Relaxation energies and excited state structures of poly(para-phenylene)

TL;DR

This study examines the relaxation energies and excited state structures of poly(para-phenylene) using advanced modeling, revealing significant differences in lattice relaxation among various excited states and their implications for light-emitting polymers.

Contribution

It provides detailed computational analysis of excited state geometries and relaxation energies in poly(para-phenylene), highlighting differences linked to soliton types and their impact on the exchange gap.

Findings

The $1^1B_{1u}^-$ state has a small relaxation energy (~0.1 eV).

The $1^3B_{1u}^+$ and $2^1A_g^+$ states have larger relaxation energies (~0.5 and 1.0 eV).

Differences in relaxation energies explain about one-third of the exchange gap.

Abstract

We investigate the relaxation energies and excited state geometries of the light emitting polymer, poly(para-phenylene). We solve the Pariser-Parr-Pople-Peierls model using the density matrix renormalization group method. We find that the lattice relaxation of the dipole-active $1^1B_{1u}^-$ state is quite different from that of the $1^3B_{1u}^+$ state and the dipole-inactive $2^1A_g^+$ state. In particular, the $1^1B_{1u}^-$ state is rather weakly coupled to the lattice and has a rather small relaxation energy ca. 0.1 eV. In contrast, the $1^3B_{1u}^+$ and $2^1A_g^+$ states are strongly coupled with relaxation energies of ca. 0.5 and ca. 1.0 eV, respectively. By analogy to linear polyenes, we argue that this difference can be understood by the different kind of solitons present in the $1^1B_{1u}^-$, $1^3B_{1u}^+$ and $2^1A_g^+$ states. The difference in relaxation energies of the $1^1B_{1u}^-$ and $1^3B_{1u}^+$ states accounts for approximately one-third of the exchange gap in light-emitting polymers.