Singlet fission in linear π-conjugated systems

Singlet fission (SF) is a process in which a singlet excitation splits into two uncoupled triplet excitations. SF represents one strategy to overcome the Shockley-Queisser efficiency limit of solar cells, with photovoltaic devices utilising singlet fission having achieved quantum yields of over 100%. The singlet fission process is thought to involve triplet-pair singlet intermediates: one such intermediate is the 1(TT) state which forms after the initial photoexcitation, and another example is the 1(T · · · T) state which is produced when the constituent triplets of the 1(TT) state lose electronic interaction and only spin coherences persist.
One of the major classes of SF materials is conjugated linear polymers. In these systems, the first optically active excitation is to the 11Bu+ singlet state. However, this state is not the lowest energy singlet state. The 21Ag- , 31Ag- , 11Bu− states can fall below the optical 11Bu+ state depending on electronic screening and conjugation length. These states have triplet-pair character and this thesis explores which of the eigenstates contribute to the 1(TT) and 1(T ···T) states.
Firstly, using density matrix renormalisation group (DMRG) calculations of the Pariser-Parr-Pople-Peierls Hamiltonian, the Hellmann-Feynman relaxed geometries of the eigenstates are found. The 21Ag- , 11Bu− and 31Ag- states’ triplet-triplet characters are confirmed by calculations of bond dimerization, spin-spin correlation and wavefunction overlap with products of triplet states.
It is found that there is a family of singlet excitations (i.e., 21Ag-, 11Bu−, 31Ag- , ···), composed of both triplet-pair and electron-hole character, which are fundamentally the same excitation, but have different centre-of-mass energies. The lowest energy member of this family, the 21Ag- state, cannot undergo singlet fission. However, higher energy members (e.g., the 31Ag-) state, owing to their increased kinetic energy and reduced electron- lattice relaxation, can undergo singlet fission for specific chain lengths, with the 11Bu− and 31Ag− states being candidates for the 1(TT) state.
Following on from these calculations, the first step of singlet fission, where the photoexcited state evolves into the 1(TT) correlated triplet pair state, is probed. This step is referred to as state interconversion. Both Ehrenfest dynamics and dynamics with quantised phonons were performed for the UV-Peierls model using time-dependent density matrix renormalisation group (t-DMRG). State interconversion was found to be ultrafast, occurring in 10s fs. Additionally, it was found that the electronic environment determines to which triplet-pair eigenstate the photoexcited state evolves. Changing the Coulombic parameter, U , causes state interconversion shift from 11Bu+ → 21Ag- to 11Bu+ → 31Ag-. These are the first dynamics results that show the formation of the 31Ag- state and they have important consequences for explaining intramolecular singlet fission observed in carotenoids.

Keywords: Density Matrix Renormalization Group
Photoexcitation
Photovoltaics
Singlet Fission
π-conjugated systems
Polyenes
Quantum Mechanics
Advisor: Barford, W