Triplet-Pair Character of the $2^1A_g$ Dark State of Polyenes
We define and calculate the triplet-pair population of the $2^1A_g$ dark state in polyenes, as predicted by the $π$-electron Pariser-Parr-Pople (PPP) model, for chains of 8 to 14 C-atoms and Coulomb interaction parameter between 4-14 eV. Our definition of the triplet-pair population is motivated by a two-particle model of the $2^1A_g$ state. We use DMRG to solve the PPP model and we exploit the MPS representation of the DMRG wavefunction to compute the triplet-pair population. Using our results for short chain sizes, we predict a finite-size scaling value of the triplet-pair population of ca. 75% for realistic Coulomb interactions for polyene chains. Our results agree with other theoretical work on the doubly-excited character of polyenes, and represents further evidence that the $2^1A_g$ state is predominantly triplet-pair in character - with implications for singlet fission mechanisms in polyenes.