Metallic crystals with a three-dimensional narrow band based on an aromatic hydrocarbon derivative

Abstract

The properties and crystal structures of molecular conductors depend on the intermolecular interactions between their planar parts each comprising of a conjugated molecule. Such interactions frequently produce low-dimensional band structures that are susceptible to perturbation and to lose the electrical conductivity. To extend the intra- and intercolumnar interactions, heteroatoms such as chalcogen atoms are often introduced at the periphery of the constituent molecules. Yet this strategy inevitably encounters difficulties, as such molecules would be more and more difficult to synthesize with increasing the number of heteroatoms and the molecular weights, while they would still produce highly anisotropic conductors. Herein, we report an extended intermolecular interaction pattern in a newly synthesized charge-transfer complex (EtHAC)₂I₃, which includes ten ethyl groups around the periphery of its fused aromatic rings HAC. The (EtHAC)₂I₃ crystal contains columns of stable EtHAC radical cations with intercolumnar interactions by Et–Et contacts. Theoretical calculations indicate that intramolecular Et-HAC and intermolecular Et–Et interactions enable formation of three-dimensional (3D) EtHAC network. Additionally, charge-transfer interactions via Et–I contacts lead to carrier doping into the EtHAC network. These effects are combined to produce a stable 3D metallic ground state, accounting for their high 3D electrical conductivity (ca. 10–2500 S cm⁻¹) down to ∼2 K. The unique metallic properties of (EtHAC)₂I₃ are further corroborated by the calculated band structures and polarized reflectance spectra, both indicating 3D metallic characteristics. The electron spin resonance spectra of (EtHAC)₂I₃ suggest that the highly mobile unpaired electrons behave as if they are free electrons with long relaxation times. These findings add a different strategy to develop the molecular conductors and magnets.

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1. Introduction

In organic systems, aromatic compounds feature planar structures with π-conjugated delocalised electrons that serve as charge carriers in semiconducting devices.^1–10 When they form charge-transfer (CT) complexes, they range from insulating to superconducting materials. The variation in the conducting properties of the CT complexes originates from singly occupied molecular orbitals (SOMOs) that are delocalised and interconnected between adjacent molecules to form bands responsible for the electrical conduction. Thus, the conducting properties of organic materials depend on both the constituent molecules and their molecular arrangements. The π-conjugated molecules must be closely packed and face-to-face to enable the intermolecular interactions. However, such structural restriction leads to low-dimensional conductors and qualitative changes in electrical conduction depending on the temperature (T), pressure, and sample form.^1–10 Herein, we report a new compound, (EtHAC)₂I₃ (EtHAC = decaethylhexapyrrolohexaazacoronene, Fig. 1a). The characteristic molecular structure is important in the physical properties of (EtHAC)₂I₃. There are ten ethyl (Et) groups upright on the periphery of the π-conjugated moiety HAC (HAC = hexaazacoronene). About one half of the ten Et groups and the remaining Et groups extend in the opposite directions to each other as upward and downward directions relative to the HAC plane (Fig. 1b). After some trial syntheses of related molecules,^11,12 the number and length of alkyl groups were optimized to those in EtHAC regarding steric hindrance, crystallinity, and redox properties.¹³ Neutral EtHAC (Fig. S1, ESI†) was prepared as previously reported.^12,13 The synthesis of single crystals of (EtHAC)₂I₃ is described in the ESI.† All measurements in this study were performed using freshly prepared high-quality single crystals, as confirmed by X-ray oscillation images captured prior to the measurements. We first distinguished metallic from nonmetallic crystals based on their electron spin resonance (ESR) spectra and confirmed the electrical behaviour via four-probe resistivity measurements. The ESR spectra of ≥100 single crystals were examined to assess their sample dependence and reproducibility. For consistency, the structural analysis, ESR, and resistivity measurements were performed using the same single crystals selected above. Details of single-crystal X-ray structural analyses, first-principles band calculations, and physical property (electrical resistivity (ρ), ESR) measurements are given in the ESI.†

Fig. 1 (a) Molecular structure of EtHAC. Crystal structure of (EtHAC)₂I₃ without disorder (90 K, sample #31) as viewed (b) along and (c) perpendicular to the EtHAC columns. Brown, purple, pink, and violet spheres indicate C, N, H, and I atoms, respectively.

2. Results and discussion

2.1. Crystal and molecular structures

Fig. 1b and c show the crystal structure of (EtHAC)₂I₃ at 90 K. The crystal structures at different temperatures and their details are shown in the ESI† (Fig. S2a–m and Tables S1–S2), which are qualitatively identical except for the disorder of the anions and Et groups. Overlapping modes and interplanar distances remained unchanged at 90–300 K except for thermal contraction (ca. 260–80 ppm K⁻¹ in the cell volume, depending on the T-range). Notably, disorder in the Et groups enables shorter Et–Et and Et–I₃⁻ contacts in the major Et conformations than those in the ordered conformations. Considering CT interactions between cations and anions, the chemical formula of each constituent should be described as EtHAC^(0.5−δ)+˙ and I₃^(1−2δ)−˙ in (EtHAC)₂I₃. For simplicity, we describe the neutral molecules, radical cations, and anions as EtHAC, EtHAC^0.5+, and I₃⁻, respectively. The asymmetric unit contains a single EtHAC^0.5+ radical cation and half an I₃⁻ anion. Unlike neutral EtHAC (Fig. S1, ESI†),^12,13 EtHAC^0.5+ radical cations form a columnar structure along the a-axis with alternating interplanar distances of 3.373(4) and 3.403(4) Å, indicating subtle dimerization. All the I₃⁻ anions are arranged in parallel along the bc planes and at an angle of ∼20° along the b-axis. The Et groups in front of the I₃⁻ anions are disordered at T > 150 K. Regardless of the disorder, however, all single crystals exhibit identical lattice constants for (EtHAC)₂I₃. Interatomic distances comparable to or shorter than corresponding van der Waals distances exist between I₃⁻ and EtHAC^0.5+ (Fig. S2a–e, ESI†) and between EtHAC^0.5+ themselves (Fig. S2f and g, ESI†), suggesting CT interactions between all adjacent species in the crystal.

2.2. Band structures

Fig. 2a–d show the electron densities in the unit cell, band dispersion at the Fermi level, and Fermi surfaces of (EtHAC)₂I₃ calculated using a DFT method. Related figures with different isosurface values and projected density of states are shown in the ESI† (Fig. S3a–e). These calculation results are consistent with the observed 3D metallic properties as discussed below, demonstrating that loosely bound electrons are dispersed and delocalised all over the EtHAC^0.5+ and I₃⁻ species (Fig. 2a and b). The 3D molecular conductors were reported previously, yet they are based on planar molecules.⁹ The band structure (Fig. 2c) shows important features: a pair of narrow bands are nearly degenerate at the Fermi level E_F (each bandwidth ΔW(E_F) ≲ 50 meV) providing 1D and 3D Fermi surfaces, respectively (Fig. 2d). The two nearly degenerate bands originate from the SOMOs of the subtly dimerized EtHAC^0.5+ in the columns. The subtle dimerization originates from the unique effects of the Et groups. Firstly, the Et groups prevent the strong dimerization between facing HAC moieties within a column by steric hindrance between the crowded Et groups extending to both sides of the HAC planes. Secondly, by the intercolumnar interactions via the Et groups, a part of electron density is removed from the HAC moiety to be shared between the Et groups, as there is intramolecular interaction between HAC moiety and Et groups (Fig. 2a and b). This could be regarded as hyperconjugation between the HAC moiety (π) and Et groups (σ).¹⁴ Based on the DFT calculation, the band fillings are 57.5% and 92.5% for the upper and lower bands, respectively, resulting in EtHAC^(0.5−δ)+˙ (δ ∼ 0.1) on average. The small amount of CT is qualitatively supported by the Raman spectra (Fig. S5 and Table S3, ESI†) of the I₃⁻ anions. The relationship between Raman shifts (cm⁻¹) and oxidation states of polyiodide anions is established,^15,16 which indicates slight oxidation of the I₃⁻ anions in (EtHAC)₂I₃. Both bandwidths ΔW(E_F) are exceptionally small for metals. In one-dimensional (1D) conductors, such narrow metallic bands seldom occur because the metal instability characteristic to 1D or narrow bands transform them into insulator bands.^1–10 Furthermore, unless the lower band is also located at E_F, the upper band at E_F should be effectively half-filled based on the stoichiometry of (EtHAC)₂I₃. The half-filled bands are unstable for metals and transform (EtHAC)₂I₃ into an insulator called Mott insulator.^1–10 However, intramolecular HAC-Et and intercolumnar Et–Et interactions add weak 3D character to the electronic system and deviate it from the half-filled system. In this way, a stable, weakly 3D, and dilute carrier system is formed in (EtHAC)₂I₃, where the Et groups play an indispensable role. As a result, the band structure of (EtHAC)₂I₃ is quite different from those of the known molecular conductors. The metallic properties of (EtHAC)₂I₃ remind us of those of doped polyacetylenes (PAs).^17,18 Yet, there is a qualitative difference in the conduction mechanism. The metallic PAs are an assembly of 1D metallic chains of PA, where interchain electrical conduction is based on variable range hopping, requiring thermal activation energies (E_a > 0) and being different from metallic conduction (E_a = 0). Meanwhile, the electrical conduction of (EtHAC)₂I₃ is based on band conduction in all directions, being independent of E_a. Such difference originates from the absence/presence of overlaps between neighbouring SOMOs. There are hardly any overlaps of SOMOs between PA chains, which require hopping of carriers for electrical conduction from chain to chain. The hopping requires E_a, the values of which depend on the details of local structures of the two chains where the carriers hop. Yet, in (EtHAC)₂I₃, there are overlaps between SOMOs forming crystal orbitals, i.e., partially filled valence bands, continuously extending from end to end in the crystal in a 3D way. Such overlaps serve as conduction pathways. They are based on the well-defined atomic arrangements in the crystal and are independent of temperature and E_a. The SOMO bands enable intra- and intercolumnar metallic conduction in (EtHAC)₂I₃. Similarly, there are rich examples of works using alkyl chains to control the packing motifs of molecular conductors including polymer-based semiconductors.^1–10 However, there is no report in the literature where the alkyl chains also serve as metallic conduction pathways. In this regard, metallic properties in the ground state based on aromatic hydrocarbon derivatives have not been reported, let alone a 3D metal with a small bandwidth at the Fermi level ΔW(E_F). Narrow band metals have been paid attention to for a long time given their unique conducting and magnetic properties.^19–31

Fig. 2 Calculated electronic structures of (EtHAC)₂I₃ based on the observed structure at 90 K (sample #31). (a) and (b) Electron density maps as isosurface of the value indicated above each panel, where a₀ indicates the Bohr radius, (c) band dispersion, and (d) 3D Fermi surfaces. In Fig. 2c, Y, Γ, X, V, R, U, and Z indicate (0, 0.5, 0), (0, 0, 0), (0.5, 0, 0), (0.5, −0.5, 0), (0.5, −0.5, −0.5), (0.5, 0, −0.5), and (0, 0, 0.5), respectively.

2.3. Electrical properties

The details of band structures and intermolecular interactions are manifested in the anisotropy and temperature dependence of electrical resistivity. ρ(T) curves of the single crystal of (EtHAC)₂I₃ in Fig. 3 shows that it exhibits a nearly T-independent ρ (Fig. 3, T ≥ 30 K). The resistivity is lower than those of other organic metals (typically, 10⁰–10² Ω cm at 300 K) by several orders of magnitude.^1–10 It does not exhibit a metal–insulator (MI) transition to retain the low resistivity in 2–300 K. The gradual increase in ρ is observed at a wide T-range (Fig. S4a–c, ESI†) but is not reproduced by an Arrhenius model (Fig. S4d–g, ESI†), excluding the possibility that (EtHAC)₂I₃ should be a band insulator in the ground state. Rather, both T-dependence and the values of ρ are quantitatively close to those of metals with strong electron correlation, i.e., the metals with narrow bands.^19–31 The electrical behaviour of materials with narrow bands are intriguing as ΔW(E_F) ∼ 0 suggests that the average kinetic energy of carriers should be close to 0 as if they are immobile. The intriguing electrical properties of (EtHAC)₂I₃ provide a valuable opportunity for experimental studies on how they carry charge as electric current. In summary, the conduction pathways of (EtHAC)₂I₃ is not hindered by the counter ions (I₃⁻) despite strong EtHAC–I₃ interactions. As a result, (EtHAC)₂I₃ does not exhibit characteristics of low-dimensional conductors, contrasting with various iodine-based CT complexes such as α-ET₂I₃ (ET = bis(ethylenedithio)tetrathiafulvalene).^1–10

Fig. 3 Temperature (T) dependence of the electrical resistivity (ρ) of (EtHAC)₂I₃ measured by a standard four-probe method using the single crystals with a direct current applied along the (a) a-, (b) b-, (c) c-, and (d) (b−c)-axes. Red and blue curves, which completely overlap with each other at some temperature ranges for some samples, represent the heating and cooling processes, respectively. To illustrate sample dependence and reproducibility, the results of different samples in independent measurements are shown. The single crystals are sequentially numbered. The cooling-rate-dependence of the electrical resistivity and detailed analyses of each data in Fig. 3 are shown in the ESI† (Fig. S4a–i). Small accidental jumps in cooling data in (b) (∼230 K and ∼60 K) and (c) (∼70 K) were extrinsic.

2.4. Electron spin resonance spectra

ESR spectra provide complementary information to crosscheck the consistency in the observed behaviour of carriers. In this work, we measured the ESR spectra of (EtHAC)₂I₃ using the single crystals to elucidate the anisotropy of motion of the carriers. Fig. 4a–c show the ESR results depicting the anisotropy, i.e. the dependence on the relative angle between the magnetic field and the selected crystallographic axis in the g-values, linewidths (Γ), and intensities (I) of metallic EtHAC₂I₃. The ESR results show unusually small anisotropies in I, g-value, and Γ, indicating the essential three-dimensionality of the carrier motion originating from the 3D Fermi surface as small hole pockets (Fig. 2d). The directions corresponding to the maximal and minimal I, g-value, and Γ directions are approximately parallel and perpendicular to the EtHAC columns, respectively. These results indicate the coexisting one-dimensionality originating from the 1D Fermi surfaces as slightly warped parallel planes (Fig. 2d). Thus, the observed (an)isotropies in the ESR results and ρ are consistent with the calculated band structure (Fig. 2c and d). Additionally, the ESR spectra show an unusually narrow Γ (ca. 60–80 μT in any direction) for metallic carriers (Fig. S6 and Table S5, ESI†): Γ is typically a few mT in the molecular conductors.^32–48 Narrow ESR lines are often observed for isolated spins in insulating materials. However, if (EtHAC)₂I₃ contains localised and isolated spins, hyperfine structures (hfs) assigned to ¹H, ¹⁴N or ¹²⁷I should be observed, which is not the case (Fig. S6, ESI†). The metallic carriers with high mobility account for the absence of hfs. The metallic carriers in known materials give characteristically broad ESR peaks because of the significantly short relaxation times τ. The values of τ are particularly short in the dense carrier systems, as carriers frequently collide with each other to exchange their energies during the travel in the solid as electric current. However, in (EtHAC)₂I₃, the carriers are divided in the two bands at E_F, forming two dilute and non-interacting carrier systems. In such carrier systems, the values of τ could be as long as those of localised electrons in insulators. This is why such high-mobility carriers exhibit the unusually narrow Γ (∝ τ⁻¹) in (EtHAC)₂I₃.

Fig. 4 Angle dependence of the ESR spectra of metallic (EtHAC)₂I₃ (single crystal, sample #156, 296 K). (a) θ and (b) ϕ dependencies of the linewidth (Γ) and g value. (c) θ and ϕ dependencies of the intensity (I). The rotation angles are defined in the ESI.† The sinusoidal curves are the best-fitting curves of g-values (a and b, red), intensity during φ-rotation (c, red), intensity during θ-rotation (c, black), and linewidths Γ (a and b, black) (see Table S5 for details, ESI†). The magnetic field H was applied perpendicular to the indicated molecular arrangements.

2.5. Reflectance spectra

Using the single crystals and microspectroscopy, polarized infrared (IR) reflectance spectra were measured for additional crosscheck on the 3D metallic character of the carrier system in (EtHAC)₂I₃. Previous organic metals and superconductors are known to exhibit Drude-type dispersions.^49–54 Corresponding to the values of E_a = 0 in metallic carrier systems, the Drude peak in the conductivity spectrum centres at 0 cm⁻¹. Accordingly, the reflectivity, which is almost 100% at sufficiently low temperature and low wavenumber, would exhibit an increase in reflectivity (Drude edge) as a tail of the Drude-type dispersion typically in the range of ca. 3000–10 000 cm⁻¹ depending on the carrier density. Thus, one can observe the Drude edge in the infrared region for the metallic molecular conductors. For example, the two-dimensional molecular conductors such as α-ET₂I₃ exhibit the Drude-type dispersion in response to the two independent polarization directions but not to the third direction. On cooling, it disappears at lower temperature than the MI transitions.⁵⁵Fig. 5 shows the reflectance spectra of (EtHAC)₂I₃ with different polarization angles and temperatures. We also measured spectra at selected temperatures in both cooling and heating processes to examine hysteresis (Fig. S7a–c, ESI†). The spectra were measured in the ab and ac planes using different single crystals along the parallel and perpendicular to the a-axis in each crystal face. For simplicity, we will call the polarization angles //a, //a*(ab), and //a*(ac), respectively. The //a spectra of different single crystals, different crystal faces (ab or ac planes), and independent measurements were consistent with each other. The temperature dependence and anisotropy of the reflectance spectra qualitatively agree with the observed electrical properties (Fig. 3a–d), which are also hardly temperature dependent. Although the spectra are quantitatively anisotropic, they manifest the Drude dispersion in three orthogonal directions unlike the known low-dimensional molecular conductors. In this sense, the band structure is 3D and metallic. In the cooling process, all the temperature except for 200 K, the reflectance spectra are nearly identical with each other in the respective polarization angles //a, //a*(ab), and //a*(ac). The values of reflectance at 200 K, R(200 K), in the cooling process in all polarization angles are evidently higher than those at other temperatures. As R(200 K) in the heating process are rather low in all polarization angles, hysteresis in reflectance spectra is largest at ∼200 K in all polarization angles (Fig. S7a–c, ESI†). Similarly, different extents of hysteresis in the spectra are also observed at 294 K in all polarization angles. This is largely consistent with the observed electrical properties (Fig. 3a–d). The vibration peaks are assigned to the ethyl groups, which appeared at ∼2800 to 3100 cm⁻¹ with different intensities and linewidths depending on the temperatures and polarization angles (broken squares in Fig. 5b, d, and f). Finally, the feature at <1000 cm⁻¹ can be interpreted as the tail of Drude-type dispersion at each polarization direction, which reaches ∼20 to 80% in reflectance at 750 cm⁻¹ depending on the temperatures and polarization angles. From 294 K to 6.8 K, the Drude-type dispersion gradually enhances with decreasing temperature in all directions (Fig. 5b, d, f and Fig. S9a–c, ESI†), consistent with the 3D metallic properties. Based on the discussion thus far, the reflectance spectra indicate that (EtHAC)₂I₃ should be an anisotropic 3D metal, where the electronic band structure is stable at 294–6.8 K, making a sharp contrast with low-dimensional molecular conductors exhibiting MI transitions.

Fig. 5 Polarised reflectance spectra of metallic (EtHAC)₂I₃ at indicated temperatures and polarisation angles (single crystal, sample #212 for (a)–(d) and #218 for (e) and (f)). All the spectra in (a)–(f) were measured in the cooling processes. (a), (c) and (d) Spectra after removing the CO₂ noise (∼2300–2380 cm⁻¹). (b), (d) and (f) Offset spectra in the order of temperature. (b), (d) and (f) are based on the same spectra with those in (a), (c) and (e), respectively. Broken squares in (b), (d), and (f) indicate the vibration modes (C–H and C–C) assigned to ethyl groups.

3. Conclusions

(EtHAC)₂I₃ exhibits a stable 3D delocalised electron system based on intermolecular interactions between EtHAC radical cations. The band structure at the Fermi level is characteristic of nearly doubly degenerate narrow bands with long relaxation times and high conductivity. Our findings provide an alternative strategy for designing and understanding molecular conducting and magnetic materials based on intermolecular interactions between planar parts of conjugated molecular species.

Author contributions

T. N. conceived the idea, designed the experiments, and supervised the project. Y. S., Y. F., and M. T. synthesized neutral EtHAC and optimized the condition of crystal growth of (EtHAC)₂I₃. M. I. prepared the single crystals to perform the X-ray structural analyses, measurements of electrical resistivity, electron spin resonance and Raman spectra with the aid of S. M., K. K., K. O., and H. T. M. I. and T. N. measured the reflectance spectra with the aid of A. M. S., Y. M., and R. M. M. I. also conducted the analyses of the experimental results with T. N. H. D. calculated the first-principles electronic structures, which were discussed and interpreted with T. N. T. N. wrote the paper. All the authors read, commented on and agreed with the manuscript.

Data availability

The authors confirm that the data supporting the findings of this study are available within the article and its ESI.†

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Infrared spectroscopy was performed using the facilities of the Materials Design and Characterization Laboratory in the Institute for Solid State Physics (ISSP), the University of Tokyo (ISSPkyodo-202410-MCBXU-0122).

Notes and references

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Footnote

† Electronic supplementary information (ESI) available. CCDC 2394976–2394979, 2394981, 2350026 and 2405509. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d5tc01367d

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