Photoexcited state dynamics in carotenoids
Keywords: excited state dynamics
density matrix renormalisation group
singlet fission
many-body physics

Carotenoids are an important class of biomolecules found in nature with exquisite photo- physical properties. The quasi-one-dimensional nature of carotenoids enhances the roles of the electron-electron interactions and electron-nuclear coupling in their π-conjugated systems. This gives rise to a fascinating excited state structure with a nonemissive ‘dark’ excited state, labelled S1/2 1Ag- , of energy below the photoexcited ‘bright’ state, labelled S2/1 1Bu+. This energetic reversal gives rise to the nonemissive properties of carotenoids, their photoprotection properties in light harvesting complexes, and the ability to undergo singlet fission.
Singlet fission (SF) is a process by which a singlet excitation dissociates to form two spin-uncorrelated triplet excitations. In carotenoids, the first step of SF is thought to be internal conversion of the photoexcited 11Bu+ state to a correlated triplet-pair state. The low-lying excited states of polyenes are studied using the density matrix renormal- isation group (DMRG) method to solve the Pariser−Parr−Pople-Peierls (PPPP) model of π-conjugated systems. The triplet-pair nature of 21Ag-, 11Bu-, and 31Ag- states are established via calculation of excitation energies, bond dimerisations, and exciton wave- functions. Importantly, the 11Bu- state is identified as a potential intermediate state for the internal conversion process in carotenoids.
Following the static DMRG calculations, the internal conversion process is probed dynamically using the adaptive time-dependent density matrix renormalisation group method with Ehrenfest dynamics describing the nuclear motion (tDMRG-Ehrenfest). Us- ing the UV-Peierls (UVP) Hamiltonian, two sets of parameters are used to account for the theoretical and experimental uncertainty surrounding the ordering of excited state en- ergies around the Franck-Condon point. Using these two sets of parameters, two internal conversion pathways are investigated, using two different carotenoids as model systems. For both pathways, for both molecules, ultrafast internal conversion of the 11Bu+ state to a triplet-pair state is observed within ∼ 5 fs. For all simulations, a triplet-pair yield of ∼ 65% is attained within ∼ 50 fs. These results present the first instance of a dynamical simulation of the internal conversion process in carotenoids.
The calculation of theoretical transient spectra using Lanczos-DMRG is incorporated to the dynamical simulation scheme to relate to the available spectroscopic data. The dominant spectral features exhibit a blue shift as the nuclei relax, confirming the 11Bu+ → 21Ag- internal conversion. Following the calculation of exciton wavefunction of the state dipole connected to the 2 1Ag- state, these dominant transitions are assigned to the charge-transfer character of the 2 1Ag- state.
The electron transfer process surrounding the internal conversion is scrutinised using a two-level toy model. Using the Landau-Zener theory of electronic transition, it is shown that the electronic transition during the internal conversion evolves from a non-adiabatic transition to a primarily adiabatic transition as the magnitude of the symmetry breaking increases. It is shown that for parameters relevant to carotenoids, the internal conversion process lies in the adiabatic limit.