Tuning the role of charge-transfer states in intramolecular singlet exciton fission through side-group engineering

Understanding the mechanism of singlet exciton fission, in which a singlet exciton separates into a pair of triplet excitons, is crucial to the development of new chromophores for efficient fission-sensitized solar cells. The challenge of controlling molecular packing and energy levels in the solid state precludes clear determination of the singlet fission pathway. Here, we circumvent this difficulty by utilizing covalent dimers of pentacene with two types of side groups. We report rapid and efficient intramolecular singlet fission in both molecules, in one case via a virtual charge-transfer state and in the other via a distinct charge-transfer intermediate. The singlet fission pathway is governed by the energy gap between singlet and charge-transfer states, which change dynamically with molecular geometry but are primarily set by the side group. These results clearly establish the role of charge-transfer states in singlet fission and highlight the importance of solubilizing groups to optimize excited-state photophysics.

and (b,d,f) selected kinetics integrated over the indicated spectral regions. The formation of the structureless, red-shifted emissive CT species can be directly resolved in the data. Its spectral position progressively red-shifts with solvent polarity. Raw data sets from TGPL were analysed with Singular Value Decomposition to determine the number of real components and to remove experimental noise. From the relative magnitude of the eigenvalues, we determined that only two significant spectral components were present in the data. Thus only the first two components with the highest eigenvalues are used and plotted here.  Figure 11. Two-species SF dynamics in DP-Mes. Normalised population kinetics of different excited species in DP-Mes in various solvents from spectral decomposition (shaded regions). The scatter plots represent the raw kinetics averaged in the region of GSB (610-620 nm, black), primarily TT PIA (520-530 nm, red) and S 1 SE (665-670nm, blue). We note that the nearly invariant GSB kinetic over the triplet formation timescale indicates that essentially no population is lost during SF: molecules either form triplet pairs or remain in S stab . Figure 12. DP-Mes reference spectra. Transient absorption features of DP-Mes triplet state, obtained by the same sensitisation protocol as above for DP-TIPS, as well as anion and cation spectra. The latter were obtained by chemical oxidation or reduction of DP-Mes in solution, and were converted into ΔT/T units for comparison. In the latter the CT spectrum of DP-TIPS has been shifted uniformly so that the GSB peaks align, revealing striking similarity to the DP-Mes singlet PIA spectrum in the NIR. This similarity is presumed to reflect the significant CT component in the initial singlet state in DP-Mes. We note, however, that there are also important differences in the spectral shapes, due to the singlet character of the DP-Mes excited state.        The support of the NGWFs is strictly confined to a chosen localisation radius (a convergence parameter).

Supplementary
In ONETEP, a conjugate gradients optimisation scheme is used to minimise the total energy with respect to both the density kernel (subject to the constraints of idempotency and normalisation), and the NGWFs. The NGWFs are optimised in an underlying basis set of "psinc" functions, i.e. delta functions commensurate with the simulation box and with a finite cutoff. These have the desirable property of being equivalent to plane waves.
The central idea of constrained-DFT (c-DFT) is to add terms to the DFT total energy functional that impose desired constraints on the charge density of a system. 3,4 In the case of intramolecular CT states of pentacene dimers, these constraints are one fewer charge on the donor unit and one additional charge on the acceptor unit, relative to the ground state.
In this work we impose the constraints using monomer-localised projection operators to partition the density. Within the linear-scaling DFT framework it is a natural choice to make use of the localised NGWFs to define projection operators. 5 Here, we resort to a fixed set of NGWFs from a ground-state calculation for this purpose.
To obtain CT excitation energies, we first optimise the molecular geometry in the ground state (resulting in an orthogonal configuration with approximate D2d symmetry for both pentacene dimers). This gives both a total energy for the relaxed ground state and a set of converged ground-state NGWFs which are then employed as cDFT projectors. Vertical CT excitation energies are calculated as the difference between the constrained total energy and the ground state total energy.
To incorporate the electrostatic effects of different solvent environments, we employ an implicit solvent model with open boundary conditions. 6 In the ONETEP implementation the molecule occupies a smooth dielectric cavity in an otherwise uniform, infinite dielectric. The nonhomogeneous Poisson equation is solved to obtain the potential due to the molecular density in the dielectric.
For all DFT calculations we use the LDA functional and norm-conserving pseudopotentials. The energy cutoff is set to 750 eV which results in well-converged energies for organic molecules using the pseudopotentials we employ Mes is distinctly smaller than in DP-TIPS (0.10 eV vs 0.14 eV in vacuum).

Supplementary Note 2: Triplet yield calculation
As described in the Methods section, the triplet yield was determined from the ratio of S 1 to T 1 molar extinction coefficient, which was in turn established through normalization against the GSB region 635-640 nm. The calculations for DP-Mes and DP-TIPS take the extinction ratio from previous publication 1 and Fig. S19 respectively.
The peak S 1 population was taken to be at the 100 fs time-slice, while the T 1 value was taken at 10 ps (any delay in the range ~5 ps to ~50 ps gives equivalent results). For triplet yield calculated in solvent with S stab , the ΔA(T 1 ) at 10 ps used in the calculation is corrected for the underlying ΔA(S stab ) that does not undergo singlet fission. The yield is still calculated against the full initial singlet population.
For DP-TIPS in hexane, calculation at ~ 520 nm: For triplet yield calculated in solvent with residual S stab or CT, the ΔA(T 1 ) at 10 ps used in the calculation is corrected for the underlying ΔA(S stab ) or ΔA(CT) that does not undergo singlet fission. The yield is still calculated against the full initial singlet population.