Photoreactivity Score in Photochemical Systems

• Photoreactivity score is a scalar metric that compresses complex photophysical data into a dimensionless ranking variable, defined contextually for different applications.
• It is operationalized via distinct formulations in semiconductors, photodynamic therapy, and photocatalytic reactors, using normalized transition probabilities, absorption, or quantum yields.
• The metric enables direct comparison across candidate materials or conditions by integrating multidimensional photochemical parameters into a single actionable value.

Searching arXiv for the cited papers and topic. “Photoreactivity score” denotes a scalar quantity used to rank or compare light-driven chemical performance, but the literature assigns the term to different observables depending on the physical scale and application. In semiconductors, it is an orientation-resolved fraction of optical transition probability associated with a surface normal; in cancer-targeted photodynamic therapy, it is a composite score combining normalized absorption in the 700–850 nm therapeutic window with a normalized intersystem-crossing proxy; in a benchmark H$_2$-photoproduction reactor, it is the overall quantum yield defined as the ratio of hydrogen-production rate to absorbed-photon rate (Ricca et al., 2022, Zhou et al., 17 Dec 2025, Supplis et al., 2020).

1. Terminological scope and domain-specific definitions

The term is used for quantitatively different constructs that share a common purpose: condensing a photophysical or photochemical workflow into a single ranking variable. The cited literature does not present a single universal definition; instead, it presents three domain-specific operationalizations.

Domain	Score definition	Interpretation
Semiconductor photochemistry	$$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$	Fraction of all photo-excited carriers generated within a chosen angular cap around surface normal $\hat n$
PDT photosensitizers	$S_i=(w_A\bar A_i+w_k\bar k_i)$ or $S_i=(\bar A_i)^{w_A}(\bar k_i)^{w_k}$	Composite ranking from normalized therapeutic-window absorption and normalized ISC proxy
Photoreactor H$_2$ production	$\Phi=\dfrac{\langle r_{H_2}\rangle}{\bar G_{abs}}$	Overall quantum yield, i.e. mol H$_2$ per mol photon absorbed

In all three cases, the score is dimensionless after normalization or ratio formation, and each formulation is intended to support comparison across candidates: crystal facets, molecular photosensitizers, or photocatalytic operating conditions. A plausible implication is that the phrase “photoreactivity score” should be interpreted contextually rather than as a standardized metric across subfields.

2. Orientation-resolved score in semiconductor photochemistry

For semiconductors, the score is constructed from the Fermi–Golden-Rule rate of vertical optical transitions at crystal momentum $\mathbf k$ under monochromatic illumination (Ricca et al., 2022). The directional optical transition probability is written as

$$P(\mathbf k;\nu)\propto \sum_{v\in \mathrm{VB}}\sum_{c\in \mathrm{CB}} |\mu_{cv}(\mathbf k)|^2\, \delta(E_{c,\mathbf k}-E_{v,\mathbf k}-\hbar\nu),$$

with transition-dipole matrix element

$$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$0

The $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$1-function enforces energy conservation and encodes the joint density of states at $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$2. An equivalent notation introduces

$$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$3

so that

$$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$4

The practical quantity is obtained by coarse-graining over a finite energy window, typically from the band gap $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$5 up to $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$6: $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$7 Each $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$8 is normalized to $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$9, and the weights $\hat n$0 are interpolated onto a regular $\hat n$1 grid on the unit sphere to form a continuous spherical heat map

$\hat n$2

To isolate carriers generated toward a surface with normal $\hat n$3, the construction restricts to a spherical cap

$\hat n$4

where $\hat n$5 is a small half-angle, e.g. $\hat n$6. The raw score is

$\hat n$7

and the normalized photoreactivity score is

$\hat n$8

In discrete form,

$\hat n$9

with $S_i=(w_A\bar A_i+w_k\bar k_i)$0 the integration weight. For a regular Monkhorst–Pack mesh one may take $S_i=(w_A\bar A_i+w_k\bar k_i)$1.

This formulation is designed to identify the surfaces associated with the largest number of photo-generated carriers. The underlying significance is that photochemical reactions on semiconductors are anisotropic, and the score supplies a facet-resolved ranking that uses all possible transitions weighted by their transition dipole moments rather than band dispersion alone.

3. Hybrid-DFT implementation and the rutile TiO$S_i=(w_A\bar A_i+w_k\bar k_i)$2 example

The semiconductor implementation is specified within hybrid-DFT in the independent-particle approximation (Ricca et al., 2022). The exchange–correlation functional is HSE06 with 25% exact exchange; the plane-wave cutoff is 500 eV; PAW potentials are used as in Table S1 of the paper; and transition matrix elements are computed via the PAW $S_i=(w_A\bar A_i+w_k\bar k_i)$3-operator. For rutile TiO$S_i=(w_A\bar A_i+w_k\bar k_i)$4, the Brillouin zone is sampled with a $S_i=(w_A\bar A_i+w_k\bar k_i)$5 $S_i=(w_A\bar A_i+w_k\bar k_i)$6-centered mesh, giving $S_i=(w_A\bar A_i+w_k\bar k_i)$7 k-points. The energy window extends from the PBE-HSE gap $S_i=(w_A\bar A_i+w_k\bar k_i)$8 up to $S_i=(w_A\bar A_i+w_k\bar k_i)$9, intended to mimic visible/near-UV excitation.

The worked example uses rutile TiO$S_i=(\bar A_i)^{w_A}(\bar k_i)^{w_k}$0 with $S_i=(\bar A_i)^{w_A}(\bar k_i)^{w_k}$1 eV and $S_i=(\bar A_i)^{w_A}(\bar k_i)^{w_k}$2 eV. Choosing $S_i=(\bar A_i)^{w_A}(\bar k_i)^{w_k}$3, the discrete evaluation yields

$S_i=(\bar A_i)^{w_A}(\bar k_i)^{w_k}$4

Under this definition, roughly 42% of all photo-excited carriers are generated within $S_i=(\bar A_i)^{w_A}(\bar k_i)^{w_k}$5 of the [001] direction, compared to 22% within $S_i=(\bar A_i)^{w_A}(\bar k_i)^{w_k}$6 of [101]. The paper interprets this as quantifying the stronger photoreactivity expected for the TiO$S_i=(\bar A_i)^{w_A}(\bar k_i)^{w_k}$7(001) facet under near-band-gap illumination.

The methodological significance lies in the contrast with conventional band-structure inspection. The results indicate that it is generally possible to correlate the heat maps with anisotropy visible in conventional band-structure plots, but they also demonstrate that band-structure plots do not always provide all the informations. Taking into account the contribution of all possible transitions weighted by their transition dipole moments is therefore presented as crucial for a complete picture.

4. Composite score for cancer-targeted photosensitizers

For photodynamic therapy, the score is built from two observables that the study identifies as central to photosensitizer performance: cumulative absorption in the therapeutic window and the efficiency of singlet–triplet intersystem crossing (Zhou et al., 17 Dec 2025). The one-photon absorption cross-section is

$S_i=(\bar A_i)^{w_A}(\bar k_i)^{w_k}$8

and the total absorption in the 700–850 nm window is

$S_i=(\bar A_i)^{w_A}(\bar k_i)^{w_k}$9

In the stick-spectrum limit $_2$0,

$_2$1

The second ingredient is an intersystem-crossing proxy. In the weak-coupling regime, the true ISC rate out of the first singlet into triplets is, to leading order, proportional to $_2$2. Instead of computing every spin–orbit matrix element, the study defines

$_2$3

and states that for $_2$4,

$_2$5

The composite photoreactivity score is then formed by combining normalized absorption and normalized ISC proxy. For candidate $_2$6,

$_2$7

and one may define

$_2$8

In its simplest form, equal weights $_2$9 may be used. An alternative geometric mean is also given: $\Phi=\dfrac{\langle r_{H_2}\rangle}{\bar G_{abs}}$0 The text states that the geometric mean can be used if one wants to penalize poor performance in either channel more sharply.

By ranking molecules by $\Phi=\dfrac{\langle r_{H_2}\rangle}{\bar G_{abs}}$1, the study frames the score as a physically meaningful Pareto-optimal trade-off between deep-tissue absorption and spin-flip efficiency. This differs structurally from the semiconductor score: there the score is a directional fraction of transition probability, whereas here it is an explicit multi-objective aggregation over normalized molecular descriptors.

5. Fault-tolerant quantum workflow and resource estimates

The PDT formulation is explicitly tied to a fault-tolerant quantum workflow for BODIPY derivatives, including heavy-atom and transition-metal-substituted systems that are described as challenging for classical methods (Zhou et al., 17 Dec 2025). To compute $\Phi=\dfrac{\langle r_{H_2}\rangle}{\bar G_{abs}}$2 without resolving every spectral peak, the method prepares the normalized dipole-acted ground state

$\Phi=\dfrac{\langle r_{H_2}\rangle}{\bar G_{abs}}$3

block-encodes the electronic Hamiltonian $\Phi=\dfrac{\langle r_{H_2}\rangle}{\bar G_{abs}}$4 in a low-rank THC form, and then uses qubitization plus generalized Quantum Signal Processing to build two Heaviside-style projectors, one onto energies $\Phi=\dfrac{\langle r_{H_2}\rangle}{\bar G_{abs}}$5 and one onto energies $\Phi=\dfrac{\langle r_{H_2}\rangle}{\bar G_{abs}}$6. In each shot, both filters are applied and a single ancilla qubit is measured; if its value is $\Phi=\dfrac{\langle r_{H_2}\rangle}{\bar G_{abs}}$7, then repeating $\Phi=\dfrac{\langle r_{H_2}\rangle}{\bar G_{abs}}$8 shots yields

$\Phi=\dfrac{\langle r_{H_2}\rangle}{\bar G_{abs}}$9

To achieve a sampling error $_2$0 with confidence $_2$1, the shot count is

$_2$2

The specific example uses $_2$3, $_2$4, and therefore $_2$5. Each shot costs two QSP projections, each of degree $_2$6 calls to the walk operator $_2$7.

For ISC, the method prepares a two-branch superposition of singlet and triplet reference states via the sum-of-Slaters method and a single-sided QSP-based low-energy projector, evolves under the one-body $_2$8, and then performs a modified Hadamard test to read off $_2$9 and $\mathbf k$0 from ancilla $\mathbf k$1 and $\mathbf k$2 measurements. Repetition to precision $\mathbf k$3 requires $\mathbf k$4 shots; for $\mathbf k$5, $\mathbf k$6. The workflow also describes a vibronic alternative based on the spin-vibronic Koppel–Domcke–Cederbaum Hamiltonian

$\mathbf k$7

with rate extraction from

$\mathbf k$8

The resource estimates state that active spaces ranging from 11 to 45 spatial orbitals can be simulated using 180–350 logical qubits and Toffoli gate depths between $\mathbf k$9 and $$P(\mathbf k;\nu)\propto \sum_{v\in \mathrm{VB}}\sum_{c\in \mathrm{CB}} |\mu_{cv}(\mathbf k)|^2\, \delta(E_{c,\mathbf k}-E_{v,\mathbf k}-\hbar\nu),$$0. The detailed workflow specifies active-space construction for four BODIPY derivatives, Hamiltonian factorization with PySCF followed by THC or compressed double factorization, and sum-of-Slaters state preparation with depth $$P(\mathbf k;\nu)\propto \sum_{v\in \mathrm{VB}}\sum_{c\in \mathrm{CB}} |\mu_{cv}(\mathbf k)|^2\, \delta(E_{c,\mathbf k}-E_{v,\mathbf k}-\hbar\nu),$$1 for $$P(\mathbf k;\nu)\propto \sum_{v\in \mathrm{VB}}\sum_{c\in \mathrm{CB}} |\mu_{cv}(\mathbf k)|^2\, \delta(E_{c,\mathbf k}-E_{v,\mathbf k}-\hbar\nu),$$2 determinants. A width–depth trade-off in the QROM-based SELECT gives cumulative-absorption costs up to $$P(\mathbf k;\nu)\propto \sum_{v\in \mathrm{VB}}\sum_{c\in \mathrm{CB}} |\mu_{cv}(\mathbf k)|^2\, \delta(E_{c,\mathbf k}-E_{v,\mathbf k}-\hbar\nu),$$3 Toffolis per shot and ISC-proxy costs up to $$P(\mathbf k;\nu)\propto \sum_{v\in \mathrm{VB}}\sum_{c\in \mathrm{CB}} |\mu_{cv}(\mathbf k)|^2\, \delta(E_{c,\mathbf k}-E_{v,\mathbf k}-\hbar\nu),$$4 per shot; multiplying by the required $$P(\mathbf k;\nu)\propto \sum_{v\in \mathrm{VB}}\sum_{c\in \mathrm{CB}} |\mu_{cv}(\mathbf k)|^2\, \delta(E_{c,\mathbf k}-E_{v,\mathbf k}-\hbar\nu),$$5–$$P(\mathbf k;\nu)\propto \sum_{v\in \mathrm{VB}}\sum_{c\in \mathrm{CB}} |\mu_{cv}(\mathbf k)|^2\, \delta(E_{c,\mathbf k}-E_{v,\mathbf k}-\hbar\nu),$$6 shots yields total Toffoli budgets $$P(\mathbf k;\nu)\propto \sum_{v\in \mathrm{VB}}\sum_{c\in \mathrm{CB}} |\mu_{cv}(\mathbf k)|^2\, \delta(E_{c,\mathbf k}-E_{v,\mathbf k}-\hbar\nu),$$7–$$P(\mathbf k;\nu)\propto \sum_{v\in \mathrm{VB}}\sum_{c\in \mathrm{CB}} |\mu_{cv}(\mathbf k)|^2\, \delta(E_{c,\mathbf k}-E_{v,\mathbf k}-\hbar\nu),$$8 in the worst case, but $$P(\mathbf k;\nu)\propto \sum_{v\in \mathrm{VB}}\sum_{c\in \mathrm{CB}} |\mu_{cv}(\mathbf k)|^2\, \delta(E_{c,\mathbf k}-E_{v,\mathbf k}-\hbar\nu),$$9–$$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$00 for more moderate accuracy targets or smaller spaces.

6. Reactor-scale quantum-yield score in photocatalytic H$$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$01 production

In the benchmark photoreactor study, the photoreactivity score is the overall quantum yield $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$02, defined from the mean volumetric H$$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$03-production rate and the mean volumetric rate of radiant light absorbed (Supplis et al., 2020). In the flat-torus reactor, neglecting reflections at the walls, the mean volumetric rate of photon absorption is

$$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$04

with illuminated specific surface $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$05. The incoming monochromatic hemispherical photon flux density is $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$06, and the outgoing flux is $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$07. The integration limits are $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$08 nm and $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$09 nm. The probability that an absorbed photon is absorbed by eosin Y rather than by the catalyst is

$$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$10

Hydrogen production is measured from pressure rise in the sealed headspace. Under continuous stirring at 1000 rpm and isothermal conditions $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$11, the steady-regime balance gives

$$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$12

with $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$13 mL, $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$14 mL, $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$15, $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$16, and $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$17 K. The pressure rise is recorded by a Keller PA 33X transducer and Read 30 software, while online GC confirms that the only evolving gas is H$$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$18.

Plotting $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$19 versus $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$20 gives a straight line through the origin, yielding the linear coupling law

$$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$21

The score is then defined as

$$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$22

which is dimensionless and reported as mol H$$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$23 per mol photon. An equivalent expression uses total absorbed photons per second, $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$24: $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$25

Typical values at $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$26 mM and $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$27 mM give

$$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$28

while other runs varying $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$29 give $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$30 in the range $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$31–$$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$32 with uncertainties of $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$33–$$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$34. The protocol is explicitly generalized to other photocatalytic systems by characterizing incident and transmitted spectra, computing $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$35, measuring the reaction rate, testing linear or non-linear coupling, and extracting the slope as $$S(\hat n)=\dfrac{\int_{\Omega(\hat n)}P(\hat k)\,d\Omega}{\int_{4\pi}P(\hat k)\,d\Omega}$$36 or a more complex function if non-linear.

7. Comparative interpretation, methodological cautions, and recurring misconceptions

Across the three formulations, the score always compresses a high-dimensional photophysical problem into a scalar, but the compressed object differs substantially. In the semiconductor case, the score is an angularly restricted share of total transition probability. In PDT molecular screening, it is a weighted combination of two normalized observables. In the photoreactor study, it is a process-level ratio between chemical productivity and absorbed radiant input (Ricca et al., 2022, Zhou et al., 17 Dec 2025, Supplis et al., 2020).

A recurrent misconception is to treat band-structure anisotropy by itself as a sufficient predictor of facet photoreactivity. The semiconductor study explicitly states that conventional band-structure plots do not always provide all the informations, and that a complete picture requires all possible transitions weighted by their transition dipole moments. Another potential misconception is to regard any photoreactivity score as intrinsically universal. The cited literature instead shows that normalization conventions, observables, and intended use cases are domain dependent. This suggests that cross-study comparison is meaningful only after verifying what has been normalized, over which energy or wavelength window, and whether the score measures directionality, molecular trade-offs, or reactor-scale quantum yield.

The three definitions also differ in what they omit. The semiconductor score is constructed within hybrid-DFT in the independent-particle approximation. The PDT score may use an ISC proxy, with vibronic dynamics introduced only where appropriate. The reactor score is valid within the measured radiative balance and can support either linear or non-linear coupling analysis, depending on the observed behavior. These are not contradictions; they are differences in modeling target and experimental or computational granularity.

Taken together, the literature supports using “photoreactivity score” as a family of operational metrics for ranking light-driven systems. The common structure is not a shared formula but a shared function: converting absorption, transition probability, spin conversion, or chemical output into a dimensionless or normalized ranking variable that is specific to the photochemical question being asked.