Kinetics of Palladium(0)‐Allyl Interactions in the Tsuji‐Trost Reaction, derived from Single‐Molecule Fluorescence Microscopy

Single‐molecule (SM) chemistry is devoted to unravel reaction steps which are hidden in cuvette experiments. Controversies about the substrate activation during the Tsuji‐Trost deallylation motivated us to study, on the single‐molecule level, the kinetics of the catalyst precursor Pd(PPh3)4 with our recently designed two‐color fluorescent probes. Photochemical, metal‐free bypass reactions were found and taken into account by the combination of spectrally separated single‐molecule TIRF‐microscopy and state‐of‐the art analysis procedures. Unselective π‐complex formation (KD≈103 M−1) precedes the insertion of the active catalyst into the C−OR bond (RO−=leaving group), indicated by the lacking immediate change of fluorescence color. The formed intermediate then decomposes on a time scale of≥2 – 3 s to the deallylated product.


Introduction
Over the last decade, single-molecule fluorescence spectroscopy (SMFS) emerged as a tool to bring insights into the microscopic behavior of molecular, chemical systems. [1][2][3][4][5] When ensemble measurements conceal uncommon events, single-molecule observation has the potential to provide a deeper understanding of chemical processes. [6][7][8] In these first studies, it was shown that even text book reactions can show furcations of reaction pathways, still leading to an identical product. [9] Hidden intermediates [10] or static disorder is revealed for single nanoparticles and enzymes. [11,12] Reactivity mapping of heterogeneous catalysts has been accomplished with spatial resolution. [13] Ligand exchange [14,15] and polymerization [16] reactions have been investigated in model systems for homogeneous catalysis. [17] To further advance this field in direction of recent synthetic chemistry, we previously introduced multi-emissive probes for the so-called participant approach. [18][19][20][21] The Tsuji-Trost allylic substitution provides an example of a well-known and widely-used organometallic reaction. [22][23][24] We have chosen to study this reaction as only few components are involved and there are still some mechanistic details under discussion. The putative active catalyst is PdL 2 (L = Ligand, e. g. PPh 3 ), which is formed during dissociation from a Pd 0 -precursor like Pd(PPh 3 ) 4 . [25] The catalytic cycle then consists of two separable reactions, the displacement of allylic substrates, [26] also utilized for cleavage of allyl protective groups, [27] and the allylic alkylation. [28,29] This second half of the catalytic cycle is described by the nucleophilic attack of a wide variety of nucleophiles [22] on the Pd-allyl-complex, finally forming CÀ C, CÀ N and CÀ O bonds. [30] In our study, we focus on the primary activation step. Here, the catalytic active Pd 0 L 2 species stands in equilibrium with a Pd-η 2 -allylcomplex in equation (1).

ð1Þ
Via this transient complex, a cationic η 3 -allyl-complex is yielded. Especially for this part of the reaction, the Pdmediated deallylation, ambiguity exists regarding the progression of the oxidative addition of allylic substrates to Pd 0 . The latter step may proceed similar to a S N 2 reaction [31] with immediate release of the leaving group [eq. (2)].

ð2Þ
Alternatively, the Pd-center may insert into the CÀ ORbond [30,32] (RO À = leaving group). Here, an oxidative association with formation of either a π-allylic η 3 -intermediate or a η 1 -Pd-complex [33,34] are proposed, with the leaving group temporarily bound in the ligand sphere. From these intermediates a consecutive dissociation step then is expected. [35] With the aim of obtaining new insights into the mechanisms of leaving group release, we studied the interactions of Pd 0 with our recently introduced, dualemissive and immobilizable substrates: [36] During this reaction, tetrakis(triphenylphosphine)-palladium(0) (Pd 0 ) causes a strong bathochromic shift in substrate fluorescence (SI Figure S2).
To probe the early events during the interaction of Pd 0 with the substrate, i. e. the equilibrium of complex formation, we used time-correlated single photon counting (TCSPC) [37] and analyzed the quenching behavior by a Stern-Volmer (SV)-analysis. Monitoring fluorescence emission of individual reactive chromophores with two-channel detection in total-internal reflection fluorescence microscopy (TIRFM) [38] should then enable conclusions about the role of Pd during chemical transformation. In addition, we investigated several data analyzation routines for adaption to irreversible reactions. Hidden Markov modelling [39] or Bayesian statistical analysis, [40] very well suited for the analysis of Förster resonance energy transfer (FRET) trajectories in equilibria, allow for extracting kinetic or mechanistic data from two channel SM fluorescence trajectories. Problems may occur when applied to a single reaction step with superimposed fluorescence quenching. We therefore searched for an unbiased statistical analysis of obtained single-molecule data. At first, we pursued noise-cancelling auto-and cross-correlation analyses of single particle emission [41] for extraction of substrate decay and product rise. Subsequently, we compared the outcome with the results from analyzing the histograms of substrate fluorescence termination and product fluorescence formation events. With these methods, kinetic information of the reaction steps in equation (1) and (2) could be extracted, but photochemical bypass reactions were deciphered as well.

Results and Discussion
We synthesized pyrene-based, reactive fluorophores 2 a, 2 b and 2 c from 1 a, 1 b and 1 c according to existing procedures [36,37] (scheme 1). The benzylated probes 3 a, 3 b and 3 c were synthesized in a similar fashion (SI pp.: 4-7). Compounds 2 a, b and 3 a, b were used for kinetic experiments in cuvette whereas 2 c and 3 c were used for immobilization on quartz surfaces prior to SM visualization. [36] All probes 2 a, 2 b, 3 a and 3 b were stable in ethanol at standard conditions in the time span of these experiments. In steady-state experiments with 3 a and 3 b, no product formation at RT was noticed, neither in presence of Pd 0 , nor in combination with Pd 0 and the nucleophiles ethylmalonate and acetoacetate [28] (SI Figure S3). Due to the lacking reactivity at RT towards Pd 0 , the benzylated derivatives served as control probes in this study. Electronic spectra and photophysical properties of all compounds were determined and are compiled in table S1 (SI Figure S1).
We performed steady-state and time resolved measurements in solution for characterizing the Pd 0 interaction with the substrate prior to the reaction. With addition of various amounts of Pd 0 up to a saturated solution (150 μM), fluorescence emission of unreactive 3 a, 3 b and 1 b was quenched (SI Figure S4). Association constants K SV of1 0 3 M À 1 were obtained from a SV plot [42] (Figure 1a). Fluorescence lifetimes of 2 a, 2 b and 3 a, 3 b, on the other hand, remained unchanged shortly after addition of Pd 0 (SI Figure S5). These findings indicate static quenching by Pd 0 , i. e. complex formation. [43] Scheme 1. Synthesis of reactive (2 a,b,c) and reference probes (3 a,b,c) for the Tsuji-Trost deallylation reaction [36,37] performed in acetone or dimethylformamide.

Fluorescence Correlation Spectroscopy (FCS)
FCS was performed in oxygen-free ethanol to further determine the underlying kinetics (SI pp. 17). We used compounds 3 b and 1 b as control probes, with enough brightness and photostability for FCS under short wavelength excitation (λ exc = 445 nm and 488 nm; SI Figure S7). Moreover, reactive 2 b was investigated as well, shortly after addition of Pd 0 . As the measurement time was limited due to the consumption of 2 b, we exploited high excitation intensities for obtaining reasonable FCS curves ( Figure 1b). Autocorrelation curves revealed a dark state in the presence of Pd 0 , the ligand PPh 3 (1 mM) and only in the absence of oxygen. Consequently, strong fluorescence fluctuations cannot unambiguously be traced back to the interaction with the catalyst.
Moreover, since the amplitude and the contrast of the fast fluctuations depend on illumination intensities, these observations point to typical light driven processes. [44] However, photochemical release of a phosphine ligand [45] could not be excluded. Equation (3) therefore represents the kinetic description of a reversible dark state formation from autocorrelation curves.
Through application of equation (3), effective dark state formation and decomposition rates k dark; eff and k bright in the μs-time regime were obtained. While on the μs-time scale hardly any significant differences between 3 b and 2 b are found in FCS, we noticed a distinct reduction of apparent diffusion time t diff from 160 �36 ð Þ ms to < 40 �4 ð Þ ms upon addition of Pd 0 only in 2 b. Although the interpretation of apparent t diff requires caution, [46] we conclude that the extracted k � 1:5 � 10 4 s À 1 , that is k 1 or k 2 in equation (2), appears as the upper limit for the reaction of 2 b with Pd 0 L x . Still, this upper limit is several orders of magnitude above the rate constants of the conversion in cuvette experiments (k � 2 � 10 À 2 s À 1 ), [36] and thus may not reflect the putative S N 2-like short cut in equation (2). In summary, the only specific interaction with Pd 0 , which is not seen in the control experiment, is the reduction of t diff . Due to resulting limited observation time window, that is the diffusion time through the detection volume, FCS in solution can neither clearly distinguish between the pathways of fluorescence loss in eq. (2) nor does provide the kinetics of eq. (1) in its present configuration.

TIRF-microscopy
For exploring the Pd 0 interaction during chemical conversion, the deallylation reaction was visualized on the SM level. Simultaneous observation of substrate and product with low background was achieved with a prism-based TIR [38] excitation in a custom built setup [36,47] and dualchannel detection. Excitation and emission spectra of silanes 1 c and 2 c in solution as well as utilized laser lines and detection channels are shown in Figure 2a. Dyes 1 c, 2 c and 3 c were immobilized on a, with methylsilane passivated quartz surface, as described before, [36] leading to 1 imm (product), 2 imm (reactive substrate), and 3 imm (reference substrate) (SI Figure S10). Movies (100 ms/frame) of immobilized substrates 2 imm and 3 imm were recorded in ethanol before, during and after addition of 100 μM Pd 0 . With 2 imm , a clear shift of emitting molecules from the "blue" (417-477 nm) to the "orange" (500-600 nm) detection channel was observed, which was initiated by Pd 0 (PPh 3 ) 4 ( Figure 2b). Single-molecule fluorescence trajectories with apparent noise were extracted with the selection criterion of single bleaching steps. Finally, 1741 SM-trajectories from 9 samples of 3 independent preparations of 2 imm from movies during addition of Pd 0 were collected (amount of all trajectories: see SI p. 24).
To attain the temporal evolution from the starting material to product without any data preselection (except the mentioned single step in the blue channel), correlation analyses [41] were conducted. Autocorrelation decays provide the time constant for molecule disappearance (due to reaction or photobleaching) as in FCS but also do not distinguish between these processes. Cross-correlation analysis, in contrast, is specific for the reaction and yields the time constant for product formation once a substrate molecule is identified. Moreover, artifacts and random noise are cancelled out in correlation functions [48] and the time resolution of the acquisition frequency (10 Hz b ¼100 ms) is sustained in contrast to our later analyses based on binning. Emission trajectory pairs of each measurement were aligned into single paired data series. Subsequently, the overall correlation curves were calculated, which were corrected for spectral cross-talk according to the method described by Bacia et.al. [49] (SI pp. 25). The obtained corrected crosscorrelation G t i;j À � curves of measurements with introduction of Pd 0 show positive amplitudes (Figure 3a). In the conversion of 2 imm by Pd 0 a pronounced maximum is seen, while corresponding curves of 3 imm only show a weak maximum (Figure 3a and SI Figure S11b). Kinetic constants were derived from mono-or biexponential fits of these curves, in which the rising component is interpreted as product formation. A time constant of t form; orange of 15:7 �1:5 ð Þ s of 2 imm with presence of Pd 0 results from this analysis (SI Figure S16). This time constant is considerably lower, by a factor 4, than the previously determined time constant of product formation in a fluorogenic approach, that is when only the formed product molecules were excited. [36] However, if we take the competing photobleaching of the substrate 2 imm into account (i. e. the decay of the blue autocorrelation functions of control 3 imm and 2 imm without Pd 0 , see Figure 4 and SI Figure S11), then a reduced time constant t red ¼ 6:2 �1:9 ð Þ s is expected (SI p. 34). The significant retardation from the expected 6 to the observed 16 s putatively points to an intermediate, specific to an interaction with Pd 0 , before 1 imm is produced in the reaction. However, no conclusions about its nature or any reaction branching as inferred from eq. (2) can be drawn from these correlation analyses. If fluorescent intermediates with a different emission spectrum were present, then signal-pair histograms [48,50] (SI Figure S14), created from the paired emission trajectories, could suggest their presence. However, such an analysis provided no unambiguous indication for spectrally shifted intermediates specific to the presence of Pd 0 . We therefore interpret any putative intermediate as dark state in the reaction from 2 imm to 1 imm . Please note that even the cross-correlation curves of 2 imm without Pd 0 shows  We subsequently chose an analysis method for extracting information out of individual trajectories, finally yielding conventional histograms. In contrast to the former analyses, any dark state is directly detected as discontinuity of fluorescence to agree with the outcome of the former analyses. A simple algorithm was used to sort trajectories into groups of reactive and non-reactive molecules. At first, normalized intensity trajectories were transformed into a binary signal via a threshold to exclude 99 % of data points, which may correspond to zero emission (SI Figure S12). Then, for recognition of product formation, the orange intensity had to exceed the corresponding threshold for at least one second (Figure 2c, d). Consecutively, all trajectories showing conversion were selected and the number of reactive molecules was determined. Roughly 28 % of trajectories of 2 imm ( b ¼487 of 1741 trajectories) with Pd 0 was deemed reactive with a significant rise in orange fluorescence during the observation window (Figure 2c), whereas the rest of molecules were considered to photobleach. We certainly lost a wealth of trajectories by these strict criteria and, therefore, overestimated photobleaching. In the first control experiment, that is 2 imm in ethanol, but without Pd 0 , however, also around 12 % of fluorescence trajectories with similar behavior ( b ¼280 of 2330 trajectories) were identified (Figure 2d). Moreover, experiments with benzylated dye 3 imm , also revealed approximately 6 % of trajectories with rising orange fluorescence, independent of Pd 0 influence ( b ¼25 trajectories with Pd 0 and 51 without Pd 0 ). These findings are in agreement with the almost vanishing cross-correlations (see Figure 3a and SI Figure S11). Interestingly, and most significant for the reaction mechanism, only a minor fraction of trajectories ( b ¼ 60 of 487 reactive trajectories or 12 %) exhibited a sudden color shift (� 0:1 s).  Figure S11); b) exemplary SM trajectories with sliding average over 1 s; scheme of extracted t 1 , t 2 and delay time Dt; c) histogram of normalized product formation events t 2 regarding 2 imm and 3 imm with and without Pd 0 . The shaded area represents the additional amount of formed product 1 imm through influence of Pd 0 on 2 imm resp. the Tsuji-Trost deallylation reaction; d) histogram of lag times Dt; arrows indicate the shift in kinetics upon addition of Pd 0 (SI Figure S16). The timepoints of substrate emission termination t 1 and product fluorescence formation t 2 were resolved from the binary fluorescence trajectories and accumulated (Figure 3b). The resulting histograms were subsequently fitted with monoexponential functions (SI p. 33 and Figure 3c, extracted from Figure S13). The kinetics of the decay of 2 imm , expressed by equation (4) shows a faint acceleration by Pd 0 as expected (Figure 4).
The influence of Pd 0 on 3 imm is less clear, as the error margins hide any measurable effect. Altogether, the obtained rate constants are in a similar range like those of the correlation analysis (Figure 4). Conversion of 2 imm /3 imm to the fluorescent product support a photochemical bypass reaction for both substrates to 1 imm with an apparent quantum yield of about F Ph; reac � 5:5 � 10 À 6 and 2:8 � 10 À 6 for 2 imm and 3 imm , respectively. The most likely interpretation therefore is a photoinduced deprotection reaction, presumably via homolytic CÀ O cleavage [51] or photoionization reaction [52] (SI Scheme S2 p. 36). Its competition to the metal-organic reaction of 2 imm (SI p. 34) causes the seeming acceleration compared to the experiments in a fluorogenic approach. [36] More relevant for mechanistic insight is the analysis of the lag time Dt between the disappearance of the blue fluorescence and appearance of orange fluorescence, that is, the lifetime of the dark intermediate (Figure 3b,d). To perform an unbiased analysis of dark state evolution in regard to its mechanism, an empirical biexponential fit of Dt was utilized.
Firstly, the relative amplitudes of a fast (A short ) and a slow (A long ) decay component are resolved, normalized on the absolute number of reactive trajectories (SI Figure S16). For inert substrate 3 imm , addition of Pd 0 makes the short component disappear, leading to a monoexponential decay. This behavior is opposed to the reactive substrate 2 imm , where the amplitude of the faster decay component of the allylated 2 imm absolutely increases (Figure 3d). Although the relative amplitude A short of the biexponential fit increases only by~one third (from 0.28 to 0.38), the absolute raise corresponds to 7 % of all trajectories of 2 imm during the presence of Pd 0 (� 120trajectories of 487 reactive trajectories) and, hence, to roughly half of the increase of reactive trajectories upon addition of Pd(0). Thus, this faster process is related to the synthetic reaction mechanism, although it competes here with photochemical conversion. An absolute increase of the slow component is noticed as well.
Secondly, the obtained rate constants are compared. Addition of Pd 0 extends the dark state lifetime of inert substrate 3 imm to a single value t dark � 30 �5 ð Þ s (Figure 3d). This time constant, however, may not necessarily reflect the binding time of Pd 0 to the substrate. Considering the benzylated derivatives 3 are not prone to conversion by Pd 0 , this latter, slower process is not related to the catalytic cycle. This interpretation becomes important, as the same lifetime is found for the reactive substrate 2 imm as well. Here, Pd 0 also elongates the long component of dark state lifetime (denoted by horizontal arrow in Figure 3d). At the same time, its short component lifetime slightly shortens upon addition of Pd 0 from t short ¼ 3:1 �0:5 ð Þ s to t short;Pd ¼ 2:4 �0:4 ð Þ s opposed to its absence in the reaction of benzylated counterpart 3 imm (SI Figure S16b). Still, the observation of (at least) two lifetimes may also hint to more than one process being involved. The question therefore arises whether a distribution of rate constants is here a more appropriate description.
For analysis of kinetics with an intrinsic dispersion of rate constants, a Weibull analysis is employed. [53] Here, a βvalue results from a stretched exponential fit of the dataset with an effective rate constant k eff . The larger the discrepancy of β from 1 is, the more pronounced is the distribution of rates around k eff . Applied on the presented data, this analysis shows an increase of complexity of dark state kinetics of 2 imm through addition of Pd 0 , indicated by a decrease of the corresponding β-value. With the inert substrate 3 imm , Pd 0 exerts the opposite effect with a β-value close to one with the transition metal present (SI Figure S13d,e). One interpretation are additional contributions to reactive trajectories by e. g. the reaction of a mixture of various reactive Pd-ligand species [25,54] or the presence of different intermediate states like η 1 or η 3 -complexes. [33,34] In summary, no more evidence for a distinct, sudden change than before results from the kinetics dispersion.
Nevertheless, having the previously discussed lack of a fast rising component in the cross-correlation (Figure 3a in equation (2), rather pointing to the proposed mechanisms involving a Pd 0 insertion into the CÀ O-bond. [33,35]

Conclusion
The interaction of Pd 0 with allyl-protected substrate molecules 2 and its chemically inert, benzylated counterpart 3 has been studied by fluorescence spectroscopy and microscopy. Steady-state unselective fluorescence quenching provides evidence for formation of a π-complex with Pd 0 L x moieties. The reduced t diff in FCS, only observed in the allylated compounds, is suggestive of formation of a chemically relevant intermediate. SM experiments with twochannel detection were performed to cover the time regime well above 0.1 s. Noise insensitive correlation analyses and noise affected analysis of fluorescence event histograms result in similar time-constants for the substrate decay and product formation, but only the latter method shows the kinetics of presumably photoinduced dark states and reveals the existence of a Pd II intermediate with a lifetime of 2-3 s. The present experiments are more in line with insertion of Pd 0 into the CÀ O-bond (in a S N 2-like mechanism we would expect an instantaneous release of the product 1 imm ), but may reflect a selected mechanism for the Tsuji-Trost-deallylation. As our pyrene derivatives provide an excellent leaving group, the result may only be transferred to comparable substituents. Experiments with other allylated fluorophores [55,56] are a convenient way to find out distinctions. It is yet unclear to which extent the investigated conversion, with simultaneous excitation of product and substrate agrees with the findings of our previous study based on a fluorogenic approach. [36] However, an intermediate, as found here with a lifetime � 60 s, would hardly be detected in a conventional fluorogenic approach or kinetic analyses in an ensemble and underpins the benefits of single-molecule studies.