Manuscript no.: PC-045
Theoretical Investigation of Covalently Linked Diphenylhexatriene Dimers as Potential Intramolecular Singlet Fission Chromophores
a Department of Chemical Sciences, Indian Institute of Science Education and Research (IISER) Kolkata, Mohanpur, West Bengal - 741246, India
b Centre for Advanced Functional Materials (CAFM), Indian Institute of Science Education and Research (IISER) Kolkata, Mohanpur, West Bengal - 741246, India
E-mail: mn22rs001@iiserkol.ac.in
Singlet fission (SF) splits a high-energy singlet exciton (S1) into two triplet excitons (T1), enhancing the efficiency of organic photovoltaics beyond the Shockley–Queisser limit. Intramolecular SF (iSF) offers an advantage over intermolecular SF (xSF) using covalently linked dimers, eliminating the need for crystal engineering. Recently Millington et. al, reported six phenylene-bridged DPH dimers as efficient SF materials. In this work, we studied these systems using the Pariser–Parr–Pople (PPP) Hamiltonian with DMRG and TD-DFT. Excited-state energetics were consistent with experiments and SF criterions, affirming their role as efficient SF materials for advanced solar cell applications.
1. Introduction
Singlet fission (SF), first observed in 1965 as the splitting of a singlet (S1) exciton into two triplet (T1) excitons, offering a pathway to surpass the Shockley–Queisser limit in solar cells. [1] SF has attracted interest for photovoltaics and transistors as it enables efficient harvesting of high-energy photons otherwise lost as heat.[2] Efficient SF requires long triplet lifetimes. Traditionally studied in crystalline systems (xSF), where molecular packing governs efficiency, SF can also occur intramolecularly (iSF) in covalently linked dimers, eliminating crystal engineering constraints. iSF proceeds through the conversion of S1 to subsequent triplet pair separation via (1TT) state through direct or charge-transfer (CT) mediated pathways.[3],[4] The necessary energetic condition for iSF is S1≥2T1 .[1] Millington et al. synthesized six phenylene-bridged DPH dimers, demonstrating their potential as efficient iSF chromophores.[5] Herein, we investigated these dimers using the Pariser–Parr–Pople (PPP) Hamiltonian with DMRG, along with DFT and TD-DFT, to explore their low-lying excited states and assess their suitability for advanced next generation solar energy applications.
2. Experimental Section
Ground-state geometries of the dimers were optimized using DFT in Gaussian16 with the CAM-B3LYP functional and 6-31G(d,p) basis set. Excited-state properties were computed using TD-DFT at the same level. To capture strong correlation effects in π-conjugated systems, we employed the Pariser–Parr–Pople (PPP) Hamiltonian at DFT-optimized geometries. The PPP model accounts for both on-site Hubbard interactions and long-range Coulomb interactions.[6] Low-lying excited states were further investigated via the density matrix renormalization group (DMRG) within the PPP model.[6],[7] Dimers were constructed iteratively within the DMRG framework to resolve singlet and triplet manifolds. We employed a 600 density matrix eigenvector (DMEV) cutoff to ensure convergence and accurately evaluate the ordering of S₁, T₁, and dark (D) states. Finally, spin–orbit coupling matrix elements (SOCMEs) were computed using PySOC to assess singlet–triplet interactions relevant to fission dynamics. Frontier molecular orbitals, Natural transition orbitals (NTOs) and non covalent interactions were also computed to further explore photophysical properties of these dimers.
3. Results & Discussion
The DPH dimers (a)–(f) differ in connectivity where (a) and (b) are para-linked, (c) and (d) are meta-linked, and (e) and (f) are ortho-linked relative to the central phenyl ring.
To validate the accuracy of the DMRG approach, ground state energies were benchmarked against exact diagonalization in the non-interacting Hückel limit. With a cutoff of 600 DMEV, molecules (a), (b), and (c) showed excellent agreement, with errors of 0.18%, 0.02%, and 0.49%, respectively. The higher deviation in molecule (c) arises from the lack of C₂ symmetry, while molecules (a) and (b) exhibit more regular structures. Molecules (d–f), which are more distorted, were modeled with TD-DFT.
The PPP-DMRG calculations are in excellent agreement with experimental excited-state energies. For molecule (a), S₁ appears at 3.35 eV (exp. 3.17 eV), with a dark "D" state below at 2.87 eV. The small S₁–2T₁ gap (0.09 eV) and negative 2D–2T₁ gap confirm favorable energetics for iSF. Molecule (b) shows S₁ at 3.56 eV, close to experiment, with a similarly small fission-driving gap. Molecule (c) yields S₁ at 3.39 eV (exp. 3.26 eV) and a 0.19 eV S₁–2T₁ gap, also indicating efficient iSF feasibility.
Further bond-order analysis shows electron redistribution. in S₀, fluctuations occur on the monomeric sides; in S₁, they localize in the molecular core, and in the D state, they extend across both hexatriene and the central bridge favouring the triplet exciton separation.
Excited-state analysis of meta-meta and ortho dimers via TD-DFT further supports efficient iSF, with S₁–2T₁ gaps of 0.44–0.56 eV. Molecules (e) and (f) also exhibit close agreement with experiment and favorable gaps. Vertical excitation energies confirm that S₁ > 2T₁ in all systems, with (a) and (e) showing especially balanced energetics for CT-mediated iSF.
Spin–orbit coupling values are uniformly weak (<1 cm⁻¹), with molecule (a) at 0.558 cm⁻¹. Such small SOC strengths suggest long triplet lifetimes and minimal triplet–singlet back conversion, key for efficient harvesting.
Frontier orbitals show delocalized HOMO/LUMO states and separated SOMOs in the triplets, consistent with correlated but spatially distinct triplet excitons. NTO analysis reveals that in molecule (a), S₁ is charge-transfer in nature, S₂ is locally excited, while higher states mix CT and LE character. Molecule (b) displays multiexcitonic S₁/S₂, whereas molecule (c) shows mixed CT–ME character in low-lying states facilitating the iSF process.
NCI (Non-Covalent Interaction) analysis highlights weak π–π stacking and dispersive contacts between dimer subunits, especially in para- and meta-linked systems, which facilitate exciton delocalization and stabilize multiexcitonic states. In contrast, ortho-linked dimers show stronger steric repulsion, leading to localized states. These observations demonstrate how electronic and non-covalent structural features together govern singlet fission efficiency in DPH dimers.
4. References
1. M. B. Smith and J. Michl, Annual review of physical chemistry, 2013 (64), 361-386.
2. I. Paci et al., Journal of the American Chemical Society, 2006, 128(51), 16546-16553.
3. K. Ranabhat et al., Journal of Applied Engineering Science, 2016,14(4), 481-491.
4. J. T. Blaskovits et al., Chemistry of Materials, 2020, 32(15), 6515–6524.
5. O. Millington et al., Journal of the American Chemical Society, 2023, 145(4), 2499–2510.
6. R. Pariser, R.G. Parr, The Journal of Chemical Physics, 1953, 21(5), 767-776.
7. S.R. White, Physical review B, 1993, 48 (14), 10345.