3.2.5. (TMTSF)4(I3)4·THF

The average of Δ*E*<sup>0</sup> − Δ*E*1<sup>+</sup> of K, L, M, and L in the 4:4 salt is 0.151 eV and it is relatively high in Figure 12d. This is consistent with the average valence 1+ expected from the composition. On the other hand, we see that these crystallographically independent TMTSF molecules naturally give the relatively large distribution of Δ*E*<sup>0</sup> − Δ*E*1+, namely 0.083 eV (M), 0.140 eV (N), 0.180 eV (K), and 0.201 eV (L), respectively.

The distribution poses an interesting possibility that some of the TMTSF molecules have the valence larger than a unity (>1+). One will easily understand that it is certainly possible by taking a look at the crystal structure in Figure 8a.

In a simplified picture, the 4:4 salt has an elongated rock-salt structure, but the cation and anion units are composed of not by single atoms such as Na<sup>+</sup> and Cl<sup>−</sup> but by the tetramers of molecules. Therefore, the electrons do not have to distribute uniformly within each tetramer.

Indeed, the TMTSF molecules K and L are surrounded by more I− <sup>3</sup> anions than M and N. Especially, the molecule M is next to a neutral THF molecule instead of an I− <sup>3</sup> anion. Thus, the molecules K and L can possess more positive charge than M; and N will be in between them. Considering it like this, the order of the height of bars in Figure 12b,d is understood naturally.

#### 3.2.6. Ionization Potentials

The difference between the total energy obtained for the optimized structure at "neutral" state (*E*0(optimized for 0)) and that for the "cationic" state (*E*1+(optimized for 1+)) corresponds to the adiabatic ionization potential *I*a of the TMTSF molecule as,

$$I\_{\mathbf{a}} = E\_{\mathbf{l}+} \text{(optimized for } \mathbf{1}+) - E\_{\mathbf{0}} \text{(optimized for } \mathbf{0}).\tag{1}$$

On the other hand, the difference between *E*0(optimized for 0) and the total energy of the cationic state with the structure optimized for the "neutral" state (*E*1+(optimized for 0)) gives the vertical ionization energy *I*v as,

$$I\_\mathbf{v} = E\_{1+} \text{(optimized for 0)} - E\_0 \text{(optimized for 0)}.\tag{2}$$

Comparison of the *I*a and *I*v values by the present calculations with the experimental ones will be a good test for knowing the reliability of the fundamental values of *E*<sup>0</sup> and *E*1+ in Tables 3 and 4.

By the present calculations, the values *I*<sup>a</sup> = 5.81 eV (DFT) and 5.65 eV (MP2); and *I*<sup>v</sup> = 6.09 eV (DFT) and 6.01 eV (MP2) are obtained for the isolated TMTSF molecule, while the values *I*<sup>a</sup> = 6.27 eV and *I*<sup>v</sup> = 6.58 eV were determined by the photoelectron spectroscopy for that in gas phase [84]. The calculated values are fairly close to the experimental ones, though the former is 7–9% smaller than the latter.

We confirmed that the agreement is much more improved (within ∼1%), when Møller–Plesset correlation energy calculations, in combination with the basis set cc-pVTZ, is truncated at fourth order (MP4(SDQ)), as *I*<sup>a</sup> = 6.17 eV and *I*<sup>v</sup> = 6.55 eV, respectively. Therefore, the results in Figure 12c,d will be further refined by the MP4 calculations (in progress), though it takes much longer machine time than the DFT and MP2 ones.

#### **4. Materials and Methods**

#### *4.1. Sample Preparation*

All the present I3 salts were grown by the electrochemical oxidation using stick-type platinum electrodes.

The single crystals of the 8:5 and 5:2 salts were obtained from the mixed solution of TMTSF (22.7 mg) and tetrabutylammonium triiodide (8.7 mg) with THF (98%, 30 mL) as the solvent. The constant DC electrical current of 2 μA was applied between electrodes for 143 h in air at 20 ◦C.

The crystals of both the 8:5 and 5:2 salts grew together on the anode. The crystals are black cuboids for the 8:5 salt and black needle-like for the 5:2 salt, respectively. After the crystals were removed from the electrode, they were washed by ethanol and dried in air.

The single crystals of the 4:4 salt were obtained from the mixed solution of TMTSF (22.8 mg) and tetrabutylammonium triiodide (9.0 mg) with THF (98%, 30 mL) as the solvent. The constant DC electrical current of 5 μA was applied between electrodes for 45 h in air at 20 ◦C.

The crystals of the 4:4 salt grew on the anode, but the major product was the 5:2 salt. The crystals of the 4:4 salt are black plate-like and most of them are much larger than those of the 5:2 salt.

#### *4.2. X-ray Crystal Structure Analysis*

Data collections for the present I3 salts were performed using a MSC Mercury CCD X-ray system (Rigaku, Tokyo, Japan) equipped with MoK*α* radiation (*λ* = 0.7107 Å) at room temperature. All the structures were solved by the direct method using SHELXS-97 software package and were refined by the full-matrix least-squares method. The refinement data are summarized in Table 1.

#### *4.3. Measurement of Electrical Resistivity*

The electrical resistance was measured by a standard four-probe technique. Annealed gold wires (10 μm in diameter) were attached as electrodes with carbon paste (XC-12, Fujikura-kasei Co., Tokyo, Japan). The DC electrical current of 1–10 μA was applied by a current source (7651, Yokogawa, Tokyo, Japan) and the voltage signal was measured by a nano-volt/micro-ohm-meter (34420A, Keysight Technologies, Santa Rosa, CA, USA) or a digital multi-meter (34970A, Keysight Technologies, CA, USA). The polarity of the electrical current was switched to eliminate the parasitic voltage. Thus, the electrical resistance was determined as the slope of the voltage to the current. The electrical resistivity *ρ* was calculated using the size of each crystal assuming their shapes are rectangular.

The temperature dependence of the *ρ* at ambient pressure was measured in the vacuum chamber of a home-made cryostat. A clamped-type pressure cell made of BeCu was used for the measurement under pressure. We used Daphne 7373 (Idemitsu Kosan Co., Tokyo, Japan) as the pressure transmitting medium. The pressure inside was corrected by the clamped pressure at room temperature and the temperature dependence of the inside pressure in the previous reports [74,75].

After the measurement was finished, the lattice parameters of the samples #1908 and #1910 were determined by the X-ray diffraction pattern and they were identified as the 8:5 and 5:2 salts, respectively.

#### **5. Conclusions**

Three types of novel TMTSF salts (TMTSF)8(I3)5, (TMTSF)5(I3)2, and (TMTSF)4(I3)4·THF were synthesized and their crystal structures were solved at room temperature. The electrical resistivity was measured for (TMTSF)8(I3)5 and (TMTSF)5(I3)2 at ambient pressure and under hydrostatic pressure up to 1.73 GPa.

The X-ray crystal structure analyses revealed that the 8:5 and 5:2 salts have one-dimensional TMTSF stacks made of TMTSF trimers. The TMTSF stacks are separated by TMTSF monomers in these salts. On the other hand, the crystal structure of the 4:4 salt is regarded as an elongated rock-salt type, where a TMTSF tetramer is surrounded by six I− <sup>3</sup> tetramers and vice versa.

#### *Crystals* **2020**, *10*, 1119

The electrical resistivity of (TMTSF)8(I3)5 is metallic for the electrical current along the highest conducting direction. The resistivity shows rapid increase below 88 and 53 K suggesting two phase transitions or changes in electronic states. The analysis of the *ρ* revealed the possibility of the third change in the electronic state above 310 K.

The electrical resistivity of (TMTSF)5(I3)2 is semiconducting below room temperature. It shows the change in slope in the Arrhenius plot suggesting a kind of change in electronic state or a crossover from a wider-band-gap to a narrow-band-gap states around 190 K.

No large change in the behavior of the electrical resistivity was observed for the 8:5 and 5:2 salts by the application of hydrostatic pressures up to 1.73 GPa.

The valence of the crystallographically independent TMTSF molecules in the three I3 salts has been estimated on the basis of the quantum mechanical calculations of the total energy. The method was found to give the plausible valence of each TMTSF molecule.

The large unit cell of the 8:5 salt is probably results in a number of energy bands separated by small band gaps. The estimated TMTSF valence ((5/8)+ on average) gives the band filled by 5/16 with holes in total, though crystallographically independent TMTSF molecules P, Q, and R are probably less oxidized in this order.

The electronic state of the 5:2 salt is semiconducting and this is consistent with the trimer structures with TMTSF(2/3)+ since the TMTSF monomer C is most likely neutral.

The average valence of TMTSF molecules is 1+ in the 4:4 salt, but the quantum mechanical calculations and its crystal structure strongly suggest that the valence of two TMTSF molecules K and L in the tetramer is higher than 1+.

It is concluded that the quantum mechanical energy calculations give relative change in the non-integer valence of TMTSF molecules in the I3 salts, in spite of the limitation that the Gaussian package can accept only the integer valence as an input parameter for single molecule.

On the other hand, there exist more direct and powerful methods to determine not only valence but also the charge distribution within a molecule as well as a unit cell. For example, the electron density analysis based on the synchrotron X-ray diffraction has been successfully applied to investigate the charge-ordering transitions of *α*-(BEDT-TTF)2I3 (BEDT-TTF = bis(ethylenedithio)tetrathiafulvalene) [85] and (TMTTF)2PF6 (TMTTF = tetramethyltetrathiafulvalene) [86].

Please note that the Gaussian package provides a function to calculate the electron density map under the periodic boundary condition. In our calculation environment, however, the DFT calculations fail in case of, for example, the 4:4 salt due to the limitation of the number of atoms or basis sets. In addition, even though the electron density map has been obtained, there should be the problem in defining the borders between neighboring molecules to integrate the electron density numerically. This type of estimation of molecular valence in a crystal with a large unit cell will be another challenge.

The present method, however, provides a quick and convenient way to estimate the more precise valence of donors and acceptors than that just by comparing the bond lengths before trying a time-consuming method.

**Author Contributions:** Sample preparation, Y.I.; X-ray crystal structure analyses, R.T.; electrical resistivity measurements, H.Y., Y.I., Y.T. and C.M.; quantum-mechanical calculations, H.Y.; interpretation of results, H.Y.; writing—original draft preparation, H.Y.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by JSPS KAKENHI Grant Number JP25400380.

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