The numerical simulations perform all calculations with wavelength-dependent parameters. Emission spectra of LED 2 and 3 as well as the transmittance of the glass vials is shown in Fig. 2a. The initially obtained data of the spectra are represented by mathematical expressions, which can easily be processed in a numerical simulation. The transmittance gradually decreases from the visible wavelengths to about 315 nm, in line with previously reported values^22,23. Further into the UV range, the transmittance dramatically decreases. For quantitative work, this cannot be ignored, and it was previously found that also quartz glass has a transmittance below 95%, despite being less dependent on the wavelength²⁴. Furthermore, the emission spectrum of any LED shows that LEDs are not nearly monochromatic light sources, although the width of the emission spectra is usually <60 nm, while the full width at half maximum is in a range of 10–15 nm. Under the paradigm of precision photochemistry any wavelength dependence needs to be considered quantitatively, as even a minor part of a spectrum can have noticeable effects²³. If an undesired overlap of emission spectrum and absorbance occurs in a complex photoreactive system, unwanted side products can be formed²⁵.

The absorbance of A, NEM, and AP was reported previously^21,26, but is shown in Fig. 2b to allow comparison with wavelength-dependent reaction quantum yields, obtained in this study from experiments that were carried out in triplicate, refer to Supplementary Information, section 2.2.1. As identified previously, the photoenol ligation using A is possible up to the wavelength of 420 nm²¹. Here, we report that the reaction quantum yield at this wavelength, Φ_{420 nm, 2.3 mM} = 0.0026 ± 0.0010 is particularly low and increases with decreasing wavelength to reach a plateau in the range of 345–400 nm at Φ_2.3 mM = 0.028 ± 0.0037. A further increase up to Φ_{307 nm, 2.3 mM} = 0.115 ± 0.023 is observed with decreasing wavelength to 307 nm, whereas the reaction quantum yield appears to drop for wavelengths shorter than 307 nm. These findings can tentatively be interpreted by assigning various photochemical efficiencies to the transitions that are accessible by each wavelength. We proposed a similar interpretation previously for a related compound, an alkoxy-2-methylbenzaldehyde B, refer also to Fig. 3a²³. While the assignment of an n → π* and a π → π* transition was straightforward with the alkoxy-derivative, the thioether-substituted compound appears to have less clearly separated transitions and the mixing between n → π* and π → π* states can occur.

Generally, a plateau in wavelength-dependent reaction quantum yields is in both cases an indication that the underlying transition is the main contributor to the absorption spectrum in the respective region and excitation into different vibrational levels within the same excited state quickly leads to the lowest vibrational level, respectively, before further photophysical processes occur. A slope in the plot of reaction quantum yields vs. wavelength, on the other hand, is either caused by two transitions competing for incident photons, or by a change in the efficiency of intersystem crossing to the triplet state dependent on the vibrational level that was reached by the respective wavelength. In the former case, within each electronically excited state the reaction quantum yields may potentially be independent of the vibrationally excited level. Wavelength-dependent quantum yields have been reported for a range of light-induced reactions, but the underlying physicochemical reasons for such dependencies are not easily identified^27,28,29.

An equilibrium between two or more conformations of the aldehyde functionality and adjacent PEG chain in solution can explain the peak in quantum yields at 307 nm. The relevance of conformers becomes apparent through comparison of A with related compounds benzyl ether-substituted o-methylbenzaldehyde B (methyl 4-((2-formyl-3-methylphenoxy)methyl)benzoate) and dodecyl thioether-substituted o-methylbenzaldehyde C (2-(dodecylthio)-6-methylbenzaldehyde), refer to Fig. 3 and the Supplementary Information, section 2.4. The broad absorbance feature from 300 to 400 nm in the absorbance spectrum of A is not caused by a single electronic transition, but is rather a convoluted band, with several conformers of A contributing. The absorbance spectrum of C (Fig. 3a) shows that at least two absorbance bands contribute to the overall absorbance.

Similarly, the absorbance spectrum of A in less polar solvents, such as dichloromethane and tetrahydrofuran, refer to the Supplementary Information, section 2.4.1, confirm this observation. A conformer, in which the aldehyde oxygen and thioether sulfur are close, as shown in Fig. 3b (O-S syn), indicates the presence of an intramolecular chalcogen bond, a noncovalent interaction well studied for small molecules with related structural motifs^30,31,32 as well as enzyme catalysis³³. To gain a better understanding of relevant conformers, we carried out wavefunction and density functional theory calculations on the model molecule C^Me to confirm that C or A are likely present in solution as conformers O-S syn, Ar-SR eclipsed, O-S anti, Ar-SR eclipsed and O-S anti, Ar-SR staggered, refer to Fig. 3b. In contrast, we conclude that B is only present in solution in significant amounts as the single conformer O-O anti eclipsed, explaining the comparably well-separated transitions, refer also to Figure S25. Each conformation can be expected to have characteristic electronic (vibronic) transitions, which are to a certain degree affected by the PEG chain in case of A. We have calculated relevant transition energies for the above-mentioned conformers of model compound C^Me, refer to Fig. 3a.

Our calculations place a S₀ → S₂ transition of the O-S anti, Ar-SR staggered conformer with mixed nπ*/ππ* character at 298 nm, refer also to the Supplementary Information, section 2.4.2. We propose that a respective conformer and transition in A is responsible for a significant fraction of absorbance between 285 and 345 nm and the maximum in the reaction quantum yield as determined by the fractional absorbance of this transition, refer also to Fig. 2a. The elevated reaction quantum yield for this conformer can be rationalized by the preferential conformation of the aldehyde, allowing a sigmatropic [1,5] H-shift to occur without prior bond rotation, refer to Fig. 3d. Furthermore, the following step (likely the passing of the initially formed (E)-enol through a conical intersection (CI) to form the ground state (Z)-enol, refer to Fig. 3c), which rapidly reacts with NEM) is an efficient pathway toward formation of the cycloadduct, as we found previously²³. In contrast, we suggest that the O-S syn, Ar-SR eclipsed conformer increasingly contributes to absorbance at longer wavelengths than 307 nm, as a S₀→S₂ transition (ππ* character) is expected at 337 nm with significant oscillator intensity, refer to Fig. 3b and the Supplementary Information, section 2.4.2. We expect a lower reaction quantum yield to be associated with this transition, as bond rotation in the excited state is required, before the [1,5] H-shift can occur.

The experimental investigation of thioether o-methylbenzaldehydes surprisingly revealed that the reaction quantum yield may be concentration-dependent, with higher reaction quantum yields at a lower initial concentration of the starting materials. We performed a detailed study, refer to Supplementary Information, section 2.2, subsection 2.2.2, to find the relation between the initial concentration and the observed reaction quantum yield. Due to the low sensitivity of ¹H-NMR spectroscopy, high-resolution electrospray ionization mass spectrometry (ESI-MS) was employed for samples with low concentrations. The effect of potential ionization biases was reduced by evaluation of the double and triple charged (Na adducts) poly(ethylene glycol) bound species. A correction factor is determined, based on the measurement of samples with varied conversion of A to AP using both NMR and ESI-MS analysis. Indeed, for low initial concentrations of A, a reaction quantum yield of Φ_{382 nm, 0.13 mM} = 0.057 is found, whereas a gradual decrease toward Φ_{382 nm, 4.8 mM} = 0.016 is observed, see also the inset of Fig. 2b. The trend is qualitatively confirmed by ¹H-NMR spectroscopy of samples with varied concentration at 307 nm. While a reaction quantum yield of Φ_{307 nm, 1.1 mM} = 0.133 is observed, it decreases to Φ_{307 nm, 4.8 mM} = 0.059 with increasing concentration. Possible reasons for the dependence of the reaction quantum yields on the initial concentration include self-quenching (e.g., triplet-triplet annihilation) at higher concentrations. For each dataset involving reaction quantum yields, a mathematical expression was formulated, which represents the observed trends and values of Φ. The expressions were combined to an expression with two variables, which upon plotting lead to a map showing the extrapolated wavelength and concentration-dependent reaction quantum yields within the observed ranges, refer to Fig. 2c. The expression is included in the source code for the quantitative prediction of conversion, refer to Supplementary Information, section 2.4.

The algorithm presented in this work, a significant improvement of a previously introduced iterative method²⁶, is represented by the flow chart in Fig. S23, refer to Supplementary Information, section 2.5. Upon starting the program, information regarding the experiment that is to be simulated is requested. Combined with the absorbance spectra of relevant species, here A, NEM, and AP, all required data are collected, as the source code itself contains expressions for emission spectra, transmittance, and reaction quantum yields. The processes in the sample solution are simulated by calculation of light absorbance and reactivity within a defined number of segments, that the solution is divided into. The segments are defined by a stack of thin slices that the light sequentially penetrates.

After the prediction of the overall conversion within one second, the result is saved and subsequently a module in the code is redistributing the compounds across the segments, so that the solution is simulated to be fully mixed. This sequence is performed until the entire irradiation time is simulated and the output is saved into an excel file. Importantly, within each of these iterative (temporal) steps, an entire iteration over the segments is performed for each wavelength increment. The distinction between the wavelength increments of 0.5 nm is important to reflect the wavelength dependence in all parameters from the emission spectrum, the transmittance, and absorbance of the species to the reaction quantum yields. The division of the solution into segments is particularly important for the code to be modular, as the complete mixing module can for future work be replaced by a simulation of stepwise mixing. Such a modification would be important, if a photoreaction is simulated, where the product of the reaction significantly absorbs at the wavelengths of irradiated light. The mixing of the solution in a real batch reactor is not ideal and depending on it a minor delay of the experimental reaction progress compared to simulated progress (with the assumption of ideal mixing) is anticipated. The conceptualization of a stepwise, incomplete mixing simulation, which is not based on arbitrary parameters exceeds the scope of this work and is the subject of future projects.

The predictions resulting from the photoreaction simulation with LED 2 and the respective experimental results are compared in Fig. 4. Predictions and experiments were carried out with and without the addition of the competitive absorber 2-hydroxy-5-nitrobenzaldehyde HNBA. For details, including the absorption spectrum of HNBA, refer to Supplementary Information, sections 1.7 and 2.7. The purpose of the addition of HNBA is to establish, whether the retardation effect of other light-absorbing molecules that otherwise do not interfere in the photoreaction can be predicted correctly. HNBA is treated in the simulation as a compound that absorbs light according to its molar attenuation coefficient, thereby affecting the overall fractional absorption of light in each simulated segment (second and wavelength) but it is not expected that any energy transfer from HNBA to A or vice versa occurs. In both cases, the observed conversion only slightly deviates from the predicted values, refer to Fig. 4a. Close examination of the predicted conversion trace shows that during the first 800 s of the reaction without HNBA addition, the predicted reaction rate (derivative of the plotted curve) increases slightly, before decreasing, refer to Fig. 4b. The increase in reaction rate is caused by the concentration-dependence of the reaction quantum yields. As the reaction progresses, A and NEM are consumed, leading to their concentrations to decrease—and thereby leading to increasing quantum yields over time. The rate of reaction significantly decreases, once light increasingly passes through the solution, as seen on the light-attenuation maps below (Fig. 4c) (right light-attenuation maps). This lower rate of conversion is not due to a change in the quantum yield, rather the effect of higher quantum yields at lower concentrations on the reaction rate is offset by the slowing of time-dependent conversion due to light passing through the solution without being absorbed.

Apart from delivering a prediction of the conversion trace of the experiment, the simulation simultaneously generates the data for the light-attenuation maps. Due to the segmented iterative approach, not only changes in (local) concentrations are simulated, but the spatiotemporal and wavelength-resolved residual light intensity during the experiment is calculated. For each second, segment, and wavelength, the incident number of photons is calculated for the respective step during simulation. The code is programmed to save the respective data in four cases: Before irradiation, after a third of the simulated time, after two-thirds, and finally upon completion of the algorithm. It can be concluded from the light-attenuation maps that initially the incident light is entirely absorbed, while after full conversion of A, the beam is for the best part passing through the solution. At this stage only a remaining minor amount of NEM causes some light to be absorbed.

In case of the addition of 0.65 eq. HNBA, the reaction is not only proceeding at a lower rate overall but also the rate of the reaction is more lowered as higher conversion is reached, because with increasing reaction time a higher percentage of photons is absorbed by HNBA rather than the reactant A, refer also to Fig. 4d. Such competitive absorption effects were recently qualitatively investigated and exploited for the design of chromatically orthogonal reactions^35,36. In contrast, the results shown here impressively demonstrate that retardation effects through competitive absorption can now be predicted quantitatively. This visualization highlights that each photochemical experiment can be expected to exhibit its own specific kinetic behavior. The progress of the reaction would vary to some degree if any parameter were changed. A lower or higher amount of starting materials not only implies a change in the reaction quantum yields that are applicable, but also leads to a changed number of photons being absorbed or passing through the solution over time. One can imagine endless examples where the dimensions of the reactor, the wavelength and intensity of incident light, amount of compounds, or addition of other light-absorbing compounds could alter the progress of the reaction. We propose that the most reliable prediction of photoreaction kinetics can only be achieved through numerical iterative simulation of the individual reaction progress using a reproducible photoreaction setup. A 3D-printed reactor is an example of how defined irradiation conditions can be established.

While a monochromatic, wavelength-tunable laser allows best control over irradiation, the use of an LED and 3D-printed reactor with respective detector scaffold can provide an alternative pathway to estimate (apparent) quantum yields: The algorithm contains an option to replace the use of the quantum yield map with an arbitrary, fixed, apparent quantum yield, for details refer to the Supplementary Information, section 2.5. Thus, the conversion determined from an LED experiment can be used for the iterative determination of a quantum yield estimate, which is an approximation applicable to the wavelengths emitted by the respective LED.

To further verify the algorithm, we predicted the course of the reaction with LED 3, refer to Fig. 5. All calculations were conducted identically, whereas here the data associated with LED 3 is employed and the experiments are performed accordingly. In comparison to the previously shown experiment, a faster reaction is predicted and found here, partly caused by the stronger output of the LED, compare to the Supplementary Information, section 1.4. Similar to the results above, the derivative of the predicted curve initially slightly increases (for the first 90 s), before decreasing due to light increasingly passing through the solution instead of being absorbed, as can be traced with the light-attenuation maps (refer to Fig. 5b, c). Importantly, the experimental results closely mirror the predicted progress of the reaction. Further predictions and experiments involving LED 1 and LED 4 are shown in the Supplementary Information, section 2.8. In the case of LED 4, the emission spectrum overlaps with the absorption spectrum by only a very small degree. Yet, the predictive method provides a good conversion estimate. In case of LED 1, the prediction is correct only for small conversion values (20–30%), because with longer irradiation increasingly side products are being formed.

The precision of the predictive method for controlled photoreactions in a 3D printed LED batch photoreactor sets a new standard for photochemical experiments. Not only can monochromatic quantum yields, obtained here with a sophisticated tunable laser setup, be applied in predicting experiments conducted in an inexpensive photoreaction setup, but the methods developed here are modular in nature and can be developed further.

Both determining wavelength-dependent reaction quantum yields and predicting photochemical kinetics helps considerably in the development of reaction systems that are controlled by the wavelength and/or intensity of light. Many combinations of chromophores, which can be addressed selectively by different wavelengths, are known^37,38,39. A significant limitation of most examples is the competition between two reaction pathways, if one irradiation step activates both chromophores^40,41,42. Selectivity can be achieved through control of the photo-kinetics by tuning both the degree of absorbance and the ratio of the relevant reaction quantum yields^26,43,44,45. We have previously reported that a combination of A with a diaryltetrazole can be addressed with a very high degree of selectivity at two different wavelengths, employing LEDs centered at 285 and 380 nm²⁶. The pro-fluorescent character of tetrazoles and the high absorbance of the product pyrazoline may be a disadvantage for certain applications, for example direct laser writing. The formation of light-absorbing cross-links in a photoresist makes the writing process challenging, as so-called micro-explosions are more likely⁴⁶. In contrast, o-methylbenzaldehydes have been employed for direct laser writing in many occasions^47,48,49,50. Considering the absorbance and quantum yields of A and of previously investigated alkoxy-substituted o-methylbenzaldehydes B²³, as shown in Fig. 6, it is not self-evident, whether a selective reaction of B in the presence of A can be achieved and which wavelength and which photon count may be suited best. A selective activation of A in the presence of B can be expected at wavelengths longer than 405 nm, as previously no detectable conversion was observed after irradiation of B at 405 nm with a defined photon count.

Here, we present an algorithm capable of making wavelength-dependent predictions of the selectivity that can be expected for irradiation of a mixture of A, B, and NEM with monochromatic tunable laser light at varied wavelengths, refer to Supplementary Information, section 2.5. The output of the algorithm is the predicted conversion of both reactions of A or B with NEM at each wavelength, refer to Fig. 6. Each simulation is carried out with as many laser pulses as are required to reach a target conversion value for either of the two reactions. The conversion that is predicted for the other reaction, respectively, is a measure for the achieved selectivity, while the number of laser pulses is direct guidance for the experimental testing of the prediction. Surprisingly, despite the wavelength-dependent changes in the absorbance and the reaction quantum yields, the selectivity is predicted to be comparably good within the range of 300–330 nm. With these encouraging results, we tested the prediction experimentally, irradiating an equimolar solution of A and B with an excess of NEM in the presence of the internal standard TMB (1,3,5-trimethoxybenzene), refer to Fig. 7. Irradiation of a sample from the stock solution with the predicted number of monochromatic 325 nm tunable laser pulses at the respective laser energy (2.64 μmol total incident photons) leads to 93% conversion of B to BP, while A is mostly retained, with only 5% AP detectable. Despite the selectivity not being exactly as good as predicted, the outcome is still noteworthy and could be applied in situations where other chromophores are less suitable, such as in direct laser writing. Surprisingly, irradiation of the stock solution for 135 min at 415 nm (575 μmol total incident photons) led not only to 91% conversion of A to AP, but also caused 4% of B to be converted to BP. Yet, the reaction quantum yield of the here undesired reaction appears to be so low that even irradiation with this very high photon count only leads to a few percent conversion, allowing an overall comparably good selectivity. With an ever-increasing number of photoreactive molecules being synthesized, the possibilities to combine them in search of a specific, λ-orthogonal reaction system increase even faster: From N photoreactive substrates, N \(*\) (N − 1)/2 different combinations can be created.

Comparison with the sequence-independent λ-orthogonal ligation system that we introduced earlier²⁶ and density functional theory calculations carried out within this study led us to question, whether the critical selectivity between tetrazole D (α-methyl-ω-4-(2-(4-methoxyphenyl)-2H-tetrazol-5-yl)benzamido poly(ethylene glycol)), refer to Fig. 8, and C under irradiation with LED 1 (λ_max = 285 nm) could be different to the previously reported selectivity between D and A. To this end, we determined reaction quantum yields of the conversion of C to CP as Φ_{C→CP, 285 nm} = 0.012 ± 0.0017 and Φ_{C→CP, 360 nm} = 0.008 ± 0.0007, each significantly lower than the observed reaction quantum yield of A, refer also to the Supplementary Information, section 2.9.2. Using the observed reaction quantum yield at 285 nm as well as the quantum yield estimate of Φ_{D→DP, 285 nm} > 0.55^23,26 as apparent quantum yields, we modified the algorithm that predicts conversion of LED experiments to simulate the competing photoreaction between C and D with NEM, refer to Fig. 8. Experimentally, a faster than predicted conversion of tetrazole D is observed, with 98% conversion reached after 30 min of irradiation, while CP is undetectable both after 30 min and one hour of irradiation (C being retained quantitatively). Only after 4 h of irradiation is the undesired product CP detectable, underscoring the improved selectivity of C and D compared to A and D, despite competing absorbance and reactivity.

In contrast to the above-described combination of photoligation reactions, tetrazole D in combination with o-methylbenzaldehyde B leads to an unselective reaction outcome, as predicted and experimentally observed, refer to the Supplementary Information, section 2.9.3. Irradiation of D and B in presence of NEM and TMB was carried out at 313 nm, as the ratio of the molar attenuation coefficients of D and B at this wavelength (3.3) is the same as the one of B and A at 325 nm, compare to Fig. 6 and Fig. 7. The difference in the observed selectivity between the sets of experiments highlights that absorbance cannot be a sufficient guide for the design of selective photoreactions, but quantum yields in combination with a numerical simulation enable to predict whether good selectivity can be expected.