Teorías y prácticas a finales del siglo XX

Calculation of the energy level of HOMO and LUMO orbitals of an organic semiconductor with potential applicability in OSCs is essential as the frontier orbitals levels alignment of the donor and the acceptor active materials plays a key role in the performance of the device. HOMO and LUMO energy values can be acquired from different experimental techniques, either in solution by electrochemistry studies or on thin film, by highly accurate techniques like Ultraviolet Photoelectron Spectroscopy (UPS), X-ray Photoelectron Spectroscopy (XPS) or Photoelectron Spectroscopy in Air (PESA).

In our case, the energy level values vs. vacuum were obtained from CV experiments, using the approximation depicted in Equation 5, based on the revised potential of the Fc/Fc⁺ redox couple considering the influence of the different reference electrodes employed described by Cardona et al.:¹⁹⁴

𝐸𝐻𝑂𝑀𝑂/𝐿𝑈𝑀𝑂= −5.1 − 𝐸_{1/2,𝑜𝑥/𝑟𝑒𝑑}¹ (𝑣𝑠. 𝐹𝑐/𝐹𝑐⁺)(𝑒𝑉) (Eqn. 5) As it has been analyzed before, SubPcs render irreversible first oxidation processes that impede the correct assignment of half-wave potential values. On the other hand, all SubPcs on this study display reversible first reduction events whose half-wave potentials can be easily extracted. For this reason, Equation 5 was used to calculate the energy LUMO level ELUMO for each SubPc derivative.

Then, in order to obtain reliable HOMO energy values, the optical band gap Eg,opt, that can be directly related to the HOMO-LUMO energy gap, was estimated from the intersection of the normalized absorption and emission spectra,¹⁹⁵ and directly added to ELUMO values applying Equation 6:

𝐸𝐻𝑂𝑀𝑂= 𝐸𝐿𝑈𝑀𝑂+ 𝐸𝑔,𝑜𝑝𝑡(𝑒𝑉) (Eqn. 6) It is very important to notice that this process implies a series of unavoidable approximations that must be taken into account when comparing the HOMO and LUMO levels calculated with other SubPc derivatives molecular energy levels found in literature. SubPc researchers employ many different approaches for measuring and reporting molecular energy levels, either in the equation developed to estimate the HOMO energy level from CV measurements^42b,85,196 or in

194Cardona, C. M.; Li, W.; Kaifer, A. E.; Stockdale, D.; Bazan, G. C. Adv. Mater. 2011, 23, 2367.

195Djurovich, P. I.; Mayo, E. I.; Forrest, S. R.; Thompson, M. E. Org. Electron. 2009, 10, 515.

196a) Trasatti, S. Pure & AppL Chem. 1986, 58, 955. b) D’Andrade, B. W.; Datta, S.; Forrest, S. R.; Djurovich, P.;

Polikarpov, E.; Thompson, M. E. Org. Electron. 2005, 6, 11.

Chapter I

91 the way to obtain the wavelength value considered in the Eg,opt calculation,42b,85,97c,197

that substantially differ from the one followed in this section. Therefore, the HOMO and LUMO levels and Eg,opt values indicated in this Thesis serve only to reflect the relative positions of the transport energy levels for the different SubPc derivatives rather than representing the absolute values of these energy levels.

Finally, in order to further investigate the geometries and electronic properties of the new SubPc derivatives, computational studies were performed using Spartan ‘14 applying density functional theory (DFT) at the B3LYP/6-31G* level for the geometry optimization and the calculation of the energy levels and the potential and energy surfaces in vacuum. In order to assess the viability of the mathematical model proposed by Bender et al. for the prediction of HOMO and LUMO energy levels in SubPc macrocycles from DFT (B3LYP) computational data,⁸⁵ estimation of the theoretical EHOMO and ELUMO values were carried out applying Equation 7 and Equation 8 to the molecular orbitals energy values computationally obtained:

𝐸_{𝐻𝑂𝑀𝑂}= 1.284 × 𝐸_{𝐻𝑂𝑀𝑂}^{𝐵3𝐿𝑌𝑃}+ 1.132 ± 0.188 (Eqn. 7) 𝐸_{𝐿𝑈𝑀𝑂}= 1.176 × 𝐸_{𝐿𝑈𝑀𝑂}^{𝐵3𝐿𝑌𝑃}− 0.499 ± 0.163 (Eqn. 8) Experimental and theoretical calculations have been carried out for all SubPc derivatives 3-22.

The experimental and computational data obtained for the HOMO-LUMO levels of reference SubPcs 6c and 7c, dicyano-SubPcs 12-15, tetracyano-SubPcs 17-20 and tricyano-SubPcs C3-22 and C1-22 is summarized in Table 4 and is shown schematically in Figure 32.

The trend in LUMO energy levels calculated with Equation 5 is obviously similar to the trend in E¹1/2,red seen in CV measurements. On the other hand, experimental EHOMO values obtained from ELUMO and Eg,opt data with Equation 6 differ slightly from the relative values of E¹ox due to the previously mentioned uncertainty associated to the experimental observation of SubPc oxidation processes by voltammetric measurements. Thus, ELUMO of dicyano-SubPc derivatives ranges from around -3.9 eV for SubPcs 12-14 to -4.1 eV for SubPc 15. This lowering denotes the influence of the electron-withdrawing peripheral substituents in 15 to increase the electron-acceptor character of these derivatives. In contrast, ELUMO of tetracyano-SubPcs 17-20 barely spans 0.04 eV, from -4.20 to -4.24 eV, suggesting that the sensitivity of the acceptor character of tetracyano-SubPcs to additional peripheral substitution is reduced due to the prevailing effect of two ortho-dicyano functionalities. A range in EHOMO from -5.92 to -6.19 eV

197Sullivan, P.; Duraud, A.; Hancox, I.; Beaumont, N.; Mirri, G.; Tucker, J. H. R.; Hatton, R. A.; Shipman, M.;

Jones, T. S. Adv. Energy Mater. 2011, 1, 352.

SubPc derivatives bearing peripheral cyano groups: HOMO and LUMO levels

92

for dicyano-SubPcs 12-15 and from -6.18 to -6.30 eV for tetracyano-SubPcs 17-20 can be extracted from Equation 6.

Table 4. Experimental and theoretical HOMO-LUMO energy levels data (in eV) of reference SubPc 6c and 7c, dicyano-SubPcs 12-15, tetracyano-SubPcs 17-20 and tricyano-SubPcs C3-22 and C1-22.

SubPc

Experimental data Computational data ELUMO

(eV)

EHOMO

(eV)

Eg,opta

(eV)

ELUMOb

(eV)

EHOMOc

(eV)

6c -3.86 -6.02 2.16 (573) -4.13 -6.30

7c -4.07 -6.23 2.16 (575) -4.30 -6.38

12 -3.88 -5.95 2.07 (599) -4.16 -6.12

13 -3.93 -5.92 1.98 (625) -4.24 -6.11

14 -3.93 -6.01 2.08 (595) -4.24 -6.24

15 -4.11 -6.19 2.09 (594) -4.67 -6.73

17 -4.20 -6.22 2.02 (615) -4.89 -6.69

18 -4.20 -6.18 1.98 (626) -4.90 -6.58

19 -4.21 -6.24 2.03 (609) -4.92 -6.92

20 -4.24 -6.30 2.06 (602) -5.11 -7.14

C3-22 -3.94 -6.11 2.16 (573) -4.47 -6.64

C1-22 -3.95 -6.11 2.16 (573) -4.51 -6.64

a Intersection wavelength in nm of the normalized absorption and emission spectra in brackets. ^b Calculated using Equation 8. ^c Calculated using Equation 7.

Chapter I

93 Figure 32. Schematic representation of the calculated HOMO and LUMO energy levels of reference SubPc 6c and 7c, dicyano-SubPcs 12-15, tetracyano-SubPcs 17-20 and tricyano-SubPcs C3-22 and C1 -22.

From computational ELUMO and EHOMO data in Table 4 and Figure 32, it can be easily spotted that estimates provided by the mathematical model proposed by Bender et al. does not fit well with the new substitution pattern introduced by cyano-SubPcs, giving rise to very disparate values. As a result, in all cases, experimental HOMO and LUMO values lie between 0.2 and 0.9 eV higher in energy when compared to the value obtained by computational calculations.

With the aim at determining a correlation between computational results obtained from B3LYP calculations and experimental data from CV measurements for the influence of the incorporation of one or two ortho-dicyano functionalities to the molecular orbital energy levels of SubPc derivatives, the same procedure as the one described by Bender et al. was followed. When plotting the computational estimates from each method against the experimental data for dicyano-SubPcs 12-15 and tetracyano-SubPcs 17-20 (tricyano-SubPcs 22 were excluded from this study as the substitution pattern is different), a linear regression of

SubPc derivatives bearing peripheral cyano groups: HOMO and LUMO levels

94

each data set produced goodness of fit (R²) values of 0.946 for EHOMO values and 0.988 for ELUMO values (Figure 33). From the linear regressions, the following equations were generated to estimate the molecular orbitals energies of these SubPc derivatives using B3LYP method:

𝐸_{𝐻𝑂𝑀𝑂} = 0.4764 × 𝐸_{𝐻𝑂𝑀𝑂}^{𝐵3𝐿𝑌𝑃}− 3.2701 (Eqn. 9) 𝐸_{𝐿𝑈𝑀𝑂}= 0.4669 × 𝐸_{𝐿𝑈𝑀𝑂}^{𝐵3𝐿𝑌𝑃}− 2.4435 (Eqn. 10)

Figure 33. a) Calculated EHOMO, calc. (eV) using B3LYP versus EHOMO (eV) measured experimentally by CV for dicyano-SubPcs 12-15 and tetracyano-SubPcs 17-20. b) Calculated E_LUMO, calc. (eV) using B3LYP versus ELUMO (eV) measured experimentally by CV for dicyano-SubPcs 12-15 and tetracyano-SubPcs 17-20.

The good correlation determined between experimentally and computationally acquired ELUMO

values is especially relevant, since these peripherally cyanated SubPc derivatives might be potentially applicable as n-type materials in OPV devices. Through these correlations, we

a)

b)

Chapter I

95 would be able to rapidly predict structural factors which influence the HOMO and LUMO energy levels of other cyanated SubPcs.

Figure 34 shows the HOMO and LUMO orbitals of a series of unsymmetrical SubPcs, namely diiodo-SubPc 5b, tetraiodo-SubPc 5a, dicyano-SubPc 14 and tetracyano-SubPc 19, calculated by DFT. Among these compounds, both the HOMO and LUMO are situated entirely on the SubPc core with no contribution from axial substituent. The HOMO is evenly distributed on the carbon atoms of the macrocycle, comprising the three isoindole units, while the LUMO encompasses both the nitrogen and carbon atoms comprising the 14 π-electron system. In iodinated SubPcs 5a and 5b, no contribution from the halogen atoms is observed to the HOMO or the LUMO. On the other hand, cyano groups in SubPcs 14 and 19 are slightly involved in the HOMO orbital delocalization, while they contribute to a greater extent in the LUMO orbital density. These patterns are reproduced in the other unsymmetrical SubPc series.

Figure 34. Frontier orbitals (HOMO and LUMO) of unsymmetrical SubPcs 5a, 5b, 14 and 19 calculated at the B3LYP/6-31G* computational level.

It can be noticed that, for the LUMO orbital in tetraiodo and tetracyano substituted SubPcs 5a and 19, the unsubstituted peripheral benzene does not exhibit any participation in the orbital delocalization. Interestingly, all tetracyanated SubPcs 17-20 follow the same trend (Figure 35).

This observation visually confirms the previously mentioned limited influence of the peripheral

SubPc derivatives bearing peripheral cyano groups: HOMO and LUMO levels

96

substituents occupying the non-cyanated benzene ring in the LUMO energy level. Finally, in SubPc 18, HOMO orbital density is entirely centered in the electron-donating thioalkyl substituents of the periphery, accordingly with the presence of intense CT-bands in the UV-vis absorption spectrum of this compound.

Figure 35. Frontier orbitals (HOMO and LUMO) of tetracyano-SubPcs 17-20 calculated at the B3LYP/6-31G* computational level. In SubPc 18, thiooctyl groups have been substituted by thioethyl groups to speed up calculations.