Nature of the excited states in the eD–eA complexes

of ITIC-2Cl is on the top of the acceptor unit of BDB-T-2F is predicted to be en- ergetically more favorable than the DA configuration, where the end-group is on the top of the donor unit. This is inline with the previous MD simulations of the BDB-T-2F–ITIC systems[16, 19].

Alongside the interaction strength between the compounds, the length and degree of branching of the polymer side chains control the accessibility of the backbone and possible intercalation of fullerene derivatives between the side chains[71, 186].

As the full-length side chains have not been included here, the studied complexes do not take these factors into account, but rather give an idea of the mutual interactions between the eD and eA compounds.

B3LYP

hole electron hole electron

TQ: 99% TQ: 1% TQ: 99% TQ: 98%

OT-BNL

LE (S )2

λ = 0.74NTO

TQ: 96% TQ: 88% TQ: 70% TQ: 4%

hole electron hole electron

PC BM: 99%71

CT (S )¹ λ = 1.00NTO

1

PC BM: 1%71

CT (S )¹ λ = 0.79NTO

5

PC BM: 1%71

LE (S )4

λ = 0.97^NTO

PC BM: 2%71

PC BM: 4%71 PC BM: 12%71 PC BM: 30%71 PC BM: 96%71

Figure 4.8 NTOs (the dominant pairs) of the CT₁and LE states of the TQ–PC₇₁BM complexes calculated in vacuum with TDDFT using different functionals and the 6-31G* basis set (isoden- sity contour = 0.025). The contributions (%) of the compounds and theλNTO values are also presented. Adapted from [151] with permission from the PCCP Owner Societies.

pentacene–C₆₀by Zhang et al.[45], namely B3LYP yielded a complete CT charac- ter for the S₂state, whereas OT-LC-BLYP predicted the CT state with admixture of the excitation of C₆₀. The non-tuned LC-BLYP predicted S₂state to be a local exci- tation of C₆₀and CT state was at the higher energy. The previous experimental and theoretical studies have hinted for the possibility of the delocalized CT excitations at or near the eD–eA interface of the PSC systems, which would have an important role in decreasing the Coulomb binding energy due to the reduced electrostatic attraction between the hole and electron[3, 190]. Thus, the OT-LRC functional including the dispersion corrections appear to be the best choice for the correct description of the intermolecular distances (see Section 4.5.1) and nature of the CT states at the local interfaces of PSC systems.

In the polymer–fullerene system BDT-TFQ–PC₇₁BM, the tuning ofωseem to affect the appearance of the CT states, as the corresponding non-tuned LRC functionals ωB97X andωB97X-D do not predict any CT states among the ten lowest excited

hole electron

hole electron

hole electron hole electron

λ = 0.99^NTO CT (S )1 1

LE (S )eD 3

λ = 0.91NTO

LE (S )eA 2

λ = 0.97NTO

λ = 0.76^NTO CT (S )^{3 9}

Figure 4.9 NTOs (the dominant pairs) of the different excited states of the BDT-TzBI–NDI2OD-T complex (the AA(1) configuration) calculated in blend with TDDFT at the OT-ωB97X-D/6-31G**

level of theory (isodensity contour = 0.025). TheλNTOvalues are also presented. The states relevant for the ED and CR processes, i.e. the CT₁and LE states are highlighted with the dashed rectangle. Reproduced from Publication IV [184] - Published by The Royal Society of Chemistry.

hole electron

hole electron

λ = 0.94^NTO CT (S )1 2

LE (S )eD 7

λ = 0.66NTO

Figure 4.10 NTOs (the dominant pairs) of the CT₁ and LE states of the DTB-EF-T–ITIC-4F complex (the DA configuration) calculated in blend with TDDFT at the OT-ωB97X-D/6-31G**

level of theory (isodensity contour = 0.025). TheλNTOvalues are also presented. Reproduced from Publication IV [184] - Published by The Royal Society of Chemistry.

singlet states at the constant intermolecular distance of 3.5 Å (Publication II). How- ever, this is not a common trait for all non-tuned LRC functionals, as the non-tuned CAM-B3LYP predicts CT states for TQ–PC₇₁BM among the ten lowest excited sin- glet states (e.g. the CT state at the fifth lowest singlet excited state, see Publication

CT states are more likely governed by the differences between the studied systems and the underlying approximations in these LRC functionals. The intermolecular distance plays also a notably role on the appearance of the CT states for BDT-TFQ–

PC₇₁BM, as no CT states are observed at the optimal distance of 4.7 Å with OT- ωB97X, but at the smaller distance of 3.5 Å, the CT states can be observed.

In the case of the studied NF PSC systems, OT-ωB97X-D predicts the same order- ing of the states as the global hybrids do for the polymer–fullerene systems, i.e. the CT₁state is in the lower energy than the LE state. Interestingly, this is the oppo- site to that predicted by OT-ωB97X-D for BDT-TFQ–PC₇₁BM, i.e. the CT₁state is in the higher energy than the LE state. While differences in the OTωvalues pre- dicted for these systems might explain the different ordering of the states[45], the more likely explanation is the different type of systems, as the OTωvalue for BDT- TFQ–PC₇₁BM (0.12 bohr⁻¹, see Table 4.1) is larger than those of the polymer–SMA systems (0.10 bohr⁻¹), but smaller than that of the polymer–polymer system (0.14 bohr⁻¹).

Similarly to the polymer–fullerene systems, a small amount of a local excitation of the eA compound NDI2OD-T2 is mixed with the CT₁state in the polymer–polymer system BDT-TzBI–NDI2OD-T2 (the AA(1) configuration, Figure 4.9). However, in the polymer–SMA systems, i.e. DTB-EF-T–ITIC-4F (the DA configuration, Fig- ure 4.10) and BDB-T-2F–ITIC-2Cl (see Publication IV for the illustration of the NTOs) no contributions of the local excitations to the CT₁state are observed. In the AA(1) configuration of BDT-TzBI–NDI2OD-T2, the CT occurs from entire back- bone of BDT-TzBI to the acceptor unit of NDI2OD-T2. In the polymer–SMA sys- tems, the nature of CT is quite similar and CT occurs from the eD compound to the end-group of the ITIC derivative, although in DTB-EF-T, the hole NTO is more evenly distributed along the backbone, while in BDB-T-2F, it is mainly localized on the acceptor unit. Interestingly, in BDT-TzBI–NDI2OD-T2, a "backward" CT pro- cess is observed to take place from the thiophene donor units of the eA compound NDI2OD-T2 to the several backbone units of the eD compound BDT-TzBI (the CT₃ state in Figure 4.9). This kind of CT could correspond to the hole transfer from the eA compound to eD, i.e. Channel II CT process, that may participate in the ET process from the eD compound to eA compound during exciton generation[87].

4.6 Calculating the charge transfer rates at local eD–eA