Exchange Speed of Four-Component Nanorotors Correlates with Hammett Substituent Constants ^†

Abstract

Three distinct four-component supramolecular nanorotors were prepared, using, for the first time, bipyridine instead of phenanthroline stations in the stator. Following our established self-sorting protocol to multicomponent nanodevices, the nanorotors were self-assembled by mixing the stator, rotators with various pyridine head groups, copper(I) ions and 1,4-diazabicyclo[2.2.2]octane (DABCO). Whereas the exchange of a phenanthroline vs. a bipyridine station did not entail significant changes in the rotational exchange frequency, the para-substituents at the pyridine head group of the rotator had drastic consequences on the speed: 4-OMe (k₂₉₈ = 35 kHz), 4-H (k₂₉₈ = 77 kHz) and 4-NO₂ (k₂₉₈ = 843 kHz). The exchange frequency (log k) showed an excellent linear correlation with both the Hammett substituent constants and log K of the copper(I)–ligand interaction, proving that rotator–copper(I) bond cleavage is the key determining factor in the rate-determining step.

1. Introduction

Over the years, researchers have been probing numerous techniques to mimic the function of biological machines, such as ATP synthase [1,2], bacterial flagella [3], histidine kinase [4], etc. During the iterative and systematic optimization of manmade motors [5,6,7], increasingly better design strategies have been identified to implement intricate movements and various functions derived therefrom [8,9,10,11]. Thus, significant progress has been achieved, for instance, in the field of molecular rotors [12,13,14,15,16,17], gears [18,19,20,21], pumps [22,23,24], walkers [25,26,27] and caterpillars [28].

To mimic nature’s strategy even closer, one has to realize that life preferentially uses multicomponent assembly for building biological machines. Such approach requires a careful balance of weak interactions that allow for sufficient spatiotemporal binding between components during motion. It is unsurprising that, in the arena of artificial multicomponent devices [29,30,31], examples with sophisticated dynamic motion are still scarce [32]. Because in multicomponent devices the exchange of a single component may lead to drastically different properties, fundamental insights are needed in how structural and electronic variations will impact on the kinetics of motion.

Herein, we demonstrate that speed changes in four-component nanorotors by exclusively varying the rotator head group are linearly correlated with Hammett substituent constants. Whereas Hammett correlations are abundant for describing kinetic reactivity and thermodynamic properties of organic compounds [33], analogous correlations with supramolecular devices remain largely unexplored [34,35,36], possibly because many of the design strategies are not robust enough to tolerate larger electronic and steric changes. Although at first glance these results appear marginal, they furnish a tool to precisely predict and tune the frequency of such four-component rotors that, as we know, are catalytic machinery, where the machine speed determines the rate of catalysis [37].

The family of four-component nanorotors [38] has demonstrated, in our hands, great potential in various fields of application, ranging from catalysis [33] to molecular logic [39]. Till now, several strategies to change the rotational frequency have been explored, including adding external brake stones [40,41], changing the flexibility of the rotator arm [42], changing the number of binding sites [33] and adding nucleophilic additives [43]. All of these studies corroborated our initial hypothesis that the rate-determining step depended on the ligand–metal dissociation. Therefore, the kinetic behavior (rotational frequency of the nanorotor) should correlate with thermodynamic data (binding constant of the metal complex). The present work now sought to establish a quantitative relationship by using the well-known Hammett equation as a link between thermodynamic and kinetics. Undoubtedly, the Hammett equation [44] is known as the most important member of a large amount of linear free energy relationships (LFERs) [45].

The four-component nanorotors of this study (Figure 1) were assembled by following our established self-sorting protocol, by combining rotators 1–3 (with various pyridine head groups), stators 4 and 5, copper(I) ions and 1,4-diazabicyclo[2.2.2] octane (DABCO). In this process, the zinc porphyrin units from the stator and rotator are linked by DABCO, in a hetero-sandwich complex, whereas the copper(I)-filled phenanthroline sites of the stator are additionally connected to the pyridine nitrogen of the rotator (see, for instance, [Cu₂(1)(4)(DABCO)]²⁺) (Figure 1b). The rotators were designed in a way so as to enable electronic influence of the para-substituent onto the pyridine head group that is bound to the copper(I) ion sitting in the diimine station of the stator. Since, in the rate-determining step, the N_py→[Cu(diimine)]⁺ linkage has to be cleaved, the donor and acceptor qualities of the para-substituent were expected to impact on the exchange frequency.

Both bipyridine and phenanthroline have been amply used as bidentate ligands in supramolecular and coordination chemistry. Compared with phenanthroline, the bipyridine shows less binding strength with metal ions, but higher flexibility for complex reorganization [46]. At the onset, we wanted to evaluate the importance of the flexibility of the bipyridine binding site onto the exchange kinetics of the rotor.

2. Materials and Methods

2.1. Synthesis

Four nanorotors were synthesized by combining one of the three rotator ligands 1–3 with one of the stators 4 and 5: ROT-1a’ = [Cu₂(1)(4)(DABCO)]²⁺, ROT-1b’ = [Cu₂(1)(5)(DABCO)]²⁺, ROT-2′ = [Cu₂(2)(4)(DABCO)]²⁺ and ROT-3′ = [Cu₂(3)(4)(DABCO)]²⁺. For better characterization, equally, the static precursor assemblies containing only one copper(I) ion, here denoted as prerotors, were prepared: ROT-1a = [Cu(1)(4)(DABCO)]⁺, ROT-1b = [Cu(1)(5)(DABCO)]⁺, ROT-2 = [Cu(2)(4)(DABCO)]⁺ and ROT-3 = [Cu(3)(4)(DABCO)]⁺. All compounds and complexes were characterized by ¹H-NMR, ¹³C NMR, mass spectroscopy and elemental analysis (see Supplementary Materials).

2.2. Determination of Binding Constants

UV–Vis titrations were analyzed by fitting the recorded spectra at 0.5 nm intervals, using the SPECFIT^® global analysis system by Spectrum Software Associates (Marlborough, MA, USA) [47]. The SPECFIT^® program analyzes equilibrium datasets with the help of singular value decomposition and linear regression modeling by the Levenberg–Marquardt method, to determine cumulative binding constants.

2.3. NMR Simulation

A conventional dynamic NMR spectroscopic method [48] based on a model involving a two-spin system undergoing mutual exchange was applied to simulate the spectra and determine the exchange frequency. The NMR signal used for the simulation is indicated in the corresponding spectra by an asterisk (*). The exchange frequency that is identical with the rotational frequency was obtained from an analysis of the exchange-broadened NMR signal of proton 16-H of the stator. Activation enthalpy (ΔH^‡) and activation entropy (ΔS^‡) were determined from transition state theory. The temperature-dependent rate constants of the rotors were fitted to the Eyring equation [49]:

k = (k_BT/h)e^−ΔG‡/RT,

(1)

ln(k/T) = − ΔH^‡/RT + ln(k_B/h) + ΔS^‡/R

(2)

3. Results

3.1. Design

Previous work about Hammett correlations has mainly focused on mono-substituted aromatic systems, e.g., in equilibria and in fundamental reactions, like hydrolysis of esters, etc. [33]. However, in our rotator’s design, the pyridine head groups are disubstituted due to connections to the arm and the probing substituent. It is advisable to attach the rotator’s arm in the meta position of the pyridine, to minimize any steric hindrance in the HETPYP (heteroleptic pyridine and phenanthroline) [50] complexation to the copper(I) phenanthroline site.

To check whether the Hammett equation applies to the Lewis acid–base interaction of pyridine (N_py) → [Cu(bipyAr₂)]⁺, the copper(I)-loaded 6,6′-dimesityl-2,2′-bipyridine [Cu(bipyAr₂)]⁺, here C1 = [Cu(6)]⁺, and its complexes with substituted pyridines N_py → [Cu(bipyAr₂)] were studied. As in other HETPYP complexes [50], the steric shielding about the bipyAr₂ effectively prevents formation of homoleptic copper bipyridine complexes [Cu(bipyAr₂)₂]⁺. To quantitatively prepare complex C1, [Cu(CH₃CN)₄](PF₆) and 6 (1:1) were simply mixed in CH₂Cl₂. The 3-bromo-4-X-pyridine ligands 8–10 were titrated with a standard solution of C1 = [Cu(6)]⁺ in CH₂Cl₂ and the binding isotherms were determined by UV–Vis spectroscopy (Figures S58–S60). For comparison, the copper(I)-loaded phenanthroline C5 = [Cu(7)]⁺ was titrated with ligand 8, for determining the binding constant in C6 (Figure S61). The Gibbs free energy, ΔG₂₉₈, of C2, C3, C4 and C6 was calculated based on the binding constants (

Table 1. Substituent constants, binding constants and Gibbs free energy of C2–C4 and C6, as determined from UV–Vis titrations.

Motifs	4-X a	σp	log K	ΔG298 (kJ mol−1)
C2 = [Cu(6)(8)]+	OMe	−0.268	4.59	−26.2
C3 = [Cu(6)(9)]+	NO2	0.778	2.93	−16.7
C4 = [Cu(6)(10)]+	H	0.000	4.10	−23.4
C6 = [Cu(7)(8)]+	OMe	−0.268	4.63	−26.4

^a Substituent at 4-position of the pyridine head groups.

). Both log K and ΔG₂₉₈ show a linear correlation with σ_p (Figure 2).

3.2. Synthesis and Characterization of Four-Component Nanorotors

The strong correlation between σ_p and log K encouraged us to prepare the four-component nanorotors based on the above design of the head group. In this regard, the substituted pyridine rotators 1–3 were synthesized by Sonogashira coupling of zinc(II)-5-(4-ethynylphenyl)-10,15,20-trimesitylporphyrin (11) with 8, 9 and 10, as shown in Scheme 1.

The new bipyridine stator 4 was afforded in six steps, as outlined in Scheme 2. First, the bipyridine binding site was separately prepared in two steps: Suzuki–Miyaura coupling between 6,6′-dibromo-2,2′-bipyridine (12) and mesitylene-2-boronic acid (13)–furnished 6-bromo-6′-mesityl-2,2′-bipyridine (16) in 75% yield. On the other hand, nucleophilic substitution at isopropoxyboronic acid pinacol (15), using the lithiated species obtained from 1-iodo-2,3,5,6-tetramethyl-4-[2-(trimethylsilyl)ethynyl]-benzene (14), furnished compound 17. Thereafter, Suzuki–Miyaura coupling between 16 and 17 yielded product 18. A follow-up deprotection of the TMS-alkyne unit in the presence of NaCO₃ provided 19 in good yield. After Sonogashira coupling between 19 and zinc(II)-meso-5,15-bismesityl-10,20-bis(4-iodophenyl)porphyrin (20), the stator 4 was afforded in 45% yield (over five steps). The new ligands 1–4 were characterized unambiguously by NMR, ESI-MS, IR and elemental analysis (see Supplementary Materials).

To prepare the prerotor ROT-1a = [Cu(1)(4)(DABCO)]⁺ (Figure 3), rotator 1 was mixed with stator 4, DABCO and [Cu(CH₃CN)₄](PF₆) (1:1:1:1) in CD₂Cl₂. The ¹H NMR displayed two singlets (1:1 ratio) for protons of the bipyridine–mesityl unit, e.g., for 9-H at 7.01 and 6.92 ppm and 16-H at 2.38 and 2.33 ppm (Figure 3a). All bipyridine protons (3-H, 4-H, 5-H, 6-H, 7-H and 8-H) showed up as two sets of signals (1:1 ratio) as well. For protons [3/8]-H, the downfield-shifted set of signals corresponded to that of the coordinated bipyridine station, i.e., N_py → [Cu(bipyAr₂)]⁺, while the upfield signals originated from the unloaded bipyAr₂ (Figure S15). Two sets of broad singlets at −4.45 and −4.54 ppm, corresponding to the DABCO protons, confirmed that DABCO acted as a hinge between the two different zinc porphyrins, 1 and 4. The ¹H NMR shifts, thus, clearly confirmed formation of ROT-1a as a hetero-sandwich structure. ¹H-¹H COSY, ESI-MS, and elemental analysis further supported the assignment.

After the addition of one further equivalent of [Cu(CH₃CN)₄](PF₆) to ROT-1a, the resulting ROT-1a’ = [Cu₂(1)(4)(DABCO)]²⁺ exhibited averaged signals for protons 9-H and 16-H (Figure 3b), as well as for all other bipyridine protons (Figure S17). Eventually the ¹H-DOSY corroborated ROT-1a’ as a single species in solution (Figure S39). The dynamic behavior in the nanorotor was monitored by variable temperature (VT) ¹H NMR, in the range from 25 to −75 °C in CD₂Cl₂ (Figure 3c). During cooling, the signal of proton 16-H transformed from a sharp singlet at 25 °C (2.34 ppm) to a broad singlet at −25 °C (2.31 ppm) and then split into two singlets at −40 °C (2.32 and 2.27 ppm). These two singlets were assigned to the copper(I)-loaded bipyridine stations that were either connected to the pyridine terminal or not. The rotational frequency of the rotor was determined by simulation of the proton 16-H signal, using the WinD-NMR (Department of Chemistry, University of Wisconsin, Madison, WI, USA) software to k₂₉₈ = 3.5 × 10⁴ Hz at 25 °C and the corresponding free energy activation barrier to ΔG^‡₂₉₈ = 47.1 kJ mol⁻¹ (Figure S32).

Preparation of the prerotors ROT-1b = [Cu(1)(5)(DABCO)]⁺, ROT-2 = [Cu(2)(4)(DABCO)]⁺ and ROT-3 = [Cu(3)(4)(DABCO)]⁺ were accomplished in a similar manner as that of ROT-1a. Addition of one equiv of [Cu(CH₃CN)₄]PF₆ to ROT-1b, ROT-2 or ROT-3 afforded rotors ROT-1b’ = [Cu₂(1)(5)(DABCO)]²⁺, ROT-2′ = [Cu₂(2)(4)(DABCO)]²⁺ and ROT-3′ = [Cu₂(3)(4)(DABCO)]²⁺, respectively. Analysis of the VT ¹H NMR (Figures S31–S38) revealed an exchange frequency at 298 K of k₂₉₈ = 2.0 × 10⁴ Hz and activation free energy barrier ΔG^‡₂₉₈ = 48.6 kJ mol⁻¹ for ROT-1b’; k₂₉₈ = 8.4 × 10⁵ Hz, ΔG^‡₂₉₈ = 39.2 kJ mol⁻¹ for ROT-2′; and k₂₉₈ = 7.7 × 10⁴ Hz, ΔG^‡₂₉₈ = 45.2 kJ mol⁻¹ for ROT-3′. The rotational frequencies of the nanorotors showed significant differences (

Table 2. Experimental rotational frequency and activation barriers at 25 °C, as calculated from VT ¹H NMR.

Nanorotor	4-X	ΔG‡298 (kJ mol−1)	k298 (Hz)	log k
ROT-1a’	4-OMe	47.1	3.5 × 104	4.55
ROT-1b’	4-OMe	48.6	2.0 × 104	4.30
ROT-2′	4-NO2	39.2	8.4 × 105	5.93
ROT-3′	4-H	45.2	7.7 × 104	4.88

).

4. Discussion

4.1. Bipyridine vs. Phenanthroline Stator in Nanorotors

By comparing ROT-1a’ with ROT-1b’, the rotational frequency difference between bipyridine stator and phenanthroline stator turned out to be rather small (k₂₉₈ of ROT-1a’ and ROT-1b’ = 3.5 × 10⁴ Hz and 2.0 × 10⁴ Hz, respectively). The coalescence temperature of ROT-1a’ and ROT-1b’ in the VT ¹H-NMR was also located in the same range, around −25 °C. The similar binding constant of C2 and C6 is in full agreement with the kinetic finding.

The minor rate difference between the two rotors suggests that it is mainly the pyridine → copper(I) interaction that matters in the rate-determining step. As one would expect on the basis of the higher flexibility of the bipyridine ligand, ROT-1a’ (bipyridine station) rotates a little bit faster than ROT-1b’. We assume that the bipyridine ligand is more apt to adjust to the distortions at the chelate binding site in the transition state [42,43].

4.2. Hammett Equation Applies to Rotational Exchange in Nanorotors

The plot of the nanorotors’ rotational frequency log k/k_H and of ΔG^‡₂₉₈ of ROT-1a’, ROT-2′ and ROT-3′ against σ_p revealed a linear correlation (Figure 4a), indicating that the electronic effect of the para-substituent is the major contributing factor in the rate-determining step and that other effects are negligible. Due to the aforementioned linear relationship between log K/K_H of complex formation for C1, C2 and C3 and σ_p, a linear free energy relationship (LFER) between thermodynamic and kinetic data was established (Figure 4b), suggesting that the Hammett equation can directly be used for predicting the rotational frequency in nanorotors with other para-substituents.

log k/k_H = 0.27 σ_p + 1.00 (R² = 0.9997)

(3)

ΔG^‡₂₉₈ (kJ mol⁻¹) = −7.59 σ_p + 45.12 (R² = 0.9997)

(4)

log k₂₉₈ = −0.84 log K + 8.39 (R² = 0.9964)

(5)

One therefore expects that substituents like 4-NMe₂ (σ_p = −0.600) and 4-NMe₃⁺ (σ_p = 0.860) would result in extreme cases of the rotational frequency. By using the correlation log k₂₉₈ = 1.33 σ_p + 4.89 (Figure S62) for the rotor with the rotator head 4-NMe₂, we would expect log k₂₉₈ = 4.09, k₂₉₈ = 1.2 × 10⁴ s⁻¹ and ΔG^‡₂₉₈ = 51.7 kJ mol⁻¹, whereas, for that with rotator head 4-NMe₃⁺, the expected kinetic data are log k₂₉₈ = 6.03, k₂₉₈ = 1.1 × 10⁶ s⁻¹ and ΔG^‡₂₉₈ = 38.6 kJ mol⁻¹.

5. Conclusions

In conclusion, we herein presented a small series of four-component nanorotors for evaluating conformational and electronic effects on their rotational exchange frequency. Whereas the effect of higher flexibility at the bipyridine vs. phenanthroline binding site in the stator was rather small (less than a factor of 2), the variation of the electronic character of substituents in the para-position of the pyridine head group in the rotator led to distinct differences in rotational speed (almost 25-fold). The rotational speed, as well as the Gibbs free activation energy, shows excellent linear correlation with the Hammett substituent constant. Based on the Hammett equation, the rotational frequency of any analogously substituted nanorotor can be predicted, resulting in a 100-fold change of the exchange frequency (from -NMe₂ to -NMe₃⁺). Since the exchange frequency of this type of four-component rotor is correlated with the rate of click catalysis, as established recently [37], one should be able to more extensively test the concept that rotating catalytic machinery shows reduced product inhibition at higher machine speed.