# Second order perturbation theory to determine the magnetic state of finite size aromatic hydrocarbons molecules

## TL;DR

This paper introduces a second-order perturbation theory approach using the Hubbard Hamiltonian to accurately determine the magnetic states of finite conjugated hydrocarbons, validated against DMRG calculations.

## Contribution

The study demonstrates that second-order perturbation theory with the Hubbard model effectively predicts magnetic states in complex conjugated molecules, offering a computationally efficient alternative to existing methods.

## Key findings

- Perturbation theory accurately predicts magnetic states.
- Fused-azulene exhibits high-spin ground states due to geometric frustration.
- Method validated against DMRG calculations.

## Abstract

Conjugated system have complex behaviors when increasing the number of monomers, which is one of the reasons that makes long oligomers hard to be characterized by numerical methods. An ex- ample of this are fused-azulene, a molecule that has been reported to displays an increasing magnetic moment with system size. A similar system composed of symmetric fused-benzene rings is reported to be always no magnetic. Instead of the empiric parametrized Pariser-Parr-Pople (PPP) Hamiltonian, a standard model for conjugated molecules, we consider the Hubbard Hamiltonian to explore a range of low electronic correlation by means of perturbation theory (PT). We show that a simple second-order perturbation treatment of electronic correlations by means of Rayleigh-Schroedinger PT allow to accurately infer about the magnetic state of these long complex {\pi}-conjugated molecules. For fused-azulene our results supports the hypothesis that the high-spin ground state on azulene oligomers comes from the frustrated geometry of these chains. We validate this approach using Density Matrix Renormalization Group (DMRG) calculations. Our procedure procedure could be helpful to describe the magnetic ground state of a larger set of conjugated molecules.