Mixed-valence (partial charge transfer state) and segregated stacking are the key factors for constructing organic metals. Here, we discuss the ionicity phase diagrams for a variety of charge transfer systems to provide a strategy for the development of functional organic materials (Mott insulator, semiconductor, superconductor, metal, complex isomer, neutral–ionic system, etc.).
Numerous functional charge transfer (CT) solids have been developed based on their peculiar electronic and structural aspects (for a review, see Saito & Yoshida (2007)), such as organic superconductors (Ishiguro et al. 1998), metals (e.g. TTF.TCNQ; Ferraris et al. 1973; Jerome & Schulz 1982; Conwell et al. 1988; for chemicals in text, see figure 1b), field-effect transistors (FETs; Takahashi et al. 2006), metallic Langmuir–Blodgett (LB) films (Nakamura et al. 1994), neutral–ionic (NI) phase transition systems (Torrance et al. 1981), ferroelectrics (Horiuchi et al. 2006), organic semiconductor condenser (Niwa 1987), and switching and memory systems (Potember et al. 1980). To manifest high conductivity, the mixed valence (or partial CT state) is the most essential feature required in the electronic structure. Such a concept is also important for nonlinearity in transport and optical properties.
The transport properties of a particular CT solid strongly depend on both the ionicity and molecular stacking. The former issue was first examined experimentally by Matsunaga (1964, 1965a,b) and then discussed theoretically by McConnell et al. (1965) as(1.1)where IP is the ionization potential of an electron donor molecule; EA is the electron affinity of an electron acceptor molecule; and M is the Madelung energy.
Equation (1.1) roughly discriminates ionic (denoted I) and neutral (N) CT solids with alternating (A) stacks, namely IP−EA>M for neutral and IP−EA<M for ionic solids. For inorganic solids, an analogous classification based on the mixed-valence concept was developed by Robin & Day (1967).
Later, Torrance (1979a,b) proposed a phase diagram showing the four different phases, namely ionic alternating (type IA) stack, neutral alternating (type NA) stack, ionic segregated (type IS) stack and mixed-valence segregated (type MS, where M and S stand for mixed valence and segregated, respectively) stack, and pointed out the importance of ionicity for organic metals, Mott insulators, NI transition system, etc. Several such classifications or phase diagrams have been proposed to understand the perspectives of CT solids (Soos 1974; Tanaka & Tanaka 1985; Cowan et al. 1990; Delhaès 1990).
Since fine-tuning of both the Fermi level and the density of states is crucial in developing new electronic devices, a variety of donor and acceptor molecules covering a wide range of electron donating and accepting ability have been prepared. As numerous new CT solids were characterized, early versions of the ionicity phase diagram were found to be insufficient for understanding the whole range of properties uncovered since they lack (i) neutral segregated (type NS) stacks, (ii) metallic mixed-valence alternating (type MA) stacks, (iii) metallic segregated (type MS) layers with charge-ordered (CO) states, and (iv) 1 : 1 metallic segregated stacks with fully ionized (type IS) CT solids having a small on-site Coulomb repulsion energy (U) component. In this paper, we present a detailed discussion about the phase diagram of CT solids with respect to ionicity and molecular stacking type.
2. Ionicity and the classification of CT solids
Ionicity phase diagrams have been used for developing a variety of functional CT solids with different dimensionality or self-assembling nature. The ionicity of CT solids, (Dδ+)m(Aδ′−)n, where D is an electron donor and A is an electron acceptor, has been estimated with the aid of IR, UV–vis–NIR and Raman spectra, and electrical conductivity, magnetic properties, structural properties and/or stoichiometry of the complexes. The ionicity is usually classified as fully ionic (δ, δ′=1, I), mixed valence (1>δ, δ′>δc; in this paper, the ionicity of 1>δ, δ′≥0.5 is represented by M and that of 0.5>δ, δ′≥δc by M′, where δc is the critical degree of CT) and neutral (δc>δ, δ′≥0, N). Although the ionicity condition, 1≥δ, δ′≥0, is the most common, some solids rarely have ionicity more than unity even with metallic behaviour. In this paper, the discussion is restricted in the ionicity range of 1≥δ, δ′≥0.
There are two main modes of molecular stacking: alternating (A) and segregated (S) stacks. When the uniform ionicity and/or stacking mode are confirmed, the letter u is added (or n for non-uniform). For example, a 2 : 1 solid with δ or δ′=0.5 having a dimerized segregated stack is labelled as MuSn. It has long been known that the size and shape of the component molecules substantially affect the boundary of ionicity between fully ionic and neutral regimes (Matsunaga 1969; Matsunaga & Saito 1971). In order to have common Madelung energy, self-assembling ability and dimensionality in a particular DA system, component molecules with similar size and shape should be used in the ionicity diagram. We have proposed ionicity phase diagrams for a variety of CT systems with different dimensionality (Saito & Yoshida 2007).
3. Ionicity phase diagram
(a) Ionicity phase diagram for low-dimensional CT solids
Cowan et al. (1990) state in their review that ‘Torrance suggested that one should not look for very good donors and very good acceptors or for the very poor donors and acceptors, but a middle ground of medium donors and acceptors to seek metallic CT solids’. However, this is not an accurate statement. One has to look for appropriate ranges of (IP−EA) or solution redox potentials, ΔE(DA) (E1(D)−E1(A), where E1 is the first redox potential), to obtain the mixed-valence state.
Figure 1a is the ionicity phase diagram of structurally related acceptors (TCNQ derivatives) on the ordinate and structurally related donor molecules (mainly TTF derivatives) on the abscissa using redox potentials for the conventional low-dimensional 1 : 1 TTF.TCNQ system, in which the component molecules have weak but enough self-assembling ability to form segregated columns (Saito & Ferraris 1980). Two bold lines (a and b) in figure 1a relate to a modified equation (1.1), EA=IP−M(δ), and separate the diagram into three regions (I, M and N) based on conductivity data. The mixed-valence regime (M) is located between lines a and b as represented by equation (3.1), and a lower limit of δ(δc) is estimated to be 0.5 for the TTF.TCNQ system,(3.1)
In the mixed-valence regime, the complexes are either highly conductive (light grey circles for pellet samples) or metallic (dark grey circles for single crystals) when they have segregated stacks with uniform intermolecular distances and charges. Otherwise, they are insulators (triangles) with either non-uniform segregated stacks, charge-ordered (CO) state, spin density waves (SDWs) or ordered anions. When they form alternating stacks, they become semiconductors. Figure 2a summarizes the family tree of mixed-valence CT solids with alternating or segregated stacks, as described in more detail in §§4c and 5b, respectively. In §3b, we describe how figure 1a can be used to search for functional solids.
(b) Organic metals, Mott insulators, complex isomers and dimensionality
The 1 : 1 CT solids of the TTF.TCNQ type in the region of ΔE(DA)<−0.02 V (region I, above the upper borderline a in figure 1a) are fully ionic insulators, including Mott insulators and antiferromagnets (e.g. segregated stacks such as HMTTF.F4TCNQ (1) and HMTSF.F4TCNQ (2) in figure 1a) and spin-Peierls systems; while those in the region of ΔE(DA)>+0.34 V (region N, below the lower borderline b in figure 1a) prefer alternating stacks and thus are insulators with small ionicity (δ<0.5). Near the lower borderline, we found bistability between neutral and partial CT states, for example in TMTSF.TCNQ (4), TSF.Et2TCNQ (5) and BEDT-TTF.TCNQ (6). The former two (4 and 5) are within the mixed-valence regime in figure 1a and afford metallic segregated complexes. They also offer examples of insulating alternating stacks. Even though BEDT-TTF.TCNQ (6) is expected to be a neutral insulator based on its ΔE(DA) value, a highly conductive material has been prepared (Mizuno et al. 1978). Our subsequent work to explore the ionicity diagram (figure 1a), which originally lacked the insulating BEDT-TTF.TCNQ, afforded the neutral and insulating complex isomer. These results indicate that BEDT-TTF.TCNQ is actually located close to the boundary of complex isomerization on the neutral side and furthermore suggest that the BEDT-TTF molecule has a significant ability to form segregated columns with increased dimensionality. Accordingly, we explored the CT complexes based on the BEDT-TTF molecules and discovered the first two-dimensional conductor (Saito et al. 1982). TTF.TCNQ (3) is a typical low-dimensional metal with δ=0.59 and exhibits a Peierls transition at 59 K. Apart from 1 : 1 stoichiometry, many CT complexes with 1 : 2, 2 : 3 and 2 : 1 and other stoichiometries are known, and the m : n (m≠n) CT complexes of the TTF.TCNQ type also follow the diagram in figure 1a, when the complex has a low-dimensional electronic structure.
Figure 1a is depicted using only redox potentials of donor and acceptor molecules. Torrance et al. (1981) used an additional parameter, the first CT transition energy of the CT solid in their V-shaped diagram (figure 3), to discriminate between neutral and ionic solids having alternating stacks. Inclusion of the optical data makes such an ionicity diagram very convenient for characterizing the solid and guessing the electronic functionality. In order to make such a diagram, one needs some information concerning the correlation between the optical data, ionicity and stacking mode.
4. Mainly alternate stacks
(a) Essentially neutral CT solids (types NA and NS)
Commonly, the neutral CT solids have alternating stacks (type NA). However, neutral CT solids with segregated stacks (type NS) have been known for a long time, i.e. 4,4′-dinitrodiphenyl complexes of biphenyl and benzidine derivatives with non-1 : 1 stoichiometries. Furthermore, some 1 : 1 neutral C60 complexes with TTF derivatives have segregated stacks or layers of C60 molecules. Their optical spectra show that (i) the IR spectrum is explained by superimposing those of the component neutral molecules and (ii) the CT absorption band appears in the UV–visible region with the energy (hνCTN) expected from the equation(4.1)where C is mainly the Coulomb static energy between D+ and A−.
For a low-dimensional TTF.TCNQ system, neutral solids are obtained when ΔE(DA) satisfies the equation(4.2)and the lower limit of δ (δc) is estimated to be 0.5. Increasing the electronic (and not only the structural) dimensionality of the CT solids, such as BEDO-TTF, EOET and HMTTeF systems, decreases δc considerably.
These neutral CT solids are electrical insulators (figure 2b) and magnetically silent. Since the neutral CT solids with alternating stacks have large dipole moments in the excited state, (D(1−δ)+)m(A(1−δ′)−)n, the solids may exhibit intriguing functions such as nonlinear transport (switching and memory) or optics, ferroelectrics, FET and rectification.
(b) Essentially ionic CT solids with alternate stacks (type IA)
When the complex has a D+A− alternating stack (type IA), a band originating from the CT transition from A− to D+ (back CT) is expected at the energy hνCTI,(4.3)where αC is Madelung energy. However, in many complexes of type IA, an optical transition among the same species (B- or B′-band, see §5a) appears along the segregated direction oblique to the D+A−D+A− stacking like the case of BEDT-TTF.F2TCNQ single crystal and no back CT appears. The absence of the back CT band is open for question.
These solids are electrical insulators but exhibit other functions such as (anti)ferromagnetism, ferroelectricity and spin-Peierls transition (figure 2c).
(c) V-shaped diagrams and mixed-valence complexes with alternate stacks
The NI phase boundary condition (hνCTN=hνCTI) in figure 3 gives(4.4)which, in principle, is the same criterion as equation (1.1). In the region near the bottom of the V-shaped line, Torrance et al. (1981) discovered a new enantiotropic phase transition at 81 K for TTF.p–chloranil from the neutral (δ=0.3) to the ionic (δ=0.7) state as(4.5)Besides the δ=0.3 phase, TTF.p–chloranil affords both a 1 : 1 ionic (δ=1) insulator and a mixed-valence (δ=0.71) conductor with unknown stoichiometry under different preparation conditions. Similar to the latter conductive complex, several highly conductive ones have been prepared in the TTF.p–quinone system. Based on a plot using redox potentials similar to figure 1a, all the conductive TTF.p–quinone complexes mentioned above belong to the range(4.6)which is comparable to equation (3.1). These conductive TTF.p–quinone complexes exhibit low-energy CT bands below 5×103 cm−1 (A- or A′-band; see §5b), indicating the presence of segregated mixed-valence stacks (type MS).
Although the initial study by Torrance et al. classified the ionicity regions of alternating stacks into two types (NA and IA), later work on HMTTeF complexes with Et2TCNQ or bisthiadiazolo-TCNQ revealed a mixed-valence region where domains of δ=0, 0.2, 0.6–0.8 and 1 coexist in alternating stacks (Pac & Saito 2002). Accordingly, the initial V-shaped diagram has to be modified to include a mixed-valence region (region MA), the ΔE(DA) of which may correspond to those of conductive TTF.p–quinone ones (equation (4.6)), in figure 3. The MA region furnishes band-insulators, NI systems, ferroelectrics, highly conductive solids and so on (figure 2a).
5. Mainly segregated stacks
(a) Fully ionic CT solids with segregated or self-assembled stacks (type IS)
Strong electron donor and/or acceptor molecules may give rise to fully ionic solids with 1 : 1 stoichiometry. Depending on the electronic shell of the starting materials, fully ionic CT solids are labelled as radical cation salts D+X−, radical anion salts M+A− or simply ionic CT solids D+A−, where X− and M+ have closed shell electronic structures. The solids of type IS usually include Mott insulators, antiferromagnets, spin-Peierls systems, spin-ladders, etc. (figure 2c).
When the solid has segregated stacks (type IS), the UV–vis–NIR spectrum exhibits absorption bands ascribable to transitions both between the neighbouring radical cations D+ (denoted B-band) and between the neighbouring radical anions A− (B′-band) within the column, in addition to the intramolecular transitions of each radical species (figure 4a,b,e,f). Here, the optical transitions ascribable to donor and acceptor species are labelled as A, B, C, … and A′, B′, C′, …, respectively, in order of energy. Since the B- or B′-band arises from the process expressed by equation (5.1), the energy of the band is defined by the effective Coulomb repulsion energy (U−V), where V denotes the nearest neighbour Coulomb repulsion energy,chem-struct>(5.1)The CT energy of an isolated dimer with two electrons (D+D+→ D2+D0) is formulated as (Harris & Lange 1967)(5.2)where t is the transfer integral. Therefore, taking into account both band formation and the effect of V in the solid, the peak position of B-band is represented by(5.3)
The B- and B′-bands appear at 5−13×103 cm−1 for TTF and TCNQ systems in the solid state and disappear in dilute solution. The band moves at lower energy with decreasing U, approximately 12–13×103 cm−1 for TTF or TMTTF systems (figure 4a), 5–10×103 cm−1 for BEDT-TTF (figure 4b) or BEDO-TTF systems, and less than 5×103 cm−1 for 1 : 1 metallic radical cation salts composed of components having small U. For the last case, the optical band is best described as an intraband transition and is denoted as the A-band. When the medium is highly polarizable, the B-band is expected to exhibit a red shift according to LeBlanc's (1965) proposal for TCNQ radical anion salts.
When the segregated column is not uniform (type ISn), the transition process becomes more complicated owing to the presence of the more than one V. For a dimerized system, intra- and interdimer bands are observed as(5.4)The former is approximately represented by equation (5.3) and the latter by(5.5)where V* is the off-site Coulomb energy between dimers. The C′-band appears at approximately 11×103 cm−1 for the TCNQ system. The C′-band described by equation (5.4) grows rapidly with lattice distortion, while its energy is insensitive to the size of the counter parts (compare figure 4e,f). The lattice distortion is also marked by the appearance of IR inactive ag modes in the IR spectrum. When a solid contains isolated TCNQ− molecules or uniform columns, it shows sharp peaks in the 10–11×103 cm−1 region, similar to that of radical anion in solution. These bands of the isolated molecule are more intense and sharper than those observed in complexes with uniform stacks (compare figure 4d,c, respectively). They are labelled as CM-bands (M, monomer). The interdimer transition (C′-band) overlaps with those observed in metallic complexes having uniform segregated columns such as TTF.TCNQ (CM′-band in figure 4c).
In the case of D+D+A−A− alternating stacks (type IA2, where 2 stands for dimerized units), the first optical transition is usually assigned as the CT energy of an isolated dimer with two electrons (equation (5.6), C2-band), which appears at higher energy than either the B- or B′-band,(5.6)In the case of complexes of TTF derivatives such as TTF and TMTTF, which contain no peripheral chalcogen atoms (denoted as the C6S4 analogues), the hνCT (C2-band) appears at approximately 10.7–12.8×103 cm−1. On the other hand, in complexes of π-extended TTF derivatives such as BEDT-TTF, BEDO-TTF, etc., the hνCT(C2-band) appears at considerably low energy, 6.5−10.8×103 cm−1. Many solids of type IA2 show triplet excitons.
It should be mentioned that a broad band at 10–12×103 cm−1, which appeared for the BEDT-TTF radical cations (D-band in figure 4b), has erroneously been interpreted as an intermolecular transition among the BEDT-TTF+ molecules. In fact, the transition has an intramolecular origin (second HOMO→HOMO), which appears at a considerably lower energy in those TTF derivatives having an extended π-system compared with the C6S4 ones.
(b) Mixed-valence complexes with segregated stacks (type MS)
It is easy to identify the CT solids in this class by the presence of an A- or A′-band extending into the IR region (hνCT≤5×103 cm−1, figure 4c,d). The presence of an A- or A′-band is a necessary condition for metallic behaviour since the band arises from an intraband process (partial CT state). However, A- and A′-bands also arise from the process expressed by equation (5.7) for insulators having mixed-valence electronic structures (figure 2a; Peierls, SDW (e.g. (TMTSF)2PF6), anion-ordered (e.g. (TMTSF)2ReO4), CO insulator (MnS type, e.g. Cs2(TCNQ)3) and θ-(BEDT-TTF)2RbZn(SCN)4 (type MuSu→MnSn)), dimer-type Mott insulator with δ=0.5 and Ueff>W (MuS2 type, e.g. κ-(BEDT-TTF)2Cu[N(CN)2]Cl and κ-(BEDT-TTF)2Cu2(CN)3), together with some misfit compounds (M′uSn type). Therefore, the appearance of A- or A′-bands indicates that the solids have segregated stacks or layers composed of mixed-valence species excepting rare cases of 1 : 1 fully ionic organic metals,(5.7)
Sometimes, a B-band appears besides the A-band for systems with δ>0.5 (figure 4c).
There are several non-1 : 1 CT solids in which the minority component is fully ionized, resulting in a mixed valence for the other component. The fully ionized species act as a counter ion located between the metallic segregated stacks. Such solids exhibit both A- and B′-bands or A′- and B-bands when the counter-ion species having open shell structures also form segregated stacks. In several cases such as (TMTSF)2 (CF3TCNQ), the molecular planes of the counter ions are almost perpendicular to the molecular plane of other component and a sharp -band is observed (figure 4d) but no B′-band is found for open shell counter-anions.
As summarized in the family tree of mixed-valence segregated stacks (figure 2a), the solids of types MS and M′S usually afford metals, superconductors, CO insulators, Peierls-type band-insulators, Mott insulators including antiferromagnets, spin-liquids of dimers, non-1 : 1 spin-Peierls systems, etc.
6. Functionality versus ionicity and stacking mode
Table 1 shows the optical (first CT band), transport and magnetic properties of CT solids, parts of which are presented in figure 2. Each block includes symbols of the ionicity (I, M, M′ and N) and stacking manner (A, S and 2).
Most of the known metallic complexes belong to a limited number of classes, mainly MuSu (e.g. TTF.TCNQ system, 1>δ≥δc(=0.5)). When a complex has a high-dimensional electronic structure, δc decreases and metallic M′uSu can be formed (e.g. BEDO-TTF complexes with δc≈0.3). Even with non-uniform segregated stacks, some solids show a metallic nature when Ueff <W (e.g. κ-type dimerized systems such as κ-(BEDT-TTF)2Cu(CN)[N(CN)2], labelled as MuS2 in table 1). Exceptional metallic complexes have been obtained in ISu for 1 : 1 radical cation salts when Ueff<W, in MnSn such as (BEDT-TTF)3(AuBr2)2(AuBr4)2(solv)x in which the BEDT-TTF molecules have charge separated states in the metallic regime, and in MnAu (e.g. HMTTeF.Et2TCNQ.solvent) through the coexistence of ionic and neutral domains. To develop the field of organic functional conductors, one important objective is to find new systems occupying the empty blocks in table 1 or showing an unprecedented physical phenomenon. An example might be a Mott insulator κ-(BEDT-TTF)2Cu2(CN)3 (type MuS2), which has a spin-liquid ground state at ambient pressure and exhibits a pressure-induced anisotropic superconducting state. Other possibility is (EDO-TTF)2PF6 (type MuSu), which exhibits a metal–insulator transition near RT caused by cooperative and multifold mechanisms (Peierls, CO, anion-order and molecular deformation; type MnSn). The insulating state is converted to a highly conductive state by coherent photon irradiation within a short time (1.5 ps).
This work was in part supported by a grant-in-aid (twenty-first century COE programs on Kyoto University Alliance for Chemistry and 15205019) from the Ministry of Education, Culture, Sports, Science and Technology, Japan.
One contribution of 15 to a Discussion Meeting Issue ‘Mixed valency’.
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