Extraction of One-Handed Helical Frontier Orbital in Even [n

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Extraction of One-Handed Helical Frontier Orbital in Even [n]Cumulenes by Breaking Mirror Images of Rightand Left-Handed Helical Orbitals: Theoretical Study Yuuichi Orimoto, Yuriko Aoki, and Akira Imamura J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b01829 • Publication Date (Web): 09 Apr 2019 Downloaded from http://pubs.acs.org on April 9, 2019

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The Journal of Physical Chemistry

Extraction of One-Handed Helical Frontier Orbital in Even [n]Cumulenes by Breaking Mirror Images of Right- and LeftHanded Helical Orbitals: Theoretical Study Yuuichi Orimoto,† Yuriko Aoki,*,† and Akira Imamura‡ †Department

of Material Sciences, Faculty of Engineering Sciences, Kyushu University, 6-1 Kasuga-Park, Fukuoka 8168580, Japan ‡Hiroshima Kokusai Gakuin University, Nakano 6-20-1, Aki-ward, Hiroshima 739-0321, Japan

ABSTRACT: Even [n]cumulenes with an even number n of double bonds are known to have degenerate helical frontier orbitals even in linear-chain structures. Theoretical analysis was conducted to separate one-handed helical orbitals from the others in cumulenes to determine their enantioselective chemical/physical properties. Donor ((NH2)3C-) and acceptor ((NO2)3C-) substituents separate the degenerate energy levels of right- and left-handed helical frontier orbitals in even [n]cumulenes. Lone pairs (LPs) in the donor group can interact with helical orbitals on the cumulene backbone, leading to “LPhelical orbital” interactions. A difference in the manner of interaction between left- and right-handed orbitals, depending on the LP direction, breaks the mirror symmetry between them. Consequent energy splitting between left- and right-handed orbitals results in extraction of a one-handed helical frontier orbital only. This is the first example of extracting a one-handed helical frontier orbital while maintaining sufficiently large energy splitting in even [n]cumulene in the framework of C1 molecular symmetry by donor-acceptor substitutions.

Introduction Carbon-based linear-chain molecules, cumulenes (H2C=C=…=C=CH2),1 and their derivatives have attracted intense attention not only as interstellar space matter2 but also as promising nanomaterials in the fields of energy,3 electronics,4,5 magnetics,6 and (non-) linear optics.7,8 Cumulenes are also used as precursors for cycloaddition.9 Moreover, their fundamental properties are relevant to electronic structures,10,11 rotational barriers,12 and reactivity.13 Because of their unique conjugation properties, many theoretical calculations have been conducted on cumulenes and their analogs, allenes (H2C=C=CH2).14 In an early molecular orbital (MO) study, in 1968, ab initio MO calculations were applied to examine the rotational barrier of allenes.15 Hückel MO theory was used to explain the relationship between allene and (Möbius-) cyclobutadienes.16 In 1976, a semi-empirical MO study was performed to examine optical rotatory properties in allenes.17 Since these early studies, numerous relevant theoretical studies have been conducted. In the present century, distinctive “helical” frontier orbitals in cumulenes have attracted much interest.18–23 These are important because helical orbitals are realized in a linear-chain structure and are not due to a helical structure. In 2013, the first reports on helical frontier orbitals in cumulenes were published.18–20 Since

then, similar helical orbitals have been discovered in various research studies.6,24–28 More recently, in 2018, Garner and Hoffmann et al. analyzed helical orbitals in allene and cumulenes by considering the topological relationship between cyclic and coarctate Möbius orbitals.21 Cumulenes have two perpendicular π-systems along their molecular axis. Especially, the even [n]cumulenes (H2C=Cn−1=CH2) highlighted in this study have an even number n of double bonds connecting an odd number (n+1) of C atoms, and the two perpendicular π-systems are equivalent. In these systems, one =CH2 terminal is perpendicular to another =CH2 terminal, resulting in D2d symmetry of the system.21 In quantum chemistry calculations, precise D2d even [n]cumulenes provide two degenerate highest occupied MOs (HOMOs) with rectilinear or left-/right-handed helical shapes, depending on the algorithm for choosing the symmetry of the initial guess orbital used in selfconsistent field calculations.19,22 Energetically degenerate rectilinear HOMOs can be converted to helical HOMOs within the freedom of unitary transformation as mentioned in many studies cited here. Deviation from D2d symmetry leads to a predominance of helical orbitals and resolves the degeneracy of HOMOs. For example, enforced torsion between two =CH2 terminals lowers the D2d→D2 symmetry and produces energetically split helical orbitals, slightly destabilizing the system.19 The effect of axial torsion in cumulenes was also discussed in other studies.20,21 In another approach, substituted allene, (CH3)HC=C=CH(CH3),18 and [4]cumulene, (CH3)HC=C=C=C=CH(CH3),21 show lowered symmetry from D2d to C2, providing a helical HOMO and HOMO-1 with an energy gap of 0.002 eV. As expected, if one can extract only one-handed (right or left) helical orbitals, cumulenes are potentially useful materials for optical detection, enantioselective reactions, and screw electromagnetism. To achieve the above-mentioned utility, chemical modification such as donor-acceptor substitution was proposed as a potential method.18,21,22 In 2018, Garner and Hoffmann et al. anticipated that larger HOMO/HOMO-1 splitting can be realized by donor (D) and accepter (A) substitutions.21 In 2019, Garner et al. demonstrated such splitting using Dcumulene-D type molecules by considering D2d→C2 symmetry lowering, and circular currents by such system was theoretically predicted.23 In a related study, Hendon et al. achieved an energy separation between a HOMO and HOMO-1 by substituting oxazolidinone derivatives with oligoyne.18 To the best of our knowledge, for even [n]cumulenes, a large energy separation of degenerate HOMOs has not yet been reported for D-cumulene-A

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type molecules assuming D2d→C1 symmetry lowering. In this work, we discuss how to extract one-handed helical orbitals from even [n]cumulenes to increase their potential applications.

Model molecule and computational details We propose a donor-acceptor substituted [4]cumulene, ((NH2)3C)2C=C=C=C=C(C(NO2)3)2 (Figure 1). Donor ((NH2)3C-) and acceptor ((NO2)3C-) groups replaced H atoms at each terminal of [4]cumulene, H2C=C=C=C=CH2. We noted that (NH2)3C- and (NO2)3C- groups are “model” donor and accepter, respectively. Numerous isomers were expected due to the various orientation combinations of six NH2- and six NO2-groups. A stable system structure was explored systematically by considering various possible conformations. At the screening stage, geometric optimizations were performed using density functional theory (DFT) calculations with the B3LYP functional29–31 and 631G(d,p) basis set, as the functional was widely used even in current studies.32–34 For stable isomers obtained during the screening stage, their optimized geometries were recomputed using the Hartree-Fock (HF) method at the HF/6-311G(d,p) level rather than DFT to obtain MOs, and the same computational level was used to obtain both the molecular structure and the corresponding electronic structure. Although the use of KohnSham orbitals has been accepted,35–37 their physical meaning is still under controversial. All the calculations were performed with Gaussian 16,38 and molecular structures and MOs were depicted with GaussView 6.0.39 Computational details and calculated isomers are given in the Supporting Information.

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reduce collisions with each other (Figure 1c). NH2-groups at the donor terminal oriented to form hydrogen bonds between N and H atoms belonging to adjacent groups (Figure 1b). Three hydrogen bonds were generated using three N atoms and three H atoms. Both terminals remained almost perpendicular. As shown in Figure 2, conformer 1 shows a left-handed helical HOMO and right-handed helical HOMO-1. These MOs are clearly helical, and their energy gap was 0.18 eV. This gap is 90 times that of (CH3)HC=C=C=C=CH(CH3), which is 0.002 eV.21 In nonsubstituted cumulenes, a right-handed helical orbital is the mirror image of a left-handed one. However, donor-acceptor substitution can partially break the mirror symmetry. In conformer 1, the most important factor with respect to breaking the symmetry is one of the lone pair (LP) orbitals in the donor terminal as shown in Figure 1a and b (highlighted in light blue). Figure 3a and b show enlarged views of the HOMO and HOMO-1, respectively, from position-A indicated in Figure 2. As shown in Figure 3a, the focused LP in the HOMO interacts with the terminal of the helical orbital. In the LP-helical orbital interaction, the back lobe of the LP (denoted “back” in the illustration beneath the figure) forms an σ-type overlap with the outside lobe of the p-orbital in the adjacent C atom (denoted “outer-p”) across the C-N bond. We denote this “σouter-back” bonding. Additionally, we can consider an out-of-phase relationship between the forward lobe of the LP on the N atom and the outer-p on the adjacent C atom.

Figure 2. HOMO and HOMO-1 of the most stable conformer 1.

Figure 1. (a) The most stable conformer 1 of donor-acceptor substituted [4]cumulene, ((NH2)3C)2C=C=C=C=C(C(NO2)3)2. The light blue lone pair effectively interacts with helical orbitals, while light orange ones cannot couple effectively with them. (b) and (c) depict views from the A- and B-directions indicated in (a), respectively. Panel (b) shows only the light blue lone pair for clarity.

Results and discussion Figure 1 shows the most stable conformer 1 of the donoracceptor substituted [4]cumulene. In the conformer, NO2-groups form helically oriented structures at the acceptor terminal to

Figure 3. (a) and (b) show enlarged views of the HOMO and HOMO-1 in conformer 1, respectively, from the A-direction indicated in Figure 2. Schematics beneath each panel show expected orbital interactions. The red box shows the cumulene molecular axis.


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As shown in Figure 3b, HOMO-1 shows a different LP-helical orbital interaction from the HOMO. The back lobe of the LP forms a σ-type overlap with the inner lobe of the p-orbital in the adjacent C (denoted “inner-p”) parallel to the C-N bond. We denote this “σinner-back” bonding. We can also consider an in-phase (but weak) relationship between the forward lobe of the LP and the outer-p on the adjacent C. The out-of-phase relationship between the LP forward lobe and adjacent outer-p in the HOMO is expected to destabilize its energy level compared with HOMO1 having an in-phase relationship. The energy difference between the HOMO and HOMO-1 was caused by the difference in the manner of interaction between the focused LP and helical orbitals. The LP-helical orbital interaction breaks the mirror symmetry of the HOMO (left-handed) and HOMO-1 (right-handed), leading to separation of the one-handed helical orbital from its counterpart.

Figure 4 shows a metastable conformer (conformer 2) of the proposed cumulene. Conformer 2 was less stable than the most stable conformer 1 by +1.15 kcal/mol. The acceptor terminal in 2 (Figure 4c) has nearly the same conformation as that in 1. As shown in Figure 4b, the donor terminal in 2 adopts a different hydrogen bonding manner from 1. Three hydrogen bonds use two N atoms and three H atoms in 2. The decrease in N atoms in the hydrogen bonds, i.e. from three N atoms in 1 to two N atoms in 2, may destabilize 2 compared with 1. Figure 5 shows a right-handed helical HOMO and left-handed helical HOMO-1 in 2, both showing sufficiently clear helical shapes. Conformation 2 has the opposite helical orbital form to conformer 1, i.e., the HOMO in 1 has a left-handed orbital, while that in 2 has a right-handed orbital. The difference in the donor terminal structure may explain the change in the helical direction, as the acceptor terminals in both conformers are almost identical. More importantly, conformer 2 shows an energy gap of 0.42 eV between the HOMO and HOMO-1. This is about 2.3 times that of conformer 1, which is 0.18 eV, and 210 times larger than the value of 0.002 eV for (CH3)HC=C=C=C=CH(CH3).21 Here, the increment of HOMO/HOMO-1 energy gap in 2 compared with 1 comes from the destabilization of the HOMO level and stabilization of the HOMO-1 level from 1 to 2.

Figure 4. (a) Metastable conformer 2 (less stable than 1 by 1.15 kcal/mol) of ((NH2)3C)2C=C=C=C=C(C(NO2)3)2. Light blue lone pairs effectively interact with helical orbitals, while light orange ones cannot couple effectively with them. (b) and (c) depict views from A and B indicated in panel (a), respectively. Panel (b) shows only light blue lone pairs for clarity.

Figure 5. HOMO and HOMO-1 of metastable conformer 2.

Figure 6. (a) and (b) show enlarged views of the HOMO and HOMO-1 in conformer 2, respectively. In each panel, left and right figures show views from the A- and B-directions indicated in Figure 5, respectively. Schematics beneath each panel show expected orbital interactions. The red box shows the cumulene molecular axis.



As shown in Figure 5, two LP orbitals in the donor terminal in 2 (highlighted in light blue in Figure 4a and b) largely break the mirror symmetry between the right- and left-handed helical orbitals. Figure 6a and b show enlarged views of the HOMO and HOMO-1, respectively. In each panel, the left and right figures show the views from the A- and B-directions indicated in Figure 5, respectively. In Figure 6a showing the HOMO, the two LP orbitals interact with the helical orbital in a σouter-back bonding manner (see illustrations beneath each panel in Figure 6a). Furthermore, two LP forward lobes on N atoms have an out-ofphase relationship with the outer-p lobes on adjacent C atoms. Conversely, in Figure 6b showing HOMO-1, the two LP orbitals weakly interact with the helical orbital in a σinner-back manner (see illustrations beneath each panel in Figure 6b). In HOMO-1, two LP forward lobes have an in-phase (but weak) relationship with the adjacent outer-p lobes. In conformer 2, the two out-of-phase relationships in the HOMO largely destabilize its energy level compared with the two in-phase relationships in HOMO-1. Consequently, the energy splitting of 0.42 eV caused by the two LPs in 2 should exceed the splitting of 0.18 eV caused by one LP in conformer 1. Figure S8 shows the HOMO and HOMO-1 viewed from the acceptor terminal for conformers 1 and 2. Each MO shows a mixture of σouter-back-like and σinner-back-like interactions at the acceptor terminal. MO coefficients on -NO2 groups are relatively small and the interaction manner is more complicated compared with the donor terminal. To compare the HF results with DFT ones, the geometries of conformers 1 and 2 were re-optimized by the M06-2X40/6311G(d,p) level. Figure S9 shows the optimized geometries of 1 and 2. Conformer 2 is less stable than 1 by 0.53 kcal/mol. Both the structures of 1 and 2 are almost the same as the HF results (see Figures 1 and 4). Figures S10 and S11 show helical frontier orbitals in 1 and 2 at the M06-2X level, respectively. Similar helical MOs and orbital interactions to the HF results were found for 2 in Figure S11 (see also Figures 5, 6, and S8). In contrast, for 1 in Figure S10, both the HOMO and HOMO-1 show the same left-handed helicity, and the HOMO-2 has right-handed helicity. From the MO feature, the HOMO and HOMO-2 here correspond to the HOMO and HOMO-1 in the HF results, respectively. The HOMO-1 is the counterpart of the HOMO due to MO splitting, where an orbital-phase inversion between HOMO and HOMO-1 was found at a part of -C(NH2)3 group. The energy difference between conformers 1 and 2 is small and comparable with the thermal energy. Moreover, the strength of three N-H hydrogen bonds is moderate41 and thus the desired conformer can convert to another adjacent isomer. To isolate desired isomers in chemical synthesis, further ingenuity by chemical modification etc. should be required to realize larger difference in thermal energy from other isomers and increase the energy barrier between isomers. Our proposed molecule in this study is just a starting one for further molecular design. If one can separately synthesize these conformers by chemical modification, the one-handed helical frontier orbital in cumulenes can be extracted. It should be also noted that the -C(NH2)3 donor group in this study has been used as a reference model,42 and thus its stability is questionable.43,44 One should explore more stable substituents exhibiting similar effects to -C(NH2)3 group for the purpose. Finally, to understand more details on cumulenes and its unique electronic structures, natural bond orbital analysis45 and our developed through-space/bond interaction analysis method46,47 can be useful ways and should be applied in future work.

Conclusions

In this work, we theoretically demonstrated the first example of extracting a one-handed helical frontier orbital with sufficiently large energy splitting between the HOMO and HOMO-1 from even [n]cumulene using donor-acceptor chemical modification (D-cumulene-A) causing D2d→C1 symmetry lowering. An important conclusion is that a one-handed helical orbital can be extracted by breaking the mirror symmetry between the right- and left-handed helical orbitals of two degenerate HOMOs in nonsubstituted cumulenes. The proposed chemical modification causes a different manner of “LP-helical orbital” interaction between the right- and left-handed helical orbitals, resulting in a large energy separation between these orbitals. This finding enables useful applications of even [n]cumulenes for enantioselective reactions and photo-analysis and can contribute to developing innovative materials exhibiting enantioselective helical properties.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Computational details and calculated isomers, helical frontier orbitals: views from acceptor terminal, results calculated by density functional theory, complete references (PDF)

AUTHOR INFORMATION Corresponding Author *[email protected]

Notes The authors declare no competing financial interests.

ACKNOWLEDGMENTS The authors thank Ikuko Okawa for her technical support to this study including computations and data reduction. The authors acknowledge financial support for this work by JSPS/MEXT (KAKENHI: 23245005, 16KT0059, 25810103, 15KT0146, and 16K08321), and JST-CREST. All the computations were carried out using Linux OS systems in our group and computing facilities in the Research Institute for Information Technology, Kyushu University.

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