Correlated-Electron Theory of Triplet-Triplet Multiexciton States in Polypentacene

Technical Summary: Correlated-Electron Theory of Triplet-Triplet Multiexciton States in Polypentacene

Problem Statement
Singlet fission (SF), the conversion of a singlet exciton ($S_1$) into a correlated triplet pair ($^1(T_1T_1)$), is a potential mechanism for enhancing photocurrent in organic semiconductors. While the energetic criterion $E(S_1) \ge 2E(T_1)$ is necessary, the efficiency of SF depends on the ability of the correlated triplet pair to escape geminate recombination and separate into independent triplets. A central unresolved issue in pentacene oligomers ($nPc$) and polypentacene (PPc) is the nature of the $^1(T_1T_1)$ eigenstates. Experimental transient absorption (TA) data in longer oligomers and polymers have been interpreted as evidence of a large triplet-triplet binding energy, implying that triplets remain confined in localized, nearest-neighbor configurations. This interpretation relies on the assumption that individual localized triplet-pair configurations (e.g., triplets on adjacent monomers) are approximate eigenstates and that separation occurs via discrete jumps between them. The authors challenge this "localized-configuration" picture, proposing that the electronic structure of these systems is fundamentally different.

Methodology
The study employs correlated-electron calculations on three-unit (3Pc) and four-unit (4Pc) pentacene oligomers as microscopic models for polypentacene. The theoretical framework consists of:

• Hamiltonian: The semi-empirical Pariser-Parr-Pople (PPP) Hamiltonian, parameterized to reproduce experimental monomer and dimer energies. This includes nearest-neighbor hopping ($t_{ij}$), on-site Coulomb repulsion ($U$), and long-range Coulomb interactions ($V_{ij}$).
• Correlation Treatment: Multiple-Reference Singles and Doubles Configuration Interaction (MRSDCI). This approach incorporates high-order excitations (up to 4-electron-4-hole) essential for accurately describing the two-electron-two-hole ($2e-2h$) $^1(T_1T_1)$ states, which are beyond the scope of standard first-principles methods for systems of this size.
• Basis Set: A unique diagrammatic molecular exciton basis is utilized rather than a standard molecular orbital (MO) basis. This basis explicitly separates intramonomer Frenkel excitations, intermonomer charge-transfer (CT) configurations, and $^1(T_1T_1)$ multiexciton configurations with distinct intertriplet separations. Calculations include the 10 frontier MOs (5 bonding, 5 antibonding) per monomer, resulting in MRSDCI matrices with dimensions in the millions.
• Geometry: Calculations were performed for planar geometries, with torsional angles ($30^\circ$) analyzed in supplementary material, showing weak dependence of wavefunction nature on torsion.

Key Contributions and Results

1. Nature of $^1(T_1T_1)$ Eigenstates:
   The calculations reveal that the $^1(T_1T_1)$ eigenstates are not single localized configurations (e.g., strictly nearest-neighbor or second-neighbor triplet pairs). Instead, every eigenstate is a quantum superposition of configurations containing all accessible intertriplet separations.

   • In 3Pc, the three $^1(T_1T_1)$ states are superpositions of nearest-neighbor and second-neighbor configurations.
   • In 4Pc, the six $^1(T_1T_1)$ states are superpositions of all six possible configurations (three nearest-neighbor, two second-neighbor, one maximally distant).
   • These eigenstates form a nearly degenerate energy window located at or below the lowest optical exciton ($S_1$). The energy differences between these states are tiny.

2. Reinterpretation of Transient Absorption (TA):
   The study addresses the persistence of TA features at ~710 nm (associated with intermonomer CT between nearest-neighbor triplets) in longer oligomers and polymers.

   • Previous interpretations assumed this persistence indicated that triplets were trapped in a single localized state with high binding energy.
   • The authors demonstrate that because the $^1(T_1T_1)$ eigenstates are quantum superpositions, even states with significant "distant" character retain substantial nearest-neighbor amplitude.
   • Consequently, the observed TA signal arises from the nearest-neighbor component of the entire manifold of nearly degenerate eigenstates. The persistence of this signal does not imply a large triplet-triplet binding energy ($E_b$) or that triplets are confined to a single configuration.

3. Intramolecular vs. Intermolecular Separation:

   • Intramolecular: The electronic structure precludes the existence of a unique, energetically isolated eigenstate consisting entirely of distant triplets (e.g., triplets on the far ends of the chain). Therefore, intramolecular triplet separation into distinct, non-interacting triplets along a single chain is not supported by the correlated electronic structure.
   • Intermolecular: The paper suggests that successful triplet separation may require intermolecular interactions (e.g., in films), where triplets occupy neighboring chains rather than distant sites on the same chain. This is consistent with observations of free triplets in polytetracene films but not in solution.

4. Comparison with Polyenes:
   While sharing similarities with long polyenes (where the dark $2^1A_g$ state has two-triplet character), the acene oligomers differ significantly. In $nPc$, there is a clear energy separation between the entire collection of covalent $2e-2h$ triplet-triplet states and the $1e-1h$ charge-transfer states ($S_2$), a separation not present in polyenes due to the small size of the "monomer" (2 carbon atoms) in the latter.

Significance and Claims
The paper claims that the "localized-pair" model of triplet fission in pentacene oligomers requires substantial revision. The perceived absence of intramolecular triplet diffusion in solutions of $nPc$ and PPc is explained not by a large binding energy trapping triplets in a specific configuration, but by the fact that the $^1(T_1T_1)$ manifold consists of a quasi-continuum of nearly degenerate, configuration-mixed states.

The authors conclude that:

• The concept of a distance-dependent triplet-triplet binding energy is not applicable to these systems in the manner previously assumed.
• The increase in SF rate with oligomer length is attributed to the increased number of nearest-neighbor interactions, not to the opening of new spatial configurations for separation.
• Successful triplet separation into "free" triplets requires a unique eigenstate composed entirely of distant configurations, which is absent in the electronic structure of polypentacene.
• Future routes to efficient SF in these materials likely depend on intermolecular mechanisms (film phase) rather than intramolecular chain extension.

The work provides a unified correlated-electron framework that reconciles the observation of nearest-neighbor TA signatures with the lack of intramolecular triplet separation, emphasizing the many-body, superposition nature of the triplet-pair states.