Odd–even alternations in helical propensity of a homologous series of hydrocarbons

Odd and even homologues of some n-alkane-based systems are known to exhibit notably different trends in solid-state properties; a well-known illustration is the zigzag plot of their melting point versus chain length. Odd–even effects in the solid state often arise from intermolecular interactions that involve fully extended molecules. These effects have also been observed in less condensed phases, such as self-assembled monolayers; however, the origins of these effects in such systems can be difficult to determine. Here we combined NMR and computational analysis to show that all-syn contiguously methyl-substituted hydrocarbons, with chain lengths from C6 to C11, exhibit a dramatic odd–even effect in helical propensity. The even- and odd-numbered hydrocarbons populate regular and less-controlled helical conformations, respectively. This knowledge will guide the design of helical hydrocarbons as rigid scaffolds or as hydrophobic components in soft materials. Even- and odd-numbered homologues of some hydrocarbons are known to exhibit different trends in solid-state properties. Now, experimental and computational investigations on a homologous series of a stereochemically well-defined hydrocarbon have revealed an odd–even effect in conformational behaviour in solution that is caused by a single gauche interaction.

I n 1887, Baeyer discovered that n-alkyl carboxylic acids do not undergo a monotonic increase in melting point with increasing chain length 1 . Instead, the series of molecules that contain an even number of carbon atoms tended to have higher melting points than the series that contained an odd number of carbon atoms (Fig. 1a). X-ray crystallographic analysis later confirmed that the origin of this odd-even effect was that the even series had optimal intermolecular interactions of their termini when packed together in their fully extended zigzag conformer 2,3 . Since then, odd-even effects in other bulk properties of n-alkane-based systems have been well documented and studied 4 . Some of the most intriguing odd-even effects are those associated with the properties of self-assembled monolayers of n-alkanethiols on metal surfaces (Fig. 1b). Although these odd-even effects, which reveal themselves in surface-wetting properties 4,5 and current densities of molecular junctions 6,7 , can have significant technological implications, the origin of each effect remains poorly understood. Some have been linked to the solid-like characteristics of these semicondensed phases; for example, in the fully extended zigzag arrangement, the odd and even systems exhibit different orientations of the free-end terminal groups, which interface differently with wetting liquids 5 or, in the case of molecular junctions, with the top electrode 6 . However, recently odd-even effects were linked to the liquid-like characteristics of self-assembled monolayers, specifically the level of deviation of chains from the all-trans conformer to socalled gauche defect conformers, dynamic behaviour that appears to alternate in a zigzag fashion with increasing chain length [8][9][10] . Furthermore, molecular dynamics simulations predict odd-even effects in the stretch-induced coil-to-helix transition of isotactic polypropylenes 11 . Here we show a rare manifestation of the oddeven effect in the conformational behaviour of all-syn contiguously methyl-substituted hydrocarbons, which are useful systems for the study and exploitation of helical conformers of hydrocarbons and display marked odd-even effects in their propensity to form regular helical conformers.
Using iterative stereodefined homologation of boronic esterterminated hydrocarbons (Fig. 2a), a process termed lithiationborylation, which was recently developed in our laboratory 12 , we prepared conformationally defined contiguously methylsubstituted hydrocarbons as single enantiomers. These molecules exhibit different shapes, linear (Fig. 2b) or helical (Fig. 2c), depending on the relative configuration of the methyl groups, and thus provide access to molecular systems that can be used to both probe and exploit specific subsets of the many conformers that are accessible in the more flexible parent n-alkanes 13 . Supported by exhaustive computational modelling and NMR analysis, we proved that the disyndiotactic (alternating syn-anti) isomer 7 heavily populated a fully extended zigzag conformer (linear) in solution, whereas the corresponding threo-diisotactic (all-syn) isomer 8 heavily populated a helical conformer 13 .
This result is consistent with and can be understood by using theoretical analysis that was put forward by Hoffmann in the 1990s 14 . He articulated a useful description of the conformation of hydrocarbons as being defined by a sequence of dihedral angles that involve the carbon atoms of the principal chain, with the terms g + , g − and t denoting dihedral angles of approximately +60, −60 and 180°, respectively. For methyl-substituted hydrocarbons, when a g + dihedral angle is immediately followed by a g − dihedral angle, two carbon units (four bonds apart from each other) are brought to within about 2.5 Å. This destabilizing g + g − interaction, commonly called a syn-pentane interaction (Fig. 2d), is worth ~3.3-3.7 kcal mol −1 (ref. 15 ). To avoid these interactions, all-syn and syn-anti contiguously methyl-substituted hydrocarbons adopt alternating g + t (or g − t) and all-t dihedral angles, which describe their helical and linear shapes, respectively.
The (S,R,S,R,S,S,R,S,R,S) enantiomer of an all-syn isomer with hydroxyl and biphenyl terminal groups (8) adopted an M helix in solution, whereas its crystalline benzoate derivative (9) adopted a P helix in the solid state 13 . This result showed that both P and M helical forms were accessible to the molecule and although one helical form was favoured in solution, this preference could be Odd-even alternations in helical propensity of a homologous series of hydrocarbons Johan A. Pradeilles 1,5 , Siying Zhong 1,5 , Márton Baglyas 2,3 , György Tarczay 2,3 , Craig P. Butts 1 ✉ , Eddie L. Myers 4 ✉ and Varinder K. Aggarwal 1 ✉ Odd and even homologues of some n-alkane-based systems are known to exhibit notably different trends in solid-state properties; a well-known illustration is the zigzag plot of their melting point versus chain length. Odd-even effects in the solid state often arise from intermolecular interactions that involve fully extended molecules. These effects have also been observed in less condensed phases, such as self-assembled monolayers; however, the origins of these effects in such systems can be difficult to determine. Here we combined NMR and computational analysis to show that all-syn contiguously methyl-substituted hydrocarbons, with chain lengths from C6 to C11, exhibit a dramatic odd-even effect in helical propensity. The even-and oddnumbered hydrocarbons populate regular and less-controlled helical conformations, respectively. This knowledge will guide the design of helical hydrocarbons as rigid scaffolds or as hydrophobic components in soft materials. over-ridden by crystal packing forces in the solid state. Intrigued by this observation, we wished to understand the origin of the sense of helicity, particularly in solution. In this work, we therefore initiated a computational and experimental investigation to establish the relationship between the structure and the sense of helicity of allsyn methyl-substituted hydrocarbons, thereby building a theoretical framework from which technological applications in catalysis, materials, and medicine could emerge.

results and discussion
We decided to base our study on the C6-C11 series of all-syn contiguously methyl-substituted hydrocarbons with alkyne groups at the termini (Fig. 3d). The terminal alkyne groups were deemed suitably non-imposing to allow the methine units to dominate the control of structural order. Overlaying the C10 isomer onto the idealized diamond-lattice template revealed that only two conformers could avoid syn-pentane interactions, namely an M (left-handed) helix and a P (right-handed) helix (Fig. 3a). Following Hoffmann's notation, their dihedral angle sequences are t g + t g + t g + t g + t and g − t g − t g − t g − t g − , respectively. The corresponding Newman projections show that each t (180°) dihedral angle creates three gauche interactions, whereas each g (±60°) dihedral angle generates only two gauche interactions (Fig. 3c). To reduce the number of steric interactions, the molecule is expected to adopt a conformer that maximizes the number of g dihedral angles and minimizes the number of t dihedral angles. Therefore, this qualitative analysis predicts that C10 would adopt a right-handed helix (22 gauche interactions) in preference to a left-handed helix (23 gauche interactions), as would other homologues in the same enantiomeric series that contain an even number of methines. For homologues that contain an odd number of methine units, such as C11, which is achiral (meso) owing to the mirror plane that contains the central carbon atom and its methyl substituent, both M and P helices contain 25 gauche interactions, with g and t dihedral angles at opposing termini ( Fig. 3b). Therefore, for odd systems one would predict a 1:1 mixture of M and P helices with a high degree of regularity. To confirm Au (111) Au (111) CH 3 (CH 2 ) 6 S-Au for CH 3 (CH 2 ) n SH (n = even) CH 3 (CH 2 ) 7 S-Au for CH 3 (CH 2 ) n SH (n = odd)

Fig. 1 | Known examples of odd-even effects associated with bulk
properties. a, Graph showing the effect of chain length on the melting point of a series of n-alkyl carboxylic acids, which demonstrates a zigzag rather than a monotonic increase in melting point as the chain length increases. b, The orientation of the terminal methyl groups of selfassembled n-alkanethiolate monolayers on Au(111) is known to depend on whether there is an odd or an even number of carbon atoms in the chain. Blue and red dots represent CH 2 groups in an odd-numbered and even-numbered n-alkanethiolate carbon chain, respectively. these predictions, a detailed computational investigation of the conformational behaviour of these molecules was undertaken. A molecular mechanics conformational search of C10 found 45 conformers, which were subjected to density functional theory (DFT) geometry optimization and free-energy calculations. These DFT calculations confirmed that C10 has a strong preference for helical conformers, which constitute 79% of the total population (Fig. 4b). Of these helical conformers, which exhibit a narrow range of pitch values, 82% are P helices (g − t g − t g − t g − t g − ; 22 gauche interactions) and 18% are M helices (t g + t g + t g + t g + t; 23 gauche interactions), a diastereomeric ratio that is consistent with the extra gauche interaction (~1 kcal mol −1 ) in M helices 15 . The same computational analysis was performed on the shorter homologues, C6 and C8, which confirmed that the corresponding P and M helices, respectively, are the preferred conformers in solution, the sense of helicity following the absolute configuration of the enantiomeric series of homologues to which they belong. The C6 and C8 compounds have a strong conformational preference for fully helical conformers-the populations register 86 and 80%, respectively (Fig. 3e). The overall drop in helical population with increasing chain length is in line with the increasing entropic cost of adopting defined conformers as the number of freely rotatable bonds increases 16 . The calculated difference in energy between the M and P helices for both the C6 and C8 compounds is about ±1 kcal mol −1 , which is similar to the value calculated for C10. Overall, the C6, C8 and C10 hydrocarbons preferentially adopt helical conformers that present g dihedral angles at the termini (g − for C6/C10 and g + for C8), which thus minimizes the overall number of gauche interactions.
Computational analysis of the meso (and odd-numbered) homologues C7, C9 and C11 revealed, as predicted, a 1:1 mixture of M and P helices 17 . However, the shortest member of this series, C7, exhibited only a moderate preference for entirely helical conformers, − Left-handed helix (M) t g g + t g + t g + t g + t g + 25 gauche interactions Right-handed helix (P) g | relationships between chain length, sequence of dihedral angles and conformational behaviour. a, Even-numbered carbon chains preferentially adopt the helical conformer with g dihedral angles at both termini, which thus reduces the number of gauche interactions in the molecule. b, To fold into a helix, odd-numbered carbon chains must have one t and one g terminal dihedral angle. Both helical conformers present the same number of gauche interactions. c, Any t dihedral angle generates three gauche interactions, whereas any g dihedral angle creates only two gauche interactions. d, The preference of the termini to present a sterically favoured g dihedral angle leads the even-numbered carbon chains to strongly favour a helical conformation (both termini induce the same screw-sense), but creates a conflict in the odd-numbered carbon chains that forces them to adopt less-regular conformations. e, Graph showing the effect of chain length on the helical fraction of all-syn methyl-substituted hydrocarbons. An odd-even effect is observed where the helicity of even-numbered hydrocarbons is well controlled but odd-numbered hydrocarbons are less well controlled.
a preference that quickly vanished on increasing the length (C7, 63%; C9, 49%; C11, 27%; Fig. 3e). Closer analysis of C11 revealed that in the helical conformers, which were present in a low population (27%), one end group adopts a low-energy gauche orientation with respect to the main chain, whereas the other adopts the highenergy trans orientation. However, in most non-helical conformers, both terminal end groups adopt the low-energy gauche orientation, facilitated through the introduction of a kink 18 (or relaxed synpentane interaction) in the chain. Consequently, for these oddnumbered hydrocarbons, the helical conformers (with one end group necessarily in the costly trans orientation) and non-helical conformers (with a relaxed syn-pentane interaction in the chain) are very close in energy (<1 kcal mol −1 compared with 1.7-1.8 kcal mol −1 for C6, C8 and C10); the degeneracy suppresses control over the degree of helicity. Overall, DFT calculations predict that for compounds with an even number of methines, such as C10, the lowest-energy conformer, which is helical, presents both end groups in a gauche relationship with the main chain. Here, both end groups, which are substituents on carbon atoms of the same absolute configuration,    induce the same sense of helicity; the reinforcement leads to control over the degree of helicity, which is only relinquished gradually by the entropic cost of increasing chain length (Fig. 3d,e). The alternating preference for P and M helices is dictated by the absolute configuration of the end groups, which alternates from R to S as the chain length increases bidirectionally. For compounds with an odd number of methines in the main chain (meso homologues), such as C11, the end groups are substituents on carbon atoms of opposite absolute configuration. The end groups only induce the same sense of helicity when one end group is placed in a gauche relationship with the main chain while the other is in a higher energy trans relationship. When both end groups are placed in the low-energy gauche relationship with the main chain, they induce the opposite sense of helicity, and thus create a kink in the chain. These internally defective helical conformers are very similar in energy to the purely helical conformers, which necessarily present gauche-and trans-orientated end groups. With increasing length, the number of positions at which the defect can present itself also increases and the increasing degeneracy leads to a rapid drop in overall control of the helical character (Fig. 3d,e).
With the above predictions in hand, we needed to synthesize these molecules and examine their behaviour in solution to validate our theoretical expectations. Our group previously reported a methodology 13 for the iterative homologation of boronic esters to synthesize compounds like C10. The protocol (Fig. 2a) involves subjecting a suitable starting pinacol boronic ester to an iterative two-step process that involves (1) the formation of a boronate complex (3) by adding the pinacol boronic ester (1) to a solution of a configurationally-stable enantioenriched methyl-substituted lithium carbenoid (2) at low temperature and (2) the stereospecific 1,2-metallate rearrangement of this boronate complex, which was promoted at a higher temperature, to deliver the one-carbon extended boronic ester. Owing to the C 2 symmetry of carbon chains that contain an even number of methine units, such as C10, we decided to investigate a bidirectional homologation of a bis(boronic ester), and thus reduce the number of synthetic steps by half compared to the unidirectional strategy. At the end of the growth phase, the terminal boronic esters could then be stereospecifically converted into alkyne groups by using a methodology developed previously by our group 19 .
Rhodium-catalysed asymmetric diboration 20,21 of trans-butene (12) provided the requisite starting bis(boronic ester) (Fig. 4a). Although 2,3-bis(boronic ester) 13a was obtained with a high enantioselective ratio (>99.5:0.5 e.r.) and high diastereoselective ratio (>95:5 d.r.), it could not be separated from the 1,2-substituted regioisomer that arose from initial alkene isomerization. Pleasingly, however, after the first round of bidirectional double homologation, bis(boronic ester) 14 could be purified by recrystallization to provide a chemically and enantiomerically pure material for further homologation. At this stage, an X-ray structure confirmed the relative configuration of the four stereogenic centres. Bis(boronic ester) 14 was subjected to three further iterations of double homologations, switching the enantiomer of the lithium carbenoid used at each iteration, to deliver the all-syn bis(boronic ester) 18, which could be successfully converted into bis(alkyne) C10 by using our recently developed stereospecific alkynylation methodology 19 . Target molecules C6 and C8 were obtained with the same protocol by terminating the sequence after the second and third iterations of homologation, respectively. Notably, the use of the same bidirectional protocol to generate C6, C8 and C10 has the consequence that it delivers C6, C10 and C8 as homologues of opposing enantiomeric series (C6 and C10 have R-configured terminal methine units and C8 has S-configured terminal methine units); a common unidirectional approach would lead to C6, C8 and C10 being part of the same enantiomeric series. The meso homologues C7, C9 and C11 were prepared from the bis(boronic ester) derivatives of C6, C8 and C10, respectively, through careful alkynylation of one of the equivalent terminal boryl groups, protection of the resulting terminal alkyne as the triisopropylsilyl derivative, homologation of the remaining boronic ester with the requisite enantiomer of the lithium carbenoid, alkynylation and deprotection (Fig. 4g). With the target molecules C6-C11 in hand, their conformational behaviour in solution was then investigated by using a comparison of their computed conformers, populations and NMR parameters with experimental solution-state NMR spectroscopic data. In line with the predicted levels of conformational control, compound C10 was a crystalline solid (melting point 88-92 °C), whereas C11 was a liquid at room temperature, which demonstrates how one additional carbon can be the difference between order and chaos.
The DFT-calculated 1 H-1 H scalar coupling constants and interproton distances that would be derived from nuclear Overhauser effect (NOE) measurements for C6, C8 and C10 (each averaged across their calculated population of conformers) were compared to the experimentally measured values (Fig. 4c). The resulting goodness of fit is in line with that observed for conformational analysis of compounds of similar structural complexity 11,13 and reflects their relatively high conformational control ( 1 H-1 H coupling: mean absolute deviation (MAD) = 0.1-0.5 Hz, standard deviation (s.d.) = 0.1-0.5 Hz; NOE distances: MAD = 2.9-4.2%, s.d. = 1.8-5.4%). The experimentally acquired vibrational circular dichroism (VCD) spectrum of C10 in CDCl 3 was a close match to the DFTpredicted simulation for the C10 P helix (Fig. 4f), and thus in agreement with the predicted sense and level of helical chirality (~P/M 90:10). Additionally, that more intense VCD signals were observed at lower temperature supports the assertion that the slight drop in helicity across the even series is due to the increased entropic cost of retaining full helicity on chain elongation ( Supplementary Fig. 7b). A selection of alternative C10 molecules with other terminal groups (1-naphthyl, 31; hydroxy, 32; acetoxy, 33; amino, 35 and dibenzylamino, 36), prepared through stereospecific transformations of the intermediate bis(boronic ester) 18 and analysed as described above, all adopted the expected P helix in solution. A comparable analysis for the less-controlled odd members of the series also supports the DFT-predicted levels of helical control. C7 provides a good fit to NMR experimental results ( 1 H-1 H coupling: MAD = 0.3 Hz, s.d. = 0.2 Hz; NOE distances: MAD = 4.1%, s.d. = 6.0%). Notably, fitting the experimental NOE data to only a 1:1 mixture of M and P helices (Supplementary Table 22) provides a much worse fit, which demonstrates that non-helical conformers are, indeed, present in solution. C9 and C11 give similar outcomes ( 1 H-1 H coupling: MAD = 0.3-1.0 Hz, s.d. = 0.3-1.4 Hz; NOE distances: MAD = 5.4-6.7%, s.d. = 6.5-8.9%) with the quality of fit falling off as the chain is extended to C11, in line with the population estimates by DFT becoming more sensitive to the increased number of low-energy non-helical conformers possible in this more complex conformational landscape.

Conclusions
Our experimental and computational studies on all-syn contiguously methyl-substituted hydrocarbons revealed a rare odd-even effect in alkanes that is not associated with bulk intermolecular interactions 22,23 . For future technological applications, these fundamental findings will guide the design of molecules with desirable conformational, and thus physicochemical, properties. Carbon chains with an even number of methine groups will lead to molecules with welldefined helical conformers for their application as non-switchable rigid materials or as scaffolds for the presentation of molecular recognition elements. Carbon chains with an odd number of methine groups, although adopting less-regular conformations with identical terminal groups, provide more ready access to both M and P helical forms, which offers the potential to manipulate their conformational landscape through judicious end-group selection. Through covalent or non-covalent modification of the end groups, the conformational landscape could be switched from one screw sense to another for applications in materials. Furthermore, these results highlight the potentially important role of dynamic behaviour in the origin of bulk odd-even effects in condensed phases, a connection that has recently been proposed to explain trends in some properties of liquids 24 and self-assembled monolayers 8,25 .

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