# An Integrated Experimental/Theoretical Study of Structurally Related Poly-Thiophenes Used in Photovoltaic Systems

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## Abstract

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## 1. Introduction

## 2. Semiconductive Polythiophene Structures

## 3. Experimental Setup

_{6}> 99.9%, Sigma-Aldrich Chemie B.V., Zwijndrecht, The Netherlands) in acetonitrile (ACN) solution was used as the base electrolyte. The working electrode is obtained by drop-casting of polythiophene/CH

_{2}Cl

_{2}solution applied on freshly polished Glassy Carbon (GC) electrodes (Metrohm Schweiz AG, Zofingen, Switzerland) and HTW Sigradur (HTW Hochtemperatur-Werkstoffe GmbH, Thierhaupten, Germany). Prior to polymer drop-casting, the GC surface was mechanically polished with emery paper, then with 0.05 μm alumina (Buheler, Lake Bluff, IL, USA), finally followed by a 5 min sonication cleaning in water. The GC surface was polymer-coated by casting one drop of a 0.1 mg/mL, in CH

_{2}Cl

_{2}, polymer solution on top of the GC surface and allowing it to dry [16]. A platinum wire was used as the counter electrode. A silver wire was used as a quasi-reference electrode, whose stability was checked (at the end of each measurement session) with respect to the ferrocene/ferrocenium reversible redox couple. In the following all potential values are referred to the Ag/Ag

^{+}couple. A large number of screening experiments were carried out, varying both the dose of the drop-casting as well as the drying time. Films obtained on repeating the sequence of a single drop-cast application three times, followed by 15 min drying, allowed for the best CV reproducibility. We estimate that our reduction and oxidation potentials are affected by a 30 mV absolute error (±15 mV error). The electrochemical cell was de-aerated with argon for 15 min before any measurement session. Figure 2 shows two examples of the cyclic voltammetry data treatment, in order to show in detail how the electrochemical onset potentials were determined. Two completely different experimental behaviors are considered: Poly H characterized by a rather hill-defined/sluggish cyclic voltammetry pattern (with particular reference to the positive potential range: polymer film oxidation), Figure 2a, and Poly F which shows a rather well-defined and neat cyclic voltammetry pattern, Figure 2b.

**Figure 2.**Cyclic voltametries (

**a**,

**b**) of the Poly H and Poly F polymer films on GC surfaces (obtained by drop-casting procedure), respectively. Showing the method adopted to determine the reduction and oxidation onset potentials, which are used to calculate the so-called electrochemical band gap ($\mathsf{\Delta}{E}_{EC}$). Onset values are obtained by the intercept of the lines interpolating the baseline and redox peak currents.

**Figure 3.**Poly F UV-vis spectrum, the line used to determine the onset wavelength is shown. The intercept with the absissa allows us to determine the optical band gap ($\mathsf{\Delta}{E}_{OPT}$).

## 4. Computational Details

_{1}symmetry and are of restricted nature. The results presented in this paper are obtained both at the very basic Hartree-Fock (HF) and Becke, three-parameter, Lee-Yang-Parr (B3LYP) exchange-correlation density functional levels of the theory; the all-electron split valence plus polarization basis set 6-31G(d) was used in both HF and DFT calculations. Preliminary screening calculations were carried out using less accurate basis sets: LanL2DZ, 3-21G*, with focus on the influence of the geometry optimization as well as of the number of repetitive units in the oligomer on the variation of the HOMO-LUMO energies and band gap. Moreover, periodic boundary condition (PBC) calculations were performed, the latter results well compare with the HOMO-LUMO band gap relevant to the dimeric and trimeric species, together with the systematic calculation (again involving the mono-, di-, trimer species) of TDDFT electronic spectra [24].

## 5. Theoretical Background

#### 5.1. Orbital Energies: DFT vs. HF

#### 5.2. Computing the Band Gaps

#### 5.3. Optical and Electrochemical Band Gaps

**Figure 4.**The white circles represent holes and the black circles electrons. In (

**a**,

**b**) the pseudo-fermi level of the polarized electrode is represented by the line on top of the dark rectangle representing the conduction band of the solid; (

**c**,

**d**) depicts the intermolecular and intramolecular electronic transitions, respectively. The other lines represent the orbitals in the polymer molecules while the arrows represent the electron transfer.

## 6. Results

_{EC}(note that the difference in the onset of potentials, V, relevant to the reduction and oxidation current peaks is straight transformed in a band gap energy, eV, on the basis of the work of Trasatti [31]).

_{HF}and ΔE

_{DFT}values. Figure 5c,e patterns demonstrate that ΔE

_{HF}are overestimated with respect to both the optical and electrochemical band gap, while in Figure 5d a comparison between the DFT band gap and the optical band gap shows that DFT systematically overestimates the optical band gap. Eventually, the electrochemical band gap is compared with the DFT gap (Figure 5f), and ΔE

_{DFT}values semi-quantitatively match the electrochemical band gap: the equivalence line is almost exactly placed in the middle of the dataset. Figure 6 shows the difference between the DFT, electrochemical and optical band gap values (i.e., ($\mathsf{\Delta}{E}_{DFT}-\mathsf{\Delta}{E}_{EC}$), ($\mathsf{\Delta}{E}_{EC}-\mathsf{\Delta}{E}_{OPT}$) and ($\mathsf{\Delta}{E}_{DFT}-\mathsf{\Delta}{E}_{OPT}$) differences). Notably, the difference between electrochemical and DFT band gaps ($\mathsf{\Delta}{E}_{DFT}-\mathsf{\Delta}{E}_{EC}$) is scattered homogenously around zero, and the maximum deviation is 0.28 eV. However, the discrepancy between electrochemical and optical results is the same as the DFT and optical one: both ranging between 0.2 and 0.9 eV, highlighting that the DFT and electrochemical band gaps have the same quantitative trend.

**Figure 5.**Comparison between (

**a**) electrochemically determined and spectroscopically determined band gap; (

**b**) band gap computed by means of DFT and HF methods; (

**c**) band gap spectroscopically determined and computed by means of HF method; (

**d**) band gap electrochemically determined and computed by means of HF method; (

**e**) band gap spectroscopically determined and computed by means of DFT method; (

**f**) band gap electrochemically determined and computed by means of DFT method. All data are reported in eV. The “equivalence line” shows the ideal line featuring slope = 1 and intercept = 0.

**Figure 6.**Discrepancies between band gaps computed by means of DFT method and electrochemically determined; band gaps electrochemically and spectroscopically determined; band gaps computed by means of DFT method and spectroscopically determined.

## 7. Conclusions

- (1)
- The comparison of HF and DFT theoretical data, with both electrochemical and spectroscopic experimental band gap values, shows that the HF approach provides a dramatic overestimation of the band gap. The exchange-correlation and electron-correlation cannot be neglected; they have to be taken into account to assess the correct band gap energy. Indeed, ΔE
_{DFT}values definitively show a better quantitative match with both the electrochemical and spectroscopic band gap values, as it is shown in Figure 5 and Figure 6. - (2)
- Arguments, based both on the purely modelistic (Figure 4) and on the comparison between DFT and experimental data (Figure 5 and Figure 6), show that the most effective approach to be used when assessing the band gap characteristics for photovoltaic materials is to make a reference to both the DFT and electrochemical methods to determine the HOMO-LUMO band gap.
- (3)
- Eventually, an empirical quantitative value can be determined for the exciton stabilization energy (${J}_{e,h}$), vide infra relation 8. The close comparison of the physics underlying absorption in electronic spectra (Figure 4d) and reduction/oxidation current peaks in cyclic voltammetry measurements (Figure 4a,b) together with the systematic difference observed in Figure 5a (the least square fit yields ΔE
_{EC}= 0.53 + 0.99 ΔE_{OPT}) allow us to propose a value of about 0.5 eV (the intercept of the least square fit) as an average value for the exciton stabilization energy [30,32]. Such an estimate is further supported by the systematic shift observed in Figure 6 between the ΔE_{OPT}vs. ΔE_{DFT}pattern (red line represents the least square fitting of the ΔE_{OPT}vs. ΔE_{DFT}data) and the relevant equivalence line.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Sample Availability:**Samples of the compounds are not available from the authors.

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**MDPI and ACS Style**

Vanossi, D.; Cigarini, L.; Giaccherini, A.; Da Como, E.; Fontanesi, C.
An Integrated Experimental/Theoretical Study of Structurally Related Poly-Thiophenes Used in Photovoltaic Systems. *Molecules* **2016**, *21*, 110.
https://doi.org/10.3390/molecules21010110

**AMA Style**

Vanossi D, Cigarini L, Giaccherini A, Da Como E, Fontanesi C.
An Integrated Experimental/Theoretical Study of Structurally Related Poly-Thiophenes Used in Photovoltaic Systems. *Molecules*. 2016; 21(1):110.
https://doi.org/10.3390/molecules21010110

**Chicago/Turabian Style**

Vanossi, Davide, Luigi Cigarini, Andrea Giaccherini, Enrico Da Como, and Claudio Fontanesi.
2016. "An Integrated Experimental/Theoretical Study of Structurally Related Poly-Thiophenes Used in Photovoltaic Systems" *Molecules* 21, no. 1: 110.
https://doi.org/10.3390/molecules21010110