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

: 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 ( k 298 = 35 kHz), 4-H ( k 298 = 77 kHz) and 4-NO 2 ( k 298 = 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.

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 pre- 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 Npy→[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.

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.

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 (∆H ‡ ) and activation entropy (∆S ‡ ) were determined from transition state theory. The temperature-dependent rate constants of the rotors were fitted to the Eyring equation [49]: ln(k/T) = − ∆H ‡ /RT + ln(k B /h) + ∆S ‡ /R (2)

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.

Synthesis and Characterization of Four-Component Nanorotors
The strong correlation between σp 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-(4ethynylphenyl)-10,15,20-trimesitylporphyrin (11) with 8, 9 and 10, as shown in Scheme 1.

Synthesis and Characterization of Four-Component Nanorotors
The strong correlation between σ p and log K encouraged us to prepare the fourcomponent 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-(4ethynylphenyl)-10,15,20-trimesitylporphyrin (11) with 8, 9 and 10, as shown in Scheme 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 (k 298 of ROT-1a' and ROT-1b' = 3.5 × 10 4 Hz and 2.0 × 10 4 Hz, respectively). The coalescence temperature of ROT-1a' and ROT-1b' in the VT 1 H-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].

Hammett Equation Applies to Rotational Exchange in Nanorotors
The plot of the nanorotors' rotational frequency log k/k H and of ∆G ‡ 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 ratedetermining 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.

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 × 10 4 Hz and 2.0 × 10 4 Hz, respectively). The coalescence temperature of ROT-1a' and ROT-1b' in the VT 1 H-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].

Hammett Equation Applies to Rotational Exchange in Nanorotors
The plot of the nanorotors' rotational frequency log k/kH and of ΔG ‡ 298 of ROT-1a', ROT-2′ and ROT-3′ against σp 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/KH of complex formation for C1, C2 and C3 and σp, 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.

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 -NMe 2 to -NMe 3 + ). Since the exchange frequency of this type of fourcomponent 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.