Orbital hybridization of donor and acceptor to enhance the conductivity of mixed-stack complexes

Abstract

Mixed-stack complexes which comprise columns of alternating donors and acceptors are organic conductors with typically poor electrical conductivity because they are either in a neutral or highly ionic state. This indicates that conductive carriers are insufficient or are mainly localized. In this study, mixed-stack complexes that uniquely exist at the neutral–ionic boundary were synthesized by combining donors (bis(3,4-ethylenedichalcogenothiophene)) and acceptors (fluorinated tetracyanoquinodimethanes) with similar energy levels and orbital symmetry between the highest occupied molecular orbital of the donor and the lowest unoccupied molecular orbital of the acceptor. Surprisingly, the orbitals were highly hybridized in the single-crystal complexes, enhancing the room-temperature conductivity (10⁻⁴–0.1 S cm⁻¹) of mixed-stack complexes. Specifically, the maximum conductivity was the highest reported for single-crystal mixed-stack complexes under ambient pressures. The unique electronic structures at the neutral–ionic boundary exhibited structural perturbations between their electron-itinerant and localized states, causing abrupt temperature-dependent changes in their electrical, optical, dielectric, and magnetic properties.

Mixed-stack complexes consisting of alternating donors and acceptors typically show low electrical conductivity. Here, the authors improved the conductivity by hybridizing the frontier orbitals of the donor and acceptor at the neutral–ionic boundary.

Introduction

Organic conductors that are lightweight, flexible, and have excellent molecular designability are widely used as essential materials in modern organic electronic devices. The most industrially successful materials are polymer conductors owing to their high conductivities and ease of synthesis¹. However, analyzing their atomic-level structures and conduction mechanisms is still challenging because of the inhomogeneity of polymers with different chain lengths. To address this issue, researchers are investigating molecular conductors with precisely defined molecular weights^2–6. The crystal-based structures help to understand the structure–conductivity relationships and address the conduction mechanism. Charge-transfer complexes^3–6 are typical molecular conductors and are categorized as either “segregated-stack complexes,” in which donors (D) and acceptors (A) are separately stacked (DDDD…/AAAA…) or “(alternatingly) mixed-stack complexes,” in which donors and acceptors are alternately stacked (DADADADA….; Fig. 1a). The difference in the stacking forms of complexes composed of the common donors and acceptors dramatically affects the conductivities. Segregated-stack complexes, such as tetrathiafulvalene (TTF) analogs–7,7,8,8-tetracyano-p-quinodimethane (TCNQ) analogs (the molecular structures are shown in Supplementary Fig. 1)^7,8, hexamethylenetetraselenafulvalene–TCNQ⁹, and TTF analogs–metal dithiolenes¹⁰, exhibit excellent room-temperature conductivities (σ_rt) of up to 10³ S cm^–17,9, although variations on such highly conducting examples are still limited^5,6. Several hybrid materials between DD-stack and DA-mixed-stack complexes have shown relatively high σ_rt (10^–2 S cm^–1)^11–14. In contrast, mixed-stack complexes are typically poor electrical conductors that show low σ_rt (below 10^–4 S cm^–1)^15–21 (Fig. 1b), although they are more frequently constructed, possibly owing to the Madelung energy gain between charged donor and acceptor. Generally, mixed-stack complexes are either in a neutral state (charge-transfer degree from donor to acceptor δ < 0.5⁴, mostly 0 < δ < 0.4^5,6) with insufficient conductive carriers and weak intermolecular interactions for carrier conduction, or are in a highly ionic state (mostly δ > 0.75)^5,6, wherein the carriers are nearly localized and have low mobility, thereby suppressing conductivity. In the early 2000s, a few neutral complexes showed high conductivity^22,23, possibly due to the structural disorders within the contaminated ionic domains. However, the structural details and mechanisms remained hidden as the CCDC data were unavailable. We hypothesized that the mixed-stack complexes at the neutral–ionic (N–I) boundary (0.59 < δ < 0.74)⁵ could have numerous mobile electrons and display excellent electrical conductivity²⁴. The hypothesis was supported by the discovery of segregated-stack complexes with exceptional conductivity in the same boundary area^5–10. Preceding studies^24–26 predicted that charge transfer to form mixed-stack complexes with δ at the N–I boundary could be realized by engineering appropriate energy gaps between the highest occupied molecular orbital (HOMO) of donors and the lowest unoccupied molecular orbital (LUMO) of acceptors that satisfy the equation I_D – E_A (= ΔE_REDOX) ≈ E_M, where I_D is the ionization potential of the donor (related to its HOMO of the donor), E_A is the electron affinity of the acceptor (related to its LUMO of the acceptor), and E_M is the electrostatic Madelung energy of the donor–acceptor complex (approximately 0.2 eV; Fig. 2). In addition, a consistent orbital symmetry between the donor HOMO and acceptor LUMO²⁷ may be necessary to facilitate the hybridization of frontier orbitals and enable efficient charge transfer. Thus far, a few mixed-stack complexes have partly fulfilled these two requirements: 1) similar energy levels between the donor HOMO and the acceptor LUMO, with the appropriate energy gaps of approximately 0.2 eV, and 2) a consistent orbital symmetry between them; for example, tetrakis(methyltelluro)tetrathiafulvalene (TTeC₁-TTF)–TCNQ (δ = 0.56; d’ in Fig. 1b)²¹ and 3,3’,5,5’-tetramethylbenzidine (TMB)–TCNQ (δ = 0.49; c’ in Fig. 1b)^16,28 close to the N–I boundary exhibited relatively high σ_rt values of 10⁻² and 10⁻⁵ S cm⁻¹, respectively. Under high-pressure conditions (~9 kbar), δ of TTF–p-chloranil (CA) (v in Fig. 1b) was transiently increased to ≈0.6, exhibiting excellent σ_rt (7 S cm⁻¹)²⁹, although it exhibits δ ≈ 0.2 and σ_rt = 10^–5 S cm^–1 under ambient pressures.

Fig. 1. Structures and electrical conductivities of mixed-stack complexes.

a Molecular structures of donors (2X; X = O, S) and acceptors (F_n; n = 4, 2) in the mixed-stack complexes 2X–F_n. An illustration of the 1D packing mode of 2X–F_n is shown in the right. b σ_rt of 1D mixed-stack complexes as a function of charge-transfer degree from donor to acceptor (δ) determined for single-crystal structures. a: Benzothieno[3,2-b]benzothiophene (BTBT)–F₄¹⁵. b: 1,2-Di(2-thienyl)ethylene (DTE)–7,7,8,8-tetracyano-p-quinodimethane (TCNQ)⁵. c: Naphthalene–TCNQ⁵. d: Perylene–TCNQ⁵. e: Dithieno[3,2-b:2’,3’-d]thiophene (DTT)–TCNQ⁵. f: Anthracene–TCNQ⁵. g: trans-Stilbene–TCNQ⁵. h: trans-2,2’,5,5’-Tetramethoxystilbene–TCNQ⁵. i: Pyrene–TCNQ⁵. j: Bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF)–TCNQ⁵. k: 2,3,7,8-Tetramethoxydibenzo[b,e][1,4]thiaselenine (Vn₂SSe)–TCNQ⁶. l: 3,3’,5,5’-Tetramethylbenzidine (TMB)–p-chloranil (CA)¹⁶. m: Tetramethyltetraselenafulvalene (TMTSF)–TCNQ⁶. n: 2,3,7,8-Tetramethoxyselenanthrene (Vn₂Se₂)–TCNQ⁶. o: 1,6-Diaminopyrene (DAP)–p-bromanil (BA)²². p: 4,4’-Dimethyltetrathiafulvalene (DMTTF)–BA²⁰. q: Coronene–TCNQ⁶. r: Dibenzotetrathiafulvalene (DB-TTF)–TCNQ⁵. s: Tetrathiafulvalene (TTF)–TCNQ¹⁷. t: DMTTF–CA²⁰. u: 5,10-Dihydro-5-10-dimethylphenazine (DHMP)–TCNQ⁶. v: TTF–CA¹⁸. w: 2,5-Dichloro-1,4-phenylenediamine (Cl₂PD)–2-chloro-5-methyl-7,7,8,8-tetracyano-p-quinodimethane (ClMeTCNQ)²⁰. x: 2-Chloro-5-methyl-1,4-benzenediamine (ClMePD)–2,5-diethyl-7,7,8,8-tetracyano-p-quinodimethane (Et₂TCNQ)²⁰. y: α,α’-Dimethylquaterthiophene (DMQtT)–F₄¹⁹. z: ClMePD–2,5-dimethyl-N,N’-dicyanoquinone diimine (DMeDCNQI)²⁰. a’: Tetrakis(methylthio)tetrathiafulvalene (TTC₁-TTF)–2-fluoro-5-methyl-7,7,8,8-tetracyano-p-quinodimethane (FMeTCNQ)²⁰. b’: TMB–2,5-dimethyl-7,7,8,8-tetracyano-p-quinodimethane (Me₂TCNQ)¹⁶. c’: TMB–TCNQ¹⁶. d’: Tetrakis(methyltelluro)tetrathiafulvalene (TTeC₁-TTF)–TCNQ²¹. e’: TMB–F₂¹⁶. f’: Phenazine–TCNQ⁵. g’: TMB–F₄¹⁶. The molecular structures are shown in Supplementary Fig. 1. The δ values for 2X–F_n are shown with error bars (standard deviation).

Fig. 2. Electronic and optical properties of mixed-stack complexes.

Relationship between ΔE_REDOX and hν_CT that has two separate linear correlations in the neutral and ionic regions; the two straight lines intersect when ΔE_REDOX ≈ E_M, resulting in the hν_CT value reaches to the minimum (approximately 0.6 eV). The vertical dashed line indicates the neutral–ionic boundary (Reprinted and modified from Reference²⁶, Copyright 1985, from Taylor & Francis). A: N,N,N’,N’-Tetramethyl-p-phenylenediamine (TMPD)–F₄. B: DHMP–TCNQ. C: TMPD–TCNQ. D: TMPD–CA. E: N,N,N’,N’-Tetramethyl-1,6-pyrenediamine (TMDAP)–TCNQ. F: TTF–CA. G: TTF–p-fluoranil (FA). H: Dibenzene TTF–TCNQ. I: Diethyldimethyltetraselenafulvalene–Et₂TCNQ. J: TMDAP–FA. K: TTF–dichlorobenzoquinone. L: Perylene–F₄. M: Perylene–2,3-dichloro-5,6-dicyano-p-benzoquinone. N: Perylene–tetracyanoethylene. O: Perylene–TCNQ. P: TTF–dinitrobenzene. Q: Perylene–CA. R: Pyrene–tetracyanoethylene. S: Pyrene–CA. T: Anthracene–CA. U: Hexamethylbenzene–CA. V: Naphthalene–TCNE. X: Anthracene–pyromellitic dianhydride (PMDA). Y: Anthracene–tetracyanobenzenze. Z: Phenanthrene–PMDA. The molecular structures are shown in Supplementary Fig. 1.

In this study, we designed and synthesized mixed-stack complexes uniquely located at and near the N–I boundary, enhancing the conductivities of mixed-stack complexes. The combination of the oligo(3,4-ethylenedioxythiophene) analog 2O^30,31 or its oxygen/sulfur-substituted analog 2S with tetra- or difluorinated TCNQs F_n fulfills the two requirements for electronic structures (i.e., 2X–F_n, X = O, S in Fig. 1a). Surprisingly, the donor HOMO and acceptor LUMO with comparable energy levels and well-matched orbital symmetries were highly hybridized in the complexes, enhancing the σ_rt values of mixed-stack complexes (10⁻⁴–0.1 S cm⁻¹). The highest σ_rt value (0.1 S cm⁻¹) observed for 2S–F₄ among the combinations of donors 2X and acceptors F_n, which is located at the N–I boundary, is the highest value reported for a structurally defined 1D mixed-stack complex under ambient pressure. Furthermore, 2S–F₄ exhibited a transition in electrical conductivity to a slightly less conductive phase accompanied by significant changes in its optical, dielectric, and magnetic properties. This emphasizes the unique electronic structure of the mixed-stack complex at the N–I boundary that displays a structural perturbation between electron-itinerant and localized states.

Results and discussion

Molecular electronic structures

First, 2S with non-bulky methylthio groups was synthesized in 52% yield after three-step transformations from 2,2’-bi(3,4-ethylenedithiothiophene) 1³² (Fig. 3a, Supplementary Note 3, Supplementary Figs. 7, 41, 42, and Supplementary Table 1). The electrochemical properties of 2O³⁰ and 2S were analyzed via cyclic voltammetry (CV). The voltammograms revealed the first oxidation potentials at 0.622 and 0.805 V (vs. Ag/AgCl) for 2O and 2S, respectively (Supplementary Note 4 and Supplementary Fig. 3), estimating HOMO levels of 2O/2S (−4.94/−5.13 eV) that are comparable to the LUMO levels of F₄/F₂ (−4.98/−4.74 eV). The gaps between the donor HOMO and acceptor LUMO (i.e., ΔE_REDOX in Fig. 2) are estimated to be in the range of −0.04 to 0.39 eV (Table 1), which is consistent with those predicted by density functional theory (DFT) calculations (Fig. 4a, Supplementary Note 5, Supplementary Figs. 4, 6, Supplementary Tables 6, 7, 9, and 11). The 1e⁻-oxidized 2O/2S structures show highly symmetrical molecular orbital shapes spread over the entire molecules and consistent horizontally nodal patterns with an average periodicity of 2.0 Å that correspond well with those of 1e⁻-reduced F₄/F₂ with an average periodicity of 1.7–1.8 Å (Fig. 4b, Supplementary Fig. 5, Supplementary Tables 8, 10, and 12). Therefore, the combination of 2O/2S as donors and F₄/F₂ as acceptors ideally has similar energy levels and orbital symmetries between the HOMO of the donor and LUMO of the acceptor, possibly leading to strong hybridization between their orbitals during complexation.

Fig. 3. Synthesis of mixed-stack complexes 2X–F_n.

a Synthesis of donor 2S by bromination followed by lithiation and methylthiolation. b Synthesis of mixed-stack complexes 2X–F_n by chemical oxidation of donor (2O and 2S) by acceptors (F₄ and F₂). The δ values were determined using Kistenmacher’s equation³⁷. NBS N-bromosuccinimide, ⁿBu n-butyl, THF tetrahydrofuran, Me methyl.

Table 1.

Structural information and physical properties of mixed-stack complexes

Donor (D)–acceptor (A)	2O–F4	2O–F2	2S–F4	2S–F2
Experimental data
ΔEREDOX ( = E1/21(D) − E1/21 (A)) (V)a	−0.04	0.20	0.15	0.39
D–A interplanar distance (Å)b	3.361	3.329	3.406	3.398
δ from bond length analyses in A	0.79(2)	0.71(4)	0.69(2)	0.46(3)
σ at 300 K (σrt; S cm−1)	4.9 × 10−4	1.4 × 10−2	0.10	6.9 × 10−3
hνCT (eV)	0.83	0.73	0.64	0.50
Ea for high temperature region (eV)c	0.113(1) (290–315 K)	0.178(1) (259–337 K)	0.200(1) (288–340 K)	0.112(1) (288–312 K)
Ea for low temperature region (eV)c	0.215(2) (238–258 K)	0.225(4) (219–231 K)	0.277(3) (228–273 K)	0.0902(17) (221–244 K)
Calculated data
Eg (eV)d	0.05	<0.01e	<0.01	0.02e
W (eV)d	0.86	0.89e	0.88	0.89e
tDA (eV)f	0.203	0.209e	0.208	0.206e
Ueff (D) (eV)f	2.31	2.28e	1.89	1.89e
Ueff (A) (eV)f	2.52	2.48e	2.19	2.22e

^aEstimated from the cyclic voltammograms (see Supplementary Fig. 3 for details). The values were calibrated using the energy level of ferrocene/ferrocenium (Fc/Fc+ vs. Ag/AgCl/1 M KCl measured under identical conditions) as the reference.

^bDetermined by measuring the distances between the centroid of the ten atoms of the bithiophene in the donor and the mean plane for the eight quinoid carbons in the acceptor in the single-crystal structures.

^cDetermined from ρ–T plots using the Arrhenius equation.

^dCalculated by OpenMX^38,39 as a sum of dispersions for the bonding and antibonding bands between donor HOMO and acceptor LUMO (i.e., W_B and W_A, respectively) and energy gap between bonding and antibonding bands (i.e., E_g), if present (i.e., bandwidth W = W_B + W_A + E_g).

^eStructural data with major occupancy were used in the calculations for 2O–F₂ and 2S–F₂.

^fCalculated by Q_UANTUM Espresso (QE)^40,41 and RESPACK⁴².

Fig. 4. Electronic structure of donor 2S, acceptor F₄, and the mixed-stack complex 2S–F₄ according to theoretical calculations.

a Energy levels of orbitals for neutral 2S donor and F₄ acceptor calculated by the Gaussian09 program. The energy levels of the donor’s highest occupied molecular orbital (HOMO) and acceptor’s lowest unoccupied molecular orbital (LUMO) were comparable, which is appropriate for their strong hybridization. b Singly occupied molecular orbitals (SOMOs) of 1e^–-oxidized 2S donor and 1e^–-reduced F₄ acceptor calculated by Gaussian09 program. These orbitals have horizontally nodal patterns with an average periodicity of 1.8–2.0 Å that correspond well with each other (Supplementary Fig. 5). c Band structure calculated by OpenMX^38,39. The bandwidth (W) value was determined from the calculated density of states (DOS). The highest occupied crystal orbital (HOCO) and lowest unoccupied crystal orbital (LUCO) at the Γ-point are depicted in red and blue dots, respectively. Γ (0,0,0), P (–0.5,0,0.5), Q (–0.5,0.5,0.5), Y (0,0.5,0). d Highly hybridized HOCO and LUCO between donor and acceptor at the Γ-point calculated by OpenMX^38,39. Atoms were colored as follows; white: hydrogen; gray: carbon; blue: nitrogen, red: oxygen; light green: fluorine; yellow: sulfur. Molecular and crystal orbitals with positive and negative phases were colored with magenta and navy, respectively.

Single-crystal X-ray diffraction analyses

Motivated by the potentially ideal combination of 2O/2S donors and F₄/F₂ acceptors in the electronic structures, we investigated their complexation. The donors and acceptors were mixed in dichloromethane or THF, which led to a gradual color change of the solutions from yellow to dark green, indicative of charge transfer from the donor to the acceptor. After slow solvent evaporation over more than three days, dark-green needle-like single crystals of complexes 2O–F₄, 2O–F₂, 2S–F₄, and 2S–F₂ were isolated (Fig. 3b). These syntheses were highly reproducible and scalable to a yield of several milligrams in a single sequence of operations. The salts had an astonishingly high solubility in organic solvents such as acetonitrile and were stable for at least several weeks under atmospheric conditions.

X-ray diffraction (XRD) analyses determined that all single-crystal structures belonged to the P2₁/n space group with inversion centers at the center of gravity of the donors and acceptors and the glide plane symmetry on the 1/2 translation operation along the (a + c)/2 direction (Supplementary Note 6, Supplementary Figs. 9, 10, 12, 14, and Supplementary Table 2). The 2O and 2S donors in single-crystal complexes are nearly planar (Supplementary Fig. 11), similar to the charge-transfer salts of 2O and 2S (i.e., 2O•BF₄³⁰ and 2S•BF₄; Supplementary Figs. 2, 8, and Supplementary Table 1). The fluorine atoms in 2O–F₂ and 2S–F₂ exhibited positional disorder, with an occupancy of 94:6 and 86:14, respectively (Supplementary Fig. 9b, d). The donors and acceptors are uniformly and alternatingly π-stacked in columns along the a-axis. The donor–acceptor interplanar distances depend on the molecular size of the donor (i.e., 2O < 2S) and acceptor (i.e., F₂ < F₄); the distances increased in the order 2O–F₂ (3.329 Å) < 2O–F₄ (3.361 Å) < 2S–F₂ (3.398 Å) < 2S–F₄ (3.406 Å) (Table 1). Significant intracolumnar short contacts were not observed, suggesting the existence of 1D electronic structures favorable for strong intermolecular interactions. Notably, X-ray diffuse scattering was observed, reminiscent of structural fluctuation (Supplementary Note 6 and Supplementary Fig. 14).

Charge-transfer degree of mixed-stack complexes

The δ values of the complexes were determined using the conventional bond length analyses of the single-crystal structures for donors and acceptors⁶ in the mixed-stack complexes. An increase in the δ value of the donor from 0 (i.e., a neutral form with a benzenoid structure) to 1 (a radical cation form with a resonance structure) weakens bond alternation (i.e., C–C bonds b and d and C–S bonds g are shortened, while C=C bonds a and c are lengthened; Fig. 5a, b, c, e, f), as is apparent from the single crystals for neutral 2X (X = O³⁰ or S, δ = 0; Supplementary Fig. 7 and Supplementary Table 1) and its 1e⁻-oxidized form 2X•BF₄³⁰ (δ = 1; Supplementary Fig. 8 and Supplementary Table 1). All bond length alterations of the 2O and 2S donors in the mixed-stack complexes are located between those of 2X and 2X•BF₄, indicative of intermediate δ values for the complexes between 0 and 1. Commonly, F₄ complexes exhibited weaker bond length alternation than F₂ complexes, indicating that the F₄ complexes have higher δ values than the F₂ complexes. Likewise, the acceptor molecules F_n exhibited weakening of the bond alternation (i.e., C–C bonds i, k, and m are shortened, while C=C bonds j and l are lengthened; Fig. 5a, d, g) upon reduction from neutral^33,34 (δ = 0) to their 1e⁻–reduced forms^35,36 (δ = 1), suggesting the intermediate δ. Notably, the 2O complexes exhibited weaker bond length alternation than the 2S complexes, suggesting that the 2O complexes have higher δ values than the 2S complexes. These tendencies are consistent with the δ values determined using Kistenmacher’s equation³⁷, which assumes that the bond length changes linearly as δ increases from 0 to 1. The δ values of 2O–F₄, 2O–F₂, 2S–F₄, and 2S–F₂ were determined to be 0.79(2), 0.71(4), 0.69(2), and 0.46(3), respectively (Table 1). These values are close to the N–I boundary (0.59 < δ < 0.74), whereas that of 2S–F₂ lies at the nearly neutral state, as predicted by the comparable energy levels of the donor HOMO and acceptor LUMO by CV analyses (Supplementary Fig. 3) and DFT calculations (Fig. 4a and Supplementary Fig. 6).

Fig. 5. Bond length analysis of mixed-stack complexes.

a Bond labels of 2O, 2S, F₄, and F₂. b–g Comparison of C–C and C–S bond lengths (d_CC and d_CS, respectively) of donors and acceptors in single crystals of mixed-stack complexes, with error bars (standard deviation). The letters along the x-axes of the plots correspond to the bonds depicted in a. As a reference, the bond lengths in single crystals of neutral donors or acceptors (i.e., δ = 0) are shown with dotted lines and 1e⁻-oxidized donors or 1e⁻-reduced acceptors (i.e., δ = 1) are shown with solid lines. Observed d_CC of 2O³⁰ (b), d_CC of 2S (c), d_CC of F₄^33,35 (d), d_CS of 2O³⁰ (e), d_CS of 2S (f), and d_CC of F₂^34,36 (g). i = (i¹ + i²)/2.

Electronic structures of mixed-stack complexes

Based on the single-crystal structures of 2X–F_n as the average structures, we then obtained the band structures using first-principles calculations (OpenMX software; Supplementary Note 7)^38,39, wherein the contributions from Coulomb repulsion between the carriers (discussed later) are ignored. All complexes showed band structures with highly dispersed bonding and antibonding orbital-derived bands formed by the donor HOMO and acceptor LUMO (Fig. 4c and Supplementary Fig. 18). The bands were exclusively dispersed along the a-axis (i.e., Γ–X corresponding to the π-stacking direction). The band structures had small or negligible energy gaps (E_g) in proximity to the Fermi level (0.02–0.05 eV for 2O–F₄ and 2S–F₂ and <0.01 eV for 2O–F₂ and 2S–F₄; Table 1 and Supplementary Fig. 18). The density of states (DOS) was calculated to determine the bandwidth (W) of the complexes in the major occupancies, the values of which were 0.86 eV (2O–F₄), 0.89 eV (2O–F₂), 0.88 eV (2S–F₄), and 0.89 eV (2S–F₂) (Table 1, Fig. 4c, and Supplementary Fig. 18), where W = W^B + W^A + E_g; W^B and W^A are the band dispersions of the bonding and antibonding orbitals, respectively. Among typical organic conductors², high W values may be characteristic of 1D electronic structures, especially given the comparable energy levels of the donor HOMO and acceptor LUMO and their well-matched orbital symmetries, indicating strong intracolumnar interactions. We next quantified the transfer integrals between a donor and the six neighboring molecules in the single-crystal structures using combined Quantum ESPRESSO (QE)^40,41 and RESPACK⁴² (Supplementary Fig. 27, and Supplementary Table 3). These calculations also identified prominent intracolumnar donor–acceptor interactions (t_DA ≈ 0.21 eV in Table 1; t₁ and t₄ in Supplementary Table 3 and Supplementary Fig. 27), corresponding to W values based on the 1D tight-binding model, and negligible intercolumnar donor–acceptor and donor–donor interactions for all complexes. These findings support their 1D electronic structures, which were also suggested by the band structures. The W and intracolumnar t_DA values follow nearly consistent trends: F₄ complexes < F₂ complexes, possibly because the donor–acceptor interplanar distances are shorter for F₂ complexes (as shown in Table 1). Despite the longer interplanar distances, the trend 2O complexes < 2S complexes is primarily due to the presence of multiple S atoms with significant orbitals in the donor.

Notably, we have made a significant discovery using OpenMX calculations^38,39, which identified that the HOMO of the donor and LUMO of the acceptor are highly hybridized. The calculated highest occupied crystal orbital (HOCO) and lowest unoccupied crystal orbital (LUCO) at the Γ point of 2X–F_n appeared equivalently on the donor and acceptor, respectively (Fig. 4d and Supplementary Fig. 19). This contrasts with neutral complexes³, where HOCOs and LUCOs were localized on the donors and acceptors, respectively. This finding supports that 2X–F_n complexes around the N–I boundary have different electronic structures from previously reported neutral or ionic mixed-stack complexes^5,6,15–23, leading to significant W values based on their 1D electronic structures and unique electronic structures as discussed later.

Polarized reflectivity measurements

The polarized reflectivity spectra further support the observation that the δ values of 2X–F_n are close to the N–I boundary. The spectra obtained for the π-stacking direction of the single crystals have peak energies based on the charge-transfer band (hν_CT) at 0.50 eV (2S–F₂) < 0.64 eV (2S–F₄) < 0.73 eV (2O–F₂) < 0.83 eV (2O–F₄) (Table 1 and Fig. 6a; complexes are located exactly at the N–I boundary, whereas 2S–F₂ is nearly neutral). The spectrum of 2S–F₂ has a shoulder peak at approximately 0.64 eV. The shape of this spectrum reflects the neutral-to-N–I boundary state⁴³ (δ = 0.46(3)) or donor–acceptor π-dimerized form^43,44 (discussed later), possibly causing the plot for 2S–F₂ to deviate from the predicted value by δ in Fig. 2. The significant positional disordering of fluorine atoms in 2S–F₂ may also affect the shape of the spectrum.

Fig. 6. Polarized reflectivity of mixed-stack complexes.

a Spectra of mixed-stack complexes obtained in the electric field of light parallel to the π-stacking direction. Bars indicate the top of the peaks. The spectrum of the relatively thin single-crystal 2O–F₄ exhibits stripe-pattern signals in the low-energy region due to interference from the backside (the raw data is shown in Supplementary Fig. 34a), and thus this part of the spectrum was deleted for clarity. b Temperature-dependent reflectivity of 2S–F₄ in the electric field of light parallel (//) and perpendicular (⊥) to the π-stacking directions for the low-energy region.

Given that the strong hybridization between the donor HOMO and acceptor LUMO in the band structures with nearly negligible E_g, we considered the electronic structures of 2X–F_n to be like homogeneous donor- or acceptor-stacked charge-transfer salts, with the average structure². Under this consideration, the observed hν_CT may correspond to the difference between the bonding and antibonding orbital bands separated by carrier-to-carrier Coulomb repulsions in the solid states (U_eff), rather than the donor HOMO–acceptor LUMO energy gap for neutral complexes. Accordingly, the lower hν_CT for the 2S complexes than that for the 2O complexes may correspond to lower U_eff for the 2S complexes. Quantum calculations provided further insights into electronic structures. The U_eff values for the complexes were quantified for donors and acceptors (i.e., U_eff (D) and U_eff (A), respectively) by combining first-principles calculations (QE^40,41/RESPACK⁴² packages) based on the average single-crystal structures. These calculations identified the far lower U_eff (D) and U_eff (A) for 2S complexes compared to those of 2O complexes (Table 1, Supplementary Figs. 20–26, and 28–33), emphasizing that the combined effects of smaller δ value and the larger π-conjugate area of the donor in the complexes may favorably contribute to lowering U_eff. The cooperative reduction in U_eff (D) and U_eff (A) supports the significant orbital hybridization of donors and acceptors in single crystals. According to these calculations, the 2S complexes have slightly larger W and far lower U_eff than the 2O complexes, conferring superior electrical conductivities^45–48 upon the 2O complexes. However, it is not negligible that nearly neutral 2S–F₂ has insufficient conductive carriers and positional disorders of fluorine atoms, which may impact the electronic structures that contribute to the conductivity (Supplementary Figs. 18–20, 26, 27, 33, and Supplementary Table 3).

Structural fluctuations involved in π-dimerization

It is also notable that the polarized infrared reflectivity spectra of the complexes along the π-stacking direction exhibited multiple sharp peaks in the low-energy region of 0.14–0.19 eV, except for nearly neutral 2S–F₂ (Fig. 6b, Supplementary Figs. 34, and 35a). The optical conductivity spectrum of 2S–F₄ (Supplementary Fig. 35b) derived from the infrared spectrum showed a coincidence of the shapes to the Raman spectrum at 293 K (Supplementary Fig. 35d), with varying intensities. Considering the inversion center of the single-crystal structure in a P2₁/n space group with uniform π-stacked donors and acceptors along the C2 glide symmetry, the Raman-active modes should not be visible in IR, while the IR-active modes should not be visible in Raman. The coincidence of the spectral shapes indicates the dynamic fluctuating of donor–acceptor-π-stacking dimerization based on the electron-molecular vibration (EMV) couplings^43,44. We performed a computational study by numerical simulations using the donor–acceptor dimer model⁴⁹, confirming that the EMV coupling effect is responsible for these signals (Supplementary Note 8, Supplementary Fig. 35c, Supplementary Tables 4, and 5). These results suggest that there is inhomogeneity in the one-dimensional molecular stacking, contradicting the uniform columnar structure predicted by single-crystal XRD (Supplementary Table 2 and Supplementary Fig. 10). This inhomogeneity likely indicates dynamic fluctuations from the average structure, which is supported by the X-ray diffuse scattering observed in XRD at 300 K (Supplementary Fig. 14).

Electrical conductivity measurements

Motivated by the proximity of the δ value to the N–I boundary, high W, and low U_eff for 2S complexes, we subsequently investigated the electrical conductivity of single-crystal mixed-stack complexes (Supplementary Note 9). The σ_rt values (300 K) determined via the direct-current method along the π-stacking direction (the a-axis) were superior by a few orders of magnitude to those of previously reported typical mixed-stack complexes with σ_rt (300 K) below 10^–4 S cm^–1: 4.9 × 10⁻⁴ S cm⁻¹ (2O–F₄), 1.4 × 10⁻² S cm⁻¹ (2O–F₂), 0.10 S cm⁻¹ (2S–F₄), and 6.9 × 10⁻³ S cm⁻¹ (2S–F₂) (Fig. 1b and Table 1) within the ohmic region (Supplementary Fig. 36). Except for the nearly neutral 2S–F₂, the trend of σ_rt (2S–F₄ > 2O–F₂ > 2O–F₄) indicates that the closeness of these complexes to the N–I boundary dominantly affected the conductivity. The σ_rt of 2S–F₄ (0.10 S cm⁻¹) is the highest value reported to date for a single crystal of a 1D mixed-stack complex, and it is an order of magnitude higher than the previously highest value of 1.0 × 10⁻² S cm^−1 21. The low U_eff based on the large conjugate area may cooperatively contribute to the high σ_rt^46–48, unlike those of the other complexes at the N–I boundary (e.g., complexes e’ and f’ in Fig. 1b).

The activation energies (E_a) near room temperature were determined from the temperature (T) dependence of the resistivity (ρ = σ⁻¹) using the Arrhenius equation. The ρ–T plots are indicative of semiconducting behavior with relatively small E_a values: 0.113(1) eV (2O–F₄), 0.178(1) eV (2O–F₂), 0.200(1) eV (2S–F₄), and 0.112(1) eV (2S–F₂) around room temperature (Figs. 7, and 8a, and Table 1), indicating that these complexes are narrow-bandgap semiconductors. The E_a trend was inconsistent with those of σ_rt, the calculated E_g, and U_eff. Except for the nearly neutral 2S–F₂, the E_a values increased: 2O–F₄ < 2O–F₂ < 2S–F₄. The trend is explained by the proximity of δ to the N–I boundary which induces the π-dimerization fluctuation between the donor and acceptor; 2S–F₄ at the N–I boundary showed largest increase in ρ, and highest E_a among the three complexes.

Fig. 7. Temperature-dependent electrical conductivities of mixed-stack complexes.

ρ–T plots obtained by a four-probe method for cooling (circles) and heating (plus marks) processes are shown.

Fig. 8. Temperature-dependent physical properties of single-crystal 2S–F₄ upon cooling.

a Electrical resistivity. b Polarized reflectivity for photon energies of 144–178 meV in the electric field of light parallel to the π-stacking direction. c Real part of the dielectric constant ε_r at 1.0 MHz. d Normalized χ_spin determined from the calculation using the intensity and ΔB_pp of the electron spin resonance (ESR) signals at g ≈ 2.003. The values are normalized by the value at 340 K, with error bars (standard deviation). e ΔB_pp of the ESR signals at g ≈ 2.003, with error bars (standard deviation). Gray panel indicates the transition temperature around 282 K.

Abrupt changes in physical properties of 2S–F₄ around room temperature

The mixed-stack complex with the highest conductivity at the N–I boundary, 2S–F₄, exhibited a unique transition with a sharp increase in ρ at a transition temperature (T_c) of 282 K. The transition was followed by an increase in E_a from 0.200(1) eV at high temperatures (288–340 K) to 0.277(3) eV at low temperatures (228–273 K) without significant hysteresis upon cooling and heating (Figs. 7, 8a, and Table 1). The XRD pattern in P2₁/n space group at 300 K showed significant X-ray diffuse scattering (Supplementary Fig. 14), possibly due to the precursor phenomenon for the π-dimerization, which may result in EMV coupling-based signals at room temperature (Fig. 6b, Supplementary Figs. 34, and 35a). On the other hand, the scattering disappeared (Supplementary Figs. 15 and 16) at 200 K, and the XRD showed superlattice patterns with dimensions of a × 2b × 2c (Supplementary Figs. 13 and 17), possibly implying the π-dimerization along the a-axis (Supplementary Note 6). The broken symmetry upon the possible π-dimerization of the complex may induce the markedly intensified EMV coupling-based signals (e.g., from 0.20 to 0.25) near 282 K during the cooling process while maintaining the energy (Figs. 6b, 8b, and Supplementary Fig. 35a), as well as the large anomaly in the dielectric constants⁵⁰ (the real part of the dielectric constant is shown in Fig. 8c). The transition events did not cause any significant hysteresis for the cooling and heating processes.

Change in the magnetic characteristics at the transition

The magnetic characteristics revealed via temperature-dependent electron spin resonance (ESR) measurements helped us to address the insights into the electronic structures of the mixed-stack complexes (Supplementary Note 10). The spectra of 2S–F₄ exhibited a narrow Lorentzian signal with a peak-to-peak width (ΔB_pp) of ≈0.2 G at g ≈ 2.003, which is typical for π-electrons² (Supplementary Figs. 37–39). At 282 K, the magnetic susceptibility (χ_spin) quantified from the spectra decreased sharply to reach a nearly nonmagnetic state (Fig. 8d and Supplementary Fig. 39b), suggesting a spin-Peierls-like singlet formation based on the 1D electronic structure⁵¹ during the π-dimerization. This χ_spin decrease was accompanied by an increase in ΔB_pp (Fig. 8e and Supplementary Fig. 39c, d), supporting increased antiferromagnetic interactions in the singlet ground state in the low-temperature region. A decrease in χ_spin and increase in ΔB_pp upon cooling were likewise observed for 2O–F₂ and 2O–F₄ at approximately 240 and 200 K, respectively (Supplementary Fig. 39b–d), which may correspond to the increase in E_a in the electrical conductivity at low temperatures (Figs. 7, 8a, and Table 1). The signals of 2S–F₂ were negligible mainly due to the relatively poor electron spins in the nearly neutral state. These magnetic behaviors were also consistent with the decrease in the magnetic susceptibilities (χ) of the polycrystals of 2S–F₄ and 2O–F₄ around the temperatures using a superconducting quantum interface device (SQUID) magnetometer (Supplementary Note 11 and Supplementary Fig. 40). The χ values of 2S–F₄ and 2O–F₄ were quantified to be 1.2 × 10⁻⁴ and 2.6 × 10⁻⁴ emu mol⁻¹, respectively at 293 K. The χ values were relatively high compared to those of previously reported mixed-stack complexes^18,50,52, most of which are in nearly nonmagnetic states. These values are comparable to those of typical organic conductors², emphasizing the presence of abundant conductive electrons.

Surprisingly, in the case of 2S–F₄, another broad signal with a ΔB_pp value of ~3 G appeared at g ≈ 2.004 below 282 K (Supplementary Figs. 37–39), and overlapped with the narrow signal at g ≈ 2.003. This suggests the appearance of nearly non-correlated spins (e.g., spin solitons) originating from unpaired donors or acceptors during transient partial-π-dimerization between donor and acceptor. This observation suggests that the conductive mechanism of 2S–F₄ at the N–I boundary may involve spin solitons that exist because of topological excitations²⁹ that contribute to its high conductivity.

The abrupt change in the electrical, optical, dielectric, and magnetic properties of 2S–F₄ at high T_c (282 K) under ambient pressures (Fig. 8) may reflect structural perturbation, which can be characteristic of the mixed-stack complexes at the N–I boundary. The neutral^20,53 or highly ionic complexes⁵⁰ transitioned based on π-dimerization to form a structure with more strongly ionic behavior at lower T_c values of 49–81 K. The complexes around the N–I boundary (δ = 0.3–0.5) had relatively high T_c values of 115–220 K^20,52 under ambient pressures. Under high-pressure conditions (approximately 9 kbar), TTF–CA (δ ≈ 0.6) transiently exhibits excellent conductivity (7 S cm^–1) and a high T_c at approximately 270 K²⁹, whereas it has a low T_c of 81 K under ambient pressures (δ = 0.2, σ_rt = 10^–5 S cm^–1; v in Fig. 1b). The high T_c (282 K) and high σ_rt (0.1 S cm⁻¹) even at ambient pressures of 2S–F₄, for which δ is exactly at the N–I boundary (δ = 0.69(2)) with non-hysterical changes in their electronic functionalities such as electrical conductivity, reflectivity, dielectricity, and magnetism may involve the unique electronic perturbation at the N–I boundary between the electron-itinerant and localized states.

In conclusion, we developed highly conductive 1D mixed-stack complexes for which δ is close to the N–I boundary by combining a donor HOMO and acceptor LUMO that have similar energy levels and well-matched orbital symmetries. These complexes have highly hybridized orbitals between the donor and acceptor and exhibited high σ_rt (10⁻⁴ to 0.1 S cm⁻¹) under ambient conditions; the top σ_rt (0.1 S cm⁻¹) for 2S–F₄ at δ = 0.69(2) is the highest value reported to date for a single-crystal 1D mixed-stack complex. 2S–F₄ uniquely exhibited a non-hysterical change in its electrical conductivity at high T_c (282 K) under ambient pressure to a less conductive phase below this temperature. This behavior was simultaneously accompanied by abrupt changes in the low-energy EMV coupling-based reflectivity, dielectric constant, and magnetic properties, reminiscent of the π-dimerization fluctuation that spatiotemporally breaks the symmetry and may widen the band gap to form a band-insulating state and increase E_a. Furthermore, the appearance of a broad ESR signal suggests non-correlated spins of unpaired donors or acceptors, which may enhance the conductivity of 2S–F₄ through mechanisms such as topological excitation²⁹. In addition, mixed-stack complexes have unique advantages as conductor materials, such as high potential for solution processing and scalable synthesis without special equipment. The high conductivity, high solubility, and air stability of the conductors may provide scope for further investigation of the fundamental physical properties and applications using various external stimuli^29,50,53,54. The rich variations in the structure-determining factors in oligomer donors, e.g., monomer unit variations, oligomer length^55,56, sequences comprising multiple units⁵⁶, and end-capping structures could enable precise tuning of the electronic structures toward highly functional mixed-stack complexes.

Methods

Apparatus

Proton (¹H) and carbon (¹³C) nuclear magnetic resonance (NMR) spectra were obtained on a JEOL JNM-AL300 (¹H NMR: 300 MHz; ¹³C NMR: 75 MHz) spectrometer. ¹H NMR spectra in CDCl₃ were referenced internally to tetramethylsilane as a standard. ¹³C NMR spectra in CDCl₃ were referenced to the solvent resonance. High-resolution mass spectra (HRMS) were obtained on a JEOL JMS-AX500 with a field desorption (FD) probe in the positive mode using cholesterol as an internal standard. Single-crystal XRD measurements were performed using a Rigaku MercuryII CCD X-ray diffractometer (Mo K_α, λ = 0.71073 Å) and BL02B1 (λ = 0.30960 Å) at a synchrotron facility SPring-8 in Japan. A N₂-gas-blowing device was employed for the low-temperature measurements. Cyclic voltammetry was performed using an ALS 610DB electrochemical analyzer. Microscopic mid-infrared (mid-IR) and ultraviolet-visible (UV-vis) measurements were performed on a JASCO FT/IR-6100 and FT/IR-6200 and MSV-5200TSO, both of which are equipped with a JASCO IRT-5000 FT/IR microscope. Raman spectroscopy was performed on a RENISHAW inVia Reflex. Dielectric constant measurements were performed using a custom-built alternating-current (AC) impedance probe with a Solartron Impedance Analyzer SI 1260, a Dielectric Interface 1296, and a Quantum Design SQUID magnetometer (MPMS-XL) as the temperature controller. Resistivity measurements were performed on a Quantum Design Physical Properties Measurement System (PPMS) and HUSO HECS 994C with a high-resistance-low-current electrometer KEYTHLEY 6517B equipped with an ADVANTEST R6142 power supply, an ADVANTEST R7210 scanner, and a KEYTHELY 2001 digital multimeter. X-band continuous wave ESR measurements were performed using a Bruker EMXmicro and EMX spectrometers with a N₂ flow variable temperature unit ER4131VT and E500 spectrometer with a He flow cryostat ESR900. Static magnetic susceptibility measurements were performed using a MPMS-XL.

Synthesis

Synthesis of 5,5’-bis(methylthio)-2,2’-bi(3,4-ethylenedithiothiophene) 2S

General synthetic procedure and materials sources are shown in Supplementary Notes 1 and 2. To a solution of 2,2’-bi(3,4-ethylenedithiothiophene)³² 1 (200 mg, 0.576 mmol) in dichloromethane (20 mL) was dropwise added at 0 °C a solution of N-bromosuccinimide (NBS; 238 mg, 1.34 mmol) in dichloromethane (6 mL), and the reaction mixture was stirred for 6 h. After the addition of a saturated aqueous solution of sodium bicarbonate (100 mL), the mixture was extracted with dichloromethane (3 × 100 mL). The combined organic layer was dried over sodium sulfate and concentrated in vacuo to afford a crude material containing 2 (250 mg) which was used for the subsequent reaction without further purification. Thus, to a solution of the mixture (250 mg) in THF (12 mL) was added ⁿBuLi (1.6 M in hexane, 1.70 mL, 2.68 mmol) at −80 °C. The reaction mixture was stirred for 2 h and then allowed to warm to ambient temperature. To the mixture was dropwise added dimethyl disulfide (500 µL, 5.63 mmol), and the mixture was stirred at ambient temperature for 3 h. After the removal of volatile materials in vacuo and the subsequent addition of a saturated aqueous solution of sodium bicarbonate (100 mL), the mixture was extracted with dichloromethane (3 × 100 mL). The combined organic solvents were dried over sodium sulfate, concentrated in vacuo, and purified by GPC (eluent: chloroform) to afford 2S (131 mg, 0.298 mmol) as a yellowish white powder in 52% total yield for three-step transformations from 1. Physical data of 2S: ¹H NMR (CDCl₃, 300 MHz) δ 2.44 (s, 6H), 3.14–3.23 (m, 4H), 3.25–3.34 (m, 4H); ¹³C NMR (CDCl₃, 75 MHz) δ 20.1, 27.6, 27.7, 126.6, 126.6, 127.8, 130.5; MS (FD) calcd for C₁₄H₁₄S₈ [M^+•] 437.8834, found 437.8856. The structural integrity and purity were identified by the NMR spectra (Supplementary Figs. 41 and 42). Block-like orange single crystals were obtained by the liquid–liquid diffusion method with dichloromethane/hexane (1:1, v/v). The single-crystal XRD analyses revealed the structural details (Supplementary Table 1 and Supplementary Fig. 7), confirming a nearly planar structure. In contrast, other solvent combinations afforded crystal-like solids, while their XRD patterns were too complicated to be resolved, suggesting that neutral 2S is polymorphic and could have multiple structures, potentially influenced by molecular twisting.

Typical procedure of mixed-stack complexes

A donor (2O³⁰ or 2S, 10 µmol) was placed on one side of an H-shaped cell and an acceptor (F₄ or F₂, 10 µmol) was placed on the other side of the cell, respectively. To the cell were slowly added THF (8 mL for 2O–F₄ and 2O–F₂) or dichloromethane (8 mL for 2S–F₄ and 2S–F₂), and the mixture was kept at 25 °C in the dark. The slow evaporation of solvents from the mixture over more than three days gave dark green needle-like single crystals which were collected by paper filtration and washed with acetonitrile or 1:1 v/v dichloromethane/hexane (typical size of ~500 × ~40 × ~20 µm³). The single-crystal structures and chemical compositions were identified by single-crystal X-ray structural analyses (Supplementary Figs. 9–17 and Supplementary Table 2).

CV measurements

We performed CV in a degassed 0.6 mM solution of 2O³⁰ or 2S in dichloromethane containing 100 mM ⁿBu₄N•PF₆. We used a glassy carbon as the working electrode, a platinum wire as the counter electrode, and a silver–silver chloride electrode (Ag/AgCl in 1 M KCl) as the reference electrode (Supplementary Fig. 3).

Theoretical calculations

Energy levels and shapes of orbitals for donors and acceptors

The energy levels of orbitals for neutral donors (2O³⁰ and 2S), one-electron-oxidized donors (2O^•+ and 2S^•+), neutral acceptors (F₄ and F₂), and one-electron-reduced acceptors (F₄^•– and F₂^•–) were calculated. The calculations were performed using the optimized structures on the Gaussian09 program (Revision D.01, Gaussian, Inc., Wallingford CT, 2016. https://gaussian.com/) at the DFT level with the (unrestricted) B3LYP functional, the gradient correction of the exchange functional by Becke^57,58 and the correlation functional by Lee, Yang and Parr⁵⁹ and the 6–31G(d) split valence plus polarization basis set^60–62.

Band structure calculations

All the periodic DFT calculations were performed with the single-crystal structures of mixed-stack complexes as the average structures at 300 K. The calculations were performed by the OpenMX software^38,39, based on optimized localized basis functions and pseudopotentials. The basis functions used were H6.0-s2p1, C6.0-s2p2d1, O6.0-s2p2d1, S7.0-s2p2d1f1, N6.0-s2p2d1, and F6.0-s2p2d1 for hydrogen, carbon, oxygen, sulfur, nitrogen, and fluorine, respectively, wherein the abbreviation of basis functions such as C6.0-s2p2d1, C stands for the atomic symbol, 6.0 the cutoff radius (Bohr) in the generation by the confinement scheme, and s2p2d1 means the employment of two, two, and one optimized radial functions for the s-, p-, and d-orbitals, respectively. The radial functions were optimized by a variational optimization method^38,39. As valence electrons in the pseudopotentials (PPs), we included 1 s for hydrogen, 2 s and 2p for carbon, oxygen, nitrogen, and fluorine, and 3 s and 3p for sulfur, respectively. All the PPs and pseudo-atomic orbitals (PAOs) we used in the study were taken from the database (2019) in the OpenMX website (https://www.openmx-square.org/), which was benchmarked by the delta gauge method⁶³. Real-space grid techniques were used for the numerical integrations and the solution of the Poisson equation using FFT with the energy cutoff of 220 Ryd⁶⁴. We performed Brillouin-zone integrations on a 2 × 1 × 2 k-grid; the Fermi-Dirac distribution function at 300 K is employed as a smeared occupation function. We used a generalized gradient approximation (GGA) proposed by Perdew, Burke, and Ernzerhof to the exchange-correlation functional⁶⁵. The real parts of the HOCO and LUCO at the Γ point (0,0,0) were visualized by VESTA⁶⁶ (Fig. 4d and Supplementary Fig. 19).

Calculations of transfer integrals

The first-principles calculations were performed using the QE package^40,41 with the GGA as the exchange-correlation function⁶⁵ based on the single-crystal structure data of 2O–F₄, 2O–F₂, 2S–F₄, and 2S–F₂ at 300 K. In the calculations, SG15 Optimized Norm-Conserving Vanderbilt (ONCV) pseudopotentials⁶⁷ were used as the pseudopotentials, in which 428 bands corresponding to the electron numbers were considered. The cutoff kinetic energies for wave functions, charge densities, and the mesh of the wave numbers were set as 80, 320 Ry, and 5 × 3 × 3, respectively. After the calculations, the maximally localized Wannier functions (MLWFs) were obtained using RESPACK⁴², and four bands near the Fermi energy were selected to reproduce the MLWFs (Supplementary Figs. 21–26). Initial coordinates of the MLWFs were located at the center of gravity of crystallographically independent two donors and two acceptors in the unit cell, respectively. Supplementary Fig. 20 shows the energy bands near the Fermi energy obtained by QE^40,41 and the Wannier interpolation. Based on the MLWFs, transfer integrals (t in Supplementary Fig. 27) were calculated as summarized in Table 1 and Supplementary Table 3.

Calculations of Coulomb interactions

Effective direct Coulomb interactions for donors and acceptors (i.e., U_eff (D) and U_eff (A)) were calculated by RESPACK⁴², in which the Coulomb interaction was reduced due to screening effects from bands other than the target band. Using a constrained random phase approximation (cRPA) method, we obtained the screened Coulomb interactions by incorporating screening effects from non-target bands. Through previous reports of such applications to different organic material systems^46–48, we know that the effective model Hamiltonians derived by the cRPA method succeed in evaluating the stability of competing phases in electron-correlated systems. Thus, we estimated the Coulomb interactions by using the cRPA method. The energy cutoff for the dielectric function was set as 5.0 Ry. Static screened direct integrals were calculated as the matrix element of the shielded Coulomb interaction between the Wannier functions on the donors and acceptors, respectively (Supplementary Figs. 21–26)⁴². The values at 0 Å were used as the U_eff (D) and U_eff (A) (Table 1 and Supplementary Figs. 28–33).

Optical reflection spectroscopy measurements

Steady-state polarized reflectivity spectra of mixed-stack complexes (2O–F₄, 2O–F₂, 2S–F₄, and 2O–F₂) in the mid-IR region (0.12–0.97 eV) and UV-vis-near IR region (0.46–1.35 eV) were performed using mid-IR and UV-vis spectrometers equipped with a polarizer by applying an electric field (E) along the π-stacking directions (i.e., the a-axis) and perpendicular to the directions (Figs. 6, 8b, Supplementary Figs. 34, and 35a, b). Raman spectroscopy of 2S–F₄ was performed using an excitation wavelength of 532 nm (Supplementary Fig. 35d).

Dielectric constant measurements

AC impedance spectroscopy measurements to determine dielectric constant were carried out by the quasi-four-probe method in the frequency range of 1.0 MHz for 160–312 K. A direction parallel to the long axis direction of the crystal shape, corresponding to the π-stacking, was chosen for the AC impedance measurements. Electrodes were made on the two opposite sides of the samples using silver paste and gold wires (15 μm diameter).

Electrical resistivity measurements

Electrical resistivity (ρ) measurements of the single-crystal mixed-stack complexes were performed by the conventional a four-probe method along the long-axis direction of the crystal shape, corresponding to the π-stacking direction. Samples were prepared by attaching gold wires (15 µm diameter) of a single crystal with a conductive carbon paste. The ρ and conductivity (σ) values were derived from the following equation: ρ = σ^–1 = R × S / L (S: cross-section, L: length). The typical size of samples was ~500 × ~40 × ~20 µm³.

ESR measurements

The X-band (∼9.4 GHz) continuous wave ESR experiments were performed on single-crystal 2O–F₄, 2O–F₂, 2S–F₄, and 2S–F₂ (Fig. 8d, e and Supplementary Figs. 37–39). The ESR signals were measured by setting the long axis of the crystal (i.e., the stacking a-axis) along the direction parallel to the magnetic field (i.e., φ ~ 0° or 180°). The typical size of samples: ~500 × ~40 × ~20 µm³.

SQUID measurements

The static magnetic susceptibility of polycrystals 2O–F₄ and 2S–F₄ was measured upon cooling from 300 or 320 K to 2 K by <1 K min^–1 applying the static magnetic field of 10,000 O_e (Supplementary Fig. 40). The absence of ferromagnetic impurity in the synthesized samples was confirmed from the obtained M–H curve at 2 K around −55,000 to 55,000 O_e, which follows a typical Brillouin function. The obtained magnetic susceptibilities (χ_exp) were plotted after subtracting the contribution of the Curie impurity for S = 1/2 (χ_cw; 0.3% for 2O–F₄ and 0.2% for 2S–F₄) and the contribution from core diamagnetism of 2O–F₄ and 2S–F₄ (–3.14 × 10^–4 and –3.74 × 10^–4 emu mol^–1, respectively) estimated from Pascal’s law⁶⁸.

Author contributions

T.F. conceived the project and H.M. directed it. T.F., R.K., K.O., and K.M. performed the synthesis procedures. T.F. and S.D performed electrical conductivity and dielectric constant measurements. T.F., T.M., Z.G., and H.O. performed the optical measurements. T.F., K.O., and T.N. performed magnetic measurements. T.F. and K.Yoshimi performed the theoretical calculations for the band structures and U_eff. T.F. and H.Sato. performed in-house single-crystal XRD analyses; S.K., T.A., H.Sawa, and Y.N. performed the synchrotron single-crystal XRD analyses. K.Yamamoto., A.T., and T.F. performed simulation for EMV coupling. T.F. wrote the manuscript, and all authors discussed the results and commented on the manuscript.

Peer review

Peer review information

Nature Communications thanks the anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

The crystallographic data (CIF files) for the structures reported in this Article have been deposited with the Cambridge Crystallographic Data Centre (CCDC), under deposition numbers 2264341 (2S), 2264342 (2S•BF₄), 2264325 (2O–F₄), 2264326 (2O–F₂), 2264327 (2S–F₄), and 2264331 (2S–F₂). These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing data_request@ccdc.cam.ac.uk, or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033. All experimental data within the article and its Supplementary Information are available from the corresponding authors upon request.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-024-47298-1.