*3.3.* α*-(BETS)2(HOC2H4SO3)*·*H2O (3)*

The asymmetric unit of **3** consists of one (A in Figure 3c) and two halves (B and C) of BETS, one isethionate and one water molecule. The anion and the water molecule are disordered as schematically shown in Figure 3a, in which there are two anions having different conformations, which are superimposed at the same position. The crystal structure is shown in Figure 3b. The space group is *P*1, so four BETS molecules, two anions and two water molecules exist in the unit cell. Figure 3c shows the packing arrangement of a BETS layer, where A is a centrosymmetrically inverted A. The layer has an α-type packing motif with short side-by-side chalcogen–chalcogen contacts, indicating that the salt has 2D conducting layers. The ratio of donor to anion is 2:1 which suggests that the salt would show low resistivity (*vide infra*). Figure 3d shows a packing arrangement of the anion/water layer. Because

there are two molecular configurations (ρ and σ) in the same position and two anion positions (I and II), there are four possible patterns ((1)–(4) in Figure 3d), where ρ and σ are centrosymmetrically inverted ρ and σ, respectively. In addition, patterns (1) and (2) are centrosymmetric but (3) and (4) are not exactly centrosymmetric.

**Figure 3.** (**a**) A schematic diagram of the disorder of the isethionate anion. (**b**) Crystal structure. (**c**) Arrangement of the donor layer, in which donors A, B and C are crystallographically independent and A is the centrosymmetrically inverted A. Dashed lines indicate short S···S, Se···S and Se···Se contacts (<3.70, 3.75 and 3.80 Å, respectively). Transfer integrals are labelled as *p*1, *p*2, etc. (**d**) Four possible patterns of the donor layer of **3**. The unit cell has two disordered water molecules (W1 and W2) and two isethionate anions (I and II), the latter of which are disordered over two conformations (ρ and σ) as schematically shown in Figure 3a. ρ and σ are the symmetrically inverted ρ and σ.

The donor arrangement (α-type), the numbers of independent BETS molecules (one (A) and two halves (B and C)), and the cell parameters of **3** are quite similar to those of α-(BETS)2I3 [12], suggesting that the transport property of **3** would also be similar. α-(BETS)2I3 shows a metal–insulator (MI) transition at 50 K, and there is a shoulder at 40 K, suggesting another phase transition, below which the resistivity increases more rapidly [13]. The temperature-dependent electrical resistivity of **3** is shown in Figure 4a, where four crystals (Samples A–D) were measured at the same time; therefore, the cooling and heating rates are the same. However, the four samples show a wide variety of temperature dependences, and therefore, the samples were measured again. The resistivity curves of the second run are shown in Figure 4b. The behaviours of samples A, B and C are clearly different from each other. Moreover, each sample shows a different behaviour from the first measurement apart from sample C. The resistivity of almost all experiments shows MI transitions at around 70 K, and shoulders can be seen in some curves at around 30 K. The general behaviours are similar to those of α-(BETS)2I3. However, the ratio of the largest and smallest resistivity values (ρmax/ρmin) of sample C of **3**, which shows the sharpest MI transition of all the measured samples, and of α-(BETS)2I3 are 4.6 and 570, respectively. This observation indicates that the MI transition of **3** is much less sharp than that of α-(BETS)2I3.

**Figure 4.** Temperature dependences of electrical resistivity of four crystals of **3**, where (**a**) is the first and (**b**) is the second run.

The temperature-dependent magnetic susceptibility of α-(BETS)2I3 was fitted by χSpin = *C*/*T* exp(−Δ/*k*B*T*) (equation 1) with the gap <sup>Δ</sup>/*k*<sup>B</sup> = 290 K and a Curie constant *C* = 0.29 emu mol−<sup>1</sup> [23]. The magnetic behaviour of **3** (Figure 5) is similar to that of α-(BETS)2I3. The susceptibility decreases with decreasing temperature, where the differences in the susceptibilities between room and low temperatures are approximately 2.7 <sup>×</sup> 10−<sup>4</sup> emu mol−1, which is 1.0 <sup>×</sup> 10−<sup>4</sup> emu mol−<sup>1</sup> smaller than that of α-(BETS)2I3. The data of **3** cannot be fitted by equation 1 and are closer to a 1D Heisenberg model (green line in Figure 5) with *J* = −213 K. However, the large deviations do not suggest that the spins on the BETS layer forms a 1D chain. This may indicate that more spins or more itinerant electrons exist at low temperatures in salt **3** when compared to α-(BETS)2I3.

**Figure 5.** Temperature dependence of magnetic susceptibility of **3**. The green solid line is calculated on the basis of a 1D Heisenberg model.

The electronic structure was characterized using extended Hückel tight-binding band structure calculations of the donor layer [24] as shown in Figure 6. The Fermi surfaces are almost the same as for α-(BETS)2I3 [25]. Therefore, **3** and α-(BETS)2I3 have the same electronic structures.

**Figure 6.** Band dispersions (**left**), Fermi surfaces (**centre**) and overlap integrals (**right**) of **3**. The donor···donor interactions (*p*1, *p*2, etc.) are labelled in Figure 3c.

#### **4. Discussion**

Although the molecular structures of the triiodide and isethionate BETS salts are very different, the cell parameters of **3** are quite similar, as are the donor arrangements and band structures. The α-(BETS)2I3 salt is isomorphous to α-(BEDT-TTF)2I3, which also shows a MI transition at 135 K (*T*MI) [12]. Therefore, it is believed that both MI transition mechanisms are similar. The mechanism of the MI transition of α-(BEDT-TTF)2I3 has been widely studied ([12,13,25–28] and references therein). At room temperature, the positive charges are equally distributed in the BEDT-TTF donor layers. However, below *T*MI, two BEDT-TTF molecules (A and B) become monocations and two become neutral (A and C), which is charge ordering (CO). In addition, the space group changes into the polar space group *P*1, and the previously crystallographically equivalent A and A molecules become independent. The crystal also becomes polar below the transition temperature [29]. Recently, J.-P. Pouget and co-workers reported a more consistent mechanism of the MI transition [27,28], where modulating the strength of the donor–anion hydrogen bonding modified the charges on the HOMOs of the donors; namely, I···H-C hydrogen bonds played a key role in the MI transition. Due to the similar structural and electronic properties, we expect that the salt **3** also shows a similar CO transition.

Figure 7a,b shows the structural relationship between -SO3 <sup>−</sup> of the HOC2H4SO3 − anions and the donors. There are no short contacts between donor C (Figure 3) and the anions, suggesting that the negatively charged sulfonate groups are not close to C but are close to A, A and B. Therefore, donor C is likely to be neutral or have a small positive charge in the CO state. In our previously reported sulfonate salts with CO ground states [30–32], the donor having the shortest S(BEDT-TTF)···O(-SO3 −) contacts (especially less than 3.1 Å), which are more direct interactions between positive and negative charges than those via the hydrogen bonds [27,28], has the largest positive charge because the state has the largest Coulomb energy. Moreover, as shown in Table 2, of the two anions in the unit cell with ρ and ρ conformations, only donor B has two contacts shorter than 3.1 Å. Therefore, in this situation, for example, only donor B becomes charge-rich and A, A and C donors become charge-poor molecules. This suggests that the configuration of the anion is relevant in determining the electronic structure of the CO state. Figure 8 shows a schematic diagram of the CO state, which includes six possible CO patterns, (b)–(g), in which C is neutral in patterns (b), (d) and (g). Therefore, one of these three states is likely to be the ground state of **3**. In addition, the ground state of α-(BEDT-TTF)2I3 is represented by Figure 8b [26], suggesting that those of α-(BETS)2I3 and **3** would also be depicted by pattern (b). To strengthen this hypothesis, we calculated the Madelung energies of the CO patterns of (b)–(g) (also Table S1). In the calculations, the formula charges of each donor molecule (*Q*) were fixed to 0 or +1 for (b)–(g), which may be far from the real CO state, in which, normally, 0 < *Q* < 1. However, we believe that the calculations point to the stability of each CO pattern. The charge distributions in the component molecules were calculated using GAMESS at the BY3LP 6-31G\* level for A, B and C donors and all crystallographically independent anions of α-(BEDT-TTF)2I3, α-(BETS)2I3 and **3**, respectively. Then, each molecule's Hirshfeld population analysis was performed using Multiwfn [21]. The resultant point charges (where we did not use the point charges of all H2O molecules in **3** because of the uncertainty of hydrogen atom positions in x-ray crystal structures. We also performed the calculations in which the charges of tentatively oriented all water molecules were included as shown in Table S1. The tendency of the results is similar to that shown in Table 3) were input into Gulp [22] to calculate each Madelung energy using an Ewald method, in which we calculated only the intermolecular Coulomb interactions. The resultant Madelung energies are summarized in Table 3. The anion in **3** has two disordered configurations on a general position, so the Madelung energies were calculated of all possible combinations of each CO pattern (a)–(g), as shown in Figure 8, and each anion arrangement pattern (1)–(4), as shown in Figure 3d.

**Figure 7.** Interactions between bis(ethylenedithio)tetraselenafulvalene (BETS) and each disordered conformer ((**a**) ρ and (**b**) σ) of isethionate in **3**, where dotted lines indicate S···O contacts shorter than the van der Waals distance (3.37 Å).

**Table 2.** Numbers (*N*) of effective short S···O contacts (<3.1 Å) of **3** for four possible anion arrangements.


**Figure 8.** Schematic diagram of α-type packing arrangement of donor layer. (**b**–**g**) Schematics of the full set of six possible arrangements of neutral (white) and cationic (dark blue) donor molecules in the conduction plane, where (*wxyz*) means the molecular charges of A, A , B and C molecules (see Figure 3c) of *w*, *x*, *y* and *z*, respectively. Blue (*wxyz*) and green (*wxyz*) indicate that the charge-ordered patterns are horizontal and vertical stripes, respectively. The same colours are used in Table 3. (**a**) A schematic diagram of the non-charge-ordered state, where each molecule has a +1/2 charge (light blue).


**Table 3.** Madelung energies of α-(BEDT-TTF)2I3, α-(BETS)2I3 and **3**.

**Table 3.** *Cont.*


\*1 CO patterns = charge-ordering patterns shown in Figure 8; \*<sup>2</sup> Horizontal = horizontal stripe; \*3 Vertical = vertical stripe; \*<sup>4</sup> kJ mol−<sup>1</sup> (unit cell); \*5 Δ*<sup>E</sup>* <sup>=</sup> *<sup>E</sup>* − *<sup>E</sup>* (the lowest in the salt); \*<sup>6</sup> Configuration <sup>=</sup> Anion Configuration at I and II positions in the unit cell as shown in Figure 3d; \*7 A ditto mark.

As shown in Table 3, the Madelung energies of α-(BEDT-TTF)2I3 of four horizontal stripe-type CO patterns (Horizontal) of (b), (c), (f) and (g) are similar and smaller than those of the vertical stripe-type CO patterns (Vertical) of (d) and (e), indicating that Horizontals are more stable than Verticals. However, the difference between the largest and smallest values of the four Horizontals are small (less than 0.25 kJ mol<sup>−</sup>1) such that we cannot say which is the most stable state. Similarly, the energies of α-(BETS)2I3 of four Horizontals are similar and smaller than those of the Verticals, also indicating that Horizontals are more stable than Verticals, but it cannot be suggested which state is the most stable due to the small difference between the largest and smallest values (<0.20 kJ mol<sup>−</sup>1). A similar tendency was also observed in **3**. The averages of the Madelung energies of (1)–(4) configurations of each CO pattern suggest that Horizontals are more stable than Verticals. However, the difference between the largest and smallest values of the averages of the Horizontals of (b), (c), (f) and (g) are larger than those of the two I3 salts. Those of (c) and (f) are approximately 5 kJ mol−<sup>1</sup> smaller than those of (b) and (g), suggesting that (c) or (f) are possible ground states of **3**. Indeed, the the difference between the largest and smallest values of the Madelung energies of the (1), (2), (3) and (4) of each CO pattern is 17.7–30.9 kJ mol−1. This indicates that the conformational effect of the anion is energetically more effective than that of the CO patterns of the donor layers. Table 3 indicates that the (c)-(4) (*E* = <sup>−</sup>466.2778) and (f)-(3) states (*E* = <sup>−</sup>466.2777 kJ mol−1) have the lowest energies, where (c)-(4) is (A C σ ρ ) and (f)-(3) is (A C ρ σ ), so centrosymmetircally inverted (c)-(4) is equivalent to (f)-(3) and vice versa. This indicates that the ground state of **3** is (c)-(4) = (f)-(3). However, if the CO pattern and the anion configuration are fixed to (c)-(4) = (f)-(3), at least above *T*MI, the MI transition of **3** is likely to be as sharp as in α-(BETS)2I3, which is not the case.

The disorder of the anion as shown in Figure 3a is related to the puckering motion of the ethylene group of isethionate. Similar puckering motions are observed in several BEDT-TTF salts [33], in which a puckering motion is seen in the terminal ethylene groups of BEDT-TTF. The motion in ET salts is frozen at around 100 K, where a glass transition occurs, indicating that perfect ordering of the ethylene groups is not realized at the time scale. If the anionic puckering motion in **3** is also frozen to form a glassy state, this is a disordered state where the full set of the configurations of (1)–(4) exist below a certain temperature. Then, the CO pattern is frozen. This type of disorder would provide a relatively large random potential because the Madelung energies (1)–(4) show a larger energy variation than those of (b)–(g). This random potential would depend on the measurement and/or sample conditions. Therefore, it is speculated that this is the reason why the salt **3** shows a broad MI transition and has large variations in the resistivity measurements of repeated samples. In addition, the random potential caused by the disorder of the anion might provide paramagnetic and/or metallic islands below *T*MI, which have a non-zero magnetic susceptibility. This agrees with the fact that the smallest magnetic susceptibility value at low temperature of **3** is larger than that of α-(BETS)2I3. We anticipate that some samples of **3** show either metallic or insulating behaviours when changing the cooling rates of the resistivity measurement. An emergent, passively even superconducting, phase may arise from the phase boundaries between the metallic and insulating phase, the investigation of which is now in progress.

## **5. Conclusions**

Three purely organic charge-transfer salts—α-(BEDT-TTF)3(HOC2H4SO3)2 (**1**), β-(BEST)3(HOC2H4SO3)2·H2O (2) and α-(BETS)2(HOC2H4SO3)·H2O (**3**)—have been prepared Salts **<sup>1</sup>** and **<sup>2</sup>** are semiconducting with <sup>ρ</sup>RT of 1.15 <sup>×</sup> 102 and 4.47 <sup>Ω</sup>·cm, and *E*<sup>a</sup> of 190 and 108 meV, respectively. Salt **3** is metallic, with a broad MI transition at around 70 K. The HOC2H4SO3 − anion in **3** is disordered, the randomness of which appears to make the resistivity behaviour vary as a function of the measured sample, which is supported by Madelung energy calculations.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2073-4352/10/9/775/s1, GAMESS input options; Figure S1: Temperature dependence of electrical resistivity of **1**; Figure S2: Temperature dependence of electrical resistivity of **2**; Table S1: Madelung energies of **3** calculated excluding and including the point charges of water molecules.

**Author Contributions:** H.A. conceived and designed the experiments; K.F. synthesized the BETS molecule; Y.K. synthesized the BEST molecule and all the charge-transfer salts; H.A. and Y.K. participated in all the physical measurements; H.A., S.S.T. and Y.N. wrote and/or reviewed the paper with contributions from all authors. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was partially funded by JSPS KAKENHI, grant numbers 17K05751, 17H01144.

**Acknowledgments:** This article is dedicated to Professor Peter Day. The authors thank Shusuke Yamanaka of Osaka University for helpful discussions on Madelung energy calculations.

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