# Orbital optimization in the perfect pairing hierarchy. Applications to full-valence calculations on linear polyacenes

## TL;DR

This paper implements orbital optimization within the perfect pairing hierarchy to improve full-valence calculations on linear polyacenes, demonstrating that larger active spaces reduce apparent strong correlation effects and achieving high accuracy with novel computational methods.

## Contribution

It introduces an efficient implementation of orbital optimization for the perfect pairing hierarchy, enabling large-scale full-valence calculations on polyacenes with improved correlation energy accuracy.

## Key findings

- Orbital optimization avoids local minima and symmetry breaking issues.
- Full-valence PH calculations capture over 95% of correlation energy.
- Larger basis sets and active spaces weaken observed strong correlations.

## Abstract

We describe the implementation of orbital optimization for the models in the perfect pairing hierarchy [Lehtola et al, J. Chem. Phys. 145, 134110 (2016)]. Orbital optimization, which is generally necessary to obtain reliable results, is pursued at perfect pairing (PP) and perfect quadruples (PQ) levels of theory for applications on linear polyacenes, which are believed to exhibit strong correlation in the {\pi} space. While local minima and {\sigma}-{\pi} symmetry breaking solutions were found for PP orbitals, no such problems were encountered for PQ orbitals. The PQ orbitals are used for single-point calculations at PP, PQ and perfect hextuples (PH) levels of theory, both only in the {\pi} subspace, as well as in the full {\sigma}{\pi} valence space. It is numerically demonstrated that the inclusion of single excitations is necessary also when optimized orbitals are used. PH is found to yield good agreement with previously published density matrix renormalization group (DMRG) data in the {\pi} space, capturing over 95% of the correlation energy. Full-valence calculations made possible by our novel, efficient code reveal that strong correlations are weaker when larger bases or active spaces are employed than in previous calculations. The largest full-valence PH calculations presented correspond to a (192e,192o) problem.