In silico prediction of annihilators for triplet–triplet annihilation upconversion via auxiliary-field quantum Monte Carlo

The energy of the lowest-lying triplet state (T1) relative to the ground and first-excited singlet states (S0, S1) plays a critical role in optical multiexcitonic processes of organic chromophores. Focusing on triplet–triplet annihilation (TTA) upconversion, the S0 to T1 energy gap, known as the triplet energy, is difficult to measure experimentally for most molecules of interest. Ab initio predictions can provide a useful alternative, however low-scaling electronic structure methods such as the Kohn–Sham and time-dependent variants of Density Functional Theory (DFT) rely heavily on the fraction of exact exchange chosen for a given functional, and tend to be unreliable when strong electronic correlation is present. Here, we use auxiliary-field quantum Monte Carlo (AFQMC), a scalable electronic structure method capable of accurately describing even strongly correlated molecules, to predict the triplet energies for a series of candidate annihilators for TTA upconversion, including 9,10 substituted anthracenes and substituted benzothiadiazole (BTD) and benzoselenodiazole (BSeD) compounds. We compare our results to predictions from a number of commonly used DFT functionals, as well as DLPNO-CCSD(T0), a localized approximation to coupled cluster with singles, doubles, and perturbative triples. Together with S1 estimates from absorption/emission spectra, which are well-reproduced by TD-DFT calculations employing the range-corrected hybrid functional CAM-B3LYP, we provide predictions regarding the thermodynamic feasibility of upconversion by requiring (a) the measured T1 of the sensitizer exceeds that of the calculated T1 of the candidate annihilator, and (b) twice the T1 of the annihilator exceeds its S1 energetic value. We demonstrate a successful example of in silico discovery of a novel annihilator, phenyl-substituted BTD, and present experimental validation via low temperature phosphorescence and the presence of upconverted blue light emission when coupled to a platinum octaethylporphyrin (PtOEP) sensitizer. The BTD framework thus represents a new class of annihilators for TTA upconversion. Its chemical functionalization, guided by the computational tools utilized herein, provides a promising route towards high energy (violet to near-UV) emission.


S1.1 TTA Upconversion Analysis
Solutions were made with 1x10 − 5 M sensitizer and 1x10 − 3 M annihilator in degassed anhydrous toluene. Solutions for each sensitizer-annihilator pair were made in a nitrogen glovebox, sealed, and removed from the glovebox for upconversion photoluminescence study.
Normalized emission and absorption spectra of sensitizers PtOEP and ZnTPP are seen in figures S1 and S2, where dashed lines denote absorption and solid lines denote emission upon excitation at 365 nm.

S1.2 Phosphorescence Measurements
Time-resolved phosphorescence measurements for BTD and CN-BTD were recorded on a Fluorolog-3P fluorometer (HORIBA Jobin Yvon). Sample solutions in 3-mm quartz tubes (inner diameter) were frozen in a quartz liquid nitrogen Dewar and excited with a pulsed xenon lamp. Luminescence signal detection was delayed 10 ms (for BTD) or 1 ms (for CN-BTD) after the light pulse and collected for 20 ms (BTD) or 1 ms (CN-BTD). Phosphorescence lifetimes (T p ) at 77 K for BTD and CN-BTD were measured by multichannel scaling on an OB920 spectrometer (Edinburgh Analytical Instruments) in conjunction with a pulsed xenon lamp. Time-resolved phosphorescence measurements of MeO-BTD and Ph- BTD were measured in frozen methylcyclohexane/iodomethane (2:1, v/v) in 3 mm quartz tubes (inner diameter) at 77 K in a optical liquid N 2 quartz dewar. Iodomethane was added to increase intersystem crossing into the triplet state. The frozen samples inside the quartz dewar were excited with a pulsed Spectra Physics GCR-150-30 Nd:YAG laser (355 nm, ca. 1 mJ per pulse, 5 ns pulse length). The time-resolved phosphorescence spectra at 100 µs (for MeO-BTD) or 20 µs (for Ph-BTD) after pulsed excitation and a gate width of 500 µs

S2 Additional Calculation Details
All AFQMC calculations in this work use the same procedures and parameters (e.g. Cholesky between the TZ result and our extrapolated estimate of the CBS limit is never larger than 0.06 eV. Given that our QMC error bars are larger than this, further extrapolation of the AFQMC/U results appears to be unnecessary for screening, and the following results reflect use of the TZ basis. This is consistent with previous CC 7 and DFT 8 studies showing TZ basis sets to be sufficient for screening T1 excitation energies of organic chromophores. This was not the case for the BTD series, and we therefore make use of CBS numbers in the main text. Species with no CBS values indicate that we were unable to converge QZ DLPNO-CCSD(T) calculations in <1 week computational wall time.

S2.1 Triplet energies
Below are our calculated adiabatic T1 energies for all systems involved.

S2.2.1 Dimerization Energies
Due to prior computational evidence for strong chalcogen bonding in anti-square thiadiazole dimers, 10 we evaluated the electronic bonding energy for each pair. The bonding energies, evaluated at the KS-DFT ωB97X-V/cc-pVTZ level of theory, are shown in Table S6, in addition to DLPNO-CCSD(T)/cc-pVTZ estimations of the triplet energy for each dimer.
Each species electronically favors the dimer, with CN-BTD and BTD having the strongest and second strongest bonding energies, respectively. Moreover, the computational triplet energies agree with the experimental phosphorescence results, suggesting that the low temperature phosphorescence measurements may reflect dimerized BTD and CN-BTD species.
To further evaluate the likelihood of dimerization, we calculated the dimerization free energies at a range of temperatures (Table S7). For a concentrated solution at low temperatures, the dimer is favored in both BTD and CN-BTD at ratios of 1000:1 and 1000,000,000:1, respectively. However, the likelihood of dimerization at low concentrations such as those used in the phosphorescence measurements ( µM) is expected to be low. Table S6: Electronic bond energies (eV) for the anti-square dimer (at the wB97X-V/cc-pVTZ level of theory), along with a comparison of triplet energies (eV) for the dimer(calculated by DLPNO-CCSD(T)) and monomer (AFQMC) vs experiment. All species exhibit chalcogen bonding, with CN-BTD and BTD exhibiting the highest and second highest bonding strengths, respectively. The phosphorescence for Ph-BTD lacked the fine structure necessary to specify the 0-0 transition energy, and so we report two estimates, one based on the phosphorescence maximum, and one (in parentheses) determined from the 1/2 intensity of the phosphorescence maximum. Triplet energies for the dimers, calculated with DLPNO-CCSD(T), agree with experiment for BTD and CN-BTD, within 0.04 and 0.1 eV, respectively.  (7) 2.09 (7) 1.81(6) Table S7: Dimerization free energies evaluated using KS-DFT at the B3LYP/cc-pVTZ level. Note that a negative free energy favors the formation of a dimer; all species are monomers at room temperature, but BTD and CN-BTD transition to a favored dimer state at low temperatures. Inspection of the geometries reveal in-plane dimerization for all but Ph-BTD, which is sterically limited to out of plane, likely resulting in the higher observed dimerization free energies.

S2.3 Excited State Tuning
Here we attempt to rationalize shifts in the S0-S1 transition energies (Table S8) between functionalized chromophores based on intuitive concepts within chemistry. We find that two factors, that of π-system extension and a combination of electron-withdrawing and electronrich substituents, can be used in tandem to lower the HOMO-LUMO gap.

S2.3.1 π-extension
Extending the π system should result in lowering T1 and S1, thus substantially lowering the 2T1-S1 gap. In the series of anthracenes, it can be seen that the amount of S1 lowering from the parent system can be directly correlated to the extent of π-extension within the functional groups. Interestingly, Me groups contribute significantly to π-extension through hyper-conjugation, as seen in the HOMO-LUMO plots of DMA: Whereas these particle in a box arguments are helpful in predicting S1, T1 is much more dependent on the exact nature of the functional group. We are currently unable to resolve any correlations that could be used as a design principle for T1 in the anthracenes, and in some cases T1 actually follows opposite trends from S1 (i.e. DMA → OMe → CF3). This, however, underlines the importance of accurate computational methods such as AFQMC.  Figure S7: Difference-density plots for the S0-S1 transition for CN and MeO substituted BTD and anthracene. A red surface denotes electron loss upon excitation, while the blue is electron density gained. Note the significant charge transfer in both BTD cases from the functional groups to the sulfur ring, regardless of electron withdrawing (CN) or donating (OMe) character; withdrawal of electrons from CN likely raises the excited state energy in comparison to OMe, even with similar HOMO-LUMO π-extension. In comparison, DCA and OMe-anthracene show the opposite trend, while the difference density plot shows electron withdrawing to the CN and electron donation from the OMe.

S2.3.2 Donor-Acceptor Character
π-system extension can have neutral, donating, or withdrawing character, and excitations can involve varying degrees and directions of charge-transfer, which can in principle be harnessed to lower the ST gap via judicious choice of solvent polarity. 11 This may also be a factor in increasing the energy of certain excitation states by pulling electrons away from highly electronegative groups within certain geometries. In a similar fashion, it is well known that conjugation of an donor-acceptor pair can lead to a large decrease in the band gap. 12 We can therefore use the relative electron withdrawing/donating characters of the parent compound and functional groups to predict the extent of S1 lowering. The BTD series illustrates this well. BTD is a highly electron-poor system used frequently in donor acceptor paradigms, and so electron donating groups such as OMe lower the gap significantly more than electron withdrawing groups such as CN, even though OMe is arguably less effective at extending the π-system than CN ( Figure S7).

S2.4 Singlet Excited states using AFQMC
Ideally, one would obtain both S1 and T1 from a consistent level of theory. In the case of calculating S1 for a molecule with a singlet ground state, fixing the spin cannot be used to orthogonalize the trial wave-function against the ground state, as it can for the triplet.
In the case of anthracene, we fix the symmetry of the wavefunction to be B2u, that of the first bright excited singlet state. For a general non-symmetric molecule, one can use stateaveraging techniques to obtain orthogonal CASSCF trial wavefunctions for an arbitrary number of excited states. We include all π orbitals in the active space, and use the same random number seeds for S0, S1, and T1 calculations to accelerate the convergence of the energy gaps, as in correlated sampling (procedure outlined in Ref. 13). Since correlated sampling attains maximum efficiency when the same geometries are used, we compute the vertical excitation energies, and thus compare to experiments corrected with a geometry reorganization energy calculated with DLPNO-CCSD(T) (from which, given our results for the anthracene derivatives, we expect reasonable accuracy). Indeed, in Table S9 we report vertical excitation energies within 0.05 eV accuracy versus experiment.

S2.5 Functionalized Tetracene structures
We have used a set of structures based on functionalizing tetracene with cyano groups in order to validate the use of CAM-B3LYP TDDFT to obtain S1 energies against experiment (see Table S8). The structures for these compounds can be seen below: