# A Method for the Analysis of the Symmetry of Excited States from GW-BSE

## TL;DR

This paper introduces a method to analyze the symmetry of excited states calculated using the GW-BSE approach, enabling better classification and understanding of these states.

## Contribution

The novelty is a method to assign GW-BSE excited states to irreducible representations using symmetry operators.

## Key findings

- The method identifies how excited states transform under various symmetry operations.
- It determines if an excited state is an eigenstate of an angular momentum operator.
- Results are demonstrated on a set of small molecules.

## Abstract

We present a method for analyzing the symmetries of excited states previously calculated with the popular GW-BSE approach. These are expressed through the Tamm-Dancoff approximation using the so-called batches representation. The method allows to establish how an excited state is transformed by symmetry operators as plane-reflection, proper and improper axis-rotation, point-inversions. It can also report if an excited state is eigen-state of an angular momentum operator. This permits the assignment to an irreducible representation of the underlying symmetry group and a prompt labeling of the GW-BSE states. We show results for a significant set of small molecules. Our approach can be easily extended to TD-DFT and can be used to probe the local environment of localized excitations.