A DFT Study on Spring Property of Helicenes

doi:10.21203/rs.3.rs-3348354/v1

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A DFT Study on Spring Property of Helicenes

https://doi.org/10.21203/rs.3.rs-3348354/v1

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This study focuses on investigating the spring properties of helicenes through DFT theoretical calculations. The energy change during stretching was observed by incrementally scanning the distance between both ends of the helicene from its stable state. The stiffness (k value) of each helicene was also determined at different stretching states. Interestingly, the k value was found to be non-constant during stretching, suggesting that helicenes do not behave as ideal springs. Furthermore, the effects of heteroatom doping and lateral π-extension on [6]helicene were examined, indicating that these factors have minimal impact on the spring nature of helicenes. Additionally, the study extended to longer helicenes, namely [12] and [18]helicenes. It was observed that the stiffness at the middle part of the helicene is greater than at the terminal parts, and the helical structures begin to collapse when the stretching length reaches approximately 2.5 times the stable state. We expected this work could bring innovative concept in future design of molecular devices.

Helicenes are a type of chiral aromatic molecule composed of ortho-fused aromatic rings and possess unique helical π-conjugated structures.^1,2 Owing to this, helicenes showed potential applications in the fields of chiroptical devices,^3,4 asymmetric catalysis,⁵ spin filters,⁶ etc. Unlike the central chirality mostly seen, the chirality of helicenes comes from the steric repulsion of the two terminal rings on the helical chain. Such chirality is largely associated with the entire molecular geometry rather than fixating on one sp³ atom. The repulsion of the two terminal rings brought obvious deviation of sp² carbon atoms on helicenes from planar structures, which consequently introduced substantial molecular strain. The most common study on this molecular strain is the enantiomerization process. Since the first synthesis of [6]helicene in 1955,^7,8 the enantiomerization of helicenes has been investigated both experimentally and theoretically in detail.^9-13 Currently, the conformational pathway was considered the plausible process for this enantiomerization, and the energy change was majorly connected to the transformation of conformations.¹³ Besides, several chemical rearrangement reactions of helicenes have also been reported, demonstrating how the helicenes release the intrinsic molecular strain to form more planar structures.^14-16 These reactions indicated helicenes naturally tend to undergo planarization to reach the most stable geometry. Meanwhile, the studies by adding forces at both ends of helicene and stretching it against flattening have seldom been studied. Such investigation could consider the helicene as a molecular spring, where both of them share helical structures.

Molecular spring has been studied mostly in supramolecular chemistry, polymers, as well as helical biomacromolecules including DNA double-helix chains and protein α-helix.^17-19 For helicenes, Matsuda’s group studied the stretching behavior of π-expanded helicene theoretically, and later heterohelicenes by Choudhury’s group.^20,21 In this study, we aim to explore the spring nature of helicenes systematically, and a series of fundamental helicenes with different lengths have been studied. Both stretching energy and spring stiffness k value have been investigated, as well as using non-covalent interaction (NCI) analysis. We expected this study could bring new concepts to the design of molecular springs, giving innovative application potential on molecule engineering.

The DFT calculations were performed using Gaussian 09 software.²² Geometry optimizations were conducted using PBE0²³ as the functional and def-TZVP²⁴ as the basis set with employment of Grimme’s D3 dispersion approximation²⁵ (PBE0-D3(BJ)/def-TZVP) without any symmetry setting. The spring nature of helicenes was calculated by scanning the length of the two terminal atoms of helicenes with each step of 0.05, 0.10 or 0.15 for [6], [12] or [18]helicene, and the electronic energy was used as the internal energy of the spring (E). The k value which stands for the stiffness of spring was calculated according to Hooke’s law, and the k value could be conducted as the second derivative of E value.

$${k}_{x}=-\frac{\delta f}{\delta x}=-\frac{\delta \left(\frac{\delta E}{\delta x}\right)}{\delta x}$$

For simplicity, this research only focused on [6], [12] and [18]helicenes, where the stretching direction (the line between the two terminal atoms) is almost paralleled to the helix direction. Besides, the Non-covalent interaction (NCI) analysis²⁶ was analyzed using the Mutliwfn 3.8-dev program.²⁷

We first investigated the primitive carbo[6]helicene 6H. 6H contains six ortho-fused benzene rings for the helical skeleton, and these rings give one entire turn of the helix with a rotation of roughly 360°. To study the spring property of 6H practically, we selected the inner carbon chain for study (Fig. 1a, in red). This carbon chain also formed a spring-like structure, and the distance between a and g is calculated as 3.07 Å for the stable state without any restriction. Then we added a constraint on the distance between a and g for the geometry optimization. This constraint could be equivalent to adding a pair of forces with opposite directions. We recorded the changes in the molecular energy when gradually increasing this distance with increments up to 1.00 Å (Fig. 1b). This stretching process showed an increase of energy of 39.8 kJ mol^− 1, and the curve seemed close to a parabola (for an ideal spring, this curve should be a parabola according to Hooke’s law). Then we took a second-order differential of this energy curve and obtained the stiffness factor k. Interestingly, k did not appear as constant, and it varied along with the distance. When the molecule is at the equilibrium state (energy minimum), the k is calculated as 19.1 N m^− 1. With the increase of the distance, the k started to decrease down to 8.0 N m^− 1 when the distance increment was close to 1.00 Å. This result indicated that helicene 6H is not an ideal spring. Then, we also studied the noncovalent interaction during the stretching process using NCI analysis. From the equilibrium state of 6H (named 6H-0), we could find rich non-covalent interaction with a helical shape in the central column of 6H. The red part close to the center indicated repulsion in this area, and the green part indicated normal van der Waals interactions. With an increase in the distance increment to 1.00 Å (6H-1.0), we could find this helical belt of noncovalent interaction also stretched, but the area was shrunk.

After studying the primitive carbo[6]helicene, we then investigated several heterohelicenes. We took aza[6]helicenes as examples, and 1- to 8-aza[6]helicene (1A6H to 8A6H) have been studied (Fig. 2). The results showed that when the nitrogen position is at 3 to 8, the increased energy for 1 Å only varied between 39.4 and 40.0 kJ mol^− 1. Besides, the k value was also limited between 19.4 and 20.3 N m^− 1 at the starting, and between 7.4 and 7.8 N m^− 1 at the elongation for 1 Å. The deviations increased but were still small for 1A6H and 2A6H. 1A6H gave higher energy up to 41.1 kJ mol^− 1 for the elongation, and 2A6H gave lower energy at 38.8 kJ mol^− 1. Correspondingly, the k values were also changed especially at the beginning point, 21.0 N m^− 1 for 1A6H and 18.4 N m^− 1 for 2A6H. This result indicated that the introduction of heteroatom by changing the benzene ring to a pyridine ring was not able to obviously change the spring nature of helicenes.

We then tried to investigate the spring nature of several reported lateral π-extended [6]helicenes (E6H-1 to E6H-4^26,28–30) (Fig. 3). E6H-1 possessed three additional lateral extended benzene rings on the skeleton of [6]helicene, and it showed an increase of energy of 40.3 kJ mol^− 1 when stretching the two terminal carbon atoms for an additional 1 Å. Besides, the k value gave 20.5 at the beginning of stretching and decreased to 8.1 when the elongation reached 1 Å. Interestingly, both the energy curve and the k value curve were nearly identical to the primitive [6]helicene, suggesting that the additional fused benzene ring for E6H-1 was not able to reinforce the stiffness of the helicene spring obviously. This could be supported by the rest three π-extended [6]helicenes. For E6H-3 and E6H-4 with more additional fused benzene rings, neither the energy curve nor the k value curve showed large deviation compared to the primitive [6]helicene. Meanwhile, for E6H-2, despite the two additional lateral fused rings, the introduced nitrogen and boron atoms on the skeleton even resulted lower energy increase of 34.7 kJ mol^− 1. Besides, the k value also changed to 15.2 N m^− 1 at the initial state and 9.3 N m^− 1 when reaching to1 Å.

Consequently, we studied the longer helicenes [12]helicene (12H) and [18]helicene (18H) with two and three turns of the helical skeleton, respectively. The NCI maps as well as the energy curve and k value curve were shown in Figs. 4a and 4b. compared with 6H, the NCI maps of 12H and 18H gave large difference. Both 12H and 18H showed not only a helical non-covalent inner belt in the central column but also an additional one on the periphery between the two layers of the helicene skeleton, and unlike the inner belt that turned two turns for 12H, the outer belt turned only one turn (For 18H, inner one gave three turns, and outer two turns). This additional belt could be attributed to the π-π interaction between the two π-conjugated layers. By stretching the two terminal carbon atoms for 2 Å for 12H, we could find that the shrinkage of these non-covalent interactions was different at the different positions. The central part of the non-covalent interactions was revealed to be similar to the stable form, while the non-covalent interactions on the two terminal parts were shrunk and disappeared during the stretching. The results appeared similar for 18H when the helicene was stretched for 3 Å. This result suggested that the terminal parts of helicenes were revealed to be easier to stretch compared to the central parts. To confirm this suggestion, we studied the stiffness of each part of the helicenes. For 12H, the helicene skeleton included seven [6]helicene sub-units (e.g. the [6]helicene sub-unit with the first six benzene rings of 12H was shown in orange in Fig. 5a). We could investigate the stiffness for each [6]helicene sub-unit by stretching the two terminal carbon atoms for 1 Å (e.g. for the first [6]helicene sub-unit, the two terminal carbon should be a and g) respectively, and the results were shown in Fig. 5b (only four [6]helicene sub-units have been investigated due to the C₂-symmetry of 12H). Interestingly, all the k values for the initial state showed obvious augmentation (> 30 N m^− 1) compared with the k value of 6H (19.1 N m^− 1). This was probably attributed to the additional π-π non-covalent interaction that stuck the helicene pitch against the stretching. Notably the terminal [6]helicene sub-unit (a-g) gave the k value of 31.9 N m^− 1, while the inner [6]helicene sub-units showed k value higher than 35.0 N m^− 1. This could be ascribed to the more π-π interaction for the inner [6]helicene sub-unit that made the structure more indurative. Besides, we could also find when stretching for 1 Å, the terminal [6]helicene sub-unit gave only 53.4 kJ mol^− 1, while the inner [6]helicene sub-unit could reach 67.4 kJ mol^− 1. Therefore, it could explain why when stretching 12H, the terminal part was easier to be stretched. The results exhibited similar in the case of 18H, and in addition, we could find the inner [6]helicene sub-units showed even higher k value up to 41.5 N m^− 1 owing to the increased π-π interaction.

The above results showed the stretching of 1/2/3 Å for 6H/12H/18H, and to further investigate the limitation of these helicene springs, we continued to stretch these helicenes, and the results are depicted in Fig. 6. For 6H, with additional stretching, the helicene became longer but narrower. From the NCI analysis, the helical non-covalent interaction gradually disappeared when the elongation was added to 3.0 Å from the stable state. With further stretching, the molecule was finally broken at ca. 5.4 Å of elongation, and at this state, the distance between to terminal atoms was measured as 8.47 Å, which was 2.7 times compared with the stable state. The k value was firstly increased to ca. 18 N m^− 1, then decreased sharply. For 12H and 18H, the results were more complicated. With additional stretching, the π-interaction only kept in the middle part of the helicene, and with more stretching, this π-interaction also disappeared, and the helix was broken at 10.0 Å of elongation (15.86 Å of two terminal atoms vs. 6.26 Å of the stable state, 2.5 times). The k value was roughly kept at ca. 6 N m^− 1 but with several fluctuations. 18H gave similar results as 12H and the helix was broken at 14.7 Å of elongation (24.32 Å of two terminal atoms vs. 9.62 Å of the stable state, 2.5 times).

In conclusion, we have studied the spring nature of helicenes using DFT theoretical calculations, and a series of [6], [12] and [18]helicenes have been studied. The results indicated that the spring nature is largely related to the helical π-system, and either bringing heteroatoms (e.g. nitrogen) on the helicene skeleton or introducing fused benzene rings on the lateral side to give π-extended helicene would hardly modify the spring nature of the helicene core. Besides, for longer helicenes, the terminal rings were revealed to be easier stretched compared with the rings in the middle part. This is probably due to the rich π-π interaction of the middle part than the terminal part. Finally, with additional stretching, the π-π interaction that sticks the helicene pitch would finally vanish and the helical structure started to collapse at roughly 2.5 times the length compared with the stable state. his work provided a new concept on conformational study of helical aromatic molecules, and we expected this work could bring new inspiration on designing new functional molecules.

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Competing interests

There are no conflicts to declare.

Authors' contributions

C.S. and X.L. conceived the experiments. X.C. and X.Z. performed the DFT calculations. X.L., J.W., and C.S. analyzed the data. X.L. and C.S. wrote the manuscript. All authors discussed the results and revised the manuscript.

Funding

This work was supported by the Natural Science Foundation of Zhejiang Province (LY23B040003, LQ22B040003), the National Natural Science Foundation of China (22105172), the Key research and development program of zhejiang province (2021C01080), and the Fundamental Research Funds of Zhejiang Sci-Tech University (22062026-Y, 21062113-Y).

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Shen Y, Chen C-F. Chem. Rev. 2012; 112:1463.
Gingras M. Chem. Soc. Rev. 2013; 42:968.
Yang Y, da Costa R C, Fuchter M J, Campbell A J. Nat. Photon. 2013; 7:634.
Dhbaibi K, Abella L, Meunier-Della-Gatta S, Roisnel T, Vanthuyne N, Jamoussi B, Pieters G, Racine B, Quesnel E, Autschbach J, Crassous J, Favereau L. Chem. Sci. 2021; 12:5522.
Aillard P, Voituriez A, Marinetti A. Dalton Trans. 2014; 43:15263.
Kiran V, Mathew S P, Cohen S R, Delgado I H, Lacour J, Naaman R. Adv. Mater. 2016; 28:1957.
Newman M S, Lutz W B, Lednicer D. J. Am. Chem. Soc. 1955; 77:3420.
Newman M S, Lednicer D. J. Am. Chem. Soc. 1956; 78:4765.
Goedicke C, Stegemeyer H, Tetrahedron Lett. 1970; 11:937.
Martin R H, Marchant M J, Tetrahedron 1974; 30:937.
Grimme S, Peyerimhoff S D. Chem. Phys. 1996; 204:411.
Janke R H, Haufe G, Würthwein E U, Borkent J H. J. Am. Chem. Soc. 1996; 118:6031.
Barroso J, Cabellos J L, Pan S, Murillo F, Zarate X, Fernandez-Herrera M A, Merino G. Chem. Commun. 2018; 54:188.
Fuchter M J, Weimar M, Yang X, Judge D K, White A J P. Tetrahedron Lett. 2012; 53:1108.
Matsuda C, Igarashi R, Katagiri H, Murase T. Chem. Eur. J. 2022; 28:e202200132.
Shen C, Zhang G, Ding Y, Yang N, Gan F, Crassous J, Qiu H. Nat. Commun. 2021; 12:2786.
Murphy K E, McKay K T, Schenkelberg M, Sharafi M, Vestrheim O, Ivancic M, Li J, Schneebeli S T. Angew. Chem. Int. Ed. 2022; 61:e202209772.
Vogt M, Langecker M, Gouder M, Kopperger E, Rothfischer F, Simmel F C, List J. Nat. Phys. 2023; 19:741.
Takahashi H, Rico F, Chipot C, Scheuring S. ACS Nano 2018; 12:2719.
Nakakuki Y, Hirose T, Matsuda K. J. Am. Chem. Soc. 2018; 140:15461.
Karak P, Choudhury J. Chem. Sci. 2022; 13:11163.
Frisch M J, Trucks G W, Schlegel H B, Scuseria G E, Robb M A, Cheeseman J R, Scalmani G, Barone V, Mennucci B, Petersson G A, Nakatsuji H, Caricato M, Li X, Hratchian H P, Izmaylov A F, Bloino J, Zheng G, Sonnenberg J L, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery J A Jr, Peralta J E, Ogliaro F, Bearpark M, Heyd J J, Brothers E, Kudin K N, Staroverov V N, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant J C, Iyengar S S, Tomasi J, Cossi M, Rega N, Millam N J, Klene M, Knox J E, Cross J B, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann R E, Yazyev O, Austin A J, Cammi R, Pomelli C, Ochterski J W, Martin R L, Morokuma K, Zakrzewski V G, Voth G A, Salvador P, Dannenberg J J, Dapprich S, Daniels A D, Farkas Ö, Foresman J B, Ortiz J V, Cioslowski J, Fox D J. Gaussian 09, Revision E.01. Wallingford CT, 2013.
Adamo C, Barone V. J. Chem. Phys. 1999; 110:6158.
Schäfer A, Huber C, Ahlrichs R. J. Chem. Phys. 1994; 100:5829.
Grimme S, Antony J, Ehrlich S, Krieg H. J. Chem. Phys. 2010; 132:154104.
Johnson E R, Keinan S, Mori-Sánchez P, García-Contreras J, Cohen A J, Yang W. J. Am. Chem. Soc. 2010; 132:6498
Lu T, Chen F. J. Comput. Chem. 2012; 33 :580.
Hatakeyama T, Hashimoto S, Oba T, Nakamura M. J. Am. Chem. Soc. 2012; 134:19600.
Fujikawa T, Segawa Y, Itami K. J. Am. Chem. Soc. 2015; 137:7763.
Morita F, Nogami J, Dias A J A, Kinoshita S, Nagashima Y, Tanaka K. Eur. J. Org. Chem. 2022; 2022:e202200690.

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A DFT Study on Spring Property of Helicenes

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