation of acceptor material (PC61BM and PC71BM).106 In fact, from the devices characterization reported in the experimental works, we can see that the higher Voc is obtained for the PTI-1 polymers (0.92 V)76, while for PBDT-I and PBDTTIT were obtained 0.84 V and 0.78 V respectively.77 The LUMO values, depending on the common acceptor units, are instead quite similar between the three polymers, and they are only slightly higher than the LUMO of PCBM, suggesting a small driving force for the charge separation,107 that could be one of the cause of the quite low photocurrent obtained. Further calculations to accurately evaluate the HOMO and LUMO level alignment in the presence of the PCBM acceptor will be the object of a future work. As already found for the DiBr PTI-1 precursor monomer, MPW1K results show an overestimation of the HOMO-LUMO gaps of more than 1eV, due to a strong HOMO stabilization and a partial LUMO destabilization compared to B3LYP values. In order to deeply study the PTI-1 polymer, we tested the CAM-B3LYP functional in the electrochemical properties simulation of the PTI-1 polymer, even if this functional provided quite inaccurate results for the DiBr PTI-1 precursor monomer. The obtained results show a strong overestimation (about 2 times the experimental value) of the HOMO-LUMO gap. Also the excitation energies are worse described with respect to the other functionals, with discrepancies of 0.43eV (0.53eV at the pentamer level). So we decided not to use this functional for the simulation of the PBDT-I and PBDT-TIT polymers.


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Figure 6: Plot of B3LYP-calculated HOMO (red line, squares), LUMO (blue line, circles) and energy gap (black line, triangles) linear fit (vs 1/n) of the (a) PTI-1, (b) PBDT-I, and (c) PBDT-TIT polymers in dichloromethane solution. The experimental values are indicated as dashed lines.

3.4 Optical properties The optical properties of the three polymers were evaluated by TDDFT calculation of the lowest excitation energies, which can be directly compared to the experimental absorption spectrum of the polymers in solution. In Figure 7 we thus report the normalized experimental absorption spectra of 21 ACS Paragon Plus Environment


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the three polymers in CHCl3 solution. These are characterized by a broad and intense absorption band, with some sub-structures features, in the region between 600 and 800 nm. The PTI-1 polymer shows the most red-shifted absorption, with a λmax located at 697 nm (1.78 eV), while the PBDT-I and PBDT-TIT have their absorption maxima respectively at 685 nm (1.81 eV) and 660 nm (1.88 eV). We notice that for the PBDT-I and PBDT-TIT polymers, Ma et al.77 found only slight differences between the polymers absorption spectra in solution and in the solid state, probably due to the lack of strong aggregation phenomena in the film, caused by the branched side alkyl chains. The calculated excitation energies are summarized, along with their linear fit and the comparison with the experimental values, in Table5(see Supporting Information for the detailed list) for the PTI-1, PBDT-I and PBDT-TIT, respectively. Our calculations using both the B3LYP and MPW1K functionals show a good agreement already at the pentamer level, with a discrepancy of ∼0.2 eV. If we consider the extrapolated values to infinite chain length, we obtain values which are closer to the experimental measurements. MPW1K (B3LYP) data show an expected shift towards higher (lower) energies, compared to the experimental data for all the considered polymers (see Table 5).


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Figure 7.Experimental absorption spectra of PTI-1 (red line, i), PBDT-I (blue line, ii) and PBDTTIT (green line, iii) in CHCl3. In Figure 8 the calculated absorption spectra of all the considered oligomers of the three polymers with B3LYP, MPW1K and CAM-B3LYPfunctionals are reported. The lowest excitation energies of these structures, both in vacuo and in solution, along with their oscillator strength are summarized in Supporting Information.



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Figure 8. Calculated absorption spectra of (1) the PTI-1,(2) PBDT-I and (3) PBDT-TIT oligomers in dichloromethane solution, with the B3LYP (a), MPW1K (b) and CAM-B3LYP (c)exchangecorrelation functionals. Monomer (red line, i), dimer (green line, ii), trimer (blue line, iii), tetramer (purple line, iv) and pentamer (cyan line, v). Vertical lines correspond to calculated excitation energies and oscillator strengths. It is interesting to note that moving from the monomer up to the pentamer a gradual but consistent red shift of the absorption maximum globally of about 0.5 eV is observed, caused by the extension of the conjugation. Moreover we can notice an almost constant increase of the oscillator strength of the main optical transitions with the size of the systems, due to the increase of the molecular cross section, see Supporting Information. Moving to the direct comparison of calculated and experimental absorption spectra in solution for each polymer, reported in Figure 9, we can see as PTI-1 and PBDT-I polymers are well reproduced by B3LYP calculations, with slight red shift, within 0.1 eV, with respect to the experiment. Notice that the precise shape of the absorption profile 24 ACS Paragon Plus Environment

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is determined, among other factors, by Franck-Condon factors, which can shift the maximum from its electronic origin by up to 0.2-0.3eV.108-111This type of calculations is very time-consuming, since one has to calculated the ground and excited state geometries and vibrations frequencies, which becomes rapidly impracticable for the large oligomers investigated here. The absorption spectrum of the PBDT-TIT polymer is instead reproduced with lower accuracy, with both B3LYP and MPW1K providing respectively a red shift and a blue shift of 0.2 eV. By looking at the relative trends, both B3LYP and MPW1K predict a red shift of the PBDT-TIT absorption spectrum with respect to the PTI-1 and PBDT-I polymers, while experimentally a slight blue shift is found. The experimental trend for PTI-1 and PBDT-I is reproduced by MPW1K calculations, although a consistent blue shift compared to experimental values is observed.This slight inaccuracy in the proper description of the experimental absorption spectrum of this system could be due to the presence in the real case, at room temperature, of different geometrical conformations, with different torsion angles of the polymer backbone, that we have calculated to have low energy barrier to move from one to another structure, particularly for the PBDT-TIT polymers, in a maximum range of 5 kcal/mole, see Table 4. This modifications in the backbone dihedral angles have a small, but sizeable effect on the electrochemical and optical parameters, already at the dimer level, Supporting Informations.



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Figure 9. Comparison between experimental (blue line, i) and calculated at the pentamer level (red line, ii) absorption spectra of the (1) PTI-1, (2) PBDT-I and (3) PBDT-TIT polymers, using B3LYP (a), MPW1K (b) and CAM-B3LYP (c) exchange-correlation functionals. Red vertical lines correspond to calculated excitation energies and oscillator strengths. The intensity of the experimental spectra has been rescaled to match the calculated one.

The main absorption band is assigned to an intramolecular charge transfer transition of HOMOLUMO character (more than 60%). As we can see in Figures 10, 11 and 12, for the PTI-1, PBDT-I and PBDT-TIT, respectively, the HOMO is in all cases quite delocalized along the whole polymer chain, while the LUMO is mainly localized on the acceptor isoindigo moieties. This strong charge transfer effect is particularly evident in the case of PBDT-TIT polymer, which manifests a significant charge separation between occupied and unoccupied molecular states by increasing the polymer backbone length.At the pentamer level there is a significant component (about 15%) of the


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main absorption band due to a HOMO-1/LUMO+1 transition; these molecular orbitals are localized respectively on the donor and acceptor moieties of the terminal units, Supporting Information.Surprisingly, essentially no differences were found on the molecular orbital localization among the investigated functionals,Supporting Information.Regarding the energy level of theorbitals involved in the optically active transition,we observe a stabilization of the HOMO-1 (destabilization of the LUMO+1) with respect to the HOMO (LUMO) within 0.1 eV for the PTI-1 polymer,which is even smaller for the PBDT-I and PBDT-TIT polymers, Supporting Information.

Figure 10. HOMO-LUMO molecular orbitals of the PTI-1 monomer, trimer and pentamer, calculated by the B3LYP functional in solution (isodensity contour = 0.03).



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Figure 11. HOMO-LUMO molecular orbitals of the PBDT-I monomer, trimer and pentamer, calculated by the B3LYP functional in solution (isodensitycontour = 0.03).


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Figure 12. HOMO-LUMO molecular orbitals of the PBDT-TIT monomer, trimer and pentamer, calculated by the B3LYP functional in solution (isodensity contour = 0.03).

To fully characterize the optical properties of the considered polymers, we also estimated their extinction coefficients.This is an importantparametergoverning the efficiency of anorganic solar cell. To compare the calculated and experimental values, reported in units ofg-1*L*cm-1, we divided the calculated ε values in units of m-1*L*cm-1 by the oligomers mass weight. In Table 6the experimental and calculated extinction coefficient values for the three polymers are reported. Table 6. Experimental and calculated extinction coefficients (L*g-1*cm-1)) for the PTI-1, PBDT-I and PBDT-TIT polymers. The data refer to the pentamers, with σ = 0.17 eV. Experimental

Calculated

PTI-1

66.0

144.2

PBDT-I

37.0

110.3

PBDT-TIT

34.3

129.9

Even if the PTI1 polymer has an almost double extinction coefficient with respect to the PBDT-TIT polymer, this difference is not always coincident with an higher photocurrent value in the photovoltaic device, in the same fabrication conditions. This is mainly due to the differences in the polymer-PCBM mixing,106 and has not been evaluated in the present work. In any case our data qualitatively reproduce the experimental trend, showing a larger extinction coefficient for PTI-1 compared to PBDT-I and PBDT-TIT, although the calculated quantities are substantially overestimated (by ca. a factor 2-3). The calculated ε values depend upon two parameters, i.e. the transition oscillator strength (ƒ), which we calculate rigorously, and the σ values used to describe the band broadening, which are chosen a posteriori to match the band shapes. The results reported in Table 6were obtained using a σ of 0.17, corresponding to a FWHM of ∼0.4 eV, estimated to 29 ACS Paragon Plus Environment


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match the bandwidth of the experimental PTI-1 absorption spectrum. We considered, by observing Figure 7, that the PBDT polymers bandwidths are considerably higher with respect to that the PTI-1 polymer. So we recalculated the ε values by using σ values of respectively 0.31 and 0.25 for PBDTI and PBDT-TIT, obtained by the experimental spectra. In this way we found extinction coefficients closer to the experiment, of 62.3 and 89.4 L*g-1*cm-1for PBDT-I and PBDT-TIT.The higher extinction coefficient calculated for the PBDT-TIT with respect to the PBDT-I, not in line with the experimental trend, depends on the higher coplanarity of the PBDT-TIT backbone, due to the effect of the thiophene spacers, allowing an higher overlap of the wavefunctions.60 3.5 Effective conjugation length of the polymers The knowledge of the number of monomer units in a π-conjugated oligomer required to provide size-independent redox, optical, or other properties that correspond to those of the related infinitechain polymer is of both practical and theoretical interest. For this purpose the concept of Effective Conjugation Length (ECL) was introduced.78 The ECL defines the extent of π-conjugated systems in which the electronic delocalization is limited and at which point the optical, electrochemical, and other physical properties reach a saturation level that is common with the analogous polymer. Following a standard procedure reported in previous works,78, 112-113 we determined the ECL values of the considered systems. We thus plot the calculated HOMO-LUMO and optical band gap versus 1/n, where n is the number of oligomers units. The ECL is determined where saturation of the investigated quantities occur. For the considered PTI-1, PBDT-I and PBDT-TIT polymers we investigated a number of units from 1 to 5. We report in Figure 13 the B3LYP-calculated HOMOLUMO gaps and excitation energies in dichloromethane solutions, which better reproduce the experimental results for the three polymers.


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Figure13. HOMO-LUMO band gap (black line, i) and excitation energy (red line, ii) calculated using the B3LYP functional in solution for the (a) PTI-1, (b) PBDT-I, and (c) PBDT-TIT oligomers (monomer to pentamer).



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As it can be noticed, the considered polymers show quite a linear trend of both the HOMO-LUMO and optical band gap up to the tetramer, while moving to the pentamer we can see a partial saturation of the calculated parameters. In particular for the PBDT-TIT polymer, between tetramer and pentamer we do not observe any change in the calculated properties, so it is reasonable to conclude that an ECL of four units characterizes this system. PTI-1 and PBDT- I polymers, due to lower conjugation of their backbones, show a slight difference in the band gap of respectively 0.02 eV and 0.01 eV moving from the tetramer to the pentamer. This trend suggests an effective conjugation length of at least five (or six) repeating units for these systems. 4. Conclusions We have investigated the structural, electronic and optical properties of three isoindigo-based donor-acceptor polymers, coded as PTI-1, PBDT-I and PBDT-TIT employing various levels of calculation, within Density Functional Theory. A calibration study was carried out to check the basis set and model simplification effects on the calculated properties, along with testing different functionals (B3LYP, MPW1K and CAM-B3LYP). Our results show the adequacy of the computational set-up to reproduce the electrochemical features of the polymers, apart from a rigid shift of the calculated HOMO and LUMO values compared to experimental data. Calculated absorption spectra with the B3LYP functional are slightly red shifted with respect to the experimental ones, while the optical band gap is well reproduced. The growing-up procedure used in this work, starting from the monomer units, allowed us to determine the effective conjugation length for these polymers, which could be of great interest in the design and synthesis of similar structures.This will allowthe predictive investigation of new variants of isoindigo-based polymers with comparable accuracy.


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Acknowledgment. The authors thank FP7-ICT-2011 project “SUNFLOWER” for financial support. Supporting Information Available. Molecular structure of the PTI-1 Di-Br precursor; optimized geometries of the PTI-1, PBDT-I and PBDT-TIT oligomers; calculated dihedral angles, HOMO, LUMO, band gap and excitation energies for the PBDT-TIT dimer; calculated HOMO-LUMO energies, energy gaps and lowest excitation energies for the PTI-1, PBDT-I and PBDT-TIT oligomers; list of the calculated lowest excitation energies and oscillator strengths; energy levels and plot of the more relevant molecular orbitals of the considered polymers; isodensity plot of the PTI-1 monomer and trimer calculated by different functionals. This material is available free of charge via the Internet at http://pubs.acs.org.

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SYNOPSIS TOC

Computational modeling of Isoindigo-based polymers Used in Organic Solar Cells Paolo Salvatori, Edoardo Mosconi, ErgangWang, MatsAndersson, Michele Muccini, Filippo De Angelis a

ComputationalLaboratory for Hybrid/OrganicPhotovoltaics (CLHYO), CNR-ISTM, via Elce di Sotto, 8 I-06123, Perugia, Italy. b

c

Department of Chemistry, University of Perugia, Via Elce di Sotto 8, I-06213, Perugia, Italy.

Department of Chemical and Biological Engineering/Polymer Technology, Chalmers University of Technology, SE-412 96 Göteborg, Sweden. d

ISMN-CNR, Via P. Gobetti 101, Bologna, Italy.

CorrespondingAuthors: Dr. Edoardo Mosconi, Dr. Filippo De Angelis E-mail: [email protected]; [email protected] Phone: +39 0755855523


Computational Modeling of Isoindigo-Based ... - ACS Publications

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