Transient chirality inversion during racemization of a helical cobalt(III) complex

Significance

We first observed a transient chirality inversion on a simple unimolecular platform during the racemization of a chiral helical complex [LCo₃A₆]³⁺, i.e., the helicity changed from P-rich (right-handed) to M-rich (left-handed), which then racemized to a P/M equimolar mixture in spite of the absence of a reagent that could induce the M helix. This transient chirality inversion was observed only in the forward reaction, whereas the reverse reaction showed a simple monotonic change with an induction time. Consequently, the M helicity appeared only in the forward reaction. These forward and reverse reactions constitute a hysteretic cycle. Compounds showing such unique time responses would be useful for developing time-programmable switchable materials that can control the physical/chemical properties in a time-dependent manner.

Abstract

While most responsive molecules show a trivial first-order exponential relaxation upon stimulation, increasing interest has recently focused on unusual nontrivial time responses such as chemical clocks and chemical oscillators. These unique time profiles principally originate from complicated multistep reactions involving an autocatalytic redox process of small inorganic species such as BrO₃^– or from supramolecular assembling of organic molecules. In this study, we have found that a very unusual time response was observed in a unimolecular platform just by integrating multiple reaction centers in a molecule. A triple-helical metallocryptand, [LCo₃A₆]³⁺ (A = (S)-1-phenylethylamine), underwent a transient chirality inversion from P-rich (right-handed) to M-rich (left-handed) then racemic during the racemization driven by the multistep ligand exchange with piperidine. In contrast, the reverse reaction showed a simple monotonic change with an induction time without showing the transient chirality inversion. Consequently, the M helicity appeared only in the forward reaction. Detailed mass spectrometric analysis suggested that the forward and reverse reactions proceeded in different pathways to make a unique hysteretic cycle.

Responsive molecules play a central role in both artificial and biological functional systems (1–5). They change their molecular structure by a physical or chemical stimulus to enable subsequent functions such as signal transduction. In general, fast response has been believed to be desirable so that the next molecular functions can quickly start to work. The time profiles of the response can usually be described as a (pseudo–) first-order exponential relaxation (Fig. 1 A, i), which gives a simple monotonic change from the initial to the final values in the molecular functions or properties.

Fig. 1.

Time response of functional molecules. (A) Various types of response curves upon stimulation (green arrows): (i) exponential decay, (ii) time response in a chemical clock, (iii) time response in a chemical oscillator, (iv) normal time response in racemization, and (v and vi) transient chirality inversion during racemization. (B) Racemization of a chiral carbon compound via a single-step reaction. (C) Racemization of a helical molecule via a six-step reaction.

In contrast, there are reactions that show an unusual time response, which is far from the trivial first-order kinetics. These include chemical clocks (Fig. 1 A, ii) (6, 7) and chemical oscillators (Fig. 1 A, iii) (8–12), which are known as thermodynamically open systems (13). The unique oscillating time profiles are observed only in limited systems, although oscillation is quite a ubiquitous physical phenomenon in classical/quantum mechanics, electromagnetism, etc. The chemical oscillation originates from very complicated multistep reactions involving autocatalytic redox processes of simple inorganic species, such as the BrO₃^– ion (8–13), and this has been successfully utilized to develop oscillating materials (14–19) that enable periodic changes in various kinds of molecular functions, physical properties, or chemical reactivities upon stimulation.

Recently, unique time responses have also been observed in some dissipative supramolecular assemblies (20–25), in which their physical quantity shows one increase–decrease cycle each time a chemical fuel is added (26–30) or multiple increase–decrease cycles (31, 32). More simply, formation of self-assembled structures from small organic molecules sometimes exhibits unique nonlinear time responses with a significant lag time mainly due to the pathway complexity (33, 34). Typically, the constituent molecules first form a metastable assembly (35–42) or a kinetically trapped state prior to the assembly (43–46), which is then converted into the most thermodynamically stable state after a substantial lag time. This two-phase time course change sometimes leads to a chirality inversion with time; i.e., the right-handed helical aggregate is initially formed, but this is converted into the left-handed helical form at a later time (47–51). This observation is noteworthy because the time-dependent positive/negative inversion is one of the important features of oscillation in physical phenomena. In principle, however, these unique nonlinear time responses have been observed mostly during the formation of supramolecular polymers but not in a unimolecular system.

In this study, we have found that an unprecedented nonlinear time response with a transient chirality inversion was observed in a unimolecular system just by integrating multiple reaction centers in a triple-helical molecular scaffold; i.e., a helical cobalt(III) metallocryptand underwent a racemization with a transient chirality inversion. Racemization is a ubiquitous chemical conversion from an optically active compound to the corresponding racemic mixture (Fig. 1B). Principally, racemization is a unimolecular reaction that shows a very normal time profile described as the first-order exponential relaxation (Fig. 1 A, iv). However, if racemization is driven by a multistep reaction, the time response could be nonlinear. Indeed, the cobalt complexes [LCo₃X₆]³⁺ (Scheme 1) in this study showed quite an unusual time response with a transient chirality inversion (Fig. 1 A, v and vi) due to the multistep reaction when all six chiral ligands, A (=(S)-1-phenylethylamine), were replaced by an achiral ligand in a multistep manner (Fig. 1C). In addition, a unique hysteretic cycle was achieved thanks to this transient chirality inversion, which was not observed in the reverse reaction.

Scheme 1.

P/M helicity inversion of the helical complex [LCo₃X₆]³⁺ (X = A or pip).

Results and Discussion

Transient Chirality Inversion Driven by the Ligand Exchange.

As a platform for nontrivial time course changes driven by a multistep transformation, we used our triple-helical complex, [LCo₃X₆]³⁺ (52–54), which has six exchangeable sites to allow six-step reactions. This complex has a dynamic helical structure, whose right- and left-handed forms (P and M forms, respectively, hereafter) are in slow equilibrium on the timescale of minutes to hours. The P/M ratios of the [LCo₃X₆]³⁺ helix can be shifted by the introduction of a chiral ligand at the six exchangeable sites (Scheme 1) (54) because each of the three hexacoordinate cobalt(III) centers can undergo ligand exchange at the two axial sites (55–59). This means that [LCo₃X₆]³⁺ will undergo racemization via a six-step process, if all the chiral ligands X are replaced with achiral ones (Fig. 1C).

The helical complex [LCo₃A₆](OTf)₃ was synthesized by the reaction of the corresponding free ligand (60, 61) with cobalt(II) acetate under aerobic conditions in the presence of chiral amine A according to our previous report (54). The right-handed helix was dominant in a methanol solution, and the P/M diastereomeric ratio was 88:12 (SI Appendix, Fig. S1). We investigated the sixfold exchange of amine A with piperidine in this complex [LCo₃A₆](OTf)₃. This would cause racemization of the P-rich [LCo₃]³⁺ triple helix because the P and M forms become an enantiomer pair after complete removal of the chiral auxiliary A (Fig. 1C and SI Appendix, Fig. S2).

Interestingly, when piperidine (120 equivalents; equiv hereafter) was added to a solution of [LCo₃A₆](OTf)₃ (denoted as A6 hereafter), the intensity of circular dichroism (CD) showed an unusual time course change instead of the usual monotonic decay of racemization. The negative CD signal at 530 to 550 nm, which is indicative of the P helix, immediately decreased and turned positive after 7 min (Fig. 2A and SI Appendix, Fig. S3). After reaching a maximum after 60 to 120 min, this positive CD signal gradually decreased and became completely silent after 2 d, which implies that the [LCo₃]³⁺ triple helix was finally racemized. Since the sign of the CD signals around 530 to 550 nm directly reflects the P/M helicity of the [LCo₃]³⁺ triple helix, this time course change represents a transient chirality inversion of the [LCo₃]³⁺ triple helix, i.e., P-rich → M-rich → racemic as depicted in Fig. 1 A, vi. When the enantiomeric metallocryptand [LCo₃A′₆]³⁺ (A′ = (R)-1-phenylethylamine) with the opposite chirality was used as the starting complex, the trace of the time dependence of the CD intensities was almost the perfect mirror image of that for [LCo₃A₆]³⁺ (SI Appendix, Figs. S4 and S5). This again confirmed that the removal of the chiral source, A or A′, caused the unique transient chirality inversion during the racemization.

Fig. 2.

Ligand exchange of [LCo₃A₆]³⁺ (=A6) with piperidine (120 equiv) in methanol at 298 K monitored by time course changes of the CD and mass spectra. (A) CD intensity at 550 nm. (B) ESI-TOF mass spectra; m/z, mass-to-charge ratio. (C) MS peak intensities of A6, A4, A2, and A0.

It should be noted that the sixfold ligand exchange from [LCo₃A₆]³⁺ (=A6) to [LCo₃(pip)₆]³⁺ (=A0) was completed at a very early stage (60 to 120 min), although a positive CD signal was still observed with a significant intensity. The electrospray ionization time-of-flight (ESI-TOF) mass spectra (Fig. 2B and SI Appendix, Fig. S6) and the ¹H NMR spectra (SI Appendix, Fig. S7) after 60 to 120 min almost exclusively showed the peaks of the fully exchanged product [LCo₃(pip)₆]³⁺ (=A0) without showing significant peaks for the intermediate species [LCo₃A_n(pip)_(6–n)]³⁺ (n = 5, 4, 3, 2, and 1; denoted as A5, A4, A3, A2, and A1, hereafter, using the number of the chiral ligand A). Obviously, this unusual time response during the racemization should be ascribed to the multistep ligand exchange at the six available sites as well as the relatively slow P/M equilibrium shifts of each of the intermediates and the final product.

In order to clarify the mechanism of the unique transient chirality inversion, we carefully analyzed the time course changes in the ESI-TOF mass spectra (Fig. 2 B and C). Since this racemization involves successive exchange of the six amine ligands A with piperidine, we had expected that we could observe all the mono- to penta-exchanged intermediates, A5, A4, A3, A2, and A1, during the reaction progress. However, only the di- and tetra-exchanged intermediates, A4 and A2, were observed as a relatively intense peak. In particular, the tetra-exchanged intermediate [LCo₃A₂(pip)₄]³⁺ (=A2) was dominant, and its amount slowly decreased with the apparent half-life t_1/2(app) of 18.2 min, whereas the di-exchanged intermediate [LCo₃A₄(pip)₂]³⁺ (=A4) rapidly disappeared at an early stage (t_1/2(app) = 4.7 min).

From a statistical point of view, this successive sixfold ligand exchange from A6 to A0 could give 14 possible intermediates ranging from mono- to penta-exchanged species including regioisomers and stereoisomers (Fig. 3A). However, the mono-, tri-, and penta-exchanged intermediates, A5, A3, and A1, were formed only in very small amounts. The absence of these species can be rationally explained by assuming that both of the two axial ligands at each cobalt(III) center are replaced with piperidine at virtually the same time. If this is the case, the plausible major pathways are limited to ones that involve only the geminal isomers of the intermediates, A4g and A2g (Fig. 3A). Thus, we simplified the sixfold ligand exchange as a three-step model, A6 → A4g → A2g → A0 with P/M equilibration (Fig. 3B). Each of the three steps was treated as a pseudo–first-order reaction because we used a large excess amount (120 equiv) of piperidine. For simplicity, we assumed that the rate constants for the P and M forms are the same for each of the three steps (k_ex1, k_ex2, and k_ex3).

Fig. 3.

Proposed mechanism of the transient chirality inversion observed during the racemization of [LCo₃A₆]³⁺ driven by ligand exchange. (A) Fourteen possible intermediates during the conversion of A6 to A0. In this scheme, the P/M diastereomers are not differentiated. (B) Simplified three-step model of the ligand exchange with P/M helicity inversion. Red arrows represent the most probable paths of the conversion.

We initially analyzed the time course changes of the peak intensities in the mass spectra (MS intensities hereafter) for A6, A4g, A2g, and A0 (Fig. 2 B and C and SI Appendix, Fig. S6) without considering the P/M helicity of the [LCo₃]³⁺ triple helix. The nonlinear curve fitting analysis yielded the rate constants of k_ex1 = 0.10 s⁻¹, k_ex2 = 4.5 × 10⁻³ s⁻¹, and k_ex3 = 6.7 × 10⁻⁴ s⁻¹, where k_ex1, k_ex2, and k_ex3 are the pseudo–first-order rate constants for the three-step reaction (Figs. 2C and 3B and Table 1). The observed trend of k_ex1 > k_ex2 > k_ex3 can be explained by the increased number of bulky piperidine ligands; i.e., the ligand exchange at one site slows down the subsequent exchange reactions. This also indicated that the final-step conversion from A2g to A0 is the rate-determining step of the overall three-step process.

Table 1.

Rate constants for ligand exchange from A6 to A0 associated with helicity inversion in methanol at 298 K

Ligand exchange rates (s–1)*		M→P Helicity inversion rates (s–1)		P→M Helicity inversion rates (s–1)		P/M Equilibrium constant†
k ex1	0.10	k A6 +	2.7 × 10−2	k A6 –	3.6 × 10−3	K A6	7.3‡
k ex2	4.5 × 10−3	k A4g +	1.5 × 10−2	k A4g –	1.5 × 10−2	K A4g	0.95
k ex3	6.7 × 10−4	k A2g +	1.0 × 10−4	k A2g –	6.4 × 10−4	K A2g	0.16
		k A0 +	1.2 × 10−5	k A0 –	1.2 × 10−5	K A0	1§

*Pseudo–first-order rate constants. The rate constants k_ex1, k_ex2, and k_ex3 for P and M forms are assumed to be the same for each of the ligand exchange steps.

^†K_S = k_S+/k_S– for S = A6, A4g, A2g, and A0.

^‡K_A6 (=k_A6+/k_A6–) was fixed at 7.3 based on the equilibrium ratio of (P)-A6:(M)-A6 = 88:12.

^§K_A0 (=k_A0+/k_A0–) was fixed at 1 because (P)-A0 and (M)-A0 are enantiomers of each other.

Clearly, the observed transient chirality inversion (Fig. 2A) was caused by the P/M inversion at a later stage of the three-step conversion A6 → A4g → A2g → A0. We analyzed the time course CD intensity changes assuming that each of the species can undergo the P/M helicity inversion with different rate constants (k_S+ and k_S– for S = A6, A4g, A2g, and A0) while undergoing the ligand exchange with the rate constants (k_ex1, k_ex2, and k_ex3) determined by the above MS experiments (Fig. 3B). All the rate constants were optimized by a nonlinear least-squares regression of the overall experimental data of the CD and MS measurements (Table 1). The results unambiguously showed that the P/M helicity inversion becomes slower as more piperidine ligands are introduced. In particular, the final product, [LCo₃(pip)₆]³⁺ (=A0), has the slowest rates for the P/M helicity inversion (k_A0+ = k_A0– = 1.2 × 10⁻⁵ s⁻¹), which is consistent with the observation that the CD intensity very slowly decayed after the complete ligand exchange (after 120 min; Fig. 2A). In addition, the equilibrium constants for the P/M helicity inversion, which are calculated as K_S = k_S+/k_S– (S = A6, A4g, A2g, and A0), showed a unique trend that could explain the unprecedented transient chirality inversion. While there was almost no P/M preference for the di-exchanged intermediate A4g (K_A4g = k_A4g+/k_A4g– ∼1.0), the P/M equilibrium constant for the tetra-exchanged intermediate A2g was significantly lower than 1 (K_A2g = k_A2g+/k_A2g– = 0.16 ≪ 1). Consequently, the M form is more favorable for the tetra-exchanged intermediate A2g, whereas the P form is dominant in the starting complex A6 (K_A6 = k_A6+/k_A6– = 7.3 ≫ 1). Obviously, the helicity inversion occurred after four A ligands were replaced with piperidine. The most probable pathway, therefore, is that the starting complex A6 underwent a fourfold ligand exchange to give the intermediate (P)-A2g while keeping the right-handed helicity, which then underwent a helicity inversion to give the left-handed (M)-A2g. This complex was then converted into the fully exchanged product (M)-A0, which very slowly underwent racemization (Fig. 3B).

Time Profiles of the Reverse Reaction.

As already described, a unique transient chirality inversion was observed when [LCo₃A₆]³⁺ (=A6) loses the chiral ligands A upon the six-step ligand exchange with piperidine. In contrast, such a unique time response was not observed in the reverse reaction as we have already reported (54). Only a monotonic increase in the CD intensity was observed without showing a CD signal reversal when up to six molecules of chiral ligand A were introduced into the racemic [LCo₃(pip)₆]³⁺ (=A0). However, we have found that this reverse reaction also showed a more distinct nonlinear feature when the amount of added A was increased from 12 to 120 equiv (Fig. 4A and SI Appendix, Fig. S8). During the first 30 min, the CD intensity showed almost no increase, although mono- to tetra-exchanged products (A1, A2, A3, A4, and A5) were observed with a significant intensity in the ESI-TOF mass spectra (Fig. 4 B and C and SI Appendix, Figs. S9–11). After this induction time of ∼30 min, the CD intensity monotonically increased for 500 min. During this reverse reaction, all the intermediates from the mono- to penta-exchanged species, A1, A2, A3, A4, and A5, were detected in the ESI-TOF mass spectra, which was in sharp contrast to the forward reaction in which only the di- and tetra-exchanged intermediates, A4 and A2, were observed as dominating species (Fig. 2 B and C). In this reverse reaction, exchange of the six piperidine ligands in A0 with the chiral ligands A probably took place in a statistically random manner via 14 intermediates (Fig. 3A). As the number of chiral ligands A increased, the negative CD signals simply increased without showing the transient chirality inversion.

Fig. 4.

Ligand exchange of [LCo₃(pip)₆]³⁺ (=A0) with chiral amine A (120 equiv) in methanol at 298 K monitored by time course changes of the CD and mass spectra. (A) CD intensity at 550 nm. (B) ESI-TOF mass spectra. (C) MS peak intensities of A0, A1, A2, A3, A4, A5, and A6.

As already discussed, the amount of the chiral amine A, 12 or 120 equiv, had a significant influence on the nonlinear feature of the time response in the reverse reaction starting from [LCo₃(pip)₆]³⁺ (=A0). In contrast, the amount of the added piperidine did not significantly affect the unique time profile of the forward reaction starting from [LCo₃A₆]³⁺ (=A6). We still observed a similar transient chirality inversion that shows a CD signal inversion followed by a decay, even when the amount of piperidine was reduced from 120 to 12 equiv (SI Appendix, Figs. S12 and S13). This may be ascribed to the higher binding affinity of piperidine to the [LCo₃]³⁺ triple helix than chiral amine A. In the forward reaction with 120 equiv of piperidine, more than 99% of the coordinating amine A was exchanged with piperidine at equilibrium, which was estimated from the time course analysis of the MS intensities (Fig. 2C). In contrast, a similar analysis for the reverse reaction with 120 equiv of A indicated that only 78% of the coordinating piperidine was exchanged with the chiral amine A. A significant amount of the intermediates A2, A3, A4, and A5 still remained even at equilibrium (Fig. 4C). In order to quantitatively discuss the relative binding affinity of the amines, we defined the averaged equilibrium constant K_ex(av) for the amine exchange between the chiral amine A and piperidine as

$$\mathit{Co}\text{-}\mathbf{A}+\text{pip}\stackrel{K_{\text{ex}\left(\text{av}\right)}}{\rightleftarrows }\mathit{Co}\text{-pip}+\mathbf{A},$$

where Co-A and Co-pip denote A and piperidine that are coordinating to the cobalt(III) centers, respectively. The K_ex(av) was determined to be 6.9 from the estimated mole fractions of A0 to A6 at equilibrium in the reverse reaction, confirming that piperidine can more strongly coordinate to the cobalt(III) centers in the [LCo₃]³⁺ triple helix than the chiral amine A.

Hysteretic Cycle in the Forward and Reverse Reactions.

Based on the time dependence of the CD intensity, we found that the M helicity appeared only in the forward reaction A6 → A0 during the forward and reverse ligand exchanges between A and piperidine (Fig. 5A). Obviously, these forward and reverse reactions constitute a hysteretic cycle originating from the nonlinear feature of the six-step reactions. In fact, linearity is a feature originating from non–first-order reactions. In an ideal one-step first-order reaction X → Y, a physical quantity always changes in proportion to the reaction progress, which is defined as [Y]/([X]_initial), thus yielding a linear feature (Fig. 5B). In contrast, a two-step reaction described as XX → XY → YY does not necessarily show such a linear feature, particularly when the reaction proceeds in a stepwise manner (k₁ ≥ k₂; Fig. 5C). Since the present system [LCo₃X₆]³⁺ undergoes a six-step reaction, plots of the CD intensity vs. the reaction progress would give a nonlinear feature, which could well explain the unique hysteretic cycle.

Fig. 5.

Hysteretic cycle originating from the nonlinearity of the reactions. (A) The hysteretic cycle of the conversions of A6 → A0 and A0 → A6. The M isomer appears only in the forward reaction. (B) Linearity of an ideal first-order reaction, X → Y. The function (proportional to [Y]) plotted versus reaction progress, which is defined as [Y]/([X]_initial), always shows a straight line. (C) Linearity of an ideal two-step reaction, XX → XY → YY. The function (proportional to [YY]) plotted versus the reaction progress, which is defined as the average number of Y, (2[YY] + [XY])/([XX]_initial), shows a significant nonlinearity when k₁ ≥ k₂. (D) The plots of the CD intensity θ₅₅₀ versus the average number of chiral amine ligands n_av throughout the reaction progress for the conversions of A6 → A0 and A0 → A6 in this study.

Thus, we defined the parameter n_av, which is the average number of chiral amine ligands A in [LCo₃A_n(pip)_(6–n)]³⁺ (A0, A1, … A6) at a given time, to describe the overall reaction progress. We made a plot of the CD intensity at 550 nm (θ₅₅₀ in mdeg) versus n_av to analyze the linearity of the forward and reverse ligand exchanges (Fig. 5D). In this n_av–θ₅₅₀ plot, the pure [LCo₃A₆]³⁺ (=A6) and [LCo₃(pip)₆]³⁺ (=A0) are situated at the points P1 (n_av, θ₅₅₀) = (6, –35) and P2 (0, 0), respectively.

In the forward reaction from A6 to A0, n_av at a given time was determined by the time course changes in the mole fractions of all the major intermediates, A6, A4g, A2g, and A0 (Fig. 2C). The observed data points (n_av, θ₅₅₀) moved from P1 to P2 as time proceeded in this n_av–θ₅₅₀ plot (Fig. 5D). The trajectory of the points (n_av, θ₅₅₀) showed a distinct two-phase feature, P1 → P3 → P2, instead of a straight line corresponding to a linear relationship. In the first phase, the negative CD immediately decreased and turned positive with the reaction progress [i.e., from P1 (n_av, θ₅₅₀) = (6, –35) to P3 (0, +17)]. In the second phase, the positive CD decreased to P2 (0, 0) keeping n_av ∼ 0. This two-phase trajectory well explains the two-step feature of the transient chirality inversion observed during the forward reaction.

The reverse reaction from A0 to A6 was also analyzed by using this n_av–θ₅₅₀ plot. The n_av at a given time was determined by the mole fractions for all the intermediates, A1, A2, A3, A4, and A5, as well as A0 and A6, which were estimated by simulating the time course changes of their MS peak intensities (Fig. 4C and SI Appendix, Fig. S11). Although a seemingly simple monotonic increase in θ₅₅₀ was observed upon the exchange of the piperidine with the chiral ligand A, the n_av–θ₅₅₀ plot showed a significant nonlinear feature (Fig. 5D). During an earlier stage of the reaction, the ligand exchange caused only a small change in the CD intensity θ₅₅₀ [i.e., from P2 (n_av, θ₅₅₀) = (0, 0) to P4 (2.1, –3.5)]. This means that almost no helicity inversion occurred until two of the six piperidine ligands were replaced with the chiral ligand A. This is consistent with the fact that [LCo₃(pip)₆]³⁺ (=A0) has the slowest helicity inversion rates (k_A0+ = k_A0– = 1.2 × 10⁻⁵ s⁻¹) (Fig. 3B and Table 1). When the ligand exchange further proceeded (n_av > 2.5), the CD intensity rapidly increased from P4 (n_av, θ₅₅₀) = (2.1, –3.5) to P5 (4.6, –49). As the ligand exchange proceeds, the helicity inversion equilibrium of the [LCo₃]³⁺ triple helix becomes faster due to the loss of the bulky piperidine ligands, and the P helicity becomes more favored when more A ligands were introduced. As a result, the M helicity appeared only in the forward reaction A6 → A0, and hysteresis was observed during the erasing/writing cycle of the helicity in the cobalt(III) metallocryptand [LCo₃X₆]³⁺ by decreasing/increasing the average number of chiral amine ligands, n_av, in the range between 0 and 6 (Fig. 5A).

Conclusion

The helical complex [LCo₃X₆]³⁺ having six exchangeable ligands showed a unique time response, transient chirality inversion, during racemization. The starting P helix of [LCo₃A₆]³⁺ did not simply racemize in a monotonic fashion; the opposite M helix appeared during the stereomutation prior to the complete removal of the chiral source A, despite the absence of a reagent that could induce the M helix. Thus, the handedness of the helix changed from P-rich to M-rich, which then racemized to a P/M equimolar mixture. This overshooting profile of the time course change, i.e., sign inversion followed by a decay to zero, is quite similar to the damped oscillation observed in physics, such as classical mechanics and electromagnetism. Previously, a nontrivial time response has been observed only in complicated autocatalytic systems and in self-assembled systems. The present [LCo₃X₆]³⁺ system demonstrated that a transient chirality inversion can be observed on a unimolecular platform. One of the noteworthy features is that this transient chirality inversion was observed only in the forward reaction. The forward and reverse reactions proceeded in different pathways to make a hysteretic cycle. Moreover, the unique time course change in this system is easily observable on the timescale of minutes to hours, which would be potentially useful for time-dependent functional materials in human activities.

The development of a unimolecular system with such a nontrivial time response would enable time-programmable switches that can control the physical properties and chemical reactivities in a time-dependent manner. We believe that this result will provide an important insight into the science of autonomously driven materials. Further advanced materials with oscillating responses would be realized in combination with various types of reactions such as sequential reactions or autocatalytic reactions.

Materials and Methods

General.

[LCo₃A₆](OTf)₃ and [LCo₃(pip)₆](OTf)₃ were synthesized according to the previous report (54). The reagents and solvents were purchased from commercial sources and used without further purification. The ¹H NMR spectra were recorded on a JEOL JNM-ECS 400 (400 MHz). Chemical shifts were referenced with respect to the solvent residual peak (3.31 ppm for CD₂HOD; 1.94 ppm for CD₂HCN). The ESI-TOF MS measurements were performed on a Bruker Daltonics micrOTOF II spectrometer. The CD spectra were recorded on a JASCO J-1500 spectropolarimeter at 298 K.

Determination of Rate Constants.

Step 1: Determination of rate constants for the three-step ligand exchange A6 → A4g → A2g → A0.

Experimentally obtained time dependence of MS intensities, I_obs,S,i (S = A6, A4, A2, and A0; ith data at time t_i out of all the measured points n_MS; t_i is the time after the reaction started), was used to determine the time course change of the mole fractions. The corresponding simulated MS intensities for these species, I_sim,S,i, are given as the following equation:

$$I_{\text{sim},\text{S},i}=A_{\text{S}}•R_{\text{S}}(t_i),$$

where R_S(t) is the mole fraction of each species (S = A6, A4g, A2g, and A0) at the given time t, and A_S is a constant. The time dependence of the mole fractions, R_S(t), was simulated by numerical integration methods with the step of dt = 1 s based on the given rate constants k_ex1, k_ex2, and k_ex3, assuming that each of the three-step ligand exchange reactions of A6 → A4g → A2g → A0 is irreversible pseudo–first-order and that the P and M isomers of each species (A6, A4g, and A2g) have the same rate constants for each step. The variables of k_ex1, k_ex2, k_ex3, and A_S (S = A6, A4g, A2g, and A0) were optimized by a least-squares regression to minimize the residual r_MS defined by the following equation:

$$r_{\text{MS}}={\displaystyle \sum }_{\text{S}}\left({\displaystyle \sum }_{i=1}^{n_{\text{MS}}}{(I_{\text{obs},\text{S},i}-I_{\text{sim},\text{S},i})}^2\right)={\displaystyle \sum }_{\text{S}}\left({\displaystyle \sum }_{i=1}^{n_{\text{MS}}}{(I_{\text{obs},\text{S},i}-A_{\text{S}}•R_{\text{S}}(t_i))}^2\right),$$

using the Solver Add-In in Microsoft Excel.

Step 2: Determination of rate constants for the P/M isomerization for A6, A4g, A2g, and A0.

The experimentally obtained time dependence of the CD intensities, θ_obs,j (jth data at time t_j out of all the measured points n_CD; t_j is the time after the reaction started), was used to analyze the time course change of the CD intensities. The corresponding simulated CD intensities θ_sim,j are given as the following equation:

$${\theta }_{\text{sim},j}={\displaystyle \sum }_{\text{S}}{B}_{\text{S}}•R_{\text{S}}(t_j),$$

where R_S(t) is the mole fraction of each species [S = (P)-A6, (P)-A4g, (P)-A2g, (P)-A0, (M)-A6, (M)-A4g, (M)-A2g, (M)-A0] at the given time t, and B_S is a constant. For simplicity, |B_S| for all species is assumed to be the same as B and their signs are only dependent on the helicity as follows:

$$B_{\left(P\right)‐\mathbf{A}\mathbf{6}}=B_{\left(P\right)‐\mathbf{A}\mathbf{4}\mathbf{g}}=B_{\left(P\right)‐\mathbf{A}\mathbf{2}\mathbf{g}}=B_{\left(P\right)‐\mathbf{A}\mathbf{0}}=B,$$

$$B_{\left(M\right)‐\mathbf{A}\mathbf{6}}=B_{\left(M\right)‐\mathbf{A}\mathbf{4}\mathbf{g}}=B_{\left(M\right)‐\mathbf{A}\mathbf{2}\mathbf{g}}=B_{\left(M\right)‐\mathbf{A}\mathbf{0}}=-B,$$

because the CD intensities of each species are mostly governed by the triple-helical structures of the [LCo₃(amine)₆]³⁺ regardless of the coordinating amine ligands.

The time dependence of the mole fractions, R_S(t), was simulated by numerical integration methods with the step of dt = 1 s based on the given rate constants k_ex1, k_ex2, and k_ex3, assuming that each of the three-step ligand exchange reactions of A6 → A4g → A2g → A0 is irreversible and that the P and M isomers of each species (A6, A4g, and A2g) have the same rate constants for each step, as described for the previously mentioned step 1. The variables of k_A6+, k_A6–, k_A4g+, k_A4g–, k_A2g+, k_A2g–, k_A0+, k_A0–, and B were optimized by a further simultaneous refinement of k_ex1, k_ex2, k_ex3, and A_S (S = A6, A4g, A2g, and A0) by a least-squares regression to minimize the residual r defined as the following equation:

$$r=w_{\text{MS}}•r_{\text{MS}}+w_{\text{CD}}•r_{\text{CD}},$$

$$r_{\text{CD}}={\displaystyle \sum }_{j=1}^{n_{\text{CD}}}{({\theta }_{\text{obs},j}-{\theta }_{\text{sim},j})}^2={\displaystyle \sum }_{j=1}^{n_{\text{CD}}}{\left({\theta }_{\text{obs},j}-{\displaystyle \sum }_{\text{S}}{B}_{\text{S}}{R}_{\text{S}}(t_j)\right)}^2,$$

where w_MS and w_CD are the weights of the MS and CD measurements, respectively, using the Solver Add-In in Microsoft Excel, while applying the following constraints:

$$k_{\mathbf{A}\mathbf{6}+}:k_{\mathbf{A}\mathbf{6}-}=88:12,$$

$$k_{\mathbf{A}\mathbf{0}+}=k_{\mathbf{A}\mathbf{0}-},$$

based on the experimentally determined P/M ratio of A6 at equilibrium and that (P)-A0 and (M)-A0 constitute an enantiomer pair.

Step 3: Determination of rate constants for six-step ligand exchange in the reverse reaction.

The experimentally obtained time dependence of MS intensities, I_obs,S,i (S = A0, A1, A2, A3, A4, A5, and A6; ith data at time t_i out of all the measured points n_MS; t_i is the time after the reaction started), was used to determine the time course change in the mole fractions. The corresponding simulated MS intensities I_sim,S,i for these species are given as the following equation:

$$I_{\text{sim},\text{S},i}=A_{\text{S}}•R_{\text{S}}(t_i),$$

where R_S(t) is the mole fraction of each species (S = A0, A1, A2, A3, A4, A5, and A6) at the given time t and A_S is a constant. The time dependence of the mole fractions, R_S(t), was simulated by numerical integration methods with the step of dt = 0.1 min based on the given rate constants k'_ex1+, k'_ex1–, k'_ex2+, k'_ex2–, k'_ex3+, k'_ex3–, k'_ex4+, k'_ex4–, k'_ex5+, k'_ex5–, k'_ex6+, and k'_ex6– assuming that each of the six-step ligand exchange reactions of A0 → A1 → A2 → A3 → A4 → A5 → A6 is reversible and that all the diastereomers of each species have the same rate constants. The variables of k'_ex1+, k'_ex1–, k'_ex2+, k'_ex2–, k'_ex3+, k'_ex3–, k'_ex4+, k'_ex4–, k'_ex5+, k'_ex5–, k'_ex6+, k'_ex6–, and A_S (S = A0, A1, A2, A3, A4, A5, and A6) were optimized by the least-squares regression to minimize the residual r_MS defined by the following equation:

$$r_{\text{MS}}={\displaystyle \sum }_{\text{S}}\left({\displaystyle \sum }_{i=1}^{n_{\text{MS}}}{(I_{\text{obs},\text{S},i}-I_{\text{sim},\text{S},i})}^2\right)={\displaystyle \sum }_{\text{S}}\left({\displaystyle \sum }_{i=1}^{n_{\text{MS}}}{(I_{\text{obs},\text{S},i}-A_{\text{S}}•R_{\text{S}}(t_i))}^2\right),$$

using the Solver Add-In in Microsoft Excel.

Data Availability

All study data are included in the article and/or SI Appendix.