Singlet-oxygen production rate for the \(^{1}\Sigma_g\) oxygen state

Determine the activation energy and singlet-oxygen production rate for the \(^{1}\Sigma_g\) state of oxygen within the divide-to-conquer photochemical model, which requires locating the corresponding crossing geometry \(\mathbf{R}_x\) despite the inaccurate TDDFT excitation energy for this state.

Background

The supplementary analysis attempts to calculate singlet-oxygen production rates for both the 1Δg^{1}\Delta_g and 1Σg^{1}\Sigma_g oxygen states. For the 1Σg^{1}\Sigma_g state, the TDDFT excitation energy is substantially different from experiment, so the equation required by the divide-to-conquer model is not satisfied at any interpolated geometry between R0\mathbf{R}_0 and the minimum-energy crossing point. Without a crossing geometry Rx\mathbf{R}_x, the activation energy and rate cannot be evaluated.

References

We were not able to study the rate of production of the $1\Sigma_{g}$ state of oxygen, because Eq.~eq:get_Rx (required by the divide-to-conquer model to get the crossing structure $\mathbf{R}_x$) was never satisfied, mostly because the O$_2$ TDDFT (Time-Dependent Density Functional Theory) excitation energies for this electronic state are very far from experimental values (see Supplementary Section~\ref{subsec:tddft_excitations}). Without being able to locate $\mathbf{R}_x$, we cannot calculate the activation energy and therefore the rate.

— Measurement-efficient energy estimator for quantum chemistry of photodynamic materials  (2610.26689 - Lenihan et al., 19 Oct 2026) in Supplementary Information, Section ‘TDDFT excitation energies’