# Singlet-Triplet Energy Gaps of Organic Biradicals and Polyacenes with Auxiliary-Field Quantum Monte Carlo

## TL;DR

This paper demonstrates that phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) can accurately predict singlet-triplet energy gaps in biradical molecules and large polyacenes, enabling reliable modeling of photochemical processes.

## Contribution

The study introduces a scalable ph-AFQMC methodology with optimized trial wavefunctions for accurate singlet-triplet gap predictions in complex biradical systems and large polyacenes.

## Key findings

- Achieves ~1 kcal/mol accuracy in predicting ST gaps for small molecules.
- Validates the method's effectiveness on large polyacenes like pentacene.
- Provides a protocol for selecting trial wavefunctions based on spin-contamination.

## Abstract

The energy gap between the lowest-lying singlet and triplet states is an important quantity in chemical photocatalysis, with relevant applications ranging from triplet fusion in optical upconversion to the design of organic light-emitting devices. The ab initio prediction of singlet-triplet (ST) gaps is challenging due to the potentially biradical nature of the involved states, combined with the potentially large size of relevant molecules. In this work, we show that phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) can accurately predict ST gaps for chemical systems with singlet states of highly biradical nature, including a set of 13 small molecules and the ortho-, meta-, and para-isomers of benzyne. With respect to gas-phase experiments, ph-AFQMC using CASSCF trial wavefunctions achieves a mean averaged error of ~1 kcal/mol. Furthermore, we find that in the context of a spin-projection technique, ph-AFQMC using unrestricted single-determinant trial wavefunctions, which can be readily obtained for even very large systems, produces equivalently high accuracy. We proceed to show that this scalable methodology is capable of yielding accurate ST gaps for all linear polyacenes for which experimental measurements exist, i.e. naphthalene, anthracene, tetracene, and pentacene. Our results suggest a protocol for selecting either unrestricted Hartree-Fock or Kohn-Sham orbitals for the single-determinant trial wavefunction, based on the extent of spin-contamination. These findings pave the way for future investigations of specific photochemical processes involving large molecules with substantial biradical character.