4 RESULTS AND DISCUSSION
This chapter will summarize the key findings of this work, which have been pre- sented in more detail in Publications I–IV. First, the OTωvalues determined for all the studied compounds and their interfacial complexes are presented. After this, structural and optoelectronic properties of the individual PSC compounds will be examined to understand better their functionality and performance in the PSCs.
Then, a step towards understanding of the interactions between the eD and eA com- pounds at their local interfaces will be taken by examining the structures and CT characteristics of the selected eD–eA complexes. Finally, the results of the multi- state electronic coupling calculations together with the other CT rate parameters and rates for the ED and CR processes taking place in the eD–eA complexes are presented. In all cases, the effect of the functional and dispersion corrections on the features is closely examined. Furthermore, the effect of other calculation parameters and models used will be also considered.
Table 4.1 Optimally tuned (OT) range-separation parameters (ω, in bohr−1) of the LRC- functionals determined in vacuum.1
Model OT-ωB97X OT-ωB97X-D OT-BNL Publication
eD
BDT-TFQ 0.10 (0.11)2 0.09 (0.10)2 - II
TQ - - 0.15 III
BDT-TzBI - 0.09 (0.12)2 - IV
DTB-EF-T - 0.09 (0.11)2 - IV
BDB-T-2F - 0.10 (0.11)2 - IV
eA
PC61BM 0.16 0.15 - II
PC71BM 0.14 0.13 0.18 II&III
NDI2OD-2T - 0.12 (0.16)2 - IV
ITIC - 0.09 - IV
ITIC-4F - 0.09 - IV
ITIC-2Cl - 0.09 - IV
eD–eA
BDT-TFQ–PC71BM 0.13 0.12 - II
TQ–PC71BM - - 0.17 III
BDT-TzBI–NDI2OD-T2 - 0.14 - IV
DTP-EF-T–ITIC-4F - 0.10 - IV
BDB-T-2F–ITIC-2Cl - 0.10 - IV
1 The OTωvalues of the individual compounds and complexes were obtained with the Equation 3.1 and Equation 3.2, respectively. In Publications II and III, the 6-31G* basis set was employed in the tuning ofω, whereas in Publication IV, the 6-31G** basis set was employed.
2 The OTωvalues of the oligomeric models employed in the eD–eA complexes, i.e. the planarized trimer for BDT-TFQ and the monomer for other compounds.
In OT-ωB97X and OT-ωB97X-D, the OTω values for the oligomers of the eD D–A copolymers are generally the same, which indicates the similar extent ofπ- conjugation in their backbone with the characteristic length scales (1/ω)[173]of ca. 9–11 bohr (i.e. 5–6 Å). The SMAs ITIC and its derivatives have the same OT ωvalues as the D–A oligomers, whereas fullerene derivatives and the tetramer of the eA-type D–A copolymer P(NDI2OD-2T) have somewhat larger values due to a
smaller degree ofπ-conjugation in them[130]. Overall, the OTωvalues of the eD and eA compounds are in line with those (0.10–0.20 bohr−1) determined for other D–A copolymers[9, 12, 14]and fullerene derivatives, i.e. PC61BM and PC71BM [174, 175]. The OT ωvalues determined for the eD–eA complexes are between those of the individual molecules, although somewhat closer to those of the eA com- pounds.
When comparing different LRC functionals, it can be seen that the OTωvalues for OT-ωB97X and OT-ωB97X-D are almost the same, those of OT-ωB97X being only 0.01 bohr−1larger. As the only difference between these functionals is the empirical dispersion corrections included inωB97X-D, it can be concluded that the dispersion corrections do not have a significant effect on the OTω values and consequently the characteristic length scales. The OTωvalues for OT-BNL are generally slightly larger than those for OT-ωB97X and OT-ωB97X-D. This is most probably due to a partial SR HF exchange inωB97X andωB97X-D that is not included in BNL, leading to the larger characteristic length of the SR/LR transition for OT-ωB97X and OT-ωB97X-D[130]. Moreover, in the case of OT-BNL, the tuning of theωhas been carried out with the SP calculations using the B3LYP-optimized geometries, which may have some influence, as well (see Section 3.2.3 for the further informa- tion). However, the differences in the semilocal approximations to exchange and correlation between different LRC functionals should not affect the overall picture too much and similar results have been predicted when describing the conjugation of the system[130]and the optical properties of the D–A oligomers[9]regardless of the OT-LRC functional. Although the use of dispersion corrections can have a notable influence, as will be seen for the eD–eA complexes later on.
While OT-LRC functionals have yielded improved IEs and vertical excitation ener- gies for the D–A copolymers compared to the global hybrid and non-tuned LRC functionals, as is observed in both this work and other theoretical studies[9, 12, 14], it should be noted that in some cases the OT tuning can lead to inconsistent re- sults. For example, the BLA values predicted for highly conjugated polymers, such as polyenes[33]and a planar cyclopentadithiophene-co-benzothiadiazole based D–
A copolymer[9], do not saturate with the increasing chain length, as should be ex-
consequence of tuningωwith system size[33]. In other words, the OT-LRC func- tional approaches the semilocal functional with the increasing chain length, while losing size consistency of standard LRC functionals.
Another shortcoming of the OT-LRC functionals is the failure in combining the tun- ing ofωwith a continuum solvation model[163]. Namely, carrying out the tuning in the presence of CPCM have resulted in unreasonable small values ofωand con- sequently too low excitation energies for oligothiophenes[176]. This is because the PCM affects the total energies, but not the DFT eigenvalues, i.e. the HOMO ener- gies. One option to overcome this problem would be using an explicit solvent in the tuning calculations. While this method has potential, it has several challenges, such as large computational cost, difficulty in finding the right structure for solvent, and delocalization of the HOMO over the solvent[163, 177]. The latter problem can be overcome by using a locally projected self-consistent field[177], large computa- tional cost caused by the explicit solvent still remains. Thus, in the absence of more accurate methods at the moment, the tuning for large systems is recommended to be carried out in vacuum and use the resultingωvalues in the PCM calculations[163], as has been also done in this work.