Structural Non-Identifiability of Photochemical Reaction Yields from Linear Optical Observables
- 1Technical Institute of Physics and Chemistry
- 2Chinese Academy of Sciences
Abstract
Identical time-resolved and steady-state optical observables can correspond to different reaction quantum yields when reactive and non-reactive dark exits are not independently resolved. We formulate linear photochemical networks as stable input-output systems with kinetic matrix K, observation matrix B, and reaction output vector q. Complete integrated yields are Φobs = BRu and ΦR = q⊤Ru, where R = (−K)−1 is the cumulative residence-time matrix. Pulse-steady-state equivalence and common rate scaling are treated as auxiliary linear-system facts. The central result is a structural non-identifiability theorem: if a reactive exit qj and a dark-loss exit lj from state j are not independently observed, then any redistribution q′ j + l′j = qj + lj leaves K, all non-reactive optical observables, and all spectral signals unchanged, while the reaction yield changes by ∆ΦR = δ (Ru)j . A one-state counterexample and a Jacobian analysis of the two-state thermally activated delayed fluorescence model with eight independent parameters θ = (kF , kP , kS,nr, kT,nr, i, r, qS, qT ) show that the luminescence observation map including fluorescence and phosphorescence, Y = (kF , kS, kT , ir, kP i), has rank 5 and a three-dimensional null space. Two directions reallocate reactive and dark-loss exits on the singlet and triplet states while leaving all luminescence observables unchanged; the third reallocates internal coupling and phosphorescence, and changes ΦR if and only if the triplet reaction exit qT is nonzero. A conditional experimental design table shows how direct product detection, state-selective observations, and multi-condition quenching restore identifiability. The results clarify when lifetime, delayed fluorescence, and transient absorption can be used to infer reaction quantum yields, and when they cannot.
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BibTeX
@misc{ye2026structural,
title = {{Structural Non-Identifiability of Photochemical Reaction Yields from Linear Optical Observables}},
author = {Chen Ye},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15010306/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010306/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Structural Non-Identifiability of Photochemical Reaction Yields from Linear Optical Observables
AU - Chen Ye
PY - 2026
DA - 2026/10/12
PB - ChemRxiv
DO - 10.26434/chemrxiv.15010306/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010306/v1
AB - Identical time-resolved and steady-state optical observables can correspond to different reaction quantum yields when reactive and non-reactive dark exits are not independently resolved. We formulate linear photochemical networks as stable input-output systems with kinetic matrix K, observation matrix B, and reaction output vector q. Complete integrated yields are Φobs = BRu and ΦR = q⊤Ru, where R = (−K)−1 is the cumulative residence-time matrix. Pulse-steady-state equivalence and common rate scaling are treated as auxiliary linear-system facts. The central result is a structural non-identifiability theorem: if a reactive exit qj and a dark-loss exit lj from state j are not independently observed, then any redistribution q′ j + l′j = qj + lj leaves K, all non-reactive optical observables, and all spectral signals unchanged, while the reaction yield changes by ∆ΦR = δ (Ru)j . A one-state counterexample and a Jacobian analysis of the two-state thermally activated delayed fluorescence model with eight independent parameters θ = (kF , kP , kS,nr, kT,nr, i, r, qS, qT ) show that the luminescence observation map including fluorescence and phosphorescence, Y = (kF , kS, kT , ir, kP i), has rank 5 and a three-dimensional null space. Two directions reallocate reactive and dark-loss exits on the singlet and triplet states while leaving all luminescence observables unchanged; the third reallocates internal coupling and phosphorescence, and changes ΦR if and only if the triplet reaction exit qT is nonzero. A conditional experimental design table shows how direct product detection, state-selective observations, and multi-condition quenching restore identifiability. The results clarify when lifetime, delayed fluorescence, and transient absorption can be used to infer reaction quantum yields, and when they cannot.
ER -