A DFT-Based Computational-Experimental Methodology for

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A Computational-Experimental Methodology for Synthetic Chemistry: Example of Application to the Catalytic Opening of Epoxides by Titanocene Martin Jaraiz, Lourdes Enriquez, Ruth Pinacho, José E. Rubio, Alberto Lesarri, and José Luis López-Pérez J. Org. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.joc.7b00220 • Publication Date (Web): 13 Mar 2017 Downloaded from http://pubs.acs.org on March 16, 2017

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The Journal of Organic Chemistry

A Computational-Experimental Methodology for Synthetic Chemistry: Example of Application to the Catalytic Opening of Epoxides by Titanocene Martín Jaraíz,#* Lourdes Enríquez,# Ruth Pinacho,# José E. Rubio,# Alberto Lesarri‡, and José L. López-Pérez†§* #

Department of Electronics, ETSIT, University of Valladolid, Paseo Belén 15, 47011 Valladolid (Spain)

‡

Department of Physical Chemistry and Inorganic Chemistry, Faculty of Sciences, University of Valladolid, Paseo Belén 7, 47011 Valladolid (Spain) †

Department of Pharmaceutical Sciences - IBSAL-CIETUS, University of Salamanca, Avda. Campo Charro s/n, 37071 Salamanca (Spain) §

Department of Pharmacology, Faculty of Medicine, University of Panama, Panama.

KEYWORDS: DFT, reaction kinetics, spectroscopic data, process simulation, real-time data, IR, titanocene, epoxides.

ABSTRACT: A novel DFT-based Reaction Kinetics (DFT-RK) simulation approach, employed in combination with realtime data from reaction monitoring instrumentation (like UV-Vis, FTIR, Raman and 2D NMR benchtop spectrometers), is shown to provide a detailed methodology for the analysis and design of complex synthetic chemistry schemes. As an example, it is applied to the opening of epoxides by titanocene in THF, a catalytic system with abundant experimental data available. Through a DFT-RK analysis of real-time IR data, we have developed a comprehensive mechanistic model that opens new perspectives to understand previous experiments. Although derived specifically from the opening of epoxides, the prediction capabilities of the model, built on elementary reactions, together with its practical side (reaction kinetics simulations of real experimental conditions) makes it a useful simulation tool for the design of new experiments, as well as for the conception and development of improved versions of the reagents. From the perspective of the methodology employed, since both the computational (DFT-RK) and the experimental (spectroscopic data) components can follow the time evolution of several species simultaneously, it is expected to provide a helpful tool for the study of complex systems in synthetic chemistry.

1. INTRODUCTION The purpose of this paper is twofold. It is above all meant to provide an example of how a suitable use of a Reaction Kinetics (RK) simulator, as a bridge between DFT calculations and real-time reaction data, can turn this triple combination (DFT, RK simulator, real-time data) into a helpful methodology for the analysis and design of complex reaction systems in synthetic chemistry. And, as an example, it also reports the development of a comprehensive model for the mechanisms involved in the catalytic opening of epoxides by titanocene in THF, including the role of additives and explicit solvent molecules. Section 2 discusses the rationale for the DFT-RK methodology. Section 3 describes the specific guidelines followed in the derivation of our proposed model for the system chosen as example. Readers interested only on the methodology can skip it and jump directly to Section 4,

that presents the results and discusses them to illustrate the advantages of DFT-based RK simulation versus the customary, separate use of DFT and RK simulations. 2. THE DFT-RK SIMULATION METHODOLOGY In synthetic chemistry, a commonly used DFT study consists on proposing a set of reaction mechanisms, Scheme 1, calculating the reaction barriers, Fig. 1, (or the rate constants) and verifying that all of the forward barriers are acceptable for the experimental temperatures. Such proposed scheme has often emerged, like in the example presented here, from a previous set of RPKA (Reaction Progress Kinetic Analysis) experiments, a methodology developed to extract maximum information from a minimal number of experiments designed to be mathematically independent, via graphical manipulations of time course data.1

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However, the fact that all forward barriers are low is not enough to guarantee that the model can account for the experimental observations. Namely, it is often essential to also take into account the reverse barriers and the nonequilibrium, time-varying concentrations throughout the course of the reaction, as it will be shown for the chosen example. Although in some cases the model is also tested through, for example, a series of initial rate experiments, delayed mechanisms like catalyst deactivation may still go unnoticed. Scheme 1. Proposed catalytic cycle, without Collidine Hydrochloride, including catalyst deactivation into L*THF (reactions r8 and r9).

If present, CollHCl obstructs, by steric hindrance, the attachment of THF to the L intermediate (r9), thus suppressing catalyst trapping.

In the DFT-based RK simulation approach, instead, the goal is to quantitatively verify that the experimental transients (Fig. 2) can be reproduced with the proposed model (Scheme 1) and calculated barriers (Fig. 1). In principle, this test can be done with a reaction kinetics simulator, although, as discussed next, not directly with the ‘raw’ DFT barrier values. To find a suitable use of DFT-based RK simulations, it is important to realize that, for example, at the experimental temperature of 60 ˚̊C (the example considered here), a change of approximately 1.5 kcal/mol in a free energy barrier changes the time constant by an order of magnitude. On the other hand, the mean unsigned error of B3LYP/631+G(d,p) for a set of barrier height calculations2 is 4.86 kcal/mol, and 0.64 kcal/mol for the best ab-initio method

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tested in the same benchmark study. Moreover, this sensitivity is expected to be amplified by the fact that the reactions are not isolated but interdependent. Therefore, prediction of experimental results with the accuracy of the simulations of Fig. 2 seems to be well beyond current computation capabilities. However, as shown in Fig. 1, different DFT methods can agree in the mechanisms and give similar barrier values, within a few kcal/mol. But, as it can be verified by RK simulations, none of them ‘as is’ is likely to reproduce the experimental transients at all (see, for example, Fig. S3).

Figure 1. Free energy path for the catalytic cycle of Scheme 1, with the RK-refined barrier values. For each reaction, the barriers from B3LYP-D3 and M06-2X are also overlapped to show that the RK-refined barriers lie within the range of the calculation uncertainties. M06-2X seems to overestimate the weak Ti-O coordination energy (at reactions r4 forward and r6 reverse).

A valuable use of the RK simulator emerges here: it can be employed to see whether it is possible to find a set of refined barrier values, within the uncertainty ranges of the DFT calculations, that can reproduce the transient experimental data. And if the set is found, since the model is built on elementary reaction mechanisms, it turns out to be a useful, predictive and detailed simulation tool. It could be argued that such a pragmatic approach (DFTRK) forsakes the rigorous DFT foundations on which it was built. But it is at least better than the common usage of DFT calculations, since it imposes more stringent, quantitative constraints (reproduction of the experimental data), in addition to the customary requirement of intuitively-assessed small forward barriers. Moreover, although it does not use a particular DFT set, it stays within the boundaries of the DFT basins. And finally, even if highly accurate barriers were available, their use would reveal the need to incorporate additional reactions with minor contributions,


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and require complex reaction schemes to reproduce the experimental data with the accuracy shown in Fig. 2. Instead, the DFT-based RK approach proposed here uses DFT to obtain a plausible initial guess for the barrier values, and then RK simulations to refine them, within the barrier basins, towards a set that can accurately reproduce the experimental data, including possible second order effects.

An analogous, DFT-based Kinetic Monte Carlo combined approach,4 is currently being used in the semiconductor industry through commercial atomistic process simulators.5 Although RK simulations are already being used to fit real-time reaction data to phenomenological models (see, for example, Ref. 6), to our knowledge this is the first time that they are based on DFT-derived, elementary reactions and barrier values. This feature is especially significant because, unlike the phenomenological models, each elementary reaction (single transition state) is directly correlated to specific molecules and the barriers can be estimated by DFT. In a phenomenological model, instead, it may be necessary to resort to the introduction of, for example, global pseudo-rate constants and apparent equilibrium constants, for comparison to experimental values. And then, detailed analysis of some experimental rate laws can be complicated by the reversibility of the reactions and differences in their reaction orders.6 Finally, since they are based on elementary reactions, DFT-RK simulations can provide a particular signature, like transient spectroscopic data, for each of the intervening species simultaneously, that can be directly correlated with experimental data, as it will be discussed for Fig. 4. This is a useful feature, especially for the study of complex systems. 3. DERIVATION OF THE REACTION SCHEME AND FREE ENERGY BARRIERS 3.1. Titanocene experimental background summary Over the last 25 years, titanocene monochloride (Cp2TiCl) and variants thereof, have proven to be a prolific family of reactants and catalysts in organic synthesis7. Cp2TiCl is commonly used as a mild single-electron-transfer stoichiometric reagent for the reductive opening of epoxides. Initially, both the titanocene dichloride and the metal reductant were used in stoichiometric amounts.8

Figure 2. Experimental data (symbols, from Ref. 10) and simulation (lines, [P] + [P*Cp2TiCl]) for two sets of experiments, without CollHCl (Exp1, Exp2) and with CollHCl (Exp3, Exp4), for two initial epoxide concentrations. Only 4 data points (large symbols) of Exp1 were used to adjust the 32-barrier DFTRK simulator.

Thus, although not the ideally perfect solution, it is a step forward in the direction suggested by Dirac’s recommendation (quoted by Cheng et al.3): ”It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation”. The RK simulations can be implemented typically in less than an hour and take only a few seconds run time on a laptop computer.

Later, Gansäuer et al.9 devised a method by which the reaction could be conducted with a catalytic amount of titanocene. To achieve protonation of the metal-oxygen bond, several mild acids were tested. Collidine hydrochloride (CollHCl) was the most efficient, yielding an almost complete conversion of substrate to product, and only a small fraction of unwanted chlorohydrin. Finally, a full atom-economical, catalytic radical arylation of epoxides was developed,10 Scheme S1, that in principle requires only the amount of a metal powder necessary for the initial reduction of the precatalyst. However, deactivation of catalyst under the reaction conditions were observed. The addition of CollHCl facilitated turnover and showed results consistent with constant concentration of catalyst. 3.2. Methods Details about computational calculations and numeric results are given in the Supporting Information. In short, the main DFT calculations presented here have been performed using Gaussian09-revD11 at the B3LYP/6-31+G(d,p)



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level, including the D3 dispersion-correction scheme12 with Becke-Johnson damping.13 Solvent effects are included through the SMD solvation model14. We have made extensive use of the SCW algorithm15 included in the GRRM package16 that provides quick, rough estimates of minimum energy reaction pathways between two minima. We have also verified that the mechanisms are reproduced using the M06-2X functional17 instead of B3LYP-D3, except that M06-2X seems to overestimate the Cp2TiCl*Epoxide coordination energy, as explained below. The reaction kinetics simulations have carried out with the biochemical system simulator COPASI.18 3.3. Modelling the catalytic cycle This study is a continuation of the computational work carried out by Gansäuer et al.19 on the catalytic system shown in Scheme S1. Our catalytic cycle without CollHCl is shown in Scheme 1. According to DFT calculations (S15), the epoxide forms a complex through interaction of its oxygen with the Ti of an approaching Cp2TiCl*THF complex (Scheme 1, reaction r3) replacing the THF coordination from the opposite side. For the last two steps of Scheme S1, and like Gansäuer et al.,19 we failed to obtain their proposed, high energy ‘C’ intermediate. However, there is a low energy pathway, for the H abstraction by the O atom, that goes directly from B to the product (r6). The generated product is initially in the form of a complex with a Cp2TiCl molecule, that is easily released back to a THF solvent molecule (r7, corresponding to the reverse of the epoxide entrance, r3), thus closing the catalytic cycle of Scheme 1. Calculations with the M06-2X functional (S54) confirm the model, yielding essentially the same results (Fig. 1) except for a remarkable discrepancy at the opening of the epoxide. Since, except for this barrier (and the analogous r6 reverse barrier), the rest of the barriers and all geometries are similar for both models, it seems that, at least in the present scenario, M06-2X overestimates the weak Ti-O coordination energy because, with its predicted epoxide opening barrier, the reaction would not be possible at this temperature. 3.4. Modelling catalyst deactivation So far, only the catalytic cycle of the model has been discussed. However, RPKA “same excess” experiments10 reveal catalyst deactivation and its suppression by the addition of collidine hydrochloride (Fig. 2). Correspondingly, the simulations shown in those figures have been performed with the full model, that is derived next. The product vs. time data of Fig. 2 correspond to the growth curve for the formation of product, by in-situ monitoring of the reaction by IR spectroscopy @ 1386 wavenumbers, for two experiments (for a detailed discussion of the experiments see Ref. 10): a 55 mM (Exp1) and a 27.5 mM (Exp2) initial concentration of epoxide, respectively. While Exp2 can be fit to a single exponential, Exp1 is the sum of two exponentials, corresponding to an initial, fast transient

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that changes to a slower one after a few minutes in the present conditions, suggesting catalyst deactivation. Fig. 2 also shows the corresponding experiments carried out with CollHCl: a dramatic speed-up effect and a single exponential is now observed in the high initial concentration experiment (Exp1, Exp3). We now proceed to discuss the modelling of this catalyst deactivation effect. As a suspect to account for the deactivation and associated turnover slowdown, it can be noticed that in the A intermediate (Scheme 1) the just generated radical could easily abstract the Cl atom (r8), delaying the reaction if it can reversibly return to Ti or blocking it otherwise. This radical abstraction mechanism, with H instead of Cl, has recently been observed by ENDOR spectroscopy for the Cp2TiH catalyst by the same group20. And a Cl atom, instead of H, at the radical site has also been reported for Cp2TiCl, for example, in the unwanted chlorohydrins9. In order to explain the experimental reaction orders, they propose20 the formation of a resting state of the catalyst that reversibly binds the epoxide substrate. However, the binding energy to THF is almost the same as to the epoxide, and the THF concentration is much higher. Therefore, although the epoxide has also a small contribution that accounts for the observed reaction orders, most of the catalyst should be trapped by THF, just as in reaction r9, Scheme 1. Addition of reactions r8, r9 completes the reaction system, including catalyst deactivation. Scheme 1 corresponds to a detailed implementation of a catalytic cycle with solvent inhibition (compare with the RPKA template for product inhibition, Scheme 6 in Ref. 1a). 3.5. Modelling the effect of Collidine Hydrochloride The final task for building the model was to find the role played by CollHCl to remove the delay, either by preventing the radical abstraction of Cl or by facilitating its prompt return to Ti. A CollHCl, Cp2TiCl complex has been reported10,19 (CollH+[Cp2TiCl2]-, Fig. S1) as the resting state of Cp2TiCl in the presence of CollHCl. However, when that geometry is energy minimized in the A*CollHCl intermediate, the Cl from CollHCl is rejected by the TiIV, already bonded to the other Cl and to the oxygen. Upon minimization, CollHCl remains with its Cl attached to the two cyclopentadienyls, and the para-methyl (or one of the meta-methyls) attached to the other Cl atom, as shown in Fig. S1. The energy of this A*CollHCl complex is 18.4 kcal/mol lower than the two, separate species (S94) and a similar geometry and binding energy (18.2 kcal/mol) results for the L*CollHCl complex. The A*CollHCl ↔ L*CollHCl reaction is also reversible with forward and reverse barriers (14 and 12 kcal/mol, S88) close to the 14.5 and 13 kcal/mol of the A ↔ L reaction (r8).The key point now is that, because of the steric hindrance provided by the CollHCl shield, THF has no access to Ti to form the trap-locking assembly, and the cycle can proceed without the L*THF catalyst trapping state (the equivalent of r9 is suppressed).


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To accurately assess the effect of CollHCl it would be necessary to carry out an additional DFT/RK study including the presence of CollHCl. However, a first glance can already be gained as follows. First, we realize that, unlike the previously reported CollH+[Cp2TiCl2]- complex, in the new one CollHCl does not interact directly with Ti and thus it does not interfere with its redox activity. As a test, in addition to the A↔L comparison with and without CollHCl mentioned above, we have verified that the barriers for A↔B change from 9.7/17.8 (r5) to 13.6/19.2 kcal/mol for the A*CollHCl↔B*CollHCl reaction, at B3LYP-D3/6-31G(d) level (S95). Because of the external position of CollHCl, the rest of the steps are similarly expected to be carried out with almost the same barrier values as without CollHCl. In the presence of CollHCl the final step would, therefore, release the product plus the Cp2TiCl*CollHCl complex, initially in an arrangement (labeled CpColl in Scheme 2) like Fig. S1(b). However, the energy of CollH+[Cp2TiCl2]is about 5 kcal/mol lower and the conversion barrier, estimated by SCW, is 10 kcal/mol (S9). Thus, with CollHCl the resting state is CollH+[Cp2TiCl2]-, in agreement with experimental cyclovoltammetry measurements10,21 and the previously proposed catalytic cycle, Scheme S1. In summary, the catalyst resting state, without CollHCl, is Cp2TiCl*THF and changes to CollH+[Cp2TiCl2]- upon addition of CollHCl.

(S106) correspond to lower experimental epoxide to product conversion and higher fraction of unwanted chlorohydrin. The recent finding23 that the Cp2Ti+ catalyst does not require an additive for catalyst stabilization is also in agreement with the present model, as a consequence of the lack of a radical-quenching atom, like Cl or H (besides possible cationic effects, that may have also contributed to an increased turnover). Barrero et al.24 report the opening and high yield cyclization of an epoxygermacrolide in THF, with Cp2TiCl but without CollHCl. Following the present model, in this case there is no need for CollHCl because of the low 6-endo cyclization barrier (r5, 4 kcal/mol, S101) compared to the barrier for radical Cl abstraction (r8, typically 10-15 kcal/mol). Scheme 2. Proposed full reaction system, including catalyst deactivation and the effect of CollHCl.

Table 1. Binding energy of pyridinium hydrochlorides, epoxide to product (E:P) conversion and fraction of unwanted chlorohydrin. L-bind Kcal/mol

E : P : Chlorohydrina

Coll-HCl

15.7

2 : 96 : 2

Lut-HCl

14.6

2 : 92 : 6

Pyr-HCl

10.8

50 : 4 : 46

acid

aFrom

Ref. 22

Therefore, as a first approximation, the presence of CollHCl can be incorporated by adding an analogous cycle with the same barriers as r3 through r7, plus the above described interaction between the two cycles (r11) and the resting state relaxation (r12), as represented in the full reaction system of Scheme 2. In addition, in other experiments9, the unwanted chlorohydrin (Z in Scheme 2, r10) could result from a final protonation step of L*THF by a pyridinium hydrochloride (Y*HCl in Scheme 2, r10) with inefficient THF shielding (low binding energy to Cp2TiCl), releasing also Cp2TiCl*THF and the corresponding pyridine. At the end of the experiment, upon removal of THF, the remaining L*THF is expected to follow the lowest barrier pathway from A, towards the product. This model is in agreement with experimental results for a set of pyridinium hydrochlorides22, including CollHCl. As Table 1 shows, lower calculated complex binding energies

4. RESULTS AND DISCUSSION 4.1. The proposed DFT model put to the test: RK simulations of real-time reaction data Up to this point, we have carried out the usual DFT study to derive the reaction system (Scheme 2) and its barrier values, representative of a typical synthetic chemistry problem. It could come from a homogeneous, heterogeneous or biomolecular system, as long as the involved steps are elementary reactions and there is a DFT-computable property that can be monitored in real-time. We have implemented the full reaction system of Scheme 2 within COPASI (see S10 for details and S13 for input file). In the present study, since we wanted to test the prediction capabilities of the DFT-RK approach, we have supplied only four experimental data points from one of the transients (Fig. 2, Exp1, large symbols) to the COPASI optimizer,



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and all the results of the present study have been obtained without any further experimental data input. Since the reference experiment (Exp1) is without CollHCl, only the barriers of reactions r3 through r9 can be refined. Barriers for r13 through r18 are assumed to be equal to their corresponding r3 through r8 (an approximation verified for two of them and discussed above), and the rest are taken as calculated from DFT. Starting from the B3LYP-D3 values, the r3-r9 barriers were refined with COPASI, within the uncertainty ranges (Fig. 1), to best reproduce the experimental data. After the optimization (Table S1), we have a DFT-RK simulator for the reaction system of Scheme 2 ready to be tested.

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Again, only one of the transients was used to refine the barriers. In other words, the elementary reaction scheme seems to be the fingerprint of the system and the ground for the prediction power of the approach and this might be a real value contributed by DFT, in addition to a first approximation to a valid barrier set. In view of these results, although this methodology only tests the plausibility of the proposed model and does not rule out other possible models, at least from a practical point of view, the DFT-RK simulator can be expected to be helpful for the analysis of experiments and the design of new ones.

To begin the test, Fig. 2 shows that the simulator reproduces the Exp1 two-exponential output. Exp2, with a lower initial concentration of epoxide, is predicted to follow a single exponential, close to the experimental data. Exp3 and Exp4 are the corresponding experiments with additive. The DFT-based simulator, that has not ‘seen’ any experiments with additive, predicts the drastic suppression of catalyst deactivation, especially for Exp1-Exp3. Table 2. Experimental data (from Ref. 10) and simulated results with the 4-point refined barrier set. Entry

[E]

Catalyst

Additive

M

% mol

% mol

1

0.1

10

-

2

0.1

5

3

0.1

4

0.5

t(min)

E:P

E:P

Exper.

Simul.

30

0:100

10:90

-

30

25:75

50:50

5

10

30

0:100

0:100

1

5

120

0:100

0:100

To further test the prediction capabilities of the simulator, Table 2 lists another four experiments (from Ref. 10) for varying concentrations of epoxide, catalyst and additive. Taking into account that, other than DFT, the only guidance to optimize such a simulator with 32 barrier values has been four experimental data points from a two-exponential curve, it can be concluded that DFT is playing a key role in the predictive character of this simulator. Although this methodology still needs to be more thoroughly tested it seems that such prediction capability, rather than from the specific set of barrier values, stems from the DFTderived reaction scheme, and it is easier for different DFT functionals to agree on this point. For example, for another system25, also with more than 30 barriers (Scheme S2), already the as-calculated barriers (at M06-2X/6-311+G(d,p) level of theory, taken from the same publication) predict almost the correct shape and yields for the simultaneous transients of several reagents and products, but on a timescale about 360 times faster (Fig. 3). At the temperature of the experiment, changes of only 2-3 kcal/mol in a few barriers were enough to bring the transients to the experimental timescale and reproduce the experimental curves.

Figure 3. Experimental data (symbols, from Ref. 25), simulation with the as-calculated barriers taken from Ref. 25 (dashed lines, timescale multiplied by 360 and shifted) and with the refined barriers (solid lines). Only the experimental data of ‘Yield of 2’ were used to refine the 36-barrier DFT-RK simulator.

4.2. Exploiting the simulator The DFT-RK approach has served so far to demonstrate that the Scheme 2 model can quantitatively account for the experimental observations (Fig. 2 and Table 2). And, as a result, it has also generated a DFT-RK simulator for this particular reaction system (S13). We can now exploit this simulator and assess how detailed the insight of the mechanisms achieved with it can be. Turning again to the experimental data and simulated results (Fig. 2), Exp1 is the only one that does not reach its final asymptotic value within the reported time span. Inspection of the simulated results for an extended period of time (Fig. 4) reveals that the epoxide supply (E curve) is almost exhausted by then, and a much slower rise of the product signal is predicted to begin at that time, corresponding to the release of L from the L*THF trapping state towards the lowest energy state, the product P. This was confirmed by using only the first half of the Exp1 data points: essentially the same prediction was obtained.


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performed by a reverse barrier, would go unnoticed in a DFT study where the only constraint for the validity of a model is that the forward barriers are small. Besides, this trapping mechanism is in agreement with the kinetic isotope effect experiments that suggest that the final proton transfer is not turnover-limiting19: the use of perdeuterated phenyl groups does not affect the trapping of catalyst by the product as P*CpColl.

Figure 4. RK simulation of Exp1 for an extended time span predicting a third, slower transient (beyond the experimental data range) due to the release of the epoxide trapped in the L*THF complex (r9).

There is also a striking difference between the fit achieved for Exp2 compared to the other three experiments (Fig. 2). Even though there are so many parameters that can be adjusted, the COPASI optimizer consistently yielded a low simulated value for Exp2, indicative of incomplete substrate to product conversion. If the optimizer is forced to reproduce Exp2, then the simulated Exp1 goes far above its experimental data, yielding a much worse overall fit to these two experiments. This suggests that the model can still be improved with some second-order interactions not yet included, like catalyst trapping by the epoxide in analogy to the resting state proposed in Ref. 20. Although to a lesser extent, this peculiarity of Exp2 is already present in the reported experimental data since the missing-product values for Exp1 to Exp4, from their fittings to exponentials10 are 0.53, 1.82, 0.41 and -0.42 mM, respectively. The simulation reveals that the missing product is still trapped in the form of L*THF complex, that has no contribution to the signal at the monitored wavelength (Fig. S6). However, if there were a spectral peak specific to L, then the model provides an additional prediction (the L*THF curve of Fig. 4) that could be verified experimentally. The turnover rate-limiting step is often sought by either DFT calculations (largest forward barrier) or by model experiments.19 In the present case, however, the RK simulations indicate that the rate-limiting step is the catalyst trapping in L*THF (without CollHCl) or in P*CpColl (with CollHCl). For example, the RK simulation of Exp4 (Fig. S4) reveals a substantial trapping of catalyst by the product P. Although, as proposed in Ref. 19 based on dedicated experiments, the turnover-limiting step with CollHCl is located between B and the released product, it seems to be due to the trapping of catalyst as P*CpColl and not to any large forward barrier. If, for instance, the reverse barrier of r7 is decreased by just 2 kcal/mol, the simulation predicts a drastic increase of trapping and a much longer reaction time scale (S13, point 10). This critical turnover control,

In a preliminary example of DFT used in combination with RK26, the experimental data available was limited (only some final yields, no transient data), and thus only poor constraints could be imposed to the many parameters (activation barriers) involved in the RK simulations. The present study, though, is a better example of how useful this computational-experimental methodology can be when it is combined with real-time transient reaction data. Even the example presented here is not yet the ideal case since we have used already available experimental data. A concerted, well-planned interaction between computation and experiment might lead to a livelier pace in synthetic chemistry research. It is worth to remark a peculiarity of the DFT-RK computational approach: the RK simulation output for ‘as-calculated’ DFT barrier values is meaningless (Fig. S3, and Fig. 3 with proper timescale). However, if supplemented with experimental, real-time data to be used as a reference, the RK-refined output not only reproduces the experimental data (Fig. 2 and Fig. 3) but it can also deliver helpful insight of the actual mechanisms contributing to the experimental observations (Fig. 4). From a practical point of view, the RK simulations can also save computation time and effort during the design of the model. For example, once the catalytic cycle (r3-r7) was developed, candidate reactions to account for catalyst deactivation, like r8 and r9, can be quickly implemented and tested by RK simulations. And, instead of intuitively guessed test barrier values, approximate ones can be obtained by SCW or other computational reaction discovery tools27, before embarking in the lengthy, and not always straightforward, task of finding the transition states. 5. CONCLUSION To summarize, this paper has presented a novel computational-experimental methodology for synthetic chemistry that seems useful for the study of complex reaction systems. As an example of application, it has been used to propose a comprehensive model for the catalytic opening of epoxides by Cp2TiCl in THF, including the experimentally observed catalyst deactivation and its suppression by the addition of collidine hydrochloride. Although derived specifically from the opening of epoxides, the emerging model has a broader range of applicability since it only relies on the catalyst structure and its generated radical site, and not on any feature of the substrate.



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Regarding the computational-experimental methodology employed, it is based on a thorough DFT-RK analysis of real-time spectroscopic data obtained, in this case, from reaction monitoring by IR spectroscopy. To our knowledge, this is the first time that this type of in-depth DFT-RK study has been applied to synthetic chemistry. A key to the success has been identifying an appropriate use of RK in order to provide a computationally inexpensive, direct bridge between fundamental DFT mechanisms and parameters, and detailed real-time experimental data. And, in principle, it could be applied to homogeneous, heterogeneous or biomolecular systems, as long as the involved steps are elementary reactions and there is a DFTcomputable property that can be monitored in real-time. Since both the computational (DFT-RK simulations) and the experimental (spectroscopic data) components of the proposed methodology can follow the time evolution of several species simultaneously, it is expected to be a useful tool for complex synthetic chemistry systems, as it has been showcased here for a well-established catalytic system.

ASSOCIATED CONTENT Supporting Information. Computational methods, COPASI input files, and results. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Authors [email protected] [email protected]

ACKNOWLEDGMENTS This work was supported by the Spanish Ministerio de Economía y Competitividad y Fondo Europeo de Desarrollo Regional (MINECO/FEDER) through projects CTQ201568148-C2-2-P, CTQ2015-64049-C3-3-R, and AGL2016-79813C2-2-R.

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A DFT-Based Computational-Experimental Methodology for

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