*3.2. Electronic States and Conductivity of TTF-py2\_PF6*

To understand the electronic state of **TTF-py2\_PF6**, microscopic Raman spectrum, solid-state absorption spectrum, and ESR spectrum of **TTF-py2\_PF6** were recorded and shown in Figure 2. Microscopic Raman spectrum of **TTF-py2\_PF6** shows a strong peak around 1450 cm–1 and weak peaks around 1420 and 1520 cm–1. It is well known that there is a correlation between the valence of the TTF molecule and Raman frequency [49], and the valence corresponding to 1450 cm–1 is found to be about +0.6 based on previous studies [49]. This value is in approximate agreement with the valence obtained from the formula, +0.66. The absorption spectrum consists of major absorption bands above 1.7 eV, a broad band around 0.4 eV, and a minor band around 1.5 eV (Figure 2b). Each band was assigned by following previous reports [50–52]. Major bands above 1.7 eV correspond to the mixture of the π–π\* transition for the radical monomer trans-TTF-py2 •<sup>+</sup> and radical dimer (trans-TTF-py2 •<sup>+</sup>)2. A broad band around 0.4 eV and a minor band around 1.5 eV are characteristics of intermolecular charge transfer from trans-TTF-py2 •<sup>+</sup> to trans-TTF-py2 <sup>0</sup> (forming trans-TTF-py2 <sup>0</sup> and trans-TTF-py2 •+) and from trans-TTF-py2 •<sup>+</sup> to trans-TTF-py2 •<sup>+</sup> (forming trans-TTF-py2 <sup>0</sup> and trans-TTF-py2 <sup>2</sup>+), respectively [53]. The existence of trans-TTF-py2 •<sup>+</sup> was also supported by the results of the ESR spectrum (Figure 2c), which shows a singlet peak with *g* = 2.003 derived from a TTF radical.

**Figure 2.** (**a**) Raman spectrum, (**b**) solid-state absorption spectrum from IR to UV energy region, (**c**) ESR spectrum, and (**d**) temperature-dependent electrical conductivity of **TTF-py2\_PF6.**

A single crystal direct-current conductivity (= σ) of **TTF-py2\_PF6** along the π-stack direction is shown in Figure 2d. The electrical conductivity of **TTF-py2\_PF6** is 12 S cm–1 at RT, and the decreases with cooling temperature, suggesting semiconducting behavior. The slope of the Arrhenius plot is constant with 1000*T*–1 above 4.5 K–1. From the fitting of the Arrhenius plot above 4.5 K–1 with an Arrhenius dependence of σ = σ0exp[−(*E*g/2*kT*)] where σ<sup>0</sup> is a constant, *E*<sup>g</sup> is the bandgap and *k* is Boltzmann constant [54], it shows that the *E*g of the carriers is estimated to be 162 meV.

#### **4. Discussion**

The structural study shows short contacts by the hydrogen bondings, and the DFT calculation with the counterpoise correction shows the significant stabilization energy. It is noteworthy that although the distance of the hydrogen bonding between **A** and **B** (2.365 Å) is shorter than that between **B** and **B** (2.626 Å), the stabilization energy of the hydrogen bonding between **A** and **B** (= –0.74 kcal/mol) is less than that between **B** and **B** (= –1.72 kcal/mol). This tendency did not change even when the exchange correlation functional was changed from B3LYP to B3PW91 or PBEPBE in the DFT calculations. The nature of the hydrogen bond is complicated by the fact that the hydrogen bond has multiple parameters such as angles, distances and chemical species (elements of hydrogen donor and acceptor atoms). [17,55]. In the present case, the N···H distance seems to be less important to determine the energy of the hydrogen bond. As shown in Figure 1f,g, the angles between the axis of the pyridyl groups and the hydrogen atoms of the TTF core (∠C(position 4)···N···H) are 143.7◦ for **A** and **B** and 162.5◦ for **B** and **B**. Because the latter angle is closer to 180◦, where the lone pair of nitrogen atom is headed to the hydrogen atom, the hydrogen bonding between **B** and **B** is stronger than that between **A** and **B**. Wood et al. examined the distance- and the angle-dependence of hydrogen bondings with pyridine in terms of computational chemistry [55]. In the paper, the structural dependence of the stabilization energy varies with chemical species, and the dependence of the energy on the interatomic distance is found to be relatively weak for the weak hydrogen bondings such as those with benzene. Even in this system, the hydrogen bondings are also weak C-H···N bonds, thus the dependence of the energy on the N···H distance is small, and the change of the angle is more likely to be involved in the stabilization energy.

The temperature-dependent electrical conductivity of **TTF-py2\_PF6** shows semiconducting behavior along the *a* axis. Effective charge transfer integrals of adjacent TTF-py2 clarify the nature of one-dimensional electron conductivity along the *a* axis, which is also denoted from the band structure. Given the difference of the effective charge transfer integral between **A** and **B** (*V*eff = 390.8 meV), and **B** and **B** (*V*eff = 220.9 meV), the semiconducting behavior of **TTF-py2\_PF6** is probably due to the localization of carriers in the columnar structure. In fact, band calculation by using tight-binding approximation without structural optimization (Figure 3) shows an inherent bandgap, *E*g = 140 meV, and hence a significant localization of carrier can be assumed from the crystal structure. The Calculated bandgap is almost consistent with the bandgap acquired from temperature-dependent conductivity (*E*<sup>g</sup> = 162 meV). The carriers in the dominant part of the electron conduction were located where the path of the band structure is along *a\** axis, the direction of π–π stacking of TTF-py2. Hence, not only the effective charge transfer integrals but also the band structure show the one-dimensional conducting character of **TTF-py2\_PF6**.

**Figure 3.** Brillouin zone of TTF-py2\_PF6 (**left**) showing the path corresponding to the band structure of TTF-py2\_PF6 (**right**).

#### **5. Conclusions**

In this paper, we discussed the crystal structure and the physical properties of the molecular conductor **TTF-py2\_PF6**. It is the first molecular conductor containing trans-TTF-py2 molecules and is the second one with trans-bis-substituted TTF molecules, to the best of our knowledge. Although **TTF-py2\_PF6** has one dimensional electron transport properties, which is typical in molecular conductors, the hydrogen bondings between the pyridyl groups and the hydrogen atoms of the TTF skeleton were successfully introduced in the crystal structure. We believe that this result provides a potential for further structural explorations and physical properties of TTF-based molecular conductors with a substitution group with hydrogen bondings such as pyridyl and other moieties. Additionally, TTF-py2 is a promising ligand for constructing both conductive π-stacked arrays and coordination networks in a crystal, such as porous molecular conductors [56,57] and conductive π-stacked metal-organic frameworks [58–61].

CCDC-2040487 contains the supplementary crystallographic data for this paper. Crystal structure information is available online at the Cambridge Crystallographic Data Centre (CCDC) database via www.ccdc.cam.ac.uk/data\_request/cif.

**Author Contributions:** Conceptualization, S.K. and H.I.; methodology, S.K.; software, S.K., H.I.; validation, H.I., S.T. and M.K. (Manabu Kanno); formal analysis, S.K.; investigation, S.K., M.K. (Morio Kawai); resources, H.I., S.T., N.H., T.A.; data curation, S.K.; writing—original draft preparation, S.K.; writing—review and editing, H.I., S.T. and M.Y.; visualization, S.K.; supervision, H.I., and M.Y.; project administration, H.I. and S.T.; funding acquisition, S.K., H.I., and S.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was partly supported by JSPS KAKENHI Grant Numbers JP18H04498 (H.I.) for "Soft Crystals", JP18K14233 (H.I.), JP19H05631 (H.I., S.T. and M.Y.) and JP20J22404 (S.K.), by the Toyota Riken Scholar Program (H.I.) and by the Kato Foundation for Promotion of Science KJ-2916 (H.I.).

**Acknowledgments:** Authors acknowledge the Research and Analytical Center for Giant Molecules, Graduate School of Science, Tohoku University, for the measurement of elemental analysis and common equipment unit of Advanced Institute of Material Research, Tohoku University, for the measurement of microscopic Raman spectra.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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