Measurement of the ground-state distributions in bistable mechanically interlocked molecules using slow scan rate cyclic voltammetry

Results and Discussion

We prepared samples of the bistable [2]rotaxane R•4PF₆ and two bistable [2]catenanes, C1•4PF₆ and C2•4PF₆, to revisit their ground-state distribution constants. R⁴⁺ along with C1⁴⁺ both contain DNP as the alternative π-electron-rich unit, whereas C2⁴⁺ incorporates the much less π-electron-rich butadiyne unit. C1•4PF₆ (19) and C2•4PF₆ (20) were both synthesized using previously reported literature procedures, employing template-directed protocols in the final step to achieve the mechanically interlocked compounds. R•4PF₆ was obtained (34) using a threading-followed-by stoppering approach (35), making use of the copper(I) catalyzed 1,3-dipolar cycloaddition (36, 37) between the azide-terminated thread and the alkyne functionalized stopper precursor. The crude product was purified by preparative RP-HPLC, and R•4PF₆ was characterized by both ¹H and ¹³C NMR spectroscopies, as well as by high-resolution electrospray ionization mass spectrometry. The purity of R•4PF₆, C1•4PF₆, and C2•4PF₆ were all determined (see SI Text) by analytical RP-HPLC and ¹H NMR spectroscopy.

First of all, we focus on the results obtained for the bistable [2]rotaxane R⁴⁺ (Fig. 3A). It has been reported (33, 34, 38) that the ground-state distribution for [2]rotaxanes of this type, which contain DNP and TTF stations in its dumbbell component and are encircled by the CBPQT⁴⁺ ring, exhibit a 9∶1 distribution (K ≈ 10) favoring the encirclement of the TTF unit. This determination is made possible as a consequence of the fact that at relatively fast scan rates a modest oxidation process is observed, generally around +400 mV, corresponding to the oxidation of the MSCC to generate the TTF radical cation, and in a 1∶9 proportion with respect to the oxidation observed for the GSCC generally observed around +800 mV. A similar observation (blue trace) was made for R⁴⁺, which strongly indicates a ground-state distribution constant on the order of 10. Scanning at slower and slower scan rates, a new oxidation peak becomes increasingly apparent, until, upon using a scan rate of 10 mV s^-1, a new reversible redox process is observed with a redox potential of +0.49 V.

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Fig. 3.

Experimental data showing the transition from the fast scan rate regime (blue traces) into the slow scan rate regime (red traces). The shifting of the anodic and cathodic peaks is illustrated by the colored arrows. All scans have been normalized to the square root of the scan rate, and IR compensation was applied. (A) The bistable rotaxane R1⁴⁺: blue trace = 500 mV·s^-1, red trace = 10 mV·s^-1. (B) The bistable catenane C1⁴⁺: blue trace = 500 mV·s^-1, red trace = 10 mV·s^-1. (C) The bistable catenane C2⁴⁺: blue trace = 10 V·s^-1, red trace = 200 mV·s^-1; the scans were background subtracted.

In the case of C1⁴⁺ (Fig. 3B), which was first reported (19) in 1998, the ground-state distribution constant has never been measured carefully. CV experiments, however, suggest that the value must be significantly greater than approximately 10 as a consequence of the fact that the anodic peak corresponding to the MSCC of this bistable catenane could not be observed in the ground state at equilibrium. The technique reported herein offers, thereafter, a distinct advantage in being able to measure the ground-state distribution directly for this bistable catenane. By starting out using fast scan rates and scanning successively more slowly, we can see a new oxidation process emerge, whose redox potential was measured to be +0.58 V.

In order to demonstrate the full power of this electrochemical technique, we now turn our attention to C2⁴⁺ (Fig. 3C). Theoretical predictions suggest (20) that the distribution constant between the GSCC and the MSCC, where the CBPQT⁴⁺ encircles the butadiyne unit, is exceedingly large—indeed very much greater than in the case of R⁴⁺ or C1⁴⁺. This prediction is rationalized by the fact that, although the butadiyne unit can be considered to be a π-electron-donating unit, its ability to act as such is extremely small compared to the donor strength of either the TTF or DNP units, most likely a consequence of the highest occupied molecular orbital–lowest unoccupied molecular orbital energy mismatch. The fact that the butadiyne unit serves as such a weak recognition site for the CBPQT⁴⁺ ring has further consequences in terms of the kinetics of the switching process. On scanning at progressively slower scan rates, we observe that the new redox potential is massively shifted toward positive potentials at +0.66 V—almost entirely overlapping with the second oxidation process (MSCC⁺ → MSCC²⁺) to afford the TTF²⁺ dication.

In order to gain insight into the effect that scan rate has on the CVs observed for the bistable rotaxane and catenanes, we modeled a switching mechanism (39, 40) based on bistable MIMs incorporating TTF and an alternative binding site using an appropriate ladder-scheme mechanism (15) and began running simulations using Digisim. (For details regarding running the simulations, see SI Text. For an introduction on producing digitally simulated CV data based on a proposed mechanism, see ref. 40.) We first chose a ground-state distribution constant K = 1,000 and varied the scan rate (Fig. 4A) systematically in order to simulate the type of behavior to expect as the transition into the so-called “slow scan rate regime” begins to occur—where at every point in the (simulated) scan the redox-stimulated translational motion of the CBPQT⁴⁺ ring is allowed to come to an equilibrium. Starting out in the so-called “fast scan rate regime”—wherein the redox-stimulated translation of the CBPQT⁴⁺ ring is not given sufficient time to equilibrate as the potential is varied from point to point—we observe (33) what looks like a typical first-scan CV (blue trace) for MIMs of this type. As the scan rate is reduced progressively, we can witness quite clearly the transition into the slow scan rate regime take place. An anodic peak begins to emerge from the two-electron oxidation process observed around +0.8 V, and continues to shift toward more negative potentials. Likewise, the cathodic peak observed around +0.4 V begins to shift toward more positive potentials. We eventually reach a scan rate sufficiently slow (red trace) that these anodic and cathodic peaks shift in such a way as to form a “new” redox couple (E_eq), which is characterized by the expected approximately 60 mV separation between anodic and cathodic peaks expected for a totally reversible process. This simulation data provides further insight into the type of behavior we observe in the case of R⁴⁺, C1⁴⁺, and C2⁴⁺ as the transition from the fast scan into the slow scan rate regime begins to occur.

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Fig. 4.

Simulated CV data based on the proposed mechanism of switching. (A) Simulated data for a bistable rotaxane or catenane transitioning from the fast scan rate regime (blue trace) into the slow scan rate regime (red trace). The transition to the slow scan rate regime is characterized by the emergence of a new redox couple, E_eq. The shifting of the anodic and cathodic peaks associated with E_eq is illustrated by the colored arrows. The simulated scans have been normalized by the square root of the scan rate. (B) Simulated data showing the effect of varying the ground-state equilibrium constant (K) in the slow scan rate regime. For every order of magnitude change in K, an approximately 60 mV positive shift in the new redox potential is observed. Note: In order to arrive at a more accurate value of K obtained by least-squares fitting to simulated data, we relied upon a more sophisticated picture of the switching mechanism not represented by the ideal cases shown in this figure. See SI Text.

Next, we investigated how, by employing digital simulations, the value of the ground-state distribution constant K affects (Fig. 4B) the CVs within the slow scan rate regime in order to develop a means to quantify the value of K. From the beginning, we chose a scan rate sufficiently slow that it placed us in the slow scan rate regime, and then systematically varied the distribution constant K by factors of 10. For every order of magnitude change in K, the redox potential, E_eq, shifts approximately 60 mV toward positive potentials. This trend agrees well with Eq. 5 (see below), which also predicts an order of magnitude change in K for every integer multiple of approximately 60 mV difference between E_MSCC and E_eq. [It is important to note that data from digital simulations reveals that at the redox potential, E_eq, the quantity ([MSCC⁺])/([GSCC]) is indeed equal to unity.]

In order to offer a rationalization of the simulated data that varying K has on the new redox potential E_eq, consider the following analysis. In each case (namely, R1⁴⁺, C1⁴⁺, and C2⁴⁺), we can define the equilibrium based upon the ground-state distribution between the GSCC and the MSCC as [1]where K is the ground-state distribution constant governing the equilibrium of the GSCC, with the MSCC. It is well known (41) that there is a substantial difference in the oxidation potentials of TTF depending on whether or not it is encircled by the CBPQT⁴⁺ ring; indeed, the first oxidation potential of TTF becomes shifted by as much as approximately 400 mV. The first oxidation potential of TTF in the GSCC is, therefore, much higher than that of the MSCC. With this fact in hand, consider the following redox equilibrium:[2]From this relationship, we can invoke the use of the Nernst equation:[3]where E_MSCC is the redox potential for the electron transfer process in Eq. 2, E_Ap is the applied potential, R is the gas constant, T is the temperature, n is the number of electrons transferred, and F is Faraday’s constant. Combining Eq. 1 with Eq. 3, we can derive an expression for [MSCC] in terms of K and the [GSCC]: [4]Under the proper experimental conditions where the scan rate is sufficiently slow enough, such that at each point in the scan the redox-stimulated translational motion of the CBPQT⁴⁺ ring is allowed to reach an equilibrium as the potential is varied, there exists an applied potential E_Ap at which the quantity is equal to unity and effectively defines the new redox potential, E_eq. (To put it into more intuitive terms, if the scan rate is slow enough, as soon as the GSCC is oxidized to the GSCC⁺, it equilibrates immediately to the MSCC⁺; and conversely, as soon as the MSCC⁺ is reduced to the MSCC, it immediately equilibrates to the GSCC, at least on the time scale of the experiment.) Taking into consideration the fact that there is some applied potential, call it E_eq, at slow enough scan rates such that the expression is equal to one, solving Eq. 4 in terms of K leads us to the following expression:[5]We now have a rationale for explaining why and how K varies as a function of the redox potential E_eq and E_MSCC. (It is possible to measure the redox potential E_MSCC directly by accessing the fast scan rate regime, and the new redox potential E_eq in the slow scan rate regime. See SI Text.) This analysis of redox potentials is an extention of similar analyses that have been reported previously on metal-ligand and supramolecular complexes in order to evaluate their binding affinities quantitatively. A discussion of these procedures can be found in refs. 39 and 40.

We use the fact that we can populate the MSCC through an oxidation/reduction cycle of the TTF unit, an experiment that allows the redox potential of which, E_MSCC, to be directly measured at relatively fast scan rates (8 V s^-1). We found E_MSCC to be equal to 0.42 V. In a similar manner as the rotaxane, R⁴⁺, we took advantage of the fact that the MSCC of the catenane C1⁴⁺ can be populated by an oxidation/reduction cycle of the TTF unit. The redox potential, E_MSCC, was then measured directly at relatively fast scan rates and was found to be once again 0.42 V. The relaxation process of the populated MSCC to the GSCC following an oxidation/reduction cycle of the TTF unit in the case of C2⁴⁺ is so rapid, it has not been possible to measure the oxidation of the MSCC directly with our current instrumentation. We have assumed therefore that the redox potential of the MSCC for C2⁴⁺ is the same as that for the case of the R⁴⁺ and C1⁴⁺.

By fitting the experimental data using simulation methods (see SI Text), we find that the value of the ground-state equilibrium constant for R⁴⁺ is equal to 10 ± 2, an outcome that agrees well with that of the previously determined experimental value. The ground-state distribution constant in the case of C1⁴⁺ was measured by fitting the experimental data to the simulated curves: It was found to be K = 150 ± 20, which is an order of magnitude higher than that for R⁴⁺. We hypothesize that this difference could be a result of several factors including solvation effects and enforced side-on interactions, which are not significantly active in the bistable rotaxane, but are present in the bistable catenane. By fitting the experimental to simulated data for C2⁴⁺, we determined a ground-state distribution constant of K = 6,800 ± 300. Remarkably, the value of K is nearly three and two orders of magnitude higher (Fig. 5), respectively, when compared to the K values for R⁴⁺ and C1⁴⁺. We also used Eq. 5 to calculate K and found that the values determined from this mathematical method are in good agreement (see Fig. 5 and SI Text) with those determined from the fitting of the data to simulations.

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Fig. 5.

Graphical summary of the ground-state equilibrium distribution (K) for the bistable rotaxane R⁴⁺ and bistable catenanes C1⁴⁺ and C2⁴⁺. For each case, the value of K was determined either by X²-fitting of the data to simulations or by Eq. 5. The catenane C2⁴⁺ with the weakly π-electron-donating butadiyne station was found to have the highest ground-state distribution, followed by C1⁴⁺ with the stronger π-electron-donating DNP unit. The smallest ground-state equilibrium distribution is exemplified by R⁴⁺, which lacks any enforced side-on interactions with its DNP unit.

In order to elucidate the key factors responsible for the differences in the equillibrium between the GSCC and the MSCC for the bistable catenane C1⁴⁺ and bistable rotaxane R⁴⁺, we performed a quantum mechanical study based on density functional theory (DFT)—using the M06 suite of functionals—which has been shown (42, 43) by us to be a good choice for the study of donor–acceptor bistable MIMs. Initially, we investigated the gas-phase and MeCN solvation energy differences between the GSCC and MSCC for catenane C1•4PF₆. Using the M06 functional (43, 44) and the 6-311 ++G^∗∗ basis set, our results show that the energy difference (Fig. 6) between the GSCC and MSCC in the gas phase is 41.6 kcal/mol favoring the GSCC. This large energetic difference is not observed for the case of the rotaxane R•4PF₆, where the gas-phase energy difference is only 13.8 kcal/mol, also in favor of the GSCC. These relative gas-phase energies suggest that there are electronic effects in the catenane that are not present in the rotaxane, which cause the GSCC to be more stable by approximately 28 kcal/mol. The relative MeCN solvation energies act in the opposite direction, because the MSCC is solvated preferentially in both cases for the catenane and rotaxane. The increased solvation energy of the MSCC could be a consequence of the much higher accessibility of the more polar TTF recognition site (stronger solvation interactions) in the MSCC, when it is not encircled by the CBPQT⁴⁺ ring. In addition, our calculations show that the relative MeCN solvation energy [E_solv(GSCC) - E_solv(MSCC)] of the catenane (36.2 kcal/mol) is higher than for the rotaxane (11.0 kcal/mol). This observation suggests that the catenane’s equilibrium constant may show a stronger dependence with solvent polarity as compared to the rotaxane. These computational data suggest that it is likely that side-on interactions in the MSCC of the catenane between the unencircled TTF unit and the periphery of the CBPQT⁴⁺ ring may destabilize the recognition of the DNP unit, thus increasing the stability of the GSCC. This charge-transfer and polarization of the outside TTF unit in the MSCC also increases the solvation energy, a factor that reduces the switching free energy difference from the gas phase—or a less polar solvent. The computational results support our hypothesis that both solvation effects, as well as side-on interactions, are responsible for the difference in equilibrium constant for the GSCC and MSCC in a catenane and rotaxane, and serves to elucidate one of the fundamental physical differences between catenanes and rotaxanes. Side-on interactions present only in the catenane increase dramatically the difference in stability, whereas solvation effects mitigate this difference.

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Fig. 6.

Graphical summary of results from theoretical calculations on the difference in energy between the GSCC and the MSCC for both the catenane C1⁴⁺ and the rotaxane R⁴⁺. In both the gas phase and solution phase, the GSCC for C1⁴⁺ is substantially more favored than compared to the rotaxane R⁴⁺. All calculations were based off of DFT using the M06 functional and the 6-311 ++G^∗∗ basis set.