Electronic couplings with the multi-state treatments

4.6 Calculating the charge transfer rates at local eD–eA

Furthermore, the functional has a clear effect on the relation between the coupling values and the number of excited states used for forming the diabatic states. With the global hybrid functionals, B3LYP (Figure 4.11a) and PBE0, both the GMH and FCD scheme yield very constant couplings for the TQ–PC₇₁BM that decrease only slightly with the increasing number of states. This can be explained by the tendency of the global hybrids to predict only a small or negligible mixing of the adiabatic states (see Figure 4.8). Thus, as the adiabatic CT states are already well localized, the diabatization does not change their nature much even with larger number of the states.

However, with the LRC functionals, CAM-B3LYP and OT-BNL (Figure 4.11b), the number of the states has more notable effect on the electronic couplings. Gener- ally, the GMH and FCD ED couplings predicted with the LRC functionals decrease with the increasing number of the states, with the exception of some multi-state re- sults, which are slightly higher than the 2-state ones. Additionally, the FCD CR couplings mainly decrease with the increasing number of the states, but the GMH CR couplings do not follow such a clear trend and rather oscillate when the number of states increases. These differences in the coupling values obtained with the differ- ent number of states can be attributed to the tendency of the LRC functionals used here to predict the mixing of the local excitation with the CT₁state (see Figure 4.8).

As the sizes of the studied TQ–PC₇₁BM complexes set limitations to the computa- tional time, it is not possible to determine whether the couplings predicted by the LRC functionals have converged already to the certain values or whether more ex- cited states would have been required. Nevertheless, based on the∆q^diabvalues of the CT₁state (see the original Publication III), which are closer to the ideal value of 2 with the 11-state FCD scheme (1.8–1.9) than with the 2–4-state schemes (0.7–

1.7), the 11-state FCD couplings are excepted to be more reliable. Similarly, while not reaching the ideal dipole moments calculated for the studied TQ–PC₇₁BM com- plexes (41.1 D and 41.3 D for 3T4Q–PC₇₁BM and 3Q4T–PC₇₁BM, respectively), theµ^diabvalues of the CT₁state are closer to the ideal ones with the 11-state GMH scheme (24.5–27.9 D) than with the 2–4-state schemes (11.4–21.8 D).

Alongside the functional, other calculation settings can influence the couplings. In Publication III, the basis set, excited state method, and surrounding medium are

2 3 4 5 6 7 11 2 3 4 5 6 7 11 0

20 40 60 80 100 120140 160 180 200

GMH / FCD

/ 3T4Q–PC₇₁BM / 3Q4T–PC₇₁BM H if (meV)

Exciton dissociation

2 3 4 5 6 7 11 2 3 4 5 6 7 11 0

20 40 60 80 100 120140 160 180 200

FCD GMH

GMH / FCD

/ 3T4Q–PC₇₁BM / 3Q4T–PC₇₁BM Charge recombination

Hif (meV)

GMH FCD

(a)

2 3 4 11 2 3 4 11 0

20 40 60 80 100 120 140 160 180

200 GMH / FCD

/ 3T4Q–PC₇₁BM / 3Q4T–PC₇₁BM

Hif (meV)

Exciton dissociation

FCD

GMH 0 2 3 4 11 2 3 4 11GMH FCD

20 40 60 80 100 120 140 160 180

200 GMH / FCD

/ 3T4Q–PC₇₁BM / 3Q4T–PC₇₁BM Charge recombination

Hif (meV)

(b)

Figure 4.11 Electronic couplings obtained using the GMH and FCD schemes with different number of states (2–11) for the TQ–PC₇₁BM complexes. The calculations were carried out in vacuum with TDDFT using (a) B3LYP and (b) OT-BNL with the 6-31G* basis set. Adapted from [151] with permission from the PCCP Owner Societies.

found to have a notable effect on the GMH CR couplings when employing the LRC functionals, whereas no significant changes in the values are observed with the global

6-31G** basis set, which predicts larger couplings than the smaller 6-31G*. Further- more, the GMH CR couplings calculated either in CHCl₃or blend are larger than those obtained in vacuum. Thus, the GMH scheme is more sensitive to the differ- ent calculation settings and number of the states than the FCD scheme is, especially when using the LRC functionals. Based on these results, the use of FCD is more recommended for calculating the multi-state couplings of the PSC systems when ap- plying the LRC functionals.

This study has been extended in Publication IV, where the effect of the dispersion corrections on the prediction of the multi-state electronic couplings has been exam- ined for the polymer–polymer system BDT-TzBI–NDI2OD-T2. Both the ED and CR couplings calculated with the FCD scheme and OT-ωB97X-D are very constant regardless of the number of states. In other words, the 2-state and multi-state (for 3–26 states) values are almost the same. While the reference calculations both with- out the dispersion corrections and with the defaultωvalues have not been carried out to see, whether this is due to the dispersion corrections, OT-LRC functional used, or the studied system, the dispersion corrections are expected to be beneficial for the calculating the FCD electronic couplings for the PSC systems with the OT- LRC functionals. Similar trends are observed also for the polymer–SMA systems in Publication IV, as the 2-state and multi-state (i.e. 11-state) electronic couplings pre- dicted for them are close to each other. However, in these systems, the effect of the inclusion of more states could not be verified, as these calculations would have been computationally too demanding.

It is well known that the electronic couplings are highly sensitive to the relative ori- entations of the studied compounds[34, 91, 165, 192]. In Publication III, both the ED and CR couplings of the polymer–fullerene system TQ–PC₇₁BM are predicted to be stronger (by ca. 21–83 meV for ED and 25–252 meV for CR) when PC₇₁BM is on the top of the thiophene donor unit of TQ than when it is on the top of quinoxa- line acceptor unit. Similarly, stronger ED and CR couplings have been predicted by Wang et al. with the fragment orbital approach[97]and the non-tunedωB97X-D, when PC₇₁BM is closer to the donor unit of PBDT-TPD[18]. They have also pre- dicted stronger CR couplings with the 2-state FCD scheme and the OTωB97X-D functional when PC₇₁BM is on the donor unit of benzothiadiazole-quaterthiophene

-based copolymers[15]. However, opposite results, i.e. stronger couplings on the top of the acceptor units of the copolymers, have been observed, as well[34].

The relative orientation of the eD and eA compounds in the NF PSC systems is also observed to have a notable effect on the calculated couplings. In the case of the polymer–SMA systems, the strongest electronic couplings are predicted for the most stable, i.e. DA and AA configurations of the DBT-EF-T–ITIC-4F and BDB-T-2F–

ITIC-2Cl, respectively (see Publication IV and Table 4.7). However, the most stable, i.e. AA(1) configuration of the polymer–polymer system BDT-TzBI–NDI2OD-T2 has smaller couplings than the DA(2) configuration, which is energetically (by 0.9 kJ mol⁻1) very close to the AA(1) one. These findings highlight the previously stated fact that electronic couplings can change even by minor displacements of the inter- acting compounds[91]. It should be noted that, unlike for example in the studies of Wang et al. [15, 18], the full side chains have not been included here in the cou- pling calculations. While the long alkyl side chains can be expected to impact the preferred relative orientations and the resulting interactions between the eD and eA compounds in the real blend systems[18], the electronic couplings predicted here yield insight into the interactions between different units of the studied compounds.