This is an open access article published under an ACS AuthorChoice License, which permits copying and redistribution of the article or any adaptations for non-commercial purposes.
Reactions FIRSTFirst REACTIONS
One-Handed Helical Orbitals in Conjugated Molecules Yuriko Aoki† Yuuichi Orimoto† and Akira Imamura‡ †
Department of Material Sciences, Faculty of Engineering Sciences, Kyushu University, 6-1 Kasuga-Park, Fukuoka 816-8580, Japan
‡
Hiroshima Kokusai Gakuin University, Nakano 6-20-1, Aki-ward, Hiroshima 739-0321, Japan
Cumulenes with two degenerate helical molecular orbitals could be modified for use in spintronics, analysis, and enantioselective reactions. Figure 1. Cyclic and coarctate Möbius orbital topologies (left) and helical molecular orbitals (right) made explicit by substitution or axial torsion. [n] is depicted for an allene structure. Figure is modified and reprinted with permission from ref 1. Copyright 2018 American Chemical Society.
I
n conjugated linear molecules (H2CCn–1CH2) p-orbitals exhibit interesting shapes, depending on the number of carbon atoms in the main chain and the dihedral angle in the terminal CH2 groups. Garner et al. systematically analyzed the relationship between the structure of such conjugated π-systems, [n]cumulenes, and helical frontier molecular orbitals (MOs) using Hückel theory and density functional theory calculations.1 The authors discussed similarities between helical orbitals of even [n]cumulenes (n = even number of double bonds and odd number of carbon atoms) and those of Möbius cyclopolyenes (Figure 1). They proposed an intriguing classification of orbital nature by molecular symmetry using the Hückel method. In 1968 Buenker calculated the electronic structure of allene2 and demonstrated the rotational barriers of ethylene and allene using closed-shell self-consistent-field approach. Although many theoretical studies of chiral allenes have been reported, the existence of helical frontier MOs for even [n]cumulenes was not known until 2013.3−5 Helical MOs do not exist in odd [n]cumulenes (even number of carbon atoms), which form planar, stable structures. Garner et al. tested their approach on several existing concepts.1 Their mathematical derivation used simple Hückel theory and density functional theory calculations with large basis sets for recognizing orbital shapes. Although this approach is classical and topological, the authors produced a simple and elegant description that included important principles of basic science. The results could be extended to more quantitative discussions toward advanced molecular design. For example, the excited states of twisted structures in [n]cumulenes have been directly used in the analysis of reactions, absorption © XXXX American Chemical Society
spectra, optical and magnetic properties, etc. The symmetry within coarctate Möbius systems (Figure 1) might be an essential tool for the elucidation of coarctate transition states.6 Helical MOs7−9 were demonstrated in real systems and recognized as a key factor in various phenomena. Anderson et al. proposed experimental and computational evaluations of the rotation barrier in a butadiyne-linked porphyrin dimer.7 They showed that the transition between excited states of the molecule arises predominantly from the delocalization via helical frontier MOs on the butadiyne linker. Low et al. demonstrated helical orbitals on a butadiyne linker between diruthenium complexes.8 They proposed that the helical orbitals on the linker determined the relative orientation of the end groups. Misra et al. showed that cumulenes linking two radicals exhibit magnetic properties: ferromagnetic when cumulenes contain an odd number of carbon atoms and antiferromagnetic when the number is even.9 The work was focused on establishing relations between magnetic properties, the number of carbon atoms, and bond alternation behavior of the linker. Helical orbitals were found on the disubstituted cumulene linker when the substituents were the same type of spin center. We obtained helical orbitals for even [n]cumulenes and polyynes by starting the closed-shell self-consistent-field calculations with an initial guess having helical orbitals.4 When the program recognizes a specific symmetry in the molecular
A
DOI: 10.1021/acscentsci.8b00228 ACS Cent. Sci. XXXX, XXX, XXX−XXX
Reactions FIRSTFirst REACTIONS
ACS Central Science
the doubly degenerate helical MO levels into left-handed and right-handed, the substituent modification might be considered for the extraction of one of the two types of helices. In addition, we confirmed that the helical orbital coefficients decrease rapidly with chain length and localize into the central part when both the terminal groups are −CH2. Therefore, the conjugated “rings” are expected to produce fascinating helical orbitals designed for longer chains. For efficient and highly accurate large-ring calculations, our three-dimensional elongation method would be useful for the molecular design utilizing different substitutions and conformations.10,11
structure, the calculations start with the initial guess that initial orbitals are rectilinear, and the self-consistent-field calculations will converge to rectilinear orbitals again (Figure 2).
■
Author information Author Information
E-mail:
[email protected]. ORCID
YurikoAoki: Yuriko Aoki : 0000-0001-5243-8192 0000-0001-5243-8192 Notes
The authors declare no competing financial interest.
■
REFERENCES REFERENCES
Figure 2. Even [n]cumulenes have both frontier and degenerate (helical and rectilinear) molecular orbitals. If the degenerate helical MO levels are split by chemical modification (for example, by donor and acceptor attachments at the terminal groups), it is expected that one of the left-handed or right-handed helical orbitals will possess a special meaning as a frontier orbital and play an important role as a functional material using the nature of the anisotropic orbital.
(1) Garner, M. H.; Hoffmann, R.; Rettrup, S.; Solomon, G. C. Coarctate and Möbius: The Helical Orbitals of Allene and Other Cumulenes. ACS Cent. Sci. 2018, DOI: 10.1021/acscentsci.8b00086. (2) Buenker, R. J. Theoretical Study of the Rotational Barriers of Allene, Ethylene, and Related Systems. J. Chem. Phys. 1968, 48, 1368− 1379. (3) Hendon, C. H.; Tiana, D.; Murray, A. T.; Carbery, D. R.; Walsh, A. Helical frontier orbitals of conjugated linear molecules. Chem. Sci. 2013, 4, 4278−4284. (4) Imamura, A.; Aoki, Y. Helical molecular orbitals around straightchain polyyne oligomers as models for molecular devices. Chem. Phys. Lett. 2013, 590, 136−140. (5) Liu, M.; Artyukhov, V. I.; Lee, H.; Xu, F.; Yakobson, B. I. Carbyne from First Principles: Chain of C Atoms, a Nanorod or a Nanorope. ACS Nano 2013, 7, 10075−10082. (6) Herges, R. Coarctate Transition States: The Discovery of a Reaction Principle. J. Chem. Inf. Model. 1994, 34, 91−102. (7) Peeks, M. D.; Neuhaus, P.; Anderson, H. L. Experimental and computational evaluation of the barrier to torsional rotation in a butadiyne-linked porphyrin dimer. Phys. Chem. Chem. Phys. 2016, 18, 5264−5274. (8) Gluyas, J. B. G.; Gückel, S.; Kaupp, M.; Low, P. J. Rational Control of Conformational Distributions and Mixed-Valence Characteristics in Diruthenium Complexes. Chem. - Eur. J. 2016, 22, 16138− 16146. (9) Sarbadhikary, P.; Shil, S.; Panda, A.; Misra, A. A Perspective on Designing Chiral Organic Magnetic Molecules with Unusual Behavior in Magnetic Exchange Coupling. J. Org. Chem. 2016, 81, 5623−5630. (10) Imamura, A.; Aoki, Y.; Maekawa, K. A theoretical synthesis of polymers by using uniform localization of molecular orbitals: Proposal of an elongation method. J. Chem. Phys. 1991, 95, 5419−5431. (11) Gu, F. L.; Aoki, Y.; Springborg, M.; Kirtman, B. Calculations on Nonlinear Optical Properties for Large Systems: The Elongation Method (for example, Chapter 4.7), Springer Briefs in Molecular Science, Electrical and Magnetic Properties of Atoms, Molecules, and Clusters; Springer International Publishing, 2015.
However, when the program recognizes it as a specific molecular symmetry, even if we use helically adapted initial orbitals, the final orbitals will also be helical. The mixing of left-handed and right-handed helical orbitals also provides nonhelical (rectilinear), doubly degenerate MOs in unitary transformation frameworks without any loss of density, which is correctly pointed out in all the papers cited herein. A one-handed helical frontier orbital extracted from twisted even [n]cumulenes (odd number of carbon atoms) would play an important role in enantioselective reactions and other functional phenomena. Garner et al. suggested that the concept of helical MOs could be extended to molecular design, which could be useful for enantioselective synthesis, for example, by attaching a donor and acceptor at the terminal groups of cumulene (Figure 2). We suggest using helical frontier MOs localized into the donor to create anisotropy along the molecular chain. As a way to separate
A one-handed helical frontier orbital extracted from twisted even [n]cumulenes (odd number of carbon atoms) would play an important role in enantioselective reactions and other functional phenomena. B
DOI: 10.1021/acscentsci.8b00228 ACS Cent. Sci. XXXX, XXX, XXX−XXX
