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Internal conversion from the photoexcited state to a correlated singlet triplet-pair state is believed to be the precursor of singlet fission in carotenoids. We present numerical simulations of this process using a π-electron model that fully accounts for electron–electron interactions and electron–nuclear coupling. The time-evolution of the electrons is determined rigorously using the time-dependent density matrix renormalization group method, while the nuclei are evolved via the Ehrenfest equations of motion. We apply this to zeaxanthin, a carotenoid chain with 18 fully conjugated carbon atoms. We show that the internal conversion of the primary photoexcited state, S 2 , to the singlet triplet-pair state occurs adiabatically via an avoided crossing within ∼50 fs with a yield of ∼60%. We further discuss whether this singlet triplet-pair state will undergo exothermic versus endothermic intra- or interchain singlet fission.

We present a dynamical simulation scheme to model the highly correlated excited state dynamics of linear polyenes. We apply it to investigate the internal conversion processes of carotenoids following their photoexcitation. We use the extended Hubbard-Peierls model, H UVP , to describe the π-electronic system coupled to nuclear degrees of freedom. This is supplemented by a Hamiltonian, H , that explicitly breaks both the particle-hole and two-fold rotation symmetries of idealized carotenoid structures. The electronic degrees of freedom are treated quantum mechanically by solving the time-dependent Schrodinger equation using the adaptive time-dependent DMRG (tDMRG) method, while nuclear dynamics are treated via the Ehrenfest equations of motion. By defining adiabatic excited states as the eigenstates of the full Hamiltonian, = + H H H UVP , and diabatic excited states as eigenstates of H UVP , we present a computational framework to monitor the internal conversion process from the initial photoexcited 1 1 B u + state to the singlet triplet-pair states of carotenoids. We further incorporate Lanczos-DMRG to the tDMRG-Ehrenfest method to calculate transient absorption spectra from the evolving photoexcited state. We describe in detail the accuracy and convergence criteria for DMRG, and show that this method accurately describes the dynamical processes of carotenoid excited states. We also discuss the effect of the symmetry-breaking term, H , on the internal conversion process, and show that its effect on the extent of internal conversion can be described by a Landau−Zener-type transition. This methodological paper is a companion to our more explanatory discussion of carotenoid excited state dynamics in Manawadu, D.; Georges, T. N.; Barford, W. Photoexcited State Dynamics and Singlet Fission in Carotenoids.

Internal conversion from the photoexcited state to a correlated singlet triplet-pair state is believed to be the precursor of singlet fission in carotenoids. We present numerical simulations of this process using a π-electron model that fully accounts for electron-electron interactions and electron-nuclear coupling. The time-evolution of the electrons is determined rigorously using the time-dependent density matrix renormalization method, while the nuclei are evolved via the Ehrenfest equations of motion. We apply this to zeaxanthin, a carotenoid chain with 22 conjugated carbon atoms (i.e., 11 double bonds). We show that the internal conversion of the photoexcited state to the singlet triplet-pair state occurs adiabatically via an avoided crossing within 100 fs and we predict a yield of ∼ 50% We further discuss whether this singlet tripletpair state will undergo exothermic versus endothermic intra or inter chain singlet fission.