Organic conductors consisting of molecular donor and inorganic anion have been the subject of intense interest because of their low dimensionality, magnetism, and superconductivity [1,2,3,4]. Among them, (TMTCF)₂X (C = S; TMTTF: tetra-methyl-tetra-thia-fulvalene, C = Se; TMTSF: tetra-methyl-tetra-selena-fulvalene) salts are known as quasi-one dimensional organic conductors, and, moreover, (BEDT-TTF)₂X (BEDT-TTF: bis-(ethylene-dithio)-tetra-thia-fulvalene) salts are known as quasi-two dimensional organic conductors, where X⁻ is a monovalent inorganic anion. Figure 1 shows the molecular structure of their donors. The electronic properties emerging in these salts can be controlled by applying pressure and chemical substitutions [5].

Among (TMTSF)₂X, the so-called Bechgaard salt, (TMTSF)₂PF₆ is the first organic superconductor, and the superconductivity emerges at 1.6 K under pressure of 0.65~1 GPa [6]. In (TMTSF)₂ClO₄ which consists of the same donor molecule, the superconductivity emerges at 1.2 K at ambient pressure [7]. In TMTTF salt, (TMTTF)₂AsF₆ and (TMTTF)₂SbF₆ show charge ordered (CO) state below 100 K and 157 K, and theoretical and experimental studies have been performed from the view of the relationship between CO system and magnetism emerging at lower temperature [8,9,10]. Moreover, (TMTTF)₂Br shows commensurate antiferromagnetism below 13 K at ambient pressure [11]. With applying pressure over 0.5 GPa, the incommensurability of the magnetic state was suggested and discussed in relation to the spin density wave (SDW) in (TMTSF)₂PF₆ at ambient pressure [12]. The substitution of inorganic anions is considered to be due to the chemical pressure. The physical or chemical pressure dependence of the electronic properties was described by the universal phase diagram proposed by Jerome et al. [5].

On the other hand, the quasi-two dimensional organic conductor, (BEDT-TTF)₂X shows the various electronic properties according to the molecular arrangement. In κ-(BEDT-TTF)₂X, two BEDT-TTF molecules form a dimer, which constitutes the half-filled electronic system with the strongly-electron correlation. As a result, a similar competition occurs with adjacent and coexisting superconducting and antiferromagnetic phases as in high-T_c cuprates and heavy fermion systems at low temperatures [4,13,14]. Indeed, κ-(BEDT-TTF)₂Cu(NCS)₂ and κ-(BEDT-TTF)₂Cu[N(CN)₂]Br show superconductivity below 10.4 K and 11.6 K and κ-(BEDT-TTF)₂[N(CN)₂]Cl shows antiferromagnetic order below 27 K [15,16]. These electronic properties in κ-(BEDT-TTF)₂X are described in the phase diagram predicted by Kanoda et al., in which the physical properties can be controlled by temperature, physical pressure, and chemical substitution parameters. Since the superconductivity is close to antiferromagnetism at low temperature, theoretical studies about electronic properties in κ-(BEDT-TTF)₂X were performed from the viewpoint of the strongly-correlated electron system [17,18,19,20,21].

Salt with another packing arrangement, α-(BEDT-TTF)₂X and θ-(BEDT-TTF)₂X, has been a topic of interest due to the metal-insulator (MI) transition and charge disproportionation by off-site coulomb interaction [22,23,24,25,26,27,28,29]. In this type of organic conductor, various charge disproportionation patterns are realized, and these patterns give important information about the electronic structure. Recently, the mechanism of superconductivity by the charge fluctuation instability has also been intensively discussed [30,31,32].

Many theoretical and experimental studies of these interesting topics have been performed over the past three decades [33,34,35]. In order to reveal the electronic properties of (TMTCF)₂X and (BEDT-TTF)₂X from the microscopic view, Nuclear Magnetic Resonance (NMR) measurement is one of the most powerful tools. In ¹H-NMR, however, the spectrum showed no significant change due to the small hyperfine coupling constant and the large dipole–dipole interaction between ¹H-nuclei. Whereas the hyperfine coupling constant is large for ⁷⁷Se, there are four crystallographic independent ⁷⁷Se sites in a unit cell, and the four crystallographic independent ⁷⁷Se sites complicate the analysis of the spectrum in (TMTSF)₂X salt [36]. Moreover, there is no ⁷⁷Se site in TMTTF and BEDT-TTF. In contrast, ¹³C-NMR shows sharp spectrum with large hyperfine coupling constant. In order to reveal the electronic properties, ¹³C-NMR is suitable. However, most ¹³C-NMR studies are performed on the double-side substituted central ¹³C=¹³C in TTF skeleton because of the molecular symmetry of TTF derivatives. In the case of double-side enriched sample, two ¹³C nuclei are coupled due to the dipole–dipole interaction and the spectrum starts to become complicated (the so called Pake doublet). Therefore, TMTCF and BEDT-TTF, in which one side of the central carbon bond is substituted with ¹³C, are desired. In this paper, we first summarize the problem of Pake doublet, next we present the synthesis methods of single-site ¹³C-substituted molecules which avoid the Pake doublet problem, and demonstrate the superiority of ¹³C-NMR of these molecular crystals.

In case of the coupled spins system in the central ¹³C=¹³C bond in TTF skeleton, the nuclear dipole–dipole interaction, , is added to Zeeman interaction, . These interactions are described as,

(1)

(2)

Here, , , , , , are the spin operators of each nuclear site, the g factor of nuclei, the magnitude of the external magnetic field, the nuclear magneton, and the vector between two nuclei. This dipole–dipole interaction, , can be expressed as, using and the creation-annihilation operators, ,

(3)

Here, A~F terms are defined as,

Here, θ is the angle between the external field and the direction of the central C=C bond. Since the terms of A and B are commutative with the nuclear Zeeman interaction, terms of A and B contribute to NMR shift, whereas other anticommutative terms act in the way of the second-order perturbation. Hence, the spin states of the coupled spin system are expressed as the triplet state,

(4)

(5)

(6)

and the singlet state,

(7)

Here, . As a result, the two transitions of and between closest levels in the triplet state are allowed with same intensities. This doublet structure is the so called Pake doublet.

In realistic TMTCF and BEDT-TTF compounds, the situation is more complicated. Generally, two nuclei in ¹³C=¹³C bond are crystallographic nonequivalent even in symmetrical molecule. Defining NMR shifts at two local sites as and , the nuclear Zeeman interaction, , is modified as,

(8)

and the energy matrix is expressed as,

(9)

Here, and are the difference and the average of NMR shift between two local sites, respectively. Because of the off-diagonal elements in the energy matrix, the hybridization between the singlet and triplet states occurs and the eigenstates are expressed as follow,

(10)

(11)

(12)

(13)

As a consequence, all transitions between levels except that between and are allowed and we can observed four transitions,

(14)

(15)

(16)

(17)

These transitions are categorized into two groups with different intensities. One group is an outside pair of the quartet (O), the other group is an inside pair of the quartet (I). These shifts, , and intensities, , are expressed as,

(18)

(19)

respectively. In π electron system, δ₁₍₂₎ depends on the direction of the external field to the crystal system, and the angular dependence of δ₁₍₂₎ around a rotational axis shows a simple sinusoidal curve. However, As also depends on the angle of θ, the angular dependence of does not show a simple curve but a complicated one.

In the limit of , the mean values of two higher (lower) shift in quartet represent NMR shift at two local sites,

(20)

(21)

Whereas, the mean value does not represent the shift of the local nucleus in the case of . Since the spin susceptibility is connected to NMR shift at local nucleus via hyperfine coupling constant, NMR shift does not represent the local spin susceptibility. Since the magnitude of d isproportional to H₀⁻¹, the problems actually surface in the low field experiments, such as that under superconductivity.

The mixing of and depending on the parameter of also have an influence on the spin-lattice relaxation time, T₁, which intrinsically depends on the magnetic fluctuation at each local nucleus. Therefore, the relaxation to the mixing states is driven by the magnetic fluctuation on both sites, and the problems of Pake doublet causes great loss of the advantage of the local magnetic probe.

In the coupled spin system in the double-side ¹³C-substituted molecules, the transverse nuclear magnetization induced by RF pulse is always modulated by , which cannot be canceled by the spin echo, π/2-π pulse, sequence. Therefore, the spectrum by the fast Fourier transformation of this modulated spin echo signal contains the spurious information such as the negative intensity [37]. This modulation could be canceled by the solid echo pulse sequence [38]. There are a few experiments using solid echo pulse sequence [39]. However, this sequence requires the fast recovery RF system and restricts the advantage of the conventional spin echo. This modulation also inhibits the measurement of the spin-spin relaxation time, T₂. There are some estimations of T₂ deduced from the envelope of the modulated spin echo intensity, so called J-modulation [40,41]. However, this method estimates T₂ for overall spectrum in the coupled spin system and is not conventional.

In condensed matter physics, NMR measurement is one of the most powerful tools as the magnetometer on the specific local site. However, the coupled spin system of the double-side substituted molecule modulates NMR spectrum, mixes local spin states, and weakens the character as the local magnetic probe. The magic angle setting () is one of alternative methods to avoid Pake doublet problem [8,42]. However, the setting restricts the direction of the external field. Therefore, the single-site substituted TMTCF and BEDT-TTF are desired.

In preparing the single-site substituted TCF derivatives, a candidate reaction is the cross-coupling of a ketone and a thioketone. Figure 2 shows the use of this method to prepare one-side enriched BEDT-TTF [43]. Thioketone-Ketone coupling takes precedence over any self-coupling. We found that the treatment of the ketone-d4 and the thioketone-d0 with triethyl phosphite mainly produced BEDT-TTF-d4 with the minor product of BEDT-TTF-d8 and the trace amount of BEDT-TTF-d0 with a ratio of 0.7:0.24:0.06 from mass spectroscopy. Thus, the reaction of an enriched thioketone and non-enriched ketone produces ¹³C=¹²C molecule as major products, ¹²C=¹²C molecule as minor product, and ¹³C=¹³C molecule in only trace amounts. For ¹³C-NMR spectral purposes, the contamination by the inactive ¹²C=¹²C is unimportant, and it is important to prevent the contamination of the ¹³C=¹³C molecule which superimposes on the additional modulated resonance line. Indeed as shown in Figure 3, there are four magnetically independent central C=C sites, A-a, A-b, B, and C in the NMR spectra of α-(BEDT-TTF)₂I₃ without other additional peaks from ¹³C=¹³C molecule.

In the traditional coupling method [43], TMTTF is prepared from ¹³CS₂ as the starting material. However, we could obtain the stochastically or 100% double-side ¹³C-enriched TMTTF. For TMTSF, problems exist with the availability of the starting isotope reagent, (CH₃)₂N¹³CCl₂Cl [44], or ¹³CSe₂ [45], and we also obtain stochastically or 100% double-side ¹³C-enriched TMTSF. In a previous study [11], Barthel and Bechgaard et al. obtained ¹³C-NMR spectra of (TMTSF)₂PF₆ using stochastically 10% ¹³C-enriched molecules, but the low isotope ratio worsened the signal-to-noise ratio and restricted the measurement temperature. In the end, we could not produce TMTTF by couplings ketones, and the stochastic coupling of the corresponding carbene resulted in the contamination of the stochastic ¹³C=¹³C-enriched molecule. For TMTSF, the hetero-coupling has not been studied, and the problem of the starting material remains.

Because the well-established synthetic route to prepare TMTCF is not suitable for the isotope substitution, we explored an alternative procedure. The single-site ¹³C-substituted molecule is an unsymmetrical donor. Among the synthetic routes to prepare unsymmetrical donors, those used as symmetrical donor have not yet been considered, but may be worth consideration in the future. Figure 4 shows one such candidate, the synthetic route of Yamada et al. using dibutyltin complex [46]. Advantages of this method are that the isotope reagent dichloroacetic acid methyl ester is available and that Yamada et al. have already established the precursors of 8 and 9.

We synthesized the one-side ¹³C-enriched TMTCF by Yamada’s method and characterized the products by mass spectroscopy and ¹H-NMR. The yields with respect to the starting reagent dichloroacetic acid methyl ester were 10% for TMTTF [47], and 3% for TMTSF [48]. Compared to yields obtained by the traditional method, these yields are low. However, the method enables the preparation of enriched radical salts using the conventional electrochemical cell, and may be useful for preparing other enriched donor molecules as well.

We also made an attempt to synthesize for the selective one-side enriched BEDT-TTF by this method. Unfortunately, the yield discourages practical use. Then we explored one of the alternatives with the precursor of 11 shown in Figure 5 [49]. After purification, we obtained the selective one-side enriched BEDT-TTF with a yield of 36% based on 11 [50].

To demonstrate the suitability for ¹³C-NMR spectral purposes of enriched molecules thus prepared, we synthesized a single crystal of (TMTSF)₂PF₆ and examined its spectrum. Figure 6a shows the ¹³C-NMR spectrum for (TMTSF)₂PF₆ at 292 K [51]. There are two crystallographically non-equivalent ¹³C sites in (TMTCF)₂X salts. Hence it is expected that two peaks are observed in metallic state, and we actually observed only two peaks. The linewidth of about 30 ppm is very sharp and the small variation of NMR shift can be detected. Signal-to-Noise ratio is sufficient even at room temperature, and we can measure from room temperature.

In summary, to prevent the Pake doublet problem for ¹³C-NMR on (TMTCF)₂X and (BEDT-TTF)₂X, we synthesized a single-site ¹³C-substituted TMTCF and BEDT-TTF molecule, utilizing the coupling of the dibutyl-tin complexes with the corresponding esters developed by Yamada et al. and explored an alternative method for the pure one-side enriched BEDT-TTF.

By the determination of the hyperfine coupling tensor and chemical shift tensor of TMTCF and BEDT-TTF, we evaluated the hyperfine coupling tensor as the basic parameter for ¹³C-NMR of (TMTCF)₂X and (BEDT-TTF)₂X. These single-site ¹³C-substituted TMTCF and BEDT-TTF molecules and their hyperfine coupling and chemical shift tensors enabled us to expand the ability of ¹³C-NMR on organic conductors. We demonstrated the superiority of ¹³C-NMR of some single-site ¹³C-substituted molecular crystals. The preparation and basic parameters of single-site ¹³C-substituted TMTCF and BEDT-TTF molecules will also contribute to future ¹³C-NMR works.