Design Platform for Sustainable Catalysis with Radicals: Electrochemical Activation of Cp₂TiCl₂ for Catalysis Unveiled

Graphical Abstract

What mechanism-based screening for titanocene catalysis is all about! Combining insights from synthesis and theory with cyclic voltammetry and the rotating ring disk electrode is the deal for understanding not only how but also why condition screening for the titanocene catalyzed radical arylation works.

Abstract

The combination of synthesis, rotating ring-disk electrode (RRDE) and cyclic voltammetry (CV) measurements, and computational investigations with the aid of DFT methods shows how a thiourea, a squaramide, and a bissulfonamide as additives affect the E_qC_r equilibrium of Cp₂TiCl₂. We have, for the first time, provided quantitative data for the E_qC_r equilibrium and have determined the stoichiometry of adduct formation of [Cp₂Ti(III)Cl₂]⁻, [Cp₂Ti(III)Cl] and [Cp₂Ti(IV)Cl₂] and the additives. By studying the structures of the complexes formed by DFT methods, we have established the Gibbs energies and enthalpies of complex formation as well as the adduct structures. The results not only demonstrate the correctness of our use of the E_qC_r equilibrium as predictor for sustainable catalysis. They are also a design platform for the development of novel additives in particular for enantioselective catalysis.

Introduction

Catalysis has shaped our modern society, providing functional molecules, materials, or processes both in the lab and on industrial scale. Substituting stoichiometric reactions by catalytic alternatives offers a conceptionally straightforward approach to a more sustainable, green chemistry.¹ However, as simple this idea may appear in principle, identifying the optimal catalytic conditions usually demands laborious experimental reaction screening through expensive use of workforce, material and laboratory time. To reinforce the sustainability claim of catalysis, we propose to identify mechanistic key aspects or so-called “predictors” before setting up any reaction, avoiding both the tour de force and even the designed experimental investigation of the overall catalytic reaction. With these mechanistic key features at hand, we can then predict the optimal catalytic reaction condition based on scientific arguments rather than our usual into the blue approach, so that ideally only a few experimental combinations need to be verified. These “predictors” require either the knowledge of the overall mechanism or at least an understanding of the essentials of the catalytic cycle. We chose to illustrate our “predictor” concept with the optimization of electrochemical epoxide arylation. It is only after we exploit widely used and readily available cyclic voltammetry (CV) and DFT techniques to identify the “predictors” of this reaction that we enter the synthesis lab to try our smart guess. For catalysis in single electron steps² or metalloradical catalysis,³ cyclic voltammetry (CV) is particularly an ideal screening technique because the metals shuttle between neighboring oxidation states. Here, we demonstrate that the E_qC_r equilibrium⁴ is a predictor for the performance of the electrochemical, titanocene catalyzed radical epoxide arylation, providing understanding of the catalyst formation by bulk electrolysis of precatalyst Cp₂TiCl₂ in THF (Scheme 1).⁵ For a successful electrochemical reduction of [Cp₂Ti(IV)Cl₂] the initial product of electron transfer [Cp₂Ti(III)Cl₂]⁻ at the electrode must be transformed into arylation catalyst [Cp₂Ti(III)Cl], that is—in contrast to [Cp₂Ti(III)Cl₂]⁻—easily soluble in THF and can diffuse from the electrode. Increasing the concentration of [Cp₂Ti(III)Cl] by halide abstraction from [Cp₂Ti(III)Cl₂]⁻ will therefore facilitate bulk electrolysis of [Cp₂Ti(IV)Cl₂]. While [Cp₂Ti(III)Cl] constitutes the active catalyst for epoxide arylation, [Cp₂Ti(III)Cl₂]⁻ provides a catalytic resting state, that prevents undesired catalyst decomposition.^6c

Scheme 1

Radical arylation after electrochemical activation (top) and E_qC_r equilibrium of Cp₂TiCl₂ (middle). L denotes anion receptors allowing a shift of the E_qC_r equilibrium by reversible cleaving of Cl⁻ through hydrogen bonding.

Adjusting the relative amounts of both species in a reversible way thus allows a fine-tuning of the performance of the catalytic system. It turned out that the E_qC_r equilibrium and therefore bulk electrolysis of [Cp₂Ti(IV)Cl₂] in THF can be controlled by the addition of supramolecular additives, that bind halides through hydrogen bonding.⁷ We show then that the control of the E_qC_r equilibrium directly translates into the synthetic performance of the catalytic radical arylation⁶ in THF.

Here, we demonstrate that our qualitative analysis of the cyclic voltammograms (CVs) of the E_qC_r equilibrium as predictor for the radical arylation is applicable to bissulfonamides as another class of supramolecular additives. Moreover, it is in accord with quantitative measurements at the rotating ring-disk electrode (RRDE).⁸ The combination of the experimental results with the DFT studies of the intermediates of the E_qC_r equilibrium delivers a complete mechanistic analysis of our predictor. Our study not only leads to a better understanding of the systems already investigated. It also delivers a design platform for the use of supramolecular halide binders in enantioselective catalysis and for their use with complexes of metals other than titanium.

Results and Discussion

Cyclic voltammetry and radical arylation

A critical aspect for efficient screening is a fast and cost-efficient technique for a conclusive description of the investigated system. In our case, CV⁹ is an ideal tool because the E_qC_r equilibrium includes an electron transfer step and involves species with different redox-potentials. CV not only allows a characterization of the components of a solution. Relevant data can be obtained in short periods of time and with minor amounts of material (0.02 mmol).

Our previous studies showed that thiourea L1¹⁰ and squaramide L2¹¹ (Scheme 1) are suitable additives for the bulk electrolysis of [Cp₂Ti(IV)Cl₂] in THF and the use of the resulting solutions for radical arylation. The CVs (L1: Figure 1; L2: Figure 2) highlight the reasons for this assessment. Compared to the CV of [Cp₂Ti(IV)Cl₂] without additives (black traces), the oxidation waves pertaining to [Cp₂Ti(III)Cl₂]⁻ have a reduced intensity and that of [Cp₂Ti(III)Cl] an increased intensity. This effect is significantly more pronounced for L2 than for L1. We assumed that these effects predict a successful bulk electrolysis and catalytic radical arylation.

Figure 1

CVs of 2 mm Cp₂TiCl₂ and L1 in 0.2 m Bu₄NPF₆/THF at 0.2 Vs⁻¹.

Figure 2

CVs of 2 mm Cp₂TiCl₂ and L2 in 0.2 m Bu₄NPF₆/THF at 0.2 Vs⁻¹.

Encouraged by these successes, we extended the screening to the bissulfonamide L3 (Scheme 2).¹² The CVs (Figure 3) demonstrate that the wave originating from [Cp₂Ti(III)Cl] is visible. This predicts that addition of L3 results in an efficient bulk electrolysis and a successful radical arylation (Table 1).

Scheme 2

H-bonding anion receptor L3 investigated as additive to amplify the E_qC_r mechanism of Cp₂TiCl₂.

Figure 3

CVs of 2 mm Cp₂TiCl₂ and L3 in 0.2 m Bu₄NPF₆/THF at 0.2 Vs⁻¹.

Table 1. Results of the arylation reaction after electrochemical activation in THF with Cp₂TiCl₂ as precatalyst and L1–L3 as additives.

• Reaction conditions: Catalyst Cp₂TiCl₂, additive L, 10 mm in THF, isolated yields.

The performance of the epoxide arylation⁷ with 1 and 10 mol % electrochemically reduced Cp₂TiCl₂ in the presence of 1 equiv. of L1–L3 with respect to Cp₂TiCl₂ is summarized in Table 1. In agreement with the lowest amount of [Cp₂Ti(III)Cl] observed in the CV-screening, L1 leads to the slowest reaction and lowest yield of 2. L2 and L3 lead to a more active catalytic system giving essentially identical results after 2 h.

Besides their usefulness as predictors, the CVs highlight an interesting complexity of interactions between L1–L3 and the titanocene species. On the reductive sweep (the lower trace) all ligands L form an adduct with [Cp₂Ti(IV)Cl₂]. This adduct has a more positive reduction potential with L1 and L2 (+160 mV) showing a larger shift than L3 (+80 mV). These differences in the potentials indicate a different strength of the interactions. On the oxidative sweep (the upper trace), for all additives a complex [Cp₂Ti(III)Cl₂]⁻*L can be detected. Again, the differences in the shift of the potentials are significant. Interestingly, only L2 and L3 seem to form complexes of the type [Cp₂Ti(III)Cl]*L. The shift of the potentials relative to [Cp₂Ti(III)Cl] suggest an electron-donating interaction for L3 (−120 mV) and an electron-withdrawing interaction for L2 (+110 mV).

Studies at the rotating ring-disk electrode

Our CV experiments are an ideal tool for the rapid screening of the additives. For a quantitative analysis, CV merely allows the direct extraction of the redox potentials of the species detected and their diffusion coefficients. More complex information on pre-equilibria or follow-up reactions can only be obtained via simulation. One general shortcoming of simulation is that, frequently, several models fit the experimental data. This is especially true for situations involving several steps and a large variety of fitting parameters. We decided to provide quantitative data for our qualitative observations made by CV. To this end, we used the rotating ring-disk electrode (RRDE).⁸ This allows assessing the results of future screening experiments on a more solid mechanistic basis.

The RRDE set-up offers major advantages over CV in stagnant solution. In CV, asymmetrically shaped current waves are observed. Therefore, “real” systems cannot be fitted to a physical equation. With a RRDE set-up this becomes possible as convection results in a time-independent and well-defined thickness of the Nernstian diffusion layer. It is composed of a disk and a ring electrode surrounding the disk. Rotation ensures a steady flow of reactants from the bulk solution to the disk. From here, the electrolyte is radially forced out to the ring and the species generated at the disk can be detected with a theoretical collection efficiency N₀. They can be discerned by their individual redox potentials. The currents measured due to their electrochemical reactions are proportional to their concentration at the electrode surfaces and allow quantitative analysis of the composition of the solution. For potentials negative of the equilibrium of a reduction at the disk, the currents reach a plateau representing the diffusion limited current I_lim and can be evaluated by the Levich equation (see Supporting Information).¹³

We started our RRDE measurements of Cp₂TiCl₂ in THF with 0.2 m NBu₄PF₆ (TBAPF₆). The data are in agreement with results of the Daasbjerg group^4c-4e by means of CV simulation (see Supporting Information) and show that RRDE measurements are well suited for analyzing electrochemical systems based on Cp₂TiCl₂. Based on Daasbjerg's work we propose an extended mesh-scheme for the species present in solutions of Cp₂TiCl₂ and our additives L (Scheme 3). The monomer–dimer equilibrium of [Cp₂Ti(III)Cl] is not observed in CVs with L and thus not relevant here.

Scheme 3

Proposed mesh-scheme for the Cp₂TiCl₂/L redox system (L = L1, L2 or L3).

The RRDE measurements will provide the equilibrium constants given in Scheme 3 and an estimate of the solution composition before and after reduction. We will discuss the experimental results for sulfonamide L3 and summarize the data for L1–L3 (detailed discussion see Supporting Information).

The stabilizing effect of L3 on [Cp₂Ti(III)Cl₂]⁻ can be observed directly from the positive shift of the voltammograms detected at the disk i_D and the decreasing transfer ratios (I_R/I_D/N₀) for measurements with Cp₂TiCl₂ and L3 at a rotation frequency f of 25 Hz and a ring potential E_R of 0.05 V (Figure 4, for measurements at f = 4 Hz and E_R = 0.23, 0.42 and 0.66 V see Supporting Information). A potential of 0.05 V vs. Ag/Ag⁺ solely allows the oxidation of [Cp₂Ti(III)Cl₂]⁻ (Figure 3, please note that the Fc⁺/Fc scale is shifted by ca. −1.1 V). Thus, only this species is detected at the ring.

Figure 4

Disk current densities i_D (a), normalized ring currents I_R/N₀ (b) and transfer ratios I_R/I_D/N₀ (c) of the RRDE measurements of a solution of 2 mm Cp₂TiCl₂ in 0.2 m NBu₄PF₆/THF with different concentrations of L3 at a ring potential E_R of 0.05 V and a rotation frequency f of 25 Hz.

L3 (10 mm, 5.0 equiv.) leads to a positive shift of the reduction potential and a slight decrease of i_D in the diffusion limited region at the disk electrode from −1.54 mA cm⁻² to −1.46 mA cm⁻² (Figure 4 a) and to a significant decrease of the normalized ring current I_R/N₀ by a factor of 4 (Figure 4 b). The transfer ratio, which is directly proportional to the concentration of [Cp₂Ti(III)Cl₂]⁻ in solution (Figure 4 c), decreases from 0.85 in the base electrolyte to 0.18 when adding 10 mm (5.0 equiv.) L3.

L3 (1 mm, 0.5 equiv.) leads to the formation of a shoulder in the disk current at −0.05V (Figure 4 a), which allows us to obtain equilibrium constant K_a (Scheme 3). The decreased diffusion-limited current at the disk indicates a reaction of [Cp₂Ti(IV)Cl₂] with L3 to [Cp₂Ti(IV)Cl₂]*L3 associated with a change of the diffusion coefficient prior to the electrochemical reaction. If the reaction of L3 occurred after the electrochemical reduction of [Cp₂Ti(IV)Cl₂], this should not have an impact on the diffusion-limited current.

According to the Levich equation, the limiting current density at the disk electrode is proportional to D^2/3 (D: diffusion coefficient) and to f^1/2. Figure 5b depicts the diffusion-limited i_D of [Cp₂Ti(IV)Cl₂] and with 10 mm of L3 alongside the shoulder current density found for the measurement of L3 (1 mm, 0.5 equiv.) as a function of f^1/2. The graphical representation of the data yields straight lines. The non-zero intercept of the line representing the shoulder currents indicates that the current flow is not solely limited by diffusion. Possibly the kinetics of the reduction of the unbound species already play a minor role. We assume that in the solutions with 10 mm of L approximately all [Cp₂Ti(IV)Cl₂] is bound to L. The different slopes observed for the experiments with base electrolyte and with 10 mm L3 yield the ratio of the diffusion coefficients of [Cp₂Ti(IV)Cl₂] and [Cp₂Ti(IV)Cl₂]*L3 according to the Levich equation. The diffusion coefficient D of [Cp₂Ti(IV)Cl₂] is 1.15 times larger than that of [Cp₂Ti(IV)Cl₂]*L3 (1.15 with L1 and 1.33 with L2). In the measurement with 1 mm L3 the diffusion-limited reduction of [Cp₂Ti(IV)Cl₂]*L3 is observed as a shoulder prior to the reduction of [Cp₂Ti(IV)Cl₂], as the reaction between [Cp₂Ti(IV)Cl₂] and L3 is incomplete. From the ratio of this shoulder to the subsequent plateau, the equilibrium constant of association K_a of L3 to [Cp₂Ti(IV)Cl₂] is accessible. With a value of 1.07 mm⁻¹, L3 lies between L1 (0.69 mm⁻¹) and L2 (1.81 mm⁻¹).

Figure 5

Cut-out of the RDE measurements shown in Figure 4 a (a) highlighting the shoulder in the 1 mm L3 measurement and diffusion limited current densities (b) at the disk i_D as a function of f^1/2 for Cp₂TiCl₂ and with 10 mm of L3 or 1 mm of L3 (shoulder). The slopes of the linear fits are given as m.

We studied the composition of the reduced solutions of Ti^III to obtain K₁ to K₃ (Scheme 3) by analyzing the effect of L on the transfer ratios (compare Figure 4 c). The fixed ring potential E_R allows the detection of all species that can be oxidized up to this potential. The step-wise increase of E_R afforded transfer ratios for [Cp₂Ti(III)Cl₂]⁻, [Cp₂Ti(III)Cl₂]⁻*L3, [Cp₂Ti(III)Cl] and [Cp₂Ti(III)Cl]*L3. These transfer ratios are shown in Figure 6 as a function of the concentration of L3.

Figure 6

Transfer ratios I_R/I_D/N₀ for the measurements of Cp₂TiCl₂ and L3 at different concentrations of L3 at ring potentials of 0.05, 0.23, 0.42 and 0.66 V and at a rotation frequency f of 25 Hz.

The transfer ratios allow the calculation of the equilibrium constants between the Ti^III species (see Supporting Information for details). The association equilibrium constant K₁ of L3 to [Cp₂Ti(III)Cl₂]⁻ amounts to 0.4 mm⁻¹ (2 mm⁻¹ for L1, 0.3 mm⁻¹ for L2). Dissociation of Cl⁻*L3 from [Cp₂Ti(III)Cl₂]⁻*L3 has an equilibrium constant K₂ of 3.0 mm (2.8 mm for L1, 54 mm for L2). The formation of [Cp₂Ti(III)Cl]*L3 has a K₃ of 0.7 mm⁻¹ (0.5 mm⁻¹ for L2). This adduct is not observed for L1.

For these equilibria we have assumed the formation of 1:1 adducts. The concentration-dependent measurements can verify this assumption. The voltammograms of i_D (Figure 4 a) show a gradual shift of the reduction potential starting from a concentration of 2 mm of L3. This implies that the Nernst equation for this redox process depends on the concentration of free L3. When plotting the half-wave potential E_1/2 against the decadic logarithm of the concentration of L3 (Figure 7) a linear relation with a slope m of roughly 60 mV dec⁻¹ at all rotation frequencies is obtained.

Figure 7

Plots of the half-wave potential E_1/2 of the RRDE measurements with Cp₂TiCl₂ and L3 as a function of the decadic logarithm of the concentration of L3.

Therefore, the Nernst equation for this redox system must be linearly dependent on log(c(L3)^p) with p representing the number of L3 ligands attached to the titanocene.¹⁴ With L1 the same slope of 60 mV dec⁻¹ was obtained showing that p is equal to 1. This verifies our initial assumption. The mechanisms of chloride abstraction from the Ti^III complexes and activation of the Ti^IV complexes are likely to be similar for L1 and L3.

For L2 a slope of 30 mV dec⁻¹ was observed (Figure 8). Thus, the redox potential is proportional to log(c(L2)^q) and q = p/2. Thus, we propose the reversible formation of a 2:1 adduct between [Cp₂Ti(III)Cl] and L2 in addition to the equilibria shown in Scheme 3. For the case that only this 2:1 adduct formation between [Cp₂Ti(III)Cl] and L2 is considered (in contrast to the 1:1 adduct considered for K₁ to K₃ given above) a new set of equilibrium constants for the Ti^III species has to be calculated (K₁’ = 0.2 mm⁻¹, K₂’ = K₂ = 54 mm, K₃’ = 0.1 mm⁻²). However, it is likely that both adducts are present in the reduced solutions.

Figure 8

Plots of the half-wave potential E_1/2 of the RRDE measurements with Cp₂TiCl₂ and L2 as a function of the decadic logarithm of the concentration of L2.

The equilibrium constants obtained from the RRDE-studies together with the relative amounts of the relevant Ti^IV (in red) and Ti^III species (in green) at concentrations of 2 mm in Ti and L are summarized in Scheme 4. [Cp₂Ti(IV)Cl₂] is complexed in 40 %–60 % amounts (red numbers) by L1–L3 with L2 being slightly more efficient than the other additives as indicated by the K_a values.

Scheme 4

Mesh-scheme for the Cp₂TiCl₂/L redox system (L = L1, L2 or L3) including the equilibrium constants obtained in the RRDE measurements and the solution composition in % [Ti^IV in red, Ti^III in green].

The additives L1–L3 have a stronger influence on the equilibria involving [Cp₂Ti(III)Cl]. In the presence of L2, essentially no [Cp₂Ti(III)Cl₂]⁻*L2 is formed because L2 binds Cl⁻ too strongly. Interestingly, L2 complexes [Cp₂Ti(III)Cl] less efficiently than L3 whereas L1 forms no [Cp₂Ti(III)Cl]*L1. As a result, the use of L2 results in the highest combined relative amount (77 %) of the catalytically active [Cp₂Ti(III)Cl] and [Cp₂Ti(III)Cl]*L2. For L1 and L3, the solution contains relatively high proportions of [Cp₂Ti(III)Cl₂]⁻*L and [Cp₂Ti(III)Cl₂]⁻ that constitute the resting state of the active catalyst. This situation may be advantageous when catalyst stability is more important than catalyst activity.

The RRDE investigations underline that our use of the E_qC_r equilibrium as predictor for the performance of the bulk electrolysis of Cp₂TiCl₂ in THF as well as for the titanocene catalyzed radical arylation of epoxides has a sound mechanistic basis. Moreover, the quantitative data obtained allow an accurate prediction of the composition of an electrochemically reduced solution of Cp₂TiCl₂ containing additives that is essential for a precise control of the reaction conditions. This may be essential for applications on large scale.

Density functional theory studies

To relate the data obtained from RRDE and CV measurements to molecular properties, we studied the structures and energies of the species involved in the E_qC_r equilibrium by DFT methods. The Grimme group has recently developed a powerful multilevel approach to address such situations. It consists of the CREST code¹⁵ for searching the low-energy chemical space by tight-binding semi-empirical theory based meta-dynamics (MTD) calculations (see Ref. 16). The resulting conformer ensemble is refined efficiently in multiple DFT steps with the ENSO code¹⁷ as a driver for ORCA or TURBOMOLE quantum chemistry packages.¹⁸ For a recent overview of the main xTB code used for the GFN tight-binding or force field calculations see Ref. 19.

Accordingly, we used the xTB, CREST and ENSO programs to determine the structures with the lowest free energy in THF solution for each ligand L and all complexes. These calculations were conducted in the same workflow. Manually prepared starting structures, which are initially preoptimized with the GFN2-xTB[GBSA] tight binding model are used in the CREST program that employs MTD at the same level in order to obtain a relative complete ensemble of likely structures. The ENSO program determines the equilibrium (Boltzmann) populations for a few low-lying conformers at higher theoretical levels in three steps. First, already relatively accurate B97-3c[DCOSMO-RS(THF)] (a composite low-cost DFT method²⁰) single point energies are calculated on the CREST ensemble. Structures within an energy threshold of 4 kcal mol⁻¹ above the lowest lying structure are then fully optimized at the same level. In this first filtering step thermostatistical free energies in the modified rigid-rotor/harmonic-oscillator (mRRHO) approximation²¹ calculated with GFN2-xTB[GBSA] and the free energy of solvation in THF calculated with the accurate COSMO-RS²² solvation model are added. Finally, for all structures within a 2 kcal mol⁻¹ threshold an even better single point energy is computed at the PW6B95-D3/def2-TZVPP²³ hybrid DFT level which basically replaces the corresponding B97-3c energy. In summary, the final complete total free energy used consists of the mRRHO part from the GFN2-xTB treatment, the COSMO-RS part in THF for solvation and the basic electronic energy with the PW6B95-D3 functional. In the following, the conformer of each species with the lowest total free energy is given, if not stated otherwise.

Structures of L and Cl⁻*L

We started our investigations with the ligands L and their chloride complexes Cl⁻*L. As free species, L2 shows higher conformational rigidity than L1 and L3 (for a detailed discussion see Supporting Information). The structures of the most stable conformers were chosen as reference points for the energies of formation of all other complexes. A potential self-aggregation of L2 in THF is beyond the scope of this study.²⁴

The structures of the Cl⁻*L and energies of complexation with respect to the lowest energy conformer of the respective L are depicted in Figure 9. Cl⁻ is bound to both N−H groups of all ligands. The Cl⁻*L complexes with L1 and L2 show C_2v symmetry. Cl⁻*L2 is conformationally rigid in agreement with its X-ray structure.²⁵ Cl⁻*L1 has a second conformer 4.6 kcal mol⁻¹ higher in energy than the one shown with one NHR group rotated by almost 180° and the other bound to Cl⁻. A second conformer of Cl⁻*L3 is 2.0 kcal mol⁻¹ higher in energy and has a similar structure to the one shown. In agreement with a previous study on the chloride binding of thioureas, squaramides and sulfonamides,¹² ΔG_298.15 for Cl⁻*L show that L2 binds chloride stronger than L1 and L3. As also pointed out in that study, the strength of chloride binding does not correlate with the pK_a values of the different receptors.

Figure 9

DFT structures of the Cl⁻*L adducts of L1, L2 and L3.

Supramolecular complexes of L and Ti^III

The supramolecular complexes [Cp₂Ti(III)Cl₂]⁻*L are crucial intermediates in the electrochemical generation of [Cp₂Ti(III)Cl] from [Cp₂Ti(IV)Cl₂]. They provide a mechanism for shifting the E_qC_r equilibrium to [Cp₂Ti(III)Cl] by facilitating chloride abstraction and dissolution of [Cp₂Ti(III)Cl₂]⁻*L. Another intriguing aspect is that binding of L to [Cp₂Ti(III)Cl] directly impacts the redox properties of [Ti] in the arylation reaction.

The structures of [Cp₂Ti(III)Cl₂]⁻*L together with the corresponding values for ΔG_298.15 and ΔH_298.15 are depicted in Figure 10 and reveal that L1 and L2 bind both chloride ligands with the N−H groups, providing complexes that are C₂-symmetric within the limits of accuracy. This is exemplified by the Ti-Cl bond lengths ([Cp₂Ti(III)Cl₂]⁻*L1: 2.545 Å and 2.540 Å, [Cp₂Ti(III)Cl₂]⁻*L2: 2.547 Å and 2.550 Å).

Figure 10

DFT structures of the [Cp₂Ti(III)Cl₂]⁻*L adducts of L1, L2 and L3.

Curiously, for L3 a binding of both N−H groups was not observed. In the more stable complex (Figure 10, lowest structure) L3 only binds to one of the chloride ligands with one N−H group (Ti−Cl bond lengths: 2.53 Å and 2.50 Å). In the second most stable complex (3rd structure from the top of Figure 10), both N−H groups coordinate to one chloride in a “side-on” geometry. This results in distinctly different Ti−Cl bond lengths (2.59 Å and 2.49 Å). Enthalpically, the less stable complex is slightly favored (ΔH_298.15 = −5.3 vs. −4.6 kcal mol⁻¹). However, the entropically disfavored restriction of conformational freedom in this binding mode is the more relevant contribution to ΔG_298.15. According to the values for ΔG_298.15, the binding via both N−H and Ti−Cl groups by L1 and L2 results in a stronger binding of [Cp₂Ti(III)Cl₂]⁻.

According to the CV and RRDE measurements, L1 does not bind to [Cp₂Ti(III)Cl] whereas both L2 and L3 do. However, they bind in a different fashion as evident from the shifted oxidation potentials for [Cp₂Ti(III)Cl]*L (L2: +110 mV, L3: −120 mV). We analyzed the complex formation starting from [Cp₂Ti(III)Cl] and L and included the effect of additional coordination with THF (Figure 11, also see Supporting Information).

Figure 11

DFT structures of the [Cp₂Ti(III)Cl](THF)*L adducts of L1 and L2 and of [Cp₂Ti(III)Cl]*L3.

L1 and L2 display a similar complexation behavior. Adduct formation is substantially more favorable with [Cp₂Ti(III)Cl](THF). As for [Cp₂Ti(III)Cl₂]⁻ both additives bind the chloride ligand with both N−H groups. Adduct formation is disfavored with L1. This is in agreement with the experiment, where no [Cp₂Ti(III)Cl]*L1 was observed. The interaction of L2 with the chloride ligand leads to an increase of the Ti−Cl bond length by 0.13 Å. This is in agreement with the experimentally observed positive shift of the redox potential.

The situation is different for L3. The favored complexation mode is realized with [Cp₂Ti(III)Cl] as starting material. This is due to an intramolecular interaction of one of the sulfonamide groups with Ti that renders an additional complexation of THF superfluous. The coordination of the sulfonamide increases the electron density at Ti in agreement with the experimentally observed negative shift in the redox potential for [Cp₂Ti(III)Cl]*L3. Only the adjacent N−H group binds to the chloride ligand.

The slope of 30 mV dec⁻¹ in the RRDE measurements with L2 (Figure 8) suggests that a 2:1 stoichiometry of [Cp₂Ti(III)Cl] and L2 in the adduct formation is possible. The computed structure of the 2:1 complex with one molecule of THF and its ΔG_298.15 and ΔH_298.15 with respect to the dissociated species are depicted in Figure 12. Complex formation without THF is distinctly less favorable.

Figure 12

DFT structure of the ([Cp₂Ti(III)Cl])₂(THF)*L2 adduct.

Enthalpically, complex formation is strongly favored and the slightly positive ΔG_298.15 is due to the entropically disadvantageous formation of the complex from four components.

L2 binds the second titanocene through one of the carbonyl oxygens. At the same time, the N−H groups each bind to one of the chloride ligands of both titanocenes. This makes L2 a bifunctional ligand and provides an explanation for the broad oxidation wave in the area of Cp₂TiCl found in CVs of Cp₂TiCl₂ and L2. On the oxidative sweep ([Cp₂Ti(III)Cl])₂*L2 is oxidized first followed by [Cp₂Ti(III)Cl] and finally [Cp₂Ti(III)Cl]*L2.

Supramolecular complexes of L and Ti^IV

Finally, we investigated the adduct formation between [Cp₂Ti(IV)Cl₂] and L. This pre-equilibrium to the E_qC_r mechanism allows the use of a less negative reduction potential in bulk electrolysis (−1.3 V vs. Ag/Ag⁺ with L2, −1.4 V with L1 and L3). Figure 13 shows the structures of the hydrogen bonded adducts between [Cp₂Ti(IV)Cl₂] and L1–L3. For L2, the minimum structure of [Cp₂Ti(IV)Cl₂]*L2 is a van der Waals complex that is 0.3 kcal mol⁻¹ more stable than the complex shown (see Supporting Information for details). It is not discussed here, as it does not suggest a positive shift of the reduction potential.

Figure 13

DFT structures of the [Cp₂Ti(IV)Cl₂]*L adducts of L1, L2 and L3.

Compared to the complexes of [Cp₂Ti(III)Cl₂]⁻*L the formation of the adducts of [Cp₂Ti(IV)Cl₂]*L is less favorable. The calculated structures show that with the neutral Ti^IV complex only L2 can interact with both N−H groups. However, they both bind to the same chloride ligand. In the adducts of L1 and L3 only one of the N−H groups is coordinating chloride, the other is pointing away from the complex resulting in a noticeable conformational change of the additive.

The computed order of stability of the adducts is in agreement with the stronger binding affinity of L2 to [Cp₂Ti(IV)Cl₂] observed in the RRDE measurements.

The lower stability of [Cp₂Ti(IV)Cl₂]*L compared to [Cp₂Ti(III)Cl₂]⁻*L is most easily rationalized by the negative charge in [Cp₂Ti(III)Cl₂]⁻ that renders hydrogen bonding more attractive because of the coulomb attraction. We investigated this point by analyzing the exchange reactions shown in Scheme 5. The effect of the charge is indeed substantial as highlighted by the highly exergonic formation of the [Cp₂Ti(III)Cl₂]⁻*L adducts from their [Cp₂Ti(IV)Cl₂]*L counterparts.

Scheme 5

Gibbs energies of the exchange reaction between [Cp₂Ti(IV)Cl₂]*L and [Cp₂Ti(III)Cl₂]⁻.

Conclusions

In summary, we have demonstrated that our approach of screening the E_qC_r equilibrium as predictor for the bulk electrolysis of Cp₂TiCl₂ in THF and the titanocene catalyzed radical arylation of epoxides has a sound mechanistic basis. This was achieved by a combination of synthesis, the application of the electrochemical techniques cyclic voltammetry (CV) and rotating ring-disk electrode (RRDE) measurements, as well as DFT investigations.

We have introduced bissulfonamides as additives for enabling bulk electrolysis of Cp₂TiCl₂ in THF as well as for the titanocene catalyzed radical arylation of epoxides. For the first time, we have provided quantitative data about the E_qC_r equilibrium in the presence of a thiourea, a squaramide and a bissulfonamide and have established the stoichiometry of adduct formations between [Cp₂Ti(III)Cl₂]⁻, [Cp₂Ti(III)Cl] and [Cp₂Ti(IV)Cl₂]. By studying the complexes by DFT methods, we have provided the Gibbs energies and enthalpies of complexation as well as the adduct structures. Our studies show that a balance between activity and stability of the catalyst are vital for reaction efficiency. Changing the inorganic ligand of Cp₂TiX₂ was not investigated here. Previous investigations⁵ have shown that for Cp₂TiBr₂ derived catalysts halide abstraction is easier than for complexes derived from Cp₂TiCl₂. The intricate interactions between the additives and the titanocenes by hydrogen bonding and coordination of polar groups are not only in agreement with the electrochemical data. They also provide a design platform for the development of novel additives for catalysis in single electron steps²⁶ or metalloradical catalysis²⁷ in particular in enantioselective catalysis.

Acknowledgements

We thank the DFG (Ga 619/13-1), the “Jürgen Manchot Stiftung” (T.H.), the “Studienstiftung des deutschen Volkes” (S.K. and P.H.R.), and the “Evangelisches Studienwerk Villigst” (T.L.) Open access funding enabled and organized by Projekt DEAL.

Conflict of interest

The authors declare no conflict of interest.