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Synlett 2023; 34(17): 1978-1990
DOI: 10.1055/a-2072-2951
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Crystal Engineering, Electron Conduction, Molecular Recognition and Reactivity by Chalcogen Bonds in Tetracyanoquinodimethanes Fused with [1,2,5]Chalcogenadiazoles

Takuya Shimajiri
a   Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo, Hokkaido 060-0810, Japan
b   Creative Research Institution, Hokkaido University, Sapporo, Hokkaido 001-0021, Japan
,
Henri-Pierre Jacquot de Rouville
c   Laboratoire de Synthèse des Assemblages Moléculaires Multifonctionnels, Institut de Chimie de Strasbourg, CNRS UMR 7177, Université de Strasbourg, 4, rue Blaise Pascal, 67000 Strasbourg, France
,
Valérie Heitz
c   Laboratoire de Synthèse des Assemblages Moléculaires Multifonctionnels, Institut de Chimie de Strasbourg, CNRS UMR 7177, Université de Strasbourg, 4, rue Blaise Pascal, 67000 Strasbourg, France
,
Tomoyuki Akutagawa
d   Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai, Miyagi 980-8577, Japan
,
Takanori Fukushima
e   Laboratory for Chemistry and Life Science, Institute of Innovative Research, Tokyo Institute of Technology, Yokohama 226-8503, Japan
,
Yusuke Ishigaki 
a   Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo, Hokkaido 060-0810, Japan
,
Takanori Suzuki  ∗
a   Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo, Hokkaido 060-0810, Japan
› Author Affiliations

This work was supported by Grant-in-Aids from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan Society for the Promotion of Science (JSPS) (Grant Nos. JP20H02719 and JP20K21184 to T.Su., and JP21H01912 and JP21H05468 to Y.I.) and Japan Science and Technology Agency (JST) CREST (JPMJCR18I4 to T.F.). Additional support was received from the Research Program of ‘Five-star Alliance’, Network Joint Research Center for Materials and Devices (NJRC Mater. & Dev.), MEXT. Y.I. and T.Sh. also acknowledge the Toyota Riken Scholar Program.
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Abstract

Studies on a series of tetracyanoquinodimethanes (TCNQs) fused with [1,2,5]chalcogenadiazole rings reveals that chalcogen bonds (ChBs), through E•••N≡C (E = S or Se) contacts, are a decisive factor in determining their crystal structures, with the formation of one- or two-dimensional networks in a lateral direction. For anion-radical salts generated by one-electron reduction, electron conduction occurs in the direction of the network due to intermolecular electronic interactions involving ChBs. Based on the reliable synthon E•••N≡C for crystal engineering, molecular recognition occurs so that solid-state molecular complexes are selectively formed with certain donors, such as xylenes, among their isomers by charge-transfer-type clathrate formation. The inclusion cavity of the clathrate might provide a reaction environment for photoinduced electron transfer in the solid state. The accommodation of multiple conformers of overcrowded ethylene exhibiting thermo/mechanochromism is another example of a novel function that can be realized by ChBs through E•••N≡C contacts. Therefore, these chalcogenadiazolo-TCNQs endowed with the ability to form ChBs are promising materials for the development of novel solid-state functions.

1 Introduction

2 Bis[1,2,5]thiadiazolo-TCNQ (BTDA)

2.1 Chalcogen Bonds in Crystal Structures of BTDA and its Se Analogues

2.2 Electronic Effects of Chalcogen Bonds in Organic Conductors Consisting of BTDA

2.3 Molecular Recognition by Chalcogen Bonds in Molecular Complexes of BTDA

2.4 Single-Crystalline-State Photoreactions of Molecular Complexes of BTDA

2.5 Overcrowded Ethylene Composed of a BTDA Substructure

3 TCNQ Analogues Fused with a [1,2,5]Chalcogenadiazole

3.1 Crystal Structures of Chalcogenadiazolo-TCNQs

3.2 Crystal Structures of Chalcogenadiazolo-TCNNQs: An E•••N≡C Chalcogen Bond versus a Weak C–H•••N≡C Hydrogen Bond

3.3 Molecular Recognition by Chalcogen Bonds in TCNNQ Derivatives

4 Outlook


#

Key words

supramolecular chemistry - host–guest systems - heterocycles - electron transfer - chalcogen bond - charge-transfer complex - overcrowded ethylene - crystal structure

Biographical Sketches

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Takanori Suzuki was born in Onagawa, Miyagi Prefecture, Japan in 1961. He graduated from Tohoku University in 1984 and received his Ph.D. in 1988 under the supervision of Professors Toshio Mukai and Tsutomu Miyashi. After he worked at Tohoku University as a JSPS post-doctoral fellow (1988-1989) and a Research Associate (1989-1994), he moved to Faculty of Science, Hokkaido University and joined Professor Takashi Tsuji's group as an Associate Professor (1995-2002). He was appointed Professor at Hokkaido University in 2002. He is now working with Prof. Yusuke Ishigaki and Dr. Takuya Shimajiri in the research area of structural organic chemistry.

1

Introduction

Secondary bonding interactions (SBIs) have recently attracted a great deal of attention. They are of special importance in the field of crystal engineering[1] [2] and enable the prediction and regulation of crystal packing, thus contributing to the design of new solids with desired physical and chemical properties. Along with weak hydrogen bonds (WHBs), which involve less acidic C–H as a hydrogen donor,[3] the chalcogen bond (ChB)[4] [5] is a representative SBI that exhibits high directionality in a crystal. In an atomic array of Z-E•••LB, where E is an electrophilic chalcogen atom and Z is an electron-withdrawing group, a Lewis base (LB) is bound to E through electron donation from n(LB) to the σ*(Z–E) orbital. Electrostatic attraction also plays an important role in ChBs. Each E atom has two σ-holes, which are positively charged regions that extend in the direction opposite of each E–Z bond. Thus, the strength of the ChB is influenced by several factors including the nature of the electron-deficient Z group attached to E, the linearity of the Z-E•••LB atomic array, and the basicity of LB.[6] The E atom has dramatic effects because it becomes both more polarizable and electropositive as it grows in size. Both of these factors lead to a deeper σ-hole, and thus to a generally stronger ChB for Se than for S, as has been demonstrated for a series of compounds.[7] [1,2,5]Chalcogenadiazoles[8] possess both an E atom and imine nitrogen atoms, and thus can form ChBs via E•••N contacts among themselves. They are versatile units for the generation of supramolecular synthons with an (E•••N)2-square-dyad motif (Z = N, LB = N) with duplicate ChBs (Scheme [1a]).[9] The nitrogen atom of a cyano group is a much stronger LB than that of an imine group, and ChBs formed through E•••N≡C contacts have been reported for certain inorganic materials.[10] We previously reported that short, linear E•••N≡C contacts are quite often found in a series of tetracyanoquinodimethane (TCNQ) derivatives fused with chalcogenadiazole(s), which are characterized by the geometrical parameters shown in Scheme [1c], as in the case of WHBs (Scheme [1d]). Not only in their pristine crystals but also in their molecular complexes and anion radical salts,[11] the molecules are connected to each other by ChBs with dual E•••N≡C contacts, as shown in Scheme [1b], which induces characteristic features and functions such as molecular recognition and electrical conduction in the solid state. This account describes our journey studying a family of chalcogenadiazolo-TCNQs over the decades.

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Scheme 1 (a) (E•••N)2-square-dyad and (b) E•••N≡C motifs of chalcogen bonds (ChBs). Geometrical definitions of (c) ChBs and (d) WHBs.

# 2

Bis[1,2,5]thiadiazolo-TCNQ (BTDA)

2.1

Chalcogen Bonds in Crystal Structures of BTDA and its Se Analogues

Bis[1,2,5]thiadiazolotetracyanoquinodimethane (BTDA) (1)[11] [12] is a π-extended analogue of TCNQ that can be prepared from the corresponding quinone 4 [13] by a condensation reaction with CH2(CN)2 in the presence of TiCl4 and pyridine (Scheme [2]).[14] [15] It undergoes reversible four-stage one-electron reduction at –0.40, –0.87, –1.59, and –2.14 V vs Fc/Fc+ in MeCN. Based on a comparison of E 1 red with that of the parent TCNQ (E 1 red : –0.20 V), 1 is a slightly weaker acceptor as in the cases of other TCNQ derivatives annulated with two aromatic heterocycles.[16] Thanks to the π-extension, however, both singly charged anion radical 1 –• and doubly charged dianion 1 2– were isolated as stable salts.[17] The triply charged trianion radical 1 3–• could be generated electrochemically,[18] and an electron spin resonance study showed that it has a large spin density in the heterocyclic part. In contrast to other sterically deformed TCNQ derivatives fused with benzene rings,[19] compound 1 and its anionic states adopt planar geometries.

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Scheme 2 Preparation of BTDA (1), TSDA (2), and BSDA (3)

As revealed by X-ray crystal structure analysis (250 K), a striking feature of the crystal packing of 1 is the formation of a coplanar two-dimensional (2D) sheet-like network (Figure [1]), in which a molecule of 1 is surrounded by four neighbors connected by eight-fold S•••N≡C contacts.[11] [20] [21] The E•••N contact distance [D: 3.03(1) Å, E = S] is much smaller than the sum of the van der Waals (vdW) radii of S and N (3.35 Å). The outstanding linearity of the N–S•••N≡C atomic array is shown by the angles of N–E•••N (φ) and E•••N≡C (θ) [167.9(1)° and 170.7(1)°, respectively, E = S] (Scheme [1c]). The laterally expanded 2D sheet-like networks are regularly stacked at the heterocyclic parts with an equal interplanar distance of 3.56 Å, which is larger than the usual π–π overlap of aromatic rings (3.40 Å). Thus, we conclude that the packing arrangement of 1 is controlled by ChBs through S•••N≡C contacts.

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Figure 1 2D sheet-like network in 1 involving ChBs through S•••N≡C contacts. The distance is shown in Å.

The Se-containing analogues TSDA (2) and BSDA (3),[11] [22] in which one or both of the thiadiazole rings are replaced by selenadiazole rings, were prepared from the corresponding quinones 5 [11] and 6,[13] as shown in Scheme [2]. They adopt crystal packing isomorphous to 1, with complete positional disorder of S and Se in 2. A stronger ChB is suggested through the shorter Se•••N≡C contacts in 3 [D: 2.94(1) Å (sum of vdW radii of Se and N: 3.45 Å), φ: 169.6(1)°, θ: 169.2(1)°, measured at 250 K]. According to DFT calculations (M06-2X/6-31G**) on 1 and 3,[21] BSDA (3) has deeper σ-holes than in 1, as shown by the greater Vs,max value (+33.2 kcal mol–1 for 1 and +39.1 kcal mol–1 for 3, respectively) in their electrostatic potential maps (Figure [2]). Thus, stronger electrostatic attraction is expected via the Se•••N≡C contact. Natural bond orbital analyses showed that the E•••N≡C contact induces the donation of a lone pair of electrons from the cyano nitrogen to the antibonding E–N orbital, with a second-order perturbation stabilization of +2.05 kcal mol–1 for 1 and +4.84 kcal mol–1 for 3, respectively.

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Figure 2 Electrostatic potentials of (a) BTDA 1 and (b) BSDA 3 calculated by a DFT method (M06-2X/6-31G**) based on the crystallographic coordinates

The above X-ray analyses and DFT calculations demonstrate that bis[1,2,5]chalcogenadiazolo-TCNQs are unique electron acceptors endowed with the ability to form ChBs through E•••N≡C contacts. Despite the strong ChB in Se analogues, further studies on the exploitation of ChB-related functions have been mainly conducted using BTDA (1), based on the higher solubility and stronger electron-accepting properties of 1 than of 2 and 3 (E 1 red : –0.50 V and –0.63 V vs Fc/Fc+ in MeCN, respectively).


# 2.2

Electronic Effects of Chalcogen Bonds in Organic Conductors Consisting of BTDA

The theoretical consideration indicated that the LUMO of BTDA (1) had the same symmetry as that of TCNQ. While there are large coefficients of LUMO on cyano groups, S atoms are on the nodal plane, suggesting that stronger chalcogen bonds through S•••N≡C contacts are expected for anion-radical salts due to an increase in the negative charge density on the cyano N atoms, whereas σ-holes on S atoms are not affected by one-electron reduction. Due to its adequate electron-accepting ability, 1 was readily reduced to 1 –• upon treatment with 1.5 equivalents of an iodide, such as EtMe3N+I–, to give a stable crystalline salt of EtMe3N+ 1 –•.[23] X-ray analysis revealed the formation of a coplanar ribbon-like network of ChBs through S•••N≡C contacts (Figure [3a]), which represents a strip-subunit of a 2D sheet-like network of pristine 1.

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Figure 3 Molecular packing in the crystal of EtMe3N+ 1 –• (1:1) salt. The distances corresponding to D 1 and D 2 are shown in Å. (a) Top view showing the ribbon network, and (b) a side view showing π–π stacking. The geometrical data are as follows: D 1: 3.12 Å, φ 1: 149.3°, θ 1: 120.2°; D 2: 3.25 Å, φ 2: 150.1°, θ 2: 115.7°, respectively, for two sets of S•••N≡C contacts.

The counter cations are incorporated between the two laterally expanded ribbon networks. The N+ atom is located on the same plane as 1 –•, which maximizes the Coulombic attraction between 1 –• and the counter cation. Perpendicular to the ribbon network, a columnar π–π stack of 1 –• is formed with a short interplanar distance of 3.24 Å (Figure [3b]), which results from the orbital interaction with formation of the band structure. This salt exhibits a high electrical conductivity in the direction of π–π stacking (0.030 S cm–1), despite the completely filled conduction band of the salt with a cation/1 –• molar ratio of 1:1 (Mott insulator). This means that the disproportionation [1 –• (mol-1) + 1 –• (mol-2) ⇌ 1 0 (mol-1) + 1 2– (mol-2); mol-1 and mol-2 are the neighboring molecules in the columnar stack] in the columnar stack is facilitated by the reduced on-site Coulombic repulsion in the doubly charged species due to the enlarged π-system of 1 compared to those of other TCNQ-type electron acceptors.

The anion radical salts are sometimes formed with a molar ratio other than 1:1 (e.g., 2:3, 1:2, or 2:5), and higher conductivities are expected for such salts of 1 –• since they have a partially filled conduction band. In such salts, the electron conduction can be induced by formal electron exchange [1 –• (mol-1) + 1 0 (mol-2) ⇌ 1 0 (mol-1) + 1 –• (mol-2)]. Although such regulation of the molar ratio is usually difficult, it is easy for a series of salts of 1 –• with alkylammoniums as the counter cation, by utilizing the crystal-engineering approach based on ChBs through S•••N≡C contacts. Thus, further X-ray analyses showed that the above-mentioned ribbon-like networks were commonly observed in the crystals of two other salts [Et4N+ 1 2 –• (1:2) and nBu3MeN+ 1 2 –• (1:2)]. Again, the counter cations are incorporated between the ribbon networks. Accordingly, for the combination of 1 –• with the larger ammonium cation, the π–π stacking of 1 –• could not be retained while maintaining a molar ratio of 1:1. Thus, the ratio gradually changes to 2:3, 1:2, and then 2:5, with formal insertion of neutral 1 between the molecules of 1 –• in the columnar stack upon elongation of the side chain of the alkylammonium. In this way, small ammonium cations such as H4N+ and Me4N+ only formed 1:1 salts along with EtMe3N+, whereas Et2Me2N+ and Et4N+ only formed 2:3 and 1:2 salts, respectively. For the combination with a larger R4N+ cation, only 1:2 salts were obtained for nPr4N+ and nBu4N+, whereas nPent4N+ gave only a 2:5 salt. These salts with a partially filled conduction band are generally highly conductive [e.g., 0.32 S cm–1 measured on a compaction pellet of nBu4N+ 1 2 –• (1:2)]. Thus, modification of the molar ratio by ChB-based crystal engineering can be used to control the electron conduction of 1 –• salts.

It would be particularly interesting to clarify whether or not electron conduction can be induced along the ribbon network formed by the ChBs. Measurements performed on a single-crystalline sample of nBu3MeN+ 1 2 –• (1:2) showed that conductivity was observed not only in the direction of π–π stacking (0.59 S cm–1) but also along the ribbon network expanded laterally (0.027 S cm–1), demonstrating the 2D electronic structure of the 1 –• salts.[23] The other direction passing over the counter cation showed a resistivity 100-fold greater than that in the stacking direction. This example clearly shows that electron conduction occurs along the molecular network formed by ChBs, which plays an important role in modification of the solid-state electronic structure.[24]

Both anion radical salts and certain solid-state charge-transfer (CT) complexes of 1,[25] such as the complex with tetraceno[5,6-cd:11,12-c′d′]bis[1,2]diselenole (tetraselenatetracene) (TSeT) (7), exhibit high electrical conductivity. The crystal of the TSeT·1 (1:1) complex is a molecular metal with a partial charge transfer of 90%, the conductivity of which increases with a decrease in temperature. X-ray structural analysis revealed the formation of segregated columnar stacks for both TSeT and 1 (interplanar distance: 3.32 Å and 3.26 Å, respectively), which are the major conduction paths in the solid. Between the columnar stacks there are close contacts between the Se atoms of TSeT and the cyano groups of 1 (Figure [4a]). These ChB contacts were shown to be the key factor in stabilizing the metallic state, with suppression of the metal–insulator transition (Peierls transition), even at a very low temperature down to 1.5 K.[26]

The absence of S•••N≡C contacts in the crystal of TSeT·1 can be rationalized by considering that the stronger ChBs involving Se atoms overwhelm the ChBs through S•••N≡C contacts in 1. In other CT complexes of 1 with electron donors that lack Se atoms, the molecules of 1 are connected by S•••N≡C contacts. In the semiconducting CT complex with tetrathiafulvalene (TTF) (8)[27] with a partial charge transfer of 6%, a TTF molecule is incorporated in the cavity formed by ChBs through S•••N≡C contacts, showing that clathrate-type inclusion occurs in CT complexes of 1 with weaker electron donors (Figure [4b]).[28]

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Figure 4 (a) Molecular packing in the crystal of the TSeT·1 (1:1) CT complex viewed along the segregating stacks. The distances corresponding to D 1 and D 2 are shown in Å. The geometrical data are as follows: D 1: 3.08 Å; θ 1: 164.7°; D2: 3.10 Å; θ 2: 124.2°, respectively, for two sets of Se•••N≡C contacts, and the separation of 3.87 Å for S•••N≡C contacts is too far to be considered for ChBs. (b) Molecular packing in the crystal of the TTF·1 (1:1) CT complex viewed along the mixed stack. The distances corresponding to D 1 and D 2 are shown in Å. The geometrical data are as follows: D 1: 3.37 Å, φ 1: 125.7°, θ 1: 134.1°; D2: 3.15 Å; θ 2: 104.0°, respectively, for two sets of S•••N≡C contacts.

# 2.3

Molecular Recognition by Chalcogen Bonds in Molecular Complexes of BTDA

The molecular recognition properties of BTDA (1) upon the formation of clathrate complexes[11] via ChBs through S•••N≡C contacts were first demonstrated when finely ground yellow crystals of 1 were suspended in a liquid containing a mixture of o-, m-, and p-xylene to give a CT complex, as a red powder, which selectively includes p-xylene. The co-presence of ethylbenzene did not affect the selectivity. Heating of the resulting solid liberated pure p-xylene accompanied by the regeneration of 1, demonstrating that clathrate formation with 1 can be used to separate p-xylene from a mixture of its isomers (Scheme [3]).

X-ray analysis of p-xylene·1 (1:1) revealed that, perpendicular to an alternating donor–acceptor columnar stack, a ribbon network of 1 had formed via ChBs through S•••N≡C contacts (D 1: 3.22 Å, φ 1: 137.2°, θ 1: 112.2°; D 2: 3.24 Å, φ 2: 142.8°, θ 2: 111.1°, respectively, for two sets of S•••N≡C contacts). An inclusion cavity that incorporates p-xylene molecules is formed between the two ribbon networks, similar to that shown in Figure [4b]. Molecular recognition is the result of the molecular shapes of o- and m-xylene that are unsuitable for inclusion in the cavity formed by the ChBs. Recrystallization of 1 from pure o- and m-xylene resulted in no formation of CT complexes, which demonstrates the remarkable recognition properties of 1 via ChBs.

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Scheme 3 A simple mixing–filtration–heating process for the separation of p-xylene from a mixture of its isomers by formation of a clathrate with BTDA (1) via ChBs through S•••N≡C contacts

Selective complexation of 1 also occurs for p-chlorotoluene among its isomers (E ox: +1.74 to +1.87 V vs Fc/Fc+ in MeCN), similar to the results obtained with xylene (+1.57 to +1.69 V). On the other hand, both the p- and o-isomers of chloroanisole (+1.38 to +1.48 V) form stable CT complexes with 1. For a series of methylanisoles (+1.15 to +1.23 V), all of the isomers gave crystalline CT complexes with 1. By considering that p-methylanisole·1 (1:1) and o-methylanisole·1 (1:1) exhibit similar crystal packing with ribbon networks via ChBs through S•••N≡C contacts (Figure [5]), the enhanced CT interaction in the donor–acceptor mixed columnar stack covers up the unsuitable molecular shape of the o-isomer for location in the inclusion cavity, thus concealing the recognition properties upon clathrate formation when the CT interaction between 1 and the donor increases.

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Figure 5 (a) Molecular packing in the crystal of the p-methylanisole·1 (1:1) CT complex viewed along the mixed stack. The distance corresponding to D is shown in Å. The geometrical data are as follows: D: 3.25 Å, φ: 169.3°, θ: 174.7° for the S•••N≡C contact. The methyl and methoxy groups are positionally disordered. (b) Molecular packing in the crystal of the o-methylanisole·1 (1:1) CT complex viewed along the mixed stack. The distances corresponding to D 1 and D 2 are shown in Å. The geometrical data are as follows: D 1: 3.19 Å, φ 1: 147.0°, θ 1: 120.8°; D 2: 3.35 Å, φ 2: 137.0°, θ 2: 146.5°, respectively, for two sets of S•••N≡C contacts.

On using the weaker electron acceptor 2 instead of 1, the CT interaction decreases. Thus, selectivity for p-isomers was apparent for chloroanisoles and methylanisoles. On the other hand, while the much weaker acceptor 3 does not form any crystalline complexes with the disubstituted benzenes listed above, it does form such complexes with dimethoxybenzene isomers with much lower E ox values (+0.86 to +1.05 V). It was shown that molecular recognition of 1–3 via ChBs through E•••N≡C contacts can be realized with the appropriate combination of electron donors to attain suitable CT interactions, because the selectivity is concealed for the donors that are too strong, whereas donors that are too weak do not form CT-type clathrates with 1–3. Thus, while a complementary shape and size are important, in general, for host–guest–type complexation, the present clathrates are also stabilized by CT interactions, resulting in recognition not only by the shape but also by the electron-donating properties of the guest.


# 2.4

Single-Crystalline-State Photoreactions of Molecular Complexes of BTDA

When BTDA (1) and aryl olefins, such as styrene (STY) or o-divinylbenzenes (oDV), were mixed in MeCN, new absorption bands extending to 550 nm were observed, which correspond to the formation of CT pairs in solution. When the CT pairs were photoirradiated at their CT absorption bands, 1 and the aryl olefins were first converted into radical-ion pairs that underwent regioselective [2+2]-type cycloaddition to give adducts 9STY and 9oDV (Scheme [4]). Due to the small association constants (0.85 and 1.1 M–1 for 1/STY and 1/oDV, respectively, in MeCN at 295 K), cycloaddition was sluggish in solution. More efficient cycloaddition occurred when the CT excitation reactions were conducted with a water suspension of the crystalline CT complex of STY·1 (1:1) or oDV·1 (1:1) to give the same products in high isolated yields (e.g., 91% for 9oDV). These are the first examples of photoinduced electron-transfer reactions conducted in the solid state.[29]

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Figure 6 Molecular packing in the crystal of the o-DV·1 (1:1) CT complex viewed along the mixed stack (a) before and (b) after the single-crystal-to-single-crystal photoinduced electron-transfer reaction. The distances corresponding to D 1 and D 2 are shown in Å. The geometrical data are as follows: (a) D 1: 3.14 Å, φ 1: 142.6°, θ 1: 114.8°; D 2: 3.43 Å, φ 2: 134.7°, θ 2: 106.3°, respectively, for two sets of S•••N≡C contacts; (b) D 1: 3.35 Å, φ 1: 137.7°, θ 1: 117.6°; D 2: 3.25 Å, φ 2: 145.7°, θ 2: 117.0°, respectively, for two sets of S•••N≡C contacts.

X-ray analysis of the oDV·1 (1:1) crystal showed that it adopts molecular packing with ribbon networks formed via ChBs through S•••N≡C contacts (Figure [6a]), which is quite similar to the results with methylanisole complexes, showing that the inclusion cavity formed by ChBs in 1 provides a suitable reaction environment for oDV to undergo smooth cycloaddition with 1.

Actually, oDV·1 (1:1) is transformed into 9oDV while maintaining its single crystallinity,[30] such that the solid-state photoinduced electron-transfer reaction could be followed by X-ray analysis. The crystal structure of the as-photolyzed 9oDV is quite similar to that of oDV·1 (1:1) and exhibits ribbon networks with S•••N≡C contacts (Figure [6b]), showing that ChBs can facilitate the single-crystal-to-single-crystal transformation upon topotactic transformation.

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Scheme 4 Cycloaddition of BTDA (1) with aryl olefins under CT excitation conditions

Based on the fact that the achiral components of 1 and oDV crystallized in a chiral space group[31] (P21), the molecular arrangement in the reacting face-to-face overlap is chiral. Although such chirality is lost upon dissolution, photoconversion resulted in a transformation of the chirality of the crystal packing to point chirality in the product molecule. When a specific single crystal of oDV·1 (1:1) (right-handed crystal) was photoirradiated, (R)-(+)-9oDV was obtained in 96% ee, whereas (S)-(–)-9oDV was obtained with 95% ee upon irradiation of another single crystal (left-handed crystal), which has only the mirror-image face-to-face overlap (Scheme [5]). This photoreaction demonstrates a successful absolute asymmetric synthesis,[32] in which no external chiral element is used to generate an optically pure material.


# 2.5

Overcrowded Ethylene Composed of a BTDA Substructure

BTDA-dimer 10 [33] is a π-extended analogue with a tetracyanobiphenoquinodimethane skeleton[34] fused with four thiadiazole rings. In contrast to 1 with a planar geometry, the sterically hindered bis(tricyclic ene) structure endows 10 with unique properties as an overcrowded ethylene,[35] similar to bianthrone 11 [36] which is known to be a thermochromic and mechanochromic material (Scheme [6]). A color change of 11 upon partial isomerization from a yellow stable form with a folded geometry into a green metastable form with a twisted geometry has been postulated. However, the identity and geometrical parameters of the metastable form of 11 were not clarified for a long time since the metastable form was only isolated very recently by the introduction of appropriate substituents.[37] In contrast, the yellow folded form and violet twisted form of 10 were easily isolated and studied by X-ray analysis to confirm their geometrical features, thanks to ChB through S•••N≡C contacts.

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Scheme 5 Absolute asymmetric synthesis of 9oDV via a single-crystalline state photoinduced electron-transfer reaction of oDV·1 (1:1)
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Scheme 6 BTDA-dimer-type overcrowded ethylene 10 and bianthrone (11)

Upon treatment of (Na+)2 1 2– salt with aqueous HCl, the dihydro derivative of BTDA 12 was obtained,[17] which was further converted into mono(dicyanomethylene) derivative 13 [11] (Scheme [7]). Dehydrogenative dimerization using SeO2 gave 10. A solution in ClCH2CH2Cl exhibits a violet color characteristic of the twisted form while exhibiting reversible four-stage one-electron reduction (–0.30, –0.47, –1.48, and –1.63 V vs Fc/Fc+ in CH2Cl2). From this solution, yellow crystals were obtained upon concentration. Crushing of these yellow crystals gave a violet color (mechanochromism), whereas the yellow color returned when the crushed violet solid was heated (thermochromism). This behavior is characteristic of an overcrowded ethylene. According to DFT calculations (M06-2X/6-31G**), the folded conformer in the gas phase is marginally more stable than the twisted form by only 2.47 kcal mol–1.

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Scheme 7 Preparation of BTDA-dimer 10
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Figure 7 Molecular packing of BTDA-dimer 10 in the crystals of (a) the folded conformer and (b) the twisted conformer containing benzonitrile (solvate). The distances corresponding to D 1–D 4 are shown in Å. The geometrical data are as follows: (a) D 1: 3.30 Å, φ 1: 164.4°, θ 1: 165.3°; D 2: 3.32 Å, φ 2: 131.8°, θ 2: 108.7°; D 3: 3.36 Å, φ 3: 126.2°, θ 3: 95.3°, respectively, for three sets of S•••N≡C contacts; (b) D 1: 3.01 Å, φ 1: 150.3°, θ 1: 114.6°; D 2: 3.08 Å, φ 2: 166.8°, θ 2: 119.2°, respectively, for two sets of S•••N≡C contacts, and D 3: 3.21 Å, φ 3: 173.9°; D 4: 3.21 Å, φ 4: 171.6°, respectively, for the (S•••N)2-square-dyad motif.

In the crystal of the yellow folded form of 10, a 2D sheet-like network is formed by ChBs through S•••N≡C contacts (Figure [7a]), which stabilize the folded form in the pristine crystal. The observed network is similar to those in 1 and 13. For the latter, ChBs through S•••N≡C contacts were observed as well as a (S•••N)2-square-dyad motif (Figure [8]). On the other hand, the violet twisted form of 10 was isolated as a solvate upon recrystallization from CH2Cl2 or PhCN. X-ray analysis of the latter showed that the ChB network between 10 is partially broken into a 1D network to incorporate solvent molecules (Figure [7b]). This is the first demonstration that a change in intermolecular interactions in a crystal allows the isolation of multiple forms of overcrowded ethylenes.[38]

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Figure 8 2D sheet-like network in 13. The distances corresponding to D 1 and D 2 are shown in Å. The geometrical data are as follows: D 1: 3.04 Å, φ 1: 174.5°, θ 1: 174.6° for the S•••N≡C contact, and D 2: 3.09 Å, φ 2: 171.8° for the (S•••N)2-square-dyad motif.

#
# 3

TCNQ Analogues Fused with a [1,2,5]Chalcogenadiazole

3.1

Crystal Structures of Chalcogenadiazolo-TCNQs

Tetracyanoquinodimethanes fused to only one chalcogenadiazole (14–16)[39] were prepared from the corresponding dihalobenzochalcogenadiazoles[9g] by using Pd(0)-catalyzed coupling with NaCH(CN)2 (Scheme [8]). These compounds are strong electron acceptors (E 1 red: –0.16, –0.26, and –0.34 V vs Fc/Fc+ in MeCN for 14–16, respectively) and form highly conductive CT complexes with some derivatives of TTF.

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Scheme 8 Preparation of chalcogenadiazolo-TCNQs 14–16

After we had examined a series of crystal structures of BTDA (1) with ChBs, which induce various functions in the solid state, we unexpectedly found that the crystal of thiadiazolo-TCNQ (15) did not exhibit ChBs through S•••N≡C contacts. The molecular arrangement is similar to that of oxadiazolo-TCNQ (14). Thus, the crystal structure is characterized by a coplanar dimeric structure (Figures [9a,b]), which are connected by WHBs through C–H•••N≡C contacts (Scheme [1d]). Such observations of the WHB-dyad can be rationalized by supposing that ChBs are overwhelmed by WHBs in 15, especially because of the enhanced acidity of the C–H group on the quinoid sp2 carbon due to polarization.

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Figure 9 WHB-dyad formation in chalcogenadiazolo-TCNQs 14–16. The distances corresponding to d, D 1 and D 2 are shown in Å. The geometrical data are as follows: (a) 14: d: 2.45 Å , χ: 150°, ω: 152°; (b) 15: d: 2.53 Å, χ: 129°, ω: 169°; (c) 16: d: 2.58 Å, χ: 147°, ω: 124°, respectively, for each C–H•••N≡C contact; D 1: 3.31 Å,φ 1: 137.2°, θ 1: 104.4° for the Se•••N≡C contact; and D 2: 3.43 Å, φ 2: 154.7° for the (Se•••N)2-square-dyad motif.

On the other hand, the dimeric structure caused by WHBs is present in selenadiazolo-TCNQ (16). However, molecules are further connected by ChBs through Se•••N≡C contacts as well as the (Se•••N)2-square-dyad motif to form another dimeric structure by ChB (a ChB-dyad) (Figure [9c]). By connecting another ChB through a Se•••N≡C contact (D: 3.02 Å, φ: 169.2°, θ: 152.4°), there is a 2D sheet-like network in 16. Thus, the stronger ChB involving a Se atom can help determine the crystal packing along with WHBs.

Cooperative control of crystal packing by ChBs and WHBs occurred not only for Se-containing compounds but also with the TCNQ derivative 17,[40] which is fused with both thiadiazole and pyrazine rings leading to a weakening of the C–H-donating properties for WHBs more than in the case of 15. Thus, 17 adopts a planar geometry and forms a coplanar 2D sheet-like network, as in 1, with the formation of both a ChB-dyad and a WHB-dyad (Figure [10]).

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Figure 10 2D sheet-like network in 17. The distances corresponding to D 1, D 2, d 1, and d 2 are shown in Å. The geometrical data are as follows: D 1: 3.08 Å, φ 1: 171.6°, θ 1: 171.6°; D 2: 3.13 Å, φ 2: 157.4°, θ 2: 166.1°, respectively, for two sets of S•••N≡C contacts, and d 1: 2.54 Å, χ 1: 127°, ω 1: 112°; d 2: 2.64 Å, χ 2: 173°, ω 2: 177°, respectively, for two sets of C–H•••N≡C contacts.

# 3.2

Crystal Structures of Chalcogenadiazolo-TCNNQs: An E•••N≡C Chalcogen Bond versus a Weak C–H•••N≡C Hydrogen Bond

The crystal structures shown in the previous subsection indicate that ChBs through E•••N≡C contacts and WHBs through C–H•••N≡C contacts act cooperatively to determine the crystal packing, as found in selenadiazolo-TCNQ (16) and in pyrazine-fused derivative 17 with 2D sheet-like networks. On the other hand, WHBs predominantly determine the molecular arrangement by overwhelming ChBs, as in the crystal of 15, suggesting that ChBs and WHBs compete against each other. Based on the fact that molecular recognition by ChBs[41] is still considered to be in its infancy,[4e] further studies will be needed on tetracyanonaphthoquinodimethane (TCNNQ) derivatives with a non-planar structure, which may accommodate guest molecules more selectively when clathrate-type complexation occurs via ChBs through E•••N≡C contacts. Special attention has been focused on the relative importance of ChBs and WHBs in determining the crystal packing, and on conditions under which WHBs do not interfere with, but rather cooperate with molecular recognition via ChBs.

Thiadiazole-fused TCNNQs (18a–c) and their Se analogues 19a–c were obtained from the corresponding quinone derivatives (Scheme [9]).[12] [42] Regardless of the type of fused ring, namely, benzene (a), o-xylene (b), or naphthalene (c), they all adopt a non-planar geometry due to steric repulsion between the cyano groups and the C–H groups at peri-positions. X-ray analyses were conducted to examine whether the ChB-based dyad or the WHB-based dyad is formed in 18a–c and 19a–c to better understand the relative importance of ChBs versus WHBs in these systems (Figure [11]).

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Scheme 9 Preparation of chalcogenadiazolo-TCNNQs 18a–c and 19a–c
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Figure 11 Two types of chalcogenadiazolo-TCNNQ dyads formed via secondary bonding interactions (SBIs)

Thiadiazolo-TCNNQ (18a) existed as a WHB-dyad (Figure [12a]) and ChBs through S•••N≡C contacts are largely suppressed. On the other hand, the corresponding Se-analogue 19a showed only the presence of a ChB-dyad through Se•••N≡C contacts (Figure [12b]). This dyad is further connected by ChBs and WHBs to form a 2D sheet-like network, as detailed later. When the quinodimethane skeleton is fused with an o-xylene ring or a naphthalene ring in place of the benzene ring, quite similar ChB-dyads were found in crystals of 19b and 19c, showing that ChBs through Se•••N≡C contacts were determining factors in the selenadiazolo-TCNNQs series 19 (Figure [13]).

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Figure 12 (a) The WHB-dyad in 18a and the ChB-dyads in (b) 19a, (c) 19b, (d) 18c, and (e) 19c. The geometrical parameters are as follows: (a) d: 2.70 Å, χ: 127°, ω: 117°; (b) D: 3.16 Å, φ: 155.5°, θ: 114.5°; (c) D: 3.24 Å, φ: 153.4, θ: 123.4°; (d) D: 3.14 Å, φ: 143.6°, θ: 147.2°; (e) D: 3.06 Å, φ: 148.6°, θ: 149.3°, respectively.

In contrast to the 2D sheet-like network formed through ChBs and WHBs in 19a and 19b, WHBs in naphthalene-fused derivative 19c are less important. The weaker WHBs in 19c are the reason for the adoption of a similar ChB-dyad in S-congener 18c through S•••N≡C contacts. The above comparisons suggest that the balance of the relative importance between ChBs and WHBs can be adjusted by proper molecular design, and ChBs through Se•••N≡C contacts are robust enough even in the presence of WHBs. It is highly likely that ChBs and WHBs can cooperate to achieve superior recognition properties upon clathrate formation using 19a.

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Figure 13 Classification of crystal structures according to the type of SBI-dyad

# 3.3

Molecular Recognition by Chalcogen Bonds in TCNNQ Derivatives

Upon recrystallization of the yellow solid of selenadiazolo-TCNNQ (19a) in the presence of 2,6-dimethylnaphthalene (DMN), red crystals of the 2,6-DMN·(19a)2 CT complex were obtained.[43] On the other hand, 2,7-DMN did not form the corresponding CT complex with 19a, despite the fact that 2,6-DMN and 2,7-DMN have very similar molecular shapes and form a eutectic mixture.

Since 2,6-DMN is an important material for industrial applications,[44] the observed ability of 19a to recognize DMN isomers is outstanding.[45] By a simple mixing–filtration–heating process similar to that shown in Scheme [3], pure 2,6-DMN (97.2 wt%) was obtained with very slight contamination by 2,7-DMN (1.1 wt%) by starting from a C12 liquid containing 9.7 wt% of 2,6-DMN and 9.4 wt% of 2,7-DMN. Similar experiments using the S-congener 18a gave unfruitful results. Even when we used BTDA (1) with high recognition properties toward p-xylene, pure 2,6-DMN was not obtained (hydrocarbons obtained by thermal decomposition of CT crystals: 2,6-DMN, 77.9 wt%; 2,7-DMN, 4.5%; others, 17. 6 wt%).

To better understand the higher recognition properties of 19a toward DMN, the crystal packings of pristine 19a and 2,6-DMN·(19a)2 were analyzed in detail. In the crystal of 19a, the aforementioned ChB-dyad is connected by another ChB (along the crystallographic b axis) to form a 1D dyad-ribbon network, which is further connected by WHBs (along the c axis) into a 2D sheet-like network (Figure [14a]). In the crystal structure of 2,6-DMN·(19a)2, a very similar molecular arrangement was observed. Thus, a ChB-dyad is connected by another ChB (along the crystallographic b axis) to form a dyad-ribbon network. The original WHB in pristine 19a is broken but reconnects at the shifted positions to generate a 2D sheet-like network containing inclusion cavities in which 2,6-DMN is incorporated (Figure [14b]). The 2,6-DMN in the cavity is additionally sandwiched in a π–π stacking manner with two molecules of 19a in the neighboring 2D sheet-like networks. Such a three-dimensional cavity formed by the sterically demanding non-planar electron acceptor 19a would be key for the observed outstanding molecular recognition, which also involves WHBs.


#
# 4

Outlook

As shown above, a family of chalcogenadiazolo-TCNQs that can form ChBs are promising materials for the development of novel solid-state functions, the separation of electron-donating guest molecules upon CT complexation and for photoinduced asymmetric reactions. Furthermore, the two-dimensional network structure formed by ChBs is key for the novel electric-field-controllable conductance switching of the BTDA-dimer 10 [46] and for the mixed-valence semiconducting framework of BTDA (1),[47] both of which have been reported recently. Both the development of new members of the BTDA family[8e] [48] and a better understanding of ChBs[8f] [21] is expected to expand the chemistry of this attractive class of compounds.

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Figure 14 Crystal structures of (a) 19a and (b) 2,6-DMN·(19a)2. The distances corresponding to D, D 1, D 2, and d are shown in Å. The geometrical parameters are as follows: (a) D: 3.04 Å, φ: 176.6°, θ: 159.0°; d: 2.73 Å, χ: 127°, ω: 128°; (b) D 1: 2.99 Å, φ 1: 167.8, θ 1: 159.6°; D 2: 3.27 Å, φ 2: 153.8, θ 2: 121.2°; d: 2.72 Å, χ: 128°, ω: 146°, respectively.

#
#

Conflict of Interest

The authors declare no conflict of interest.


Corresponding Author

Takanori Suzuki
Department of Chemistry, Faculty of Science, Hokkaido University
Sapporo, Hokkaido 060-0810
Japan   

Publication History

Received: 02 April 2023

Accepted after revision: 24 April 2023

Accepted Manuscript online:
12 April 2023

Article published online:
25 May 2023

© 2023. Thieme. All rights reserved

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Scheme 1 (a) (E•••N)2-square-dyad and (b) E•••N≡C motifs of chalcogen bonds (ChBs). Geometrical definitions of (c) ChBs and (d) WHBs.
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Scheme 2 Preparation of BTDA (1), TSDA (2), and BSDA (3)
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Figure 1 2D sheet-like network in 1 involving ChBs through S•••N≡C contacts. The distance is shown in Å.
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Figure 2 Electrostatic potentials of (a) BTDA 1 and (b) BSDA 3 calculated by a DFT method (M06-2X/6-31G**) based on the crystallographic coordinates
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Figure 3 Molecular packing in the crystal of EtMe3N+ 1 –• (1:1) salt. The distances corresponding to D 1 and D 2 are shown in Å. (a) Top view showing the ribbon network, and (b) a side view showing π–π stacking. The geometrical data are as follows: D 1: 3.12 Å, φ 1: 149.3°, θ 1: 120.2°; D 2: 3.25 Å, φ 2: 150.1°, θ 2: 115.7°, respectively, for two sets of S•••N≡C contacts.
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Figure 4 (a) Molecular packing in the crystal of the TSeT·1 (1:1) CT complex viewed along the segregating stacks. The distances corresponding to D 1 and D 2 are shown in Å. The geometrical data are as follows: D 1: 3.08 Å; θ 1: 164.7°; D2: 3.10 Å; θ 2: 124.2°, respectively, for two sets of Se•••N≡C contacts, and the separation of 3.87 Å for S•••N≡C contacts is too far to be considered for ChBs. (b) Molecular packing in the crystal of the TTF·1 (1:1) CT complex viewed along the mixed stack. The distances corresponding to D 1 and D 2 are shown in Å. The geometrical data are as follows: D 1: 3.37 Å, φ 1: 125.7°, θ 1: 134.1°; D2: 3.15 Å; θ 2: 104.0°, respectively, for two sets of S•••N≡C contacts.
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Scheme 3 A simple mixing–filtration–heating process for the separation of p-xylene from a mixture of its isomers by formation of a clathrate with BTDA (1) via ChBs through S•••N≡C contacts
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Figure 5 (a) Molecular packing in the crystal of the p-methylanisole·1 (1:1) CT complex viewed along the mixed stack. The distance corresponding to D is shown in Å. The geometrical data are as follows: D: 3.25 Å, φ: 169.3°, θ: 174.7° for the S•••N≡C contact. The methyl and methoxy groups are positionally disordered. (b) Molecular packing in the crystal of the o-methylanisole·1 (1:1) CT complex viewed along the mixed stack. The distances corresponding to D 1 and D 2 are shown in Å. The geometrical data are as follows: D 1: 3.19 Å, φ 1: 147.0°, θ 1: 120.8°; D 2: 3.35 Å, φ 2: 137.0°, θ 2: 146.5°, respectively, for two sets of S•••N≡C contacts.
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Figure 6 Molecular packing in the crystal of the o-DV·1 (1:1) CT complex viewed along the mixed stack (a) before and (b) after the single-crystal-to-single-crystal photoinduced electron-transfer reaction. The distances corresponding to D 1 and D 2 are shown in Å. The geometrical data are as follows: (a) D 1: 3.14 Å, φ 1: 142.6°, θ 1: 114.8°; D 2: 3.43 Å, φ 2: 134.7°, θ 2: 106.3°, respectively, for two sets of S•••N≡C contacts; (b) D 1: 3.35 Å, φ 1: 137.7°, θ 1: 117.6°; D 2: 3.25 Å, φ 2: 145.7°, θ 2: 117.0°, respectively, for two sets of S•••N≡C contacts.
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Scheme 4 Cycloaddition of BTDA (1) with aryl olefins under CT excitation conditions
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Scheme 5 Absolute asymmetric synthesis of 9oDV via a single-crystalline state photoinduced electron-transfer reaction of oDV·1 (1:1)
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Scheme 6 BTDA-dimer-type overcrowded ethylene 10 and bianthrone (11)
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Scheme 7 Preparation of BTDA-dimer 10
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Figure 7 Molecular packing of BTDA-dimer 10 in the crystals of (a) the folded conformer and (b) the twisted conformer containing benzonitrile (solvate). The distances corresponding to D 1–D 4 are shown in Å. The geometrical data are as follows: (a) D 1: 3.30 Å, φ 1: 164.4°, θ 1: 165.3°; D 2: 3.32 Å, φ 2: 131.8°, θ 2: 108.7°; D 3: 3.36 Å, φ 3: 126.2°, θ 3: 95.3°, respectively, for three sets of S•••N≡C contacts; (b) D 1: 3.01 Å, φ 1: 150.3°, θ 1: 114.6°; D 2: 3.08 Å, φ 2: 166.8°, θ 2: 119.2°, respectively, for two sets of S•••N≡C contacts, and D 3: 3.21 Å, φ 3: 173.9°; D 4: 3.21 Å, φ 4: 171.6°, respectively, for the (S•••N)2-square-dyad motif.
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Figure 8 2D sheet-like network in 13. The distances corresponding to D 1 and D 2 are shown in Å. The geometrical data are as follows: D 1: 3.04 Å, φ 1: 174.5°, θ 1: 174.6° for the S•••N≡C contact, and D 2: 3.09 Å, φ 2: 171.8° for the (S•••N)2-square-dyad motif.
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Scheme 8 Preparation of chalcogenadiazolo-TCNQs 14–16
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Figure 9 WHB-dyad formation in chalcogenadiazolo-TCNQs 14–16. The distances corresponding to d, D 1 and D 2 are shown in Å. The geometrical data are as follows: (a) 14: d: 2.45 Å , χ: 150°, ω: 152°; (b) 15: d: 2.53 Å, χ: 129°, ω: 169°; (c) 16: d: 2.58 Å, χ: 147°, ω: 124°, respectively, for each C–H•••N≡C contact; D 1: 3.31 Å,φ 1: 137.2°, θ 1: 104.4° for the Se•••N≡C contact; and D 2: 3.43 Å, φ 2: 154.7° for the (Se•••N)2-square-dyad motif.
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Figure 10 2D sheet-like network in 17. The distances corresponding to D 1, D 2, d 1, and d 2 are shown in Å. The geometrical data are as follows: D 1: 3.08 Å, φ 1: 171.6°, θ 1: 171.6°; D 2: 3.13 Å, φ 2: 157.4°, θ 2: 166.1°, respectively, for two sets of S•••N≡C contacts, and d 1: 2.54 Å, χ 1: 127°, ω 1: 112°; d 2: 2.64 Å, χ 2: 173°, ω 2: 177°, respectively, for two sets of C–H•••N≡C contacts.
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Scheme 9 Preparation of chalcogenadiazolo-TCNNQs 18a–c and 19a–c
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Figure 11 Two types of chalcogenadiazolo-TCNNQ dyads formed via secondary bonding interactions (SBIs)
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Figure 12 (a) The WHB-dyad in 18a and the ChB-dyads in (b) 19a, (c) 19b, (d) 18c, and (e) 19c. The geometrical parameters are as follows: (a) d: 2.70 Å, χ: 127°, ω: 117°; (b) D: 3.16 Å, φ: 155.5°, θ: 114.5°; (c) D: 3.24 Å, φ: 153.4, θ: 123.4°; (d) D: 3.14 Å, φ: 143.6°, θ: 147.2°; (e) D: 3.06 Å, φ: 148.6°, θ: 149.3°, respectively.
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Figure 13 Classification of crystal structures according to the type of SBI-dyad
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Figure 14 Crystal structures of (a) 19a and (b) 2,6-DMN·(19a)2. The distances corresponding to D, D 1, D 2, and d are shown in Å. The geometrical parameters are as follows: (a) D: 3.04 Å, φ: 176.6°, θ: 159.0°; d: 2.73 Å, χ: 127°, ω: 128°; (b) D 1: 2.99 Å, φ 1: 167.8, θ 1: 159.6°; D 2: 3.27 Å, φ 2: 153.8, θ 2: 121.2°; d: 2.72 Å, χ: 128°, ω: 146°, respectively.