Triplet-Pair Character of the $2^1A_g$ Dark State of Polyenes

TL;DR

This paper calculates the triplet-pair population of the $2^1A_g$ dark state in polyenes using the PPP model and DMRG, revealing its predominantly triplet-pair character and implications for singlet fission.

Contribution

It introduces a new definition and computational approach for triplet-pair population in the $2^1A_g$ state of polyenes, extending understanding of its electronic structure.

Findings

Triplet-pair population approaches 75% in realistic polyene chains.

The $2^1A_g$ state is mainly characterized by triplet-pair configurations.

Results support the triplet-pair nature of the $2^1A_g$ state, relevant for singlet fission mechanisms.

Abstract

We define and calculate the triplet-pair population of the $2^1A_g$ dark state in polyenes, as predicted by the $\pi$-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.