Correlated shapeshifting and configurational isomerization

Herein we demonstrate that the rapid ‘shapeshifting’ constitutional isomerization of a substituted bullvalene is influenced by the E-to-Z configurational isomerization of a remote carbamate group, giving rise to correlated motion. We find that, while the E-configurational isomer of a bulky carbamate favors the β-bullvalene constitutional isomer, a noncovalent bonding interaction within the Z-carbamate tips the equilibrium toward the γ-bullvalene form. Using DFT modelling and NMR spectroscopy, this long-range interaction is identified as being between the bullvalene core and a pendant phenyl group connected to the carbamate. Coupling the constitutional changes of a bullvalene to a reciprocal configurational isomerization through a long-range interaction in this way will allow shapeshifting rearrangements to be exploited as part of collective motion in extended structures.


Introduction
The rapid, successive Cope rearrangements of bullvalenes 1 produce a series (Fig. 1a) of constitutional isomers.Recent advances in the synthesis of substituted derivatives, 2 alongside the development of related uxional cages, 3 have led to renewed interest in exploiting these 'shapeshiing' structures as part of functional molecules and materials.Part of the appeal of using bullvalene derivatives is that they juxtapose the rigidity and well-dened bond angles 1e that are typical of cage-like structures with the rapid structural dynamics that are commonly only found in exible molecules.They exhibit 'rigid dynamics' at the single-molecule level. 4Accordingly, investigations have been reported into bullvalene-containing uorophores, 5 antibiotics, 6 small-molecule receptors, 7 transition metal complexes, 8 rigid-rod polymers, 9 and single-molecule junctions. 10y contrast, most organic structures, particularly those containing rotatable single bonds, rapidly sample stereoisomeric structures through changes in bond angles and dihedral angles. 11The resulting isomerization (Fig. 1b) is not only inuenced by local electronic and steric factors, but also by long-range interactions.Bond rotations of groups that are separated by several covalent bonds but are close together in space can, therefore, become correlated with one another, 12 i.e., the isomerization or motion of one part of the molecule is coupled to a reciprocal conformational or congurational change in another part.
To exploit the shapeshiing rearrangements of bullvalenes in larger collective motions of extended structures, 12d-f it is necessary to understand how their uxional Cope rearrangements are inuenced (Fig. 1c) by isomerization of surrounding groups.Here, we report the isomeric distribution of carbamatefunctionalized bullvalenes 1 (Scheme 1) and demonstrate that, Fig. 1 The combination of (a) bullvalene shapeshifting rearrangements between constitutional isomers with (b) conformational and configurational changes by single bond rotations and E-to-Z isomerization are (c) correlated through noncovalent interactions (red) to bias the two bullvalene rearrangement equilibria in opposite directions (blue arrows).Black and purple circles represent appended functional groups.
even in this structurally simple case, conformational changes can become correlated to shapeshiing isomerization.For one of the compounds (benzhydryl derivative 1b), we nd that while the E-carbamate is most stable as its b-substituted bullvalene isomer, bond rotation to the Z-carbamate biases the bullvalene unit towards its g-substituted form instead, i.e., the energetics of bullvalene isomerization and carbamate rotation are coupled to one another.We show that through-space interactions subtly alter the energetics of the dynamic system.As part of this investigation, we have also assessed the extent to which this isomer distribution can be accurately modelled by comparing the calculated energies of the lowest energy conformers, as opposed to analyzing the full conformational landscape.

Results and discussion
We targeted (Scheme 1) tertiary carbamates 1a and 1b derived from benzylamine 2a and benzhydrylamine 2b, respectively.The partial double bond character of the carbamate C-N bond (c.f., tertiary amide C-N bonds 13 ) gives rise to E-to-Z congurational isomerization that can be slowed down and observed by dynamic NMR (DNMR) spectroscopy at low temperatures, which we reasoned would allow us to experimentally measure distributions of the congurational and constitutional isomers of 1a and 1b.
There are four possible constitutional isomers of 1 (Scheme 1b), which we label as a-d according to the attachment point of the carbamate substituent to the bullvalene cage.1e Consecutive Cope rearrangements from the a-isomer lead to the d-, b-, then g-isomers in a reversible linear sequence.Alternatively, rotation around the carbamate C-N bond interconverts the E-and Z-congurational isomers.In combination, these two pathways give rise to a set of eight isomers (Scheme 1b).
1 H NMR Spectroscopic analysis of the benzyl derivative 1a in CDCl 3 at 313 K (Fig. 2a) shows two broad resonances corresponding to the two sets of methylene protons, H1 and H2.
Rapid chemical exchange at this temperature averages out the contributions from the different isomers to these two methylene resonances and causes the signals arising from the bullvalene methine groups, Ha-Hd, to broaden and partially merge.At 219 K, the reduced rates of Cope rearrangements and carbamate rotation allow signals from the different species to be resolved.Although there are eight possible isomers, the aand d-forms of mono-substituted bullvalenes are usually several kJ mol −1 higher in energy than the olen-substituted band g-forms, 16 so they are not present in sufficient concentrations to be observed.b-Substitution is usually preferred over g-substitution by ∼1-2 kJ mol −1 .2c In keeping with this expectation, line tting of the H1 peaks indicates (Fig. 1b) that four isomers are present in a 45 : 23 : 21 : 11 ratio, which can be assigned to Z,b-1a, E,b-1a, Z,g-1a, and E,g-1a, respectively, using 2D NMR (Fig. S15-S22 †).Shapeselective crystallization ‡ 2e,17 from this mixture yields E,g-1a (the least populated of the four isomers in solution) as the sole isomer

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Chemical Science in the solid state (Fig. 2c).In energetic terms (Table 1), the solution-phase population corresponds to small Gibbs energy biases DG exp of ∼1.3 kJ mol −1 toward both b-isomers over their gsubstituted counterparts, and DG exp of ∼1 kJ mol −1 for each Zcarbamate over its corresponding E-carbamate.Therefore, for 1a, there is no evidence that the E/Z-state of the molecule substantially changes the energetics of b/g-isomerization, or vice versa.
The two isomerization processes do not appear to be correlated.This system does, however, provide an unusual case of reversible covalent changes occurring in a molecule more rapidly than its bond rotation, i.e., the carbamate isomerization of 1a proceeds at a slower rate than its Cope rearrangement.
Using 1 H-1 H Exchange NMR Spectroscopy 18 (EXSY) at 219 K (Fig. 2d), we found that the Cope rearrangements pass through transition states (TS1 and TS2, Scheme 1b) that are ∼55-57 kJ mol −1 above the lowest energy isomer, Z,b-1a, which is typical 19 for bullvalene constitutional isomerization.There are no cross peaks visible between E-and Z-isomers at this temperature because of the slow carbamate rotation rate.At the higher temperature of 308 K, 1 H NMR line-shape analysis (Fig. 2e) gives an averaged rate of carbamate rotation, k EZ , of 62 s −1 , indicating that TS3 and TS4 lie almost 10 kJ mol −1 higher than TS1 at DG exp of ∼65 kJ mol −1 relative to Z,b-1a (Table 1).
Unlike 1a, the increased steric crowding present in the benzhydryl derivative 1b leads to correlated isomerization.The additional phenyl ring of 1b experiences long-range interactions with the bullvalene that inuence the solution-phase isomerization equilibria.There are some key clues to this behavior in the variable-temperature NMR spectra (Fig. 3a).Crucially, the distribution of H1 methylene resonances (Fig. 3b) has been altered substantially relative to 1a.The Z,b-1b, E,b-1b, Z,g-1b, and E,g-1b isomers are present in a 27 : 16 : 48 : 8 ratio, as assigned by 2D NMR (Fig. S15-S22 †).Therefore, the Z,g-isomer is the most favored form of 1b, despite being only the third most populated isomer of 1a.The changes in relative Gibbs energy (G rel ) between the 1a and 1b isomers is summarized graphically as a potential energy diagram in Fig. 4. A structural change from a hydrogen substituent to a phenyl group at a remote site has overridden the inherent preference 2c, 16 for the bullvalene bisomer in the reaction network, but only when the carbamate is in its Z-form (Fig. 5a).The benzhydryl carbamate of 1b also rotates at a faster rate than the benzyl carbamate of 1a, exhibiting near-identical energy barriers of ∼54-58 kJ mol −1 for the four isomerization processes (Table 1).
To understand the unusual constitutional isomer distribution of 1b, we carried out DFT modelling.We generated all the constitutional isomers of 1a and 1b and carried out distancegeometry-based generation of their congurational and conformational isomers before optimizing the geometries at the PBE0-D3/def2-SV(P) level of theory.1e, 20 As there are several rotatable single bonds in the structure of 1, each of the isomers observed by low-temperature NMR itself represents a rapidly interconverting population of conformers.The relative energies of all the isomers are tabulated in Tables S3 and S4.† Cartesian coordinates are available in the ESI.† To take one representative example, there are six conformers of Z,b-1a spanning a range of ∼16 kJ mol −1 in energy, of which the two lowest energy structures are within just 2.5 kJ mol −1 of one another.
Despite there being numerous different structures contributing to the overall energetics of E-to-Z and b-to-g isomerization, the experimentally observed populations, p exp , can be approximated reasonably well by analyzing just the lowest energy conformers (Table 1).For 1a, the calculated energies, DG calc1 , of the lowest energy conformer for each of the four observable isomers gives a Boltzmann distribution, p calc1 , that matches closely to p exp .For 1b, however, this simplied approach incorrectly predicts that more of E,b-1b is present than Z,b-1b.Instead, it is necessary to perform a global Boltzmann population analysis (giving p calcG ) that takes into account all the accessible conformers in order to reproduce the experimentally observed hierarchy of isomers.This observation indicates that for bullvalene derivatives with several rotatable single bonds, accurate modelling of the shapeshiing rearrangements requires consideration of the full energetic landscape of accessible conformers.

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Noncovalent interaction (NCI) plots 21 generated using the DFT-optimized geometries reveal (Fig. 5b and S26-S29 †) the interactions that are responsible for the correlated isomerization of 1b.In addition to several close contacts between the crowded tert-butyl, carbonyl, and phenyl groups, which are present in all of the isomers, the lowest energy conformer of Z,g-1b shows evidence of substantial interaction between an ortho-hydrogen of one phenyl ring with the bullvalene cyclopropyl ring (Ph-BV interaction, Fig. 5b).This long-range interaction is less signicant in the NCI analyses of the other 1b isomers (Fig. S26-S29 †), such as Z,b-1b (Fig. 5b).Experimental evidence for the interaction in Z,g-1b is apparent in its lowtemperature 1 H NMR spectrum (Fig. 3a) as its Hd resonance is shied downeld relative to the Hd signals of the other isomers of 1b, which is indicative of deshielding caused by the aromatic ring current.The NOESY NMR spectrum (Fig. S23 †) also conrms Hd undergoes through-space interaction with a phenyl group.Although this Ph-BV interaction appears to be a relatively weak van der Waals contact, the combination of it together with other subtle differences in the attractive and repulsive noncovalent bonding interactions present in 1b is evidently sufficient to provide enough of an energetic bias to overcome the ∼1-2 kJ mol −1 preference for the b-isomer.

Conclusions
In summary, the shapeshiing constitutional rearrangements of even structurally simple bullvalenes can be inuenced by a complementary, remote isomerization process.Given that the energetic differences between bullvalene isomers are oen as little as a few kJ mol −1 , relatively subtle noncovalent bonding interactions, including weak van der Waals contacts, are sufficient to reshuffle the proportions of each isomer.In the system presented here, the introduction of an additional phenyl ring to the structure of 1a causes the Z,g-isomer to change from being the third most populous to being the major species of 1b as a result of a Ph-BV interaction.Programming in switchable long-range interactions may allow for control to be exercised over the large number of constitutional isomers that arise in multi-substituted bullvalene derivatives.

Fig. 2
Fig. 2 1 H DNMR (499 MHz, CDCl 3 ) and crystallographic analyses of 1a.(a) Partial 1 H NMR spectra at temperatures ranging from 219 K to 313 K. Signals are assigned using the labels in Scheme 1. Regions in orange boxes correspond to those shown in panels b, d, and e.(b) Line fitting was used to deconvolute the H1 signals at 219 K.An overlay of the experimentally measured (black) and simulated (orange) traces is shown, including the integrals of the four simulated peaks (blue).(c) Xray crystal structure of E,g-1a.(d) Partial EXSY NMR spectrum (499 MHz, CDCl 3 , t m = 500 ms).Blue boxes indicate cross peaks arising from Cope rearrangements.(e) Line-shape analysis for the H2 signal at 308 K, comparing the experimentally measured (exp.) and simulated (sim.)line shapes.See TableS1† for simulation parameters.

a
Measured at 219 K in CDCl 3 .bThe population of aand d-isomers is below the detection limit of the equipment used to acquire 1 H NMR spectra.c Population calculated as a Boltzmann distribution based on the DFT calculated energies of the most stable conformer for each constitutional and congurational isomer (DG calc1 ).d Population calculated as a global Boltzmann distribution by summing the populations of all accessible conformers calculated for each constitutional and congurational isomer (DG calcG ).e Apparent Gibbs energy barrier for carbamate rotation (weighted average of TS3 and TS4) at 308 K. f Relative Gibbs energies of only the most stable conformer for each isomer calculated at 219 K using PBE0-D3/def2-SV(P).20i-k,p g Transition states were not modelled.h Effective relative Gibbs energies based on the DFT calculated global Boltzmann distribution (p calcG ) for the purpose of comparison with DG exp .

Fig. 3
Fig. 3 1 H DNMR analysis (499 MHz, CDCl 3 ) of 1b.(a) Partial 1 H NMR spectra at temperatures ranging from 219 K to 313 K. Signals are assigned using the labels in Scheme 1.The region in an orange box corresponds to that shown in panels b and c.(b) Line fitting was used to deconvolute the H1 signals at 219 K.An overlay of the experimentally measured (black) and simulated (orange) traces is shown, including the integrals of the four simulated peaks (blue).(c) Partial EXSY NMR spectrum (499 MHz, CDCl 3 , t m = 500 ms).Blue boxes indicate cross peaks arising from Cope rearrangements.Dashed black boxes indicate cross peaks arising from carbamate rotation.

Fig. 4
Fig. 4 Potential energy diagrams for the observed isomers of (a) 1a and (b) 1b, showing the relative stabilization of Z,g-1b.Transition states in blue correspond to Cope rearrangement steps, those in purple correspond to E/Z-isomerisation.

Table 1
Populations and relative Gibbs energies of the isomers present in the dynamic mixtures and their transition states