  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.
