Krešimir Molčanov
email: kmolcano@irb.hr

Christian Jelsch
email: christian.jelsch@univ-lorraine.fr

Bruno Landeros-Rivera

Jesús Hernández-Trujillo

Emmanuel Wenger

Vladimir Stilinović

Biserka Kojić-Prodić

Eduardo C Escudero-Adán

Partially Covalent Two-Electron/Multicentric Bonding between Semiquinone Radicals

Keywords: semiquinone, charge density, crystallography, pancake bonding, cycle stacking, DFT calculations

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INTRODUCTION

Quinones and semiquinone radicals are well-known electron carriers because they easily undergo reversible oxidation-reduction reactions. Highly pronounced electron dynamics of such systems enable a wide range of redox reactions and charge transfers at close and long distances; many of them have been used by Nature in crucial life processes. For instance, new evidence of enzymes using quinones as prosthetic groups or substrates and understanding of their mechanisms will demonstrate how simple quinone molecule can exhibit very complex chemical reactions responsible for respiration, photosynthesis, and many protective mechanisms against radicals.

Coenzyme Q, the ubiquinone, is present in animals, plants, and microorganisms and is involved in electron transfer photosynthesis, oxidative phosphorylation, the bioactivity of vitamin K, and many others. [START_REF] Sies | Methods in Enzymology: Quinones and Quinone Enzymes[END_REF][START_REF] Price | Quinones: Occurence, medicinal uses and physiological importance[END_REF] Studies of mechanism for extracting photosynthetic electrons (photo system II) using exogenous quinones to produce an amenable electric current can be a bio-inspired model for green-energy production. This type of research has been put forward by using X-ray free electron laser (XFEL) revealing dynamics of photo system II macromolecular complex. [START_REF] Chapman | Femtosecond X-ray protein nanocrystallography[END_REF] Many cellular oxidoreductases participate in metabolism of quinone compounds catalysing one or two-electron reduction, such as in cytochrome P450 reductase. The two-electron reduction of quinones is an important protective mechanism against radicals in mammals. [4] In living cells quinones play crucial roles as redox mediators and to discuss their activities [START_REF] Bottow | Formation and Biological Targets of Quinones: Cytotoxic versus Cytoprotective Effects[END_REF][START_REF] Dias | Quinone-based fluorophores for imaging biological processes[END_REF] would be out of the topic of this work.

The standard redox potentials of (semi)quinone system are influenced by substituents on the (semi)quinoid ring due to an induction effect. Electronegative substituents (such as halogens, nitrile and nitro groups) raise the oxidation potential, while electron-donating ones (such as hydroxyl or methyl) lower it. Therefore, quinones with four electronegative substituents are easily reduced and form stable radicals. These unique electron characteristics of quinones are of great importance for chemical synthesis, [7,[START_REF] Ramnial | Isolation of the Latent Precursor Complex in Electron-Transfer Dynamics. Intermolecular Association and Self-Exchange with Acceptor Anion Radicals[END_REF] materials design, [START_REF] Alemany | Exploring the Electronic Structure of an Organic Semiconductor Based on a Compactly Fused Electron Donor-Acceptor Molecule[END_REF][START_REF] Yu | The first semiquinonebridged bisdithiazolyl radical conductor: a canted antiferromagnet displaying a spin-flop transition[END_REF][START_REF] Yu | Semiquinone-Bridged Bisdithiazolyl Radicals as Neutral Radical Conductors[END_REF][START_REF] Horiuchi | Hydrogen-bonded donor-acceptor compounds for organic ferroelectric materials[END_REF][START_REF] Giovannetti | Multiferroicity in TTF-CA Organic Molecular Crystals Predicted through Ab Initio Calculations[END_REF] including organic batteries, [START_REF] Ding | A Bio-Inspired, Heavy-Metal-Free, Dual-Electrolyte Liquid Battery towards Sustainable Energy Storage[END_REF][START_REF] Kim | Design Strategies for Promising Organic Positive Electrodes in Lithium-Ion Batteries: Quinones and Carbon Materials[END_REF] and in essential life processes. [START_REF] Guo | Electron Spin Resonance Investigation of Semiquinone Radicals Formed from the Reaction of Ubiquinone 0 with Human Oxyhemoglobin[END_REF][START_REF] Reece | Proton-Coupled Electron Transfer in Biology: Results from Synergistic Studies in Natural and Model Systems[END_REF][START_REF] Kopka | Electron transfer pathways in a light, oxygen, voltage (LOV) protein devoid of the photoactive cysteine[END_REF][START_REF] Postila | Atomistic determinants of co-enzyme Q reduction at the Qi-site of the cytochrome bc1 complex[END_REF] The electronic structure of the semiquinone ring has been extensively studied by quantum chemical computations, [START_REF] Boesch | π-Donor Substituent Effects on Calculated Structures and Vibrational Frequencies of p-Benzoquinone, p-Fluoranil, and p-Chloranil[END_REF][START_REF] Katan | First-principles molecular-dynamics simulations for neutral p-chloranil and its radical anion[END_REF][START_REF] Boesch | π-Donor Substituent Effects on Calculated Structures, Spin Properties, and Vibrations of Radical Anions of p-Chloranil, p-Fluoranil, and p-Benzoquinone[END_REF][START_REF] O'malley | Electronic Structure Studies of Quinones and Semiquinones: Accurate Calculation of Spin Densities and Electron Paramagnetic Resonance Parameters[END_REF] however, the results are somewhat ambiguous and depend very much on the method and basis set used. DFT calculations are able to reproduce geometry quite reasonably, [START_REF] Molčanov | Stabilisation of tetrabromo-and tetrachlorosemiquinone (bromanil and chloranil) anion radicals in crystals[END_REF] but the delocalization of the π-electron cloud still remains an issue. According to geometry and DFT-calculated harmonic oscillator model of aromaticity (HOMA) [START_REF] Akruszewski | Definition of aromaticity basing on the harmonic oscillator model[END_REF] and nucleusindependent chemical shifts (NICS) [START_REF] Schleyer | Nucleus-Independent Chemical Shifts: A Simple and Efficient Aromaticity Probe[END_REF] indices, the semiquinone ring behaves between an aromatic and a quinoid ring. [START_REF] Molčanov | Stabilisation of tetrabromo-and tetrachlorosemiquinone (bromanil and chloranil) anion radicals in crystals[END_REF] The three most common planar, conjugated rings are shown in Scheme 1: the quinoid ring (1) has distinguishable single and double bonds, while the aromatic ring of the hydroquinone (3) has a fully delocalized π-electron system. Semiquinone (2), which appears as an intermediate during reduction of the quinone and oxidation of the hydroquinone, is expected to be approximately half-way between these two. The unpaired electron and the single negative charge are delocalized throughout the ring. However, delocalization of π-electrons, bond orders, local atomic charges and local dipoles still remain open questions.

Perhalogenated and cyano-substituted semiquinone crystals are easily obtained and are often stable in air and at room temperature, [START_REF] Molčanov | Fine tuning of π-stack separation distances of semiquinone radicals affects their magnetic and electric properties[END_REF][START_REF] Molčanov | Spincoupling in dimer of 2,3-dicyano-5,6-dichlorosemiquinone radical anions characterised by ring separation distance of 2.81 Å[END_REF][START_REF] Molčanov | Spin pairing, electrostatic and dipolar interactions shape stacking of radical anions in alkali salts of 4,5-dichloro-3,6-dioxocyclohexa-1,4-diene-1,2dicarbonitrile (DDQ)[END_REF] and they are extensively used in the design and synthesis of organic molecular magnets and (semi)conductors. [START_REF] Horiuchi | Hydrogen-bonded donor-acceptor compounds for organic ferroelectric materials[END_REF][START_REF] Molčanov | Fine tuning of π-stack separation distances of semiquinone radicals affects their magnetic and electric properties[END_REF] It is possible to tune their magnetic properties and conductivity by crystal engineering. [START_REF] Molčanov | Fine tuning of π-stack separation distances of semiquinone radicals affects their magnetic and electric properties[END_REF] In these systems, the crucial component is the conjugated π-electron system; interactions between π-systems of the radicals play the key role in determining magnetic and electrical properties. [START_REF] Molčanov | Spincoupling in dimer of 2,3-dicyano-5,6-dichlorosemiquinone radical anions characterised by ring separation distance of 2.81 Å[END_REF][START_REF] Molčanov | Temperature induced magnetic bistability in a crystal of tetrachlorosemiquinone anion radical[END_REF][31][START_REF] Podzorov | Buliding molecules for a function[END_REF][START_REF] Hicks | Switchable materials: A new spin on bistability[END_REF][START_REF] Lü | Stable (Long-Bonded) Dimers via the Quantitative Self-Association of Different Cationic, Anionic, and Uncharged π-Radicals: Structures, Energetics, and Optical Transitions[END_REF][START_REF] Devic | The Maximin Principle of π-Radical Packings[END_REF][START_REF] Rosokha | Continuum of Outer-and Inner-Sphere Mechanisms for Organic Electron Transfer. Steric Modulation of the Precursor Complex in Paramagnetic (Ion-Radical) Self-Exchanges[END_REF][START_REF] Rosokha | Counter-ion modulation of longdistance π-bonding of the open-shell p-benzoquinone anions[END_REF] Two types of stacks of semiquinone radicals have been described: [START_REF] Molčanov | Fine tuning of π-stack separation distances of semiquinone radicals affects their magnetic and electric properties[END_REF] (1) stacks with alternating short (< 3.3 Å) and long (> 3.5 Å) inter-planar separations comprising dimers with diamagnetically coupled spins and (2) stacks of equidistant radicals with antiferromagnetic coupling (Figure 1). Attempts to modulate πinteractions of the radicals by crystal engineering are, however, very recent [START_REF] Molčanov | Fine tuning of π-stack separation distances of semiquinone radicals affects their magnetic and electric properties[END_REF][START_REF] Molčanov | Spincoupling in dimer of 2,3-dicyano-5,6-dichlorosemiquinone radical anions characterised by ring separation distance of 2.81 Å[END_REF][START_REF] Molčanov | Spin pairing, electrostatic and dipolar interactions shape stacking of radical anions in alkali salts of 4,5-dichloro-3,6-dioxocyclohexa-1,4-diene-1,2dicarbonitrile (DDQ)[END_REF][START_REF] Molčanov | Temperature induced magnetic bistability in a crystal of tetrachlorosemiquinone anion radical[END_REF] and little is known about the interactions between the stacked radical rings. Therefore, we focused on characteristics of electronic structure of semiquinone systems using experimental and theoretical methods. Figure 1 Two types of semiquinone radical π-stacks: [START_REF] Molčanov | Fine tuning of π-stack separation distances of semiquinone radicals affects their magnetic and electric properties[END_REF]

RESULTS AND DISCUSSION

To gain more insight into the electronic structure of the semiquinoid ring and the subtle intermolecular interactions governing magnetic properties of their crystals, we studied Nmethylpyridinium salts of tetrachlorosemiquinone anion radical (2ꞏN-MePy), previously prepared and characterised by us [START_REF] Molčanov | Fine tuning of π-stack separation distances of semiquinone radicals affects their magnetic and electric properties[END_REF] , by a combination of X-ray charge density and quantum chemical calculations. This compound is a suitable research object due to its stability in air at room temperature and because it grows into well-developed single crystals; it also lacks very heavy atoms, which would cause high X-ray absorption. Moreover, two polymorphs of 2ꞏN-MePy are known, one diamagnetic triclinic crystal with radical dimers and an antiferromagnetic one with equidistantly stacked radicals (Figure 1), making 2ꞏN-MePy an ideal system for study of stacking interactions between semiquinones. To determine the character of the electronic structure of semiquinone ring and its impact on stacking interactions, we supply X-ray charge density data of two closely related compounds, tetrachloroquinone (1) and aromatic tetrachlorohydroquinone (3).

Bond orders and interaction energies of stacking were also estimated by DFT calculations and discussed in view of experimental findings.

Electron delocalization in the semiquinone ring

Several descriptors of electron delocalization were used to quantify electron sharing and aromaticity of the semiquinone ring and to get insight into its stacking interactions. Bond orders are calculated using the three methods shown in Table 1. The topological bond orders (ntopo), as defined by Howard et al. [START_REF] Howard | Description of covalent bond orders using the charge density topology[END_REF] extracted from X-ray electron density of compounds 1-3 are in good agreement with those from quantum chemical Delocalization Indexes (DI) defined in the quantum theory of atoms in molecules (QTAIM) and Wiberg bond orders from NBO analysis. [START_REF] Bader | Spatial localization of the electronic pair and number distributions in molecules[END_REF][START_REF] Wiberg | Application of the pople-santry-segal CNDO method to the cyclopropylcarbinyl and cyclobutyl cation and to bicyclobutane[END_REF][START_REF] Foster | Natural hybrid orbitals[END_REF] Tetrachloroquinone 1 has a typical quinoid structure with very little π-electron delocalization: formally single C-C bonds have ntopo values of 0.94 and 1.00, while the formally double ones have bond orders of 1.78. Carbonyl C=O bonds have a surprisingly low ntopo of 1.35, but the maximum electron density at the critical point is 2.862 e Å -3 , which is consistent with a double bond (also the bond length is 1.2125(8) Å). In addition, delocalization indices obtained from quantum calculations also yielded similar bond orders (1.37 -1.38) for the carbonyl bond. Therefore, we conclude that this is not a result of poor parametrization or inaccurate experimental data, but a property of quinoid systems. Also, a recent X-ray charge density study of dichloroquinone [42a] , our study of partially charged semiquinones [42b] and 2,5-dihydroxyquinones [42c,d] yielded similar values. Tetrachlorohydroquinone 3 is an aromatic compound with C-C bond lengths nearly equal, and nearly pure single C-O bonds (Table 1).

In tetrachlorosemiquinone 2 there are neither single nor double C-C bonds; those that correspond to double bonds in the quinone have an ntopo of 1.45 -1.50, while those that correspond to single bonds in the quinone are weaker (ntopo of 1.07 -1.16). Two symmetry-equivalent C-O bonds have ntopo of approximately 1.5, which is higher than in compound 1; however, the electron density at the critical point is somewhat lower, ca. 2.7 e Å -3 , which is consistent with longer bond lengths of about 1.25 Å (Tables S3 andS4). Delocalization index of these C-O bonds is 1.26, which lies between values for 1 and 3 (Table 1), as expected. The same trend is observed for the NBO bond orders. Such results indicate a partial delocalization of π-electrons, which is enhanced compared to the quinone 1, but still far from a full delocalization as in the hydroquinone 3.

Electrostatic potential in the three compounds (Fig. 2) reveals pronounced differences: while in the hydroquinone 3, electrostatic potential around the carbon skeleton is quite uniform, in the quinone 1, the carbonyl C atoms are strongly electron-depleted (Fig. 2a). The same effect can be noticed in atomic charges (Tables S8-S11 in the Supporting Information). Electronic structure of semiquinone ring 2 lies between the two other compounds, however, the carbonyl C atom is still the most electron-depleted part of the molecule. The charge of the oxygen atom also shows an obvious trend: it takes the most negative value in quinone 1 while in the hydroquinone 3, the OH group actually has a total charge of -0.068 e (Tables S8 andS9 in the Supporting Information).

Again, the charge of the oxygen atom in the semiquinone 2 is between the values for two other compounds. The lower charge of the oxygen atom in the radical anion 2 seems at first counterintuitive. However, we note that the negative charge in 2 is delocalized through the entire ring (Tables S10 andS11 in the Supporting Information, Fig. 2), contributing to the stability of the radical anion. The carbonyl carbon is much less electron-depleted in 2 than in the quinone 1 (Tables S8, S10 and S11 in the Supporting Information). On the other hand, the charges of the chlorine atoms in the radical anion 2 are much more negative than in the aromatic hydroquinone and in the quinone, with negative charges increased by more than 0.1 e (Tables S10 andS11 in the Supporting Information). This is an illustrative example of the inductive effect of the electronegative chlorine substituents. Therefore, we can conclude that the electron delocalization extends beyond the carbon skeleton into the C-O bonds, and even to the substituents on the ring.

Bond orders for the C-H and C-Cl bonds keep nearly constant values in all crystallographic

systems, indicative that these bonds are not strongly affected by electron delocalization. We propose a set of aromaticity indices that share a common mathematical structure whose values depend on the used bond order definition. This model, called the 𝛽 index, is calculated as in equation (1).

𝛽 1 √6 𝛸 𝛸 1
Χ is the bond order value of the 𝑖 pair of atoms connected in the molecular ring of the studied system and Χ is the C-C bond order of benzene computed for both given models (DI and NBO), using the same level of theory. The sum runs up to six because all molecules are six-membered rings and the normalization factor √ is used to resemble a standard deviation. The 𝛽 index is defined in a similar way as previously used in term of the electron DI only [START_REF] Lü | Stable (Long-Bonded) Dimers via the Quantitative Self-Association of Different Cationic, Anionic, and Uncharged π-Radicals: Structures, Energetics, and Optical Transitions[END_REF] and measures the amount of electron delocalization with respect to benzene (purely aromatic) in terms of the variations found for bond orders. Values of the 𝛽 indices calculated with B3LYP are shown in Table 2.

The highest values of 𝛽 are found for the neutral quinone 1, which agrees with the alternation of single and double bonds of quinoid rings reported previously. The hydroquinone 3 has low 𝛽 values, which indicates its aromatic character. The semiquinone radicals in both polymorphs of 2 have intermediate values of 𝛽 between those of 1 and 3, which means that the semiquinone radical anion has partially delocalized π-electron system. These results are in agreement with our previous calculations of NICS and HOMA indices of tetrachloro-and tetrabromosemiquinone radical anions, which are also between aromatic and quinoid. [START_REF] Molčanov | Stabilisation of tetrabromo-and tetrachlorosemiquinone (bromanil and chloranil) anion radicals in crystals[END_REF] Electronic structure of N-MePy cation fulfils the Hückel rule and therefore is expected to be aromatic, which is confirmed by the low values of 𝛽 .

Stacking interaction exhibiting a partially covalent bonding (pancake bonding) in diamagnetic dimers of semiquinone rings

We have already noticed that, in diamagnetic structures, the semiquinone anion has a slightly bent, boat-like conformation with Cremer-Pople [START_REF] Cremer | General definition of ring puckering coordinates[END_REF] puckering parameter τ of 2.0 -4.3°. [START_REF] Molčanov | Stabilisation of tetrabromo-and tetrachlorosemiquinone (bromanil and chloranil) anion radicals in crystals[END_REF][START_REF] Molčanov | Spincoupling in dimer of 2,3-dicyano-5,6-dichlorosemiquinone radical anions characterised by ring separation distance of 2.81 Å[END_REF][START_REF] Molčanov | Spin pairing, electrostatic and dipolar interactions shape stacking of radical anions in alkali salts of 4,5-dichloro-3,6-dioxocyclohexa-1,4-diene-1,2dicarbonitrile (DDQ)[END_REF] The anions in the dimer are actually bent towards each other, to minimize distance between the carbon atoms of the ring skeletons (Fig. 3), indicating very strong interactions within a dimer. Such a concave shape has been observed in dimers for a number of other organic radicals. [START_REF] Cui | Double pancake bonds[END_REF][START_REF] Mou | Evidence of σ-and π-Dimerization in a Series of Phenalenyls[END_REF][START_REF] Mou | Pancake Bond Orders of a Series of π-Stacked Triangulene Radicals[END_REF][START_REF] Cui | Concave or convex π-dimers: the role of the pancake bond in substituted phenalenyl radical dimers[END_REF] In the antiferromagnetic structures, [START_REF] Molčanov | Spin pairing, electrostatic and dipolar interactions shape stacking of radical anions in alkali salts of 4,5-dichloro-3,6-dioxocyclohexa-1,4-diene-1,2dicarbonitrile (DDQ)[END_REF][START_REF] Molčanov | Temperature induced magnetic bistability in a crystal of tetrachlorosemiquinone anion radical[END_REF] the radicals are essentially planar within the experimental error, or with minor chair-like distortion (τ < 1.5 °). Topological analysis of electron density of triclinic 2ꞏN-MePy revealed a profound difference between short intra-dimer and long inter-dimer contacts (Table 3). In the short intra-dimer contact, there are six bond paths and (3,-1) saddle critical points between the rings: two C

•••C [C3•••C5 i and C5•••C3 i ; symmetry operator i) 1-x, 2-y, 1-z], two C•••O (C1•••O2 i and O2•••C1 i ) and two Cl•••Cl (Cl2•••Cl3 i and Cl3•••Cl2 i ),
with maximum electron density exceeding 0.095 e Å -3 (Table S14 in the Supporting Information, Fig. 4). In addition, there are five (3,+1) and two (3,+3) critical points (Table S14 in the Supporting Information, Fig. 4), indicating that the short contacts between two radicals close a space in a form of a cage. Since spin coupling involves some orbital mixing, this type of contact has a partial covalent character and may be regarded as a two-electron multi-centre (2e/mc) bond. [START_REF] Cui | Double pancake bonds[END_REF][START_REF] Beneberu | Bonds or not bonds? Pancake bonding in 1,2,3,5dithiadiazolyl and 1,2,3,5-diselenadiazolyl radical dimers and their derivatives[END_REF][START_REF] Preuss | Pancake bonds: π-Stacked dimers of organic and light-atom radicals[END_REF] For this type of interaction, a colourful term has been proposed, pancake bonding. [START_REF] Cui | Double pancake bonds[END_REF][START_REF] Beneberu | Bonds or not bonds? Pancake bonding in 1,2,3,5dithiadiazolyl and 1,2,3,5-diselenadiazolyl radical dimers and their derivatives[END_REF][START_REF] Preuss | Pancake bonds: π-Stacked dimers of organic and light-atom radicals[END_REF] Between the dimers, there are only four (3,-1) (corresponding to C•••Cl contacts) and three (3,+1) critical points; the maximum cp electron density does not exceed 0.045 e Å -3 (Table S14 in the Supporting Information, Fig. 4). The inter-dimer interactions are therefore similar to ubiquitous stacking of aromatic rings. a Cg = centre of gravity of the ring; b α = angle between planes of two contiguous rings; c β = angle between CgꞏꞏꞏCg line and normal to the plane of the first ring; d δ = angle between O=CꞏꞏꞏC=O axes of contiguous rings, as defined in ref. 29; e ε = angle between direction of the offset and O=CꞏꞏꞏC=O axis, as defined in ref. 29. Further insights into the nature of the 2e/mc bonding within the triclinic 2ꞏN-MePy crystal are provided by quantum chemical calculations. The di-radical feature of this system can be observed in the spin density iso-surfaces (Figure 5) where it is noticed that α and β spin populations are different for each semiquinone moiety. The two degenerate HOMOs and LUMOs of the dimer (Figures 6a and7a), obtained from the Kohn-Sham orbitals, show strong characteristics of a 2e/mc bonding. [START_REF] Cui | Double pancake bonds[END_REF] In order to quantify the degree of electrons shared in the 2e/mc bond, two intermolecular bond orders (𝐼𝐵𝑂 and 𝐼𝐵𝑂′, respectively) were proposed. The former considers all the atoms of the semiquinone molecule and the latter only the carbon skeleton. Further details are described in the section Details and protocols of theoretical calculations. From the 𝐼𝐵𝑂 and 𝐼𝐵𝑂′ values (Table 4) it can be concluded that only the intra-dimer contact exhibits properties distinctive of a 2e/mc bond, i.e., interplanar distances shorter than 3.4 Å and a non-negligible intermolecular electron delocalization. It is also inferred from the comparison of 𝐼𝐵𝑂 and 𝐼𝐵𝑂′ that pancake bonding cannot be attributed only to carbon-carbon interactions since the contribution of the rest of the atoms is also relevant. Electrostatic potential (Fig. 8a) shows a good matching between electron-rich and electron-poor areas of two radicals in the intra dimer: the closest contacts (2.86 Å) are between the electron-rich oxygen and the electron-depleted carbonyl C atoms. Therefore, we can conclude that the "longitudinal" offset [START_REF] Rosokha | Counter-ion modulation of longdistance π-bonding of the open-shell p-benzoquinone anions[END_REF] of 2.06 Å which is commonly observed in stacked semiquinones, [START_REF] Molčanov | Stabilisation of tetrabromo-and tetrachlorosemiquinone (bromanil and chloranil) anion radicals in crystals[END_REF][START_REF] Molčanov | Spincoupling in dimer of 2,3-dicyano-5,6-dichlorosemiquinone radical anions characterised by ring separation distance of 2.81 Å[END_REF][START_REF] Molčanov | Temperature induced magnetic bistability in a crystal of tetrachlorosemiquinone anion radical[END_REF][START_REF] Lü | Stable (Long-Bonded) Dimers via the Quantitative Self-Association of Different Cationic, Anionic, and Uncharged π-Radicals: Structures, Energetics, and Optical Transitions[END_REF][START_REF] Rosokha | Continuum of Outer-and Inner-Sphere Mechanisms for Organic Electron Transfer. Steric Modulation of the Precursor Complex in Paramagnetic (Ion-Radical) Self-Exchanges[END_REF][START_REF] Rosokha | Counter-ion modulation of longdistance π-bonding of the open-shell p-benzoquinone anions[END_REF] occurs because of electrostatic reasons (minimization of repulsion between the two charged anions), rather than steric ones. The short distance between the radicals is due to covalent 2e/mc bonding. However, electron-rich and electron-poor areas of contiguous rings do not match in the long-distance contact between the dimers (Fig. 8b). We can conclude that the long distance and "lateral" offset [START_REF] Rosokha | Counter-ion modulation of longdistance π-bonding of the open-shell p-benzoquinone anions[END_REF] are there to minimize both, electrostatic and steric repulsion.

To quantify the effects of the geometrical arrays discussed above, the electrostatic interaction energy was calculated using the experimental electron density, along with an estimation based on the theoretical values of the PIXEL method, [START_REF] Gavezzotti | Non-conventional bonding between organic molecules. The 'halogen bond' in crystalline systems[END_REF] providing other intermolecular contributions including the polarization energy (Table 5). DFT calculated dimerization energies (DEs) support the PIXEL analysis. The electrostatic energies obtained from the experimental and theoretical sources differ from each other in part because in the former the fragment electron densities are perturbed by the rest of the system. Therefore, a fair comparison of the experimental values should be carried out with the sum of the theoretical electrostatic plus the polarization PIXEL energies.

Such a comparison has been performed theoretically for highly polarized benzene-cation complexes [START_REF] Rocha-Rinza | The nature of benzene-cation interactions from the topology of the electron distribution[END_REF] and it is supported by the data in Table 5. Even though the semiquinone radicals are closer in the intra-dimer contact and exchange repulsion is larger due to their proximity, the PIXEL electrostatic repulsion is 4 kcal mol -1 higher for the inter-dimer contact, which may be partially explained by the differences in the electrostatic potential complementarity discussed above. Moreover, the former array has stronger polarization and dispersion components which are of an attractive nature. Accordingly, the experimental electrostatic energy is 16 kcal mol -1 larger for the latter. Nevertheless, as mentioned before, the net interaction in both dimers is repulsive because of the predominance of electrostatic forces between charged moieties. In the actual crystal, the large Madelung energy keeps the radicals together.

To understand the stability of the triclinic 2ꞏN-MePy system, it has to be considered that these repulsions are balanced by the attractions with neighbouring cations. The total interaction energies for tetramers comprising a pair of stacked semiquinones and a pair of adjacent cations are decidedly attractive (Etot < -150 kcal mol -1 , see Supplement for details). These results are consistent with the lattice energy computed with PIXEL for this system, which is -70.4 kcal mol -1 (Table S30 in the Supplement). More than 50% of the attractive contributions to the lattice energy are of electrostatic nature, in contrast with the crystals of 1 and 3, where dispersion is the driving stabilizing component (See Figure S28 in the Supplement). The strong negative electrostatic lattice energy computed from the experimental electron density corroborates this conclusion (Table 5).

In addition, a pancake bonding contribution to the interaction energy can be approximated as the SOMO-SOMO interaction (𝐸 ), which is a consequence of SOMO-SOMO overlap. [START_REF] Cui | Double pancake bonds[END_REF][START_REF] Mota | Study of the Diradicaloid Character in a Prototypical Pancake-Bonded Dimer: The Stacked Tetracyanoethylene (TCNE) Anion Dimer and the Neutral K2TCNE2 Complex[END_REF] This component is evaluated to be 𝐸 𝐸 𝐸 , where 𝐸 and 𝐸 stand for the dimerization energies calculated with low and high spin, respectively, which correspond to singlet and triplet states. This contributes with -9.4 kcal mol -1 to the intra-dimer stabilization.

Interestingly, if this value is added to the PIXEL dimerization energy, the outcome is closer to the DFT interaction energy (-46.2 and -45.1 kcal mol -1 , correspondingly). These results suggest that the interaction energies for the stacked semiquinone radicals can be approximated as 𝐸 𝐸 𝐸 𝐸 𝐸 𝐸 . a Difficult to compute, due to a half of an anion and a half of a cation in asymmetric unit.

Interactions between semiquinone rings in antiferromagnetic stacks of equidistant radicals

Geometry of the stacking interactions in the orthorhombic 2ꞏN-MePy (Table 3) shows larger inter-planar distance than the intra-dimer contact in the triclinic polymorph, but nearly identical "longitudinal" offset (2.057 Å). Electrostatic potential between two rings in the orthorhombic polymorph (Fig. 9) is also similar. The DFT DE and experimental electrostatic energies calculated for these systems are very similar to those of the intra-dimer contact of the triclinic crystal, although the PIXEL electrostatic contribution is smaller in the latter. (Table 5). However, there is considerably less electron density at the CPs between the rings than in the triclinic intra-dimer contact (Fig. 10 and Table S15 in the Supporting Information), and the maximum electron density does not exceed 0.048 e Å -3 . Consequently, Pauli (steric) repulsion is likewise reduced. Also, there are five symmetry-independent (3,-1) critical points (two CꞏꞏꞏC, two CꞏꞏꞏO and one CꞏꞏꞏCl) and eight (3,+1) critical points between two rings. A (3,+3) local minimum is also present. This indicates that interactions between radicals in the antiferromagnetic stacks are considerably weaker than in diamagnetic dimer, in agreement with a less covalent 2e/mc bonding, as can be seen in the HOMOs and LUMOS (Figures 6b and7b) and from the lower 𝐼𝐵𝑂 and 𝐼𝐵𝑂′ values (Table 4).

Accordingly, a smaller value of 𝐸 is obtained, i.e. -2.9 kcal mol -1 . However, the interactions are also much stronger than those between two diamagnetic dimers (along with a higher electron density), which explains the semiconductive properties of the antiferromagnetic crystals. [START_REF] Molčanov | Fine tuning of π-stack separation distances of semiquinone radicals affects their magnetic and electric properties[END_REF] As in the case of the model tetramers of the triclinic crystal, the interaction energies of some relevant tetramers for these systems (Etot < -150 kcal mol -1 , see Supplement for details) and the electrostatic lattice energies computed with the experimental electron density also yield favourable interactions. In the diamagnetic dimers, the inter-planar distance is the shortest due to the covalent 2e/mc bonding; apparently the interaction is significant enough to deform the molecule (Fig. 3). The C-Cl bonds are bent outward in the dimer resulting in more distant chlorine atoms (angles between C6 plane and C-Cl bonds are between 173.87 and 176.14°). The two C=O bonds are less offplane with (C6plane, C=O) = 177.9 and 179.6°. The stack of equidistant radicals has a minor intermolecular covalent component, so the inter-planar separations are larger.

Conductivity of the radical stacks therefore also depends on spin coupling, since a substantial accumulation of electron density in contiguous rings is required for electron transfer. Our previous study of two polymorphs of 2ꞏN-MePy [START_REF] Molčanov | Fine tuning of π-stack separation distances of semiquinone radicals affects their magnetic and electric properties[END_REF] clearly illustrates this. In the case of antiferromagnetic stacks in orthorhombic 2ꞏN-MePy, the electron clouds overlap throughout the entire complex so the crystals are decent semiconductors (σ ≈ 10 -6 S cm -1 ). [START_REF] Molčanov | Fine tuning of π-stack separation distances of semiquinone radicals affects their magnetic and electric properties[END_REF] In the triclinic 2ꞏN-MePy crystal, there is negligible overlap between the dimers, leading to very poor conductivity beyond the instruments' measurement range (i.e. they are insulators with σ < 10 -12 S cm -1 ). [START_REF] Molčanov | Fine tuning of π-stack separation distances of semiquinone radicals affects their magnetic and electric properties[END_REF] CONCLUSIONS Subtle differences in intermolecular stacking interactions between the radicals leading to different electrical and magnetic properties have also been determined. In the case of spin coupling, close contacts and significant accumulation of electron density between contiguous rings have been observed: intra-dimer electron density in the triclinic 2•N-MePy (diamagnetic) exceeds 0.095 e Å -3 , and the interaction can be considered as covalent 2e/mc "pancake bonding", with a bond order of 0.80. In the antiferromagnetic stacks of orthorhombic 2•N-MePy crystal, the BCP electron density between the rings is close to 0.05 e Å -3 and (3,-1) critical points are found between the rings. This interaction, with a bond order of 0.26 can still be considered as a weak "pancake bond".

In both cases, nearly identical "longitudinal" offset (i.e. along the O=CꞏꞏꞏC=O axis [START_REF] Molčanov | Spin pairing, electrostatic and dipolar interactions shape stacking of radical anions in alkali salts of 4,5-dichloro-3,6-dioxocyclohexa-1,4-diene-1,2dicarbonitrile (DDQ)[END_REF][START_REF] Rosokha | Counter-ion modulation of longdistance π-bonding of the open-shell p-benzoquinone anions[END_REF] ) of about 2.06 Å was found, and such arrangement decreases the electrostatic repulsion between the rings.

In the case of long-distance inter-dimer contacts in triclinic 2•N-MePy crystal, very low electron density between the rings was found (the bond order of 0.04 is negligible) and the "lateral" offset (i.e. normal to the O=CꞏꞏꞏC=O axis [START_REF] Molčanov | Spin pairing, electrostatic and dipolar interactions shape stacking of radical anions in alkali salts of 4,5-dichloro-3,6-dioxocyclohexa-1,4-diene-1,2dicarbonitrile (DDQ)[END_REF][START_REF] Rosokha | Counter-ion modulation of longdistance π-bonding of the open-shell p-benzoquinone anions[END_REF] ) of 2.84 Å minimizes electrostatic and steric repulsion.

Considering all these findings, we conclude that besides dispersion and polarization, the weak covalent contribution is an important factor determining the inter-planar separation in the semiquinone radical stacks, particularly for the bent diamagnetic dimers. However, the offset (shift The partial covalent character of the interaction, extending infinitely in the direction of cycle stacking can also explain the semiconductivity of the polymorph comprising the equidistant stacks of 2. [START_REF] Molčanov | Fine tuning of π-stack separation distances of semiquinone radicals affects their magnetic and electric properties[END_REF][START_REF] Molčanov | Probing semiconductivity in crystals of stable semiquinone radicals: organic salts of 5,6-dichloro-2,3-dicyanosemiquinone (DDQ) radical anion[END_REF] EXPERIMENTAL Tetrachloroquinone and tetrachlorohydroquinone were purchased form commercial sources (Sigma-Aldrich, p.a. purity) and were recrystallized from acetone and ethanol, respectively (Kemika, Zagreb, p.a. purity). N-MePy•Cl4Q was prepared according to a previously reported procedure. [START_REF] Molčanov | Fine tuning of π-stack separation distances of semiquinone radicals affects their magnetic and electric properties[END_REF] X-ray diffraction and multipolar refinement X-ray diffraction measurements for 3 was performed on a Bruker D8 Venture diffractometer at 100(2) K using MoKα radiation, to the maximum resolution of 0.50 Å. The frames were integrated with the Bruker SAINT [55] software package using a narrow-frame algorithm. Data were corrected for absorption effects using the multi-scan method (SADABS). [56] The multiple integrated reflections were averaged for the space group P 21/c using SORTAV [START_REF] Blessing | Data Reduction and Error Analysis for Accurate Single Crystal Diffraction Intensities[END_REF] adapted to area detector data.

normal
Single crystals of 1 and orthorhombic 2ꞏN-MePy were measured on an Oxford Rigaku XtaLAB Synergy diffractometer with a HyPix 6000HE detector at 104(2) and 100.01(11) K, respectively, using MoKα radiation, to the maximum resolution of 0.45 Å. Data reduction and absorption correction were done by CrysAlis PRO program package. [58] Single crystal of triclinic 2•N-MePy was measured on a Rigaku MHF007 rotating anode diffractometer with a Pilatus 200K hybrid pixel detector at 100(2) K using MoKα radiation, to the maximum resolution of 0.45 Å. Data reduction and absorption correction were done by CrysAlis PRO program package. [58] Spherical-atom model was refined using SHELXL-97; [START_REF] Sheldrick | A short history of SHELX[END_REF] atomic coordinates were taken from the room-temperature structures. [START_REF] Molčanov | Fine tuning of π-stack separation distances of semiquinone radicals affects their magnetic and electric properties[END_REF][START_REF] Van Weperen | Refinement of the crystal structure of tetrachloro-pbenzoquinone (chloranil) at 1l0 K[END_REF][START_REF] Sakurai | A nuclear quadrupole resonance and X-ray study of the crystal structure of tetrachlorohydroquinone[END_REF] Multipolar refinements were carried out vs. all reflections F 2 with program package MoPro; [START_REF] Jelsch | Advances in protein and small-molecule charge-density refinement methods using MoPro[END_REF] for triclinic and orthorhombic 2•N-MePy up to s = 1.1 Å -1 and for 1 and 3 up to s = 1.0 Å -1 . Chlorine atoms were modelled as hexadecapoles, O, N and C as octupoles and hydrogens as dipoles; loose restraints were used for multipoles and kappas of chemically equivalent atoms. In 1 Kappa 2 values for Cl and O atoms were restrained to 0.90 (5) and 1.00(1), respectively. Vibrations of chlorine atoms were refined as anharmonic using thirdorder Gram-Charlier coefficients. Anisotropic parameters for hydrogen atoms were calculated by the SHADE3 server [START_REF] Madsen | SHADE web server for estimation of hydrogen anisotropic displacement parameters[END_REF] and kept fixed in the multipolar atom refinement; O-H distances were restrained to 1.083(2) Å, aromatic C-H to 1.077(2) Å and methyl C-H to 1.083(2) Å. Geometry and charge-density calculations were performed by MoPro; [START_REF] Jelsch | Advances in protein and small-molecule charge-density refinement methods using MoPro[END_REF] molecular graphic were prepared using MoProViewer [START_REF] Guillot | Molecular recognition enrichment rules in crystals and protein/ligand complexes[END_REF] and ORTEP-3. [START_REF] Farrugia | ORTEP-3 for Windows -a version of ORTEP-III with a Graphical User Interface (GUI)[END_REF] Crystallographic and refinement data are shown in Table 6.

Topological bond orders were calculated using the fitted formula [START_REF] Zarychta | Charge-density analysis of 1-nitroindoline: refinement quality using free R factors and restraints[END_REF] ntopo = 0.00, d = 8.473; [START_REF] Howard | Description of covalent bond orders using the charge density topology[END_REF] for C-O bonds a = -0.427, b = -0.240, c = 0.280, d = 6,464; [START_REF] Tsirelson | Determination of covalent bond orders and atomic valence indices using topological features of the experimental electron density[END_REF] for C-N bonds a = -0.284, b = 0.331, c = 0.559, d = 6.569; [START_REF] Howard | Description of covalent bond orders using the charge density topology[END_REF] for C-H bonds a = -0.153, b = 0.481, c = 0.983, d = 8.087. [START_REF] Zhurova | Structure and Bonding in β-HMX-Characterization of a Trans-Annular NꞏꞏꞏN Interaction[END_REF] Atomic charges are often unreliable to be calculated and depend moreover on the charge definition. [START_REF] Kamiński | Statistical analysis of multipole-modelderived structural parameters and charge-density properties from high-resolution X-ray diffraction experiments[END_REF] An estimation of atomic charges uncertainty can be computed according to the sample standard deviation method described in Fournier et al. [START_REF] Fournier | A method to estimate statistical errors of properties derived from charge-density modelling[END_REF]

Details and protocols of quantum chemical computation

Single point calculations on the experimental geometry of the monomers and some representative arrays taken from both polymorphs were performed at the B3LYP-D3(BJ)/def2-QZVPP level of theory with Gaussian 09. [71] Dimerization energies (DEs) were computed as the energy difference between the dimer (homo or hetero) and two monomers. The advantage of using this basis set is that BSSE error is minimized, hence this correction was not included in the DFT DE values. The same methodology was applied for the calculation of interaction energies of some relevant tetramers. The semiquinone dimers behave as open-shell di-radicals and thus require a broken symmetry treatment for an appropriate description at this level of approximation. The complexes in the triplet excited state dimers were also calculated to guarantee that the lowest energy electronic state was studied; furthermore, the stability test for the open shell diradical calculation was also carried out. The multi-configurational character of the open-shell diradicals was also corroborated by CASPT2 computations for the closest contact dimers of the orthorhombic and triclinic systems using an active space of 10 π-electrons in 10 orbitals and a CASSCF wavefunction as reference, along with the Cholesky decomposition for the evaluation of the two-electron integrals. [START_REF] Beebe | Simplifications in the generation and transformation of twoelectron integrals in molecular calculations[END_REF] The CASPT2 calculations were done using Molcas. [START_REF] Aquilante | Molcas 8: New capabilities for multiconfigurational quantum chemical calculations across the periodic table[END_REF] See the Supplement for further details. In the orthorhombic and triclinic polymorphs of 2•N-MePy, tetrachlorosemiquinone and N-methylpyridium moieties were treated as anions and cations, respectively, because of the ionic character of these molecular crystals.

The bond orders (BO) of all non-equivalent pairs of atoms in each molecule in the Cl4Q (1), the orthorhombic and triclinic polymorphs of N-MePy•Cl4Q (2•N-MePy) and H2Cl4Q (3) were calculated using: i) the delocalization indices defined by the Bader space partition (QTAIM) [START_REF] Bader | Spatial localization of the electronic pair and number distributions in molecules[END_REF] and ii) the Wiberg indices based on the Natural Atomic Orbitals (NAO) analysis. [START_REF] Wiberg | Application of the pople-santry-segal CNDO method to the cyclopropylcarbinyl and cyclobutyl cation and to bicyclobutane[END_REF][START_REF] Foster | Natural hybrid orbitals[END_REF] Delocalization and Wiberg indices were calculated with AIMALL [74] and Gaussian 09, [71] respectively. In addition, the Mayer [START_REF] Mayer | bond order and valence in the AB initio SCF theory[END_REF] and Fuzzy [START_REF] Mayer | Overlap populations, bond orders and valences for 'fuzzy' atoms[END_REF] bond orders calculated with Multiwfn [START_REF] Lu | A multifunctional wavefunction analyzer[END_REF] (provided as Supporting Information) were also used, yielding in most cases a similar description of the chemical bond as with the delocalization and Wiberg indices. Intermolecular bond orders (IBO) were computed as:

𝐼𝐵𝑂 𝐵𝑂 ∈ ∈
where 𝐵𝑂 are the bond orders between the 𝑖 -th and the 𝑗 -th atoms, belonging to 𝐴 and 𝐵 molecules, respectively. In the current case, 𝑁 12, i.e., all the atoms of the semiquinone monomers are considered. Analogously, we define

𝐼𝐵𝑂 𝐵𝑂 ∈ ∈
where the sums run over bonded carbon atoms only (𝑀 6 . Delocalization index and Wiberg bond order in the Natural Atomic Orbitals (NAO) basis were used for the computations of 𝐵𝑂 .

The PIXEL method, [START_REF] Gavezzotti | Non-conventional bonding between organic molecules. The 'halogen bond' in crystalline systems[END_REF] which allows the evaluation of interaction energies from isolated molecular electron densities of two or more systems, was employed to determine the dissociation energies (DEs) as well as lattice energies (LEs) of three crystalline structures with the PIXEL-CLP program package [START_REF] Gavezzotti | Calculation of Intermolecular Interaction Energies by Direct Numerical Integration over Electron Densities. 2. An Improved Polarization Model and the Evaluation of Dispersion and Repulsion Energies[END_REF] (this requires complete molecules in order to obtain meaningful results).

While the crystalline symmetry of the Cl4Q (1) and H2Cl4Q (3) systems can be reduced so as to get complete molecules, this procedure was not affordable for orthorhombic 2ꞏN-MePy because tetrachlorosemiquinone radical and N-methylpiridinium ions are located at different special positions -i.e., an inversion centre and a mirror plane, respectively). DE and LE can be decomposed into electrostatic, polarization, dispersion and repulsion (Pauli) terms (Table S30 in Supporting Information). Since Pauli repulsion is modelled in PIXEL as proportional to the intermolecular overlap, it could be related to steric repulsion. Molecular electron densities were obtained from MP2/6-31G** calculations for this approximation, employing Gaussian 09. [71] Atomic charges of the quinone, semiquionones and hydroquinone molecules obtained from the multipole refinement and QTAIM using the DFT molecular orbitals of the monomers are reported in Tables S8 -S11 in the Supporting Information. To analyse the effect of intermolecular interactions, the QTAIM atomic charges were also analysed for the heterodimers. Discrepancies are found between the DFT monomer and the dimeric atomic charges because of the difference in chemical environments. ASSOCIATED CONTENT (Word Style "TE_Supporting_Information"). Supporting Information. Details on refinement and residual density (residual density plots, XDRK plots), details on molecular structure (deformation density maps and electrostatic potentials, details on topology of electron density, atomic charges, topology of intermolecular interactions), details on quantum chemical calculations. This material is available free of charge via the Internet at http://pubs.acs.org.

Hernández-Trujillo thank DGTIC-UNAM for supercomputer resources (project LANCAD-UNAM-DGTIC-103) and financial support from PAIP Facultad de Química UNAM (grant 5000-9004).

Notes

Any additional relevant notes should be placed here.

Table of Contents Graphic and Synopsis

A combination of experimental X-ray charge density and quantum chemical computation confirms covalent character ('pancake bonding') of π-interactions between semiquinone radical anions, which are responsible for magnetic and electrical properties of their crystals.

Figure S3

Residual electron density at the N-methylpyridinium cation in triclinic 2 in the ring plane, with a) all reflections used and b) only low-angle reflections (s< 0.7 Å -1 ) used. Contours as in Fig. S1. and Wiberg (NBO) bond orders calculated with B3LYP and M06-2X for each system are provided in Tables S18-S29.

Carbon-carbon bond orders obtained with both functionals for ethane, ethane and benzene are close to the ideal 1.5, 1.0 and 2.0 values, except for the Fuzzy BO, which is considerably larger than unity for pure single bonds in ethane.

BENZENE

INTERACTION ENERGIES

DFT dimerization energies (DE) were computed as the energy difference between the dimer (homo or hetero) and two monomers (geometries were fixed in both cases to those found in the crystal) at the same level of theory. The advantage of using the def2QZVPP basis set is that BSSE error is minimized. Pixel DE are calculated within a different approach which considers semi-classical expressions for the evaluation of the electrostatic, polarization, dispersive and repulsive terms. In order to perform a correct interpretation of interaction energies it has to be considered that, while no charge transfer is observed for Cl4Q and H2Cl4Q systems, this phenomenon is relevant in the case of the N-MePyꞏCl4Q crystals, because of the tetrachlorosemiquinone monoanion and the Nmethylpyridinium cation formation. Scheme S1 shows the DFT DE calculated with both functionals for the selected dimers of the semiquinone crystals.

Scheme S1 DFT and PIXEL dimerization energies for each selected dimer. Charge transfer calculated with AIM partition is also reported for heterodimers. Lattice energies and their decomposition in electrostatic, polarization, dispersive and repulsive terms of the Cl4Q, H2Cl4Q and N-Me-Py•Cl4Q (triclinic) systems are reported in Table S30.

Percentages of the attractive contributions to the LE are depicted in Figure S28. Just as in the molecular case, LE of the chloranil crystal is dominated by dispersion. Even though this effect is also relevant for the tetrachlorohydroquinone solid, polarization and electrostatics contribute to almost half of the energetic stabilization, result of the hydrogen bonds formation. By contrast, in the N-Me-Py•Cl4Q (triclinic) system the predominant interaction has an electrostatic origin, consequence of charge transfer. Although, LE of the N-Me-Py•Cl4Q (orthorhombic) crystal couldn't be computed for the reasons explained in the Details and protocols of quantum chemical computation of the main article, it is expected to display a similar behavior to that of the N-Me-Py•Cl4Q (triclinic) solid.

CASPT2 computations

CASPT2/aug-cc-pvdz calculations for the closest contact dimers of the semiquinone from the orthorombic and triclinic crystals were carried out to assess their multiconfigurational nature. The weights of the most important configurations are provided in Tables S31 andS32, revealing the multireferencial character of both semiquinone systems. CASSCF wavefunctions (active space of 10 electrons in 10 π-orbitals conforming the active space) were used as references for the CASPT2 computations. Cholesky decomposition for the evaluation of the two-electron integral was employed. The occupation of the ten π active orbitals is indicated by the number and spin of the electrons in each one (2 means two paired electrons; 0 no electrons; "u" a single electron with up spin and "d" a single electron with down spin).

Scheme 1

 1 Scheme 1 Three types of planar, conjugated rings studied in this paper: quinoid (tetrachloroquinone, 1), semiquinoid (tetrachlorosemiquinone, 2) and aromatic (tetrachlorohydroquinone, 3).

  Figure 1Two types of semiquinone radical π-stacks:[START_REF] Molčanov | Fine tuning of π-stack separation distances of semiquinone radicals affects their magnetic and electric properties[END_REF] a) diamagnetic stacks of closely interacting dimers and b) antiferromagnetic stacks of equidistant radicals. Short (< 3.3 Å) and long (> 3.5 Å) inter-planar separations have been indicated by letters A and B, respectively.

Figure 2 .

 2 Figure 2. Electrostatic potential plotted on an electron density isosurface of 0.5 e Å -3 of a) tetrachloroquinone 1, b) tetrachlorosemiquinone 2 from triclinic 2ꞏN-MePy and c) tetrachlorohydroquinone 3. Top row: experimental data (red: -0.1, blue: +1.0 e/Å -1 ), bottom row: DFT-calculated structures (1 -red: -0.28, blue: +0.57 e Å -1 ; 2 -red: -0.38, blue: +0.38 e Å -1 ; 3: red: -0.38, blue: +0.91 e Å -1 ).

Figure 3

 3 Figure 3 Side-view of a 'pancake-bonded' dimer of radicals in triclinic 2ꞏN-MePy viewed approximately along the O=CꞏꞏꞏC=O axis showing bent conformation of the rings.

Figure 4

 4 Figure 4 Critical points in triclinic polymorph of 2ꞏN-MePy. Close intra-dimer contact is on the top, and the longer inter-dimer contact is at the bottom; additional interactions between anions and cations are also shown. Critical points of (3,-1) type, representing bonding contacts, are shown as red spheres, those of (3,+1) type, representing ring centroids are light blue and those of (3,+3) type, representing cage centroids are violet. Bond paths are shown as red lines.

Figure 5

 5 Figure 5 Spin density maps of the semiquinone exhibiting pancake bonding in the a) orthorhombic 2ꞏN-MePy and b) triclinic 2ꞏN-MePy (isosurface = 0.001 a.u.).

Figure 6

 6 Figure 6 HOMOs of semiquinone in a) triclinic 2ꞏN-MePy and b) orthorhombic 2ꞏN-MePy. A lower degree of pancake bonding is observed for the latter system.

Figure 7

 7 Figure 7 LUMOs of semiquinone in a) triclinic 2ꞏN-MePy and b) orthorhombic 2ꞏN-MePy. A lower degree of pancake bonding is observed for the latter system.

Figure 8

 8 Figure 8 Electrostatic potential between two tetrachlorosemiquinone radical anions in triclinic polymorph of 2ꞏN-MePy on an electron density iso-surface of 0.5 e Å -3 in a) close contact (intradimer) and b) long distance (inter-dimer); orientations of the rings are approximately the same as

Figure 9

 9 Figure 9 Electrostatic potential between two tetrachlorosemiquinone radical anions in the orthorhombic polymorph of 2ꞏN-MePy on an electron density iso-surface of 0.5 e Å -3 (0.074 a.u.). Orientations of the rings are approximately the same as in the Figs. 4 and 8. a) Experimental data (red: -0.1, blue: +1.0), b) DFT-calculated structures (red: -0.19, blue: +0.66 e Å -1 ).

Figure 10

 10 Figure 10 Critical points in orthorhombic polymorph of 2ꞏN-MePy. Critical points of (3,-1) type, representing bonding contacts, are shown as red spheres, those of (3,+1) type, representing ring centroids are light blue and those of (3,+3) type, representing cage centroids are violet. Bond paths are shown as red lines.

  Parallel X-ray and quantum chemical charge density studies of analogous tetrachloro-substituted quinoid (1), semiquinoid (2) and aromatic hydroquinone (3) rings revealed the nature of delocalization of π-electrons and the negative charge in the semiquinone radical. The electronic structure of the radical is approximately half way between the quinoid and aromatic with partially delocalized π-electrons and C-O bond orders of ca. 1.5 (theoretical values are 1.25). Induction effect of the chlorine substituents, enhancing delocalization of the negative charge and thus stabilizing the radical anion has been quantitatively assessed: in the radical 2 the chlorine atoms are more negatively charged than those in the neutral tetrachloroquinone 1 and hydroquinone 3 by approximately -0.1 e.

  to the inter-planar separation) is determined by intermolecular electrostatic potential, in such a way to minimize electrostatic repulsion by allowing contacts between electron-rich and electron-poor areas of the molecules and, at the same time, lower steric repulsion. The net stacking interaction is repulsive in all cases because of the anionic nature of the semiquinone radicals. With regard to the lattice energies of the studied systems, polarization has only a small contribution and, contrary to what is obtained for other molecular solids like those of 1 and 3, dispersion, although not negligible, has a minor stabilizing role in the semiquinoid polymorphs. The most relevant attractive forces in these crystals are those between the semiquinone anions and the pyridinium cations.

  = a + b λ3 + c (λ1 + λ2) + d ρcp Coefficients a, b, c and d were taken from the literature: for C-C bonds a = -0.522, b = -1.695, c

ACKNOWLEDGMENT

  ABBREVIATIONSCl4Q, tetrachloroquinone (chloranil); Cl4Q -, tetrachlorosemiquinone radical anion; H2Cl4Q, tetrachlorohydroquinone, N-MePy, N-methylpyridinium cation; HOMA, harmonic oscillator model of aromaticity; NICS, nucleus-independent chemical shift; QTAIM, quantum theory of atoms-in-molecules; BO, bond order; IBO, intermolecular bond order.

Figure S4

 S4 Figure S4 Residual electron density at the tetraclorosemiquinone radical anion in orthorhombic 2 in the ring plane, with a) all reflections used and b) only low-angle reflections (s< 0.7 Å -1 ) used. Contours as in Fig. S1.

Figure S5

 S5 Figure S5 Residual electron density at the N-methylpyridinium cation in orthorhombic 2 in the ring plane, with a) all reflections used and b) only low-angle reflections (s< 0.7 Å -1 ) used. Contours as in Fig. S1.

Figure S6

 S6 Figure S6 Residual electron density at the tetraclorohydroquinone 3 in the ring plane, with a) all reflections used and b) only low-angle reflections (s< 0.7 Å -1 ) used. Contours as in Fig. S1.

Figure S7

 S7 Figure S7 XDRK plot for 1 showing the fit of <Yobs> vs <Ycalc> as a function of resolution.

Figure S8

 S8 Figure S8 XDRK plot for 1 showing the expected and experimental Yobs-Ycalc data profile.

Figure S9

 S9 Figure S9 XDRK plot for orthorhombic 2ꞏN-MePy showing the fit of <Yobs> vs <Ycalc> as a function of resolution.

Figure S10

 S10 Figure S10 XDRK plot for orthorhombic 2ꞏN-MePy showing the expected and experimental

Figure S11

 S11 Figure S11 XDRK plot for triclinic 2ꞏN-MePy showing the fit of <Yobs> vs <Ycalc> as a function of resolution.

Figure S12

 S12 Figure S12 XDRK plot for triclinic 2ꞏN-MePy showing the expected and experimental Yobs-Ycalc data profile.

Figure S13

 S13 Figure S13 XDRK plot for 3 showing the fit of <Yobs> vs <Ycalc> as a function of resolution.

Figure S14

 S14 Figure S14 XDRK plot for 3 showing the expected and experimental Yobs-Ycalc data profile.

Figure S16

 S16 Figure S16 Deformation density of anion 2 in orthorhombic polymorph of 2ꞏN-MePy (contours at 0.05 e Å -3 ; positive density is blue, negative is red and zero contour is a yellow dotted line) and electrostatic potential electrostatic potential mapped onto an electron density isosurface of 0.5 (red: -0.1, blue: +1.0).

Figure S17 N

 S17 Figure S17 N-methylpyridinium cation in triclinic 2ꞏN-MePy: a) deformation density (contours at 0.05 e Å -3 ; positive density is blue, negative is red and zero contour is a yellow dotted line), b) electrostatic potential mapped onto an electron density isosurface of 0.5 (red: -0.1, blue: +1.0).

Figure

  Figure S18 N-methylpyridinium cation in orthorhombic 2ꞏN-MePy: a) deformation density (contours at 0.05 e Å -3 ; positive density is blue, negative is red and zero contour is a yellow dotted line), b) electrostatic potential mapped onto an electron density isosurface of 0.5 (red: -0.1, blue: +1.0).

Figure S19

 S19 Figure S19 Electrostatic potential of Cl4Q (1) plotted onto an electron density isosurface of 0.0067 e•Å -3 : experimental (left; red; -0.05, blue: +0.05 e Å -1 ) and theoretical (right; red: -0.005, blue: +0.005 e Å -1 ).

Figure S20

 S20 Figure S20 Electrostatic potential of tetrachlorosemiquinone radical anion (2) from triclinic polymorph plotted onto an electron density isosurface of 0.0067 e•Å -3 : experimental (left; red; -0.30, blue: +0.18 e Å -1 ) and theoretical (right; red: -0.33, blue: +0.20 e Å -1 ).

Figure S21

 S21 Figure S21 Electrostatic potential of tetrachlorosemiquinone radical anion (2) from orthorhombic polymorph plotted onto an electron density isosurface of 0.0067 e•Å -3 : experimental (left; red; -0.20, blue: +0.10 e Å -1 ) and theoretical (right; red: -0.33, blue: +0.14 e Å -1 ).

Figure S22

 S22 Figure S22 Electrostatic potential of tetrachlorohydroquinone (3) plotted onto an electron density isosurface of 0.0067 e•Å -3 : experimental (left; red; -0.10, blue: +0.05 e Å -1 ) and theoretical (right; red: -0.60, blue: +0.50 e Å -1 ).

Figure S23

 S23 Figure S23Optimized structure of benzene. Bond distances depicted in green (Å).

Figure S27

 S27 Figure S27 Crystallographic structure of N-methylpyridinium cation in N-MePyꞏCl4Q (orthorhombic) crystal. Bond distances depicted in green (Å).

Figure

  Figure S30 βM, βF, βD and βN indexes calculated with B3LYP for all molecules belonging to the Cl4Q, H2Cl4Q, N-MePyꞏCl4Q (orthorhombic) N-MePyꞏCl4Q (triclinic) systems.

Figure

  Figure S31 βM, βF, βD and βN indexes calculated with M06-2X for all molecules belonging to the Cl4Q, H2Cl4Q, N-MePyꞏCl4Q (orthorhombic) and N-MePyꞏCl4Q (triclinic) systems.

Figure S32

 S32 Figure S32 SOMOs of semiquinone in a) orthorhombic and b) triclinic systems.

System N-MePyꞏCl4Q (orthorhombic) Dimer 1 :Dimer 2 :Dimer 3 :Dimer 4 :Dimer 5 :Dimer 6 :Dimer 1 :Dimer 2 :Dimer 3 :

 123456123 Intermolecular O•••H contacts involved. DE (B3LYP-D3(BJ) = -71.4 kcal/mol | CT = 0.85 electrons DE (M06-2X-D3) = -70.5 kcal/mol | CT = 0.96 electrons Intermolecular C•••C and C•••H contacts involved. DE= -3.6 kcal/mol DE (B3LYP-D3(BJ) = +59.2 kcal/mol DE (M06-2X-D3) = +60.4 kcal/mol PIXEL Intermolecular C•••C, O•••C and Cl•••Cl contacts involved. DE (B3LYP-D3(BJ) = +45.1 kcal/mol DE (M06-2X-D3) = +45.3 kcal/Intermolecular Cl•••C, O•••C and Cl•••H contacts involved. DE (B3LYP-D3(BJ) = -70.5 kcal/mol | CT = 0.85 electrons DE (M06-2X-D3) = -69.2 kcal/mol | CT = 0.95 electrons PIXEL Intermolecular Cl•••Cl contacts involved. DE (B3LYP-D3(BJ) = +33.5 kcal/mol DE (M06-2X-D3) = +33.8 kcal/No intermolecular BCP found. DE (B3LYP-D3(BJ) = +38.4 kcal/mol DE (M06-2X-D3) = +38.5 kcal/mol PIXEL Electrostatic Intermolecular C•••C, Cl•••Cl and C•••O contacts involved. DE (B3LYP-D3(BJ) = +45.1 kcal/mol DE (M06-2X-D3) = +46.0 kcal/mol PIXEL Intermolecular Cl•••C contacts involved. DE (B3LYP-D3(BJ) = +44.0 kcal/mol DE (M06-2X-D3) = +45.7 kcal/mol PIXEL Electrostatic Intermolecular Cl•••C contacts involved. DE (B3LYP-D3(BJ) = +34.1 kcal/mol DE (M06-2X-D3) = +34.5 kcal/mol PIXEL

4 Figure S33

 4S33 Figure S33 Percentages of the dispersive (Disp), polarization (Pol) and electrostatic (Elec) contributions to the attractive components of the lattice energies of the Cl4Q, H2Cl4Q and N-MePyꞏCl4Q (triclinic) systems calculated with PIXEL.

Table 1

 1

	Topological bond orders (ntopo) of compounds 1 -3 derived from X-ray charge density
	(top row, bold), AIM delocalization indices (middle row) and NBO bond orders (bottom row,

Table 3

 3 Geometric parameters of the cycles stacking.

	Symmetry operators: (i) -x, 1-y, -z: (ii) x,

Table 4

 4 IBO (top row) and IBO' (bottom row, italic) values for different contacts between the

	tetrachlorosemiquinone radicals.
	interaction	Delocalisation	Wiberg (NBO)
		index
	2ꞏN-MePy, orthorhombic	0.89	0.26
		0.18	0.09
	2ꞏN-MePy, triclinic	1.61	0.80
	intra-dimer	0.42	0.27
	2ꞏN-MePy, triclinic	0.43	0.04
	inter-dimer	0.04	0.01

Table 5

 5 Experimental

		Elec exp	Elec lattice	DFT	PIXEL total	Elec	Pol	Disp	Rep
	intra-dimer	+28.0 -266	+45.1 +55.6	+50.4 -15.5 -23.0 +43.7

electrostatic dimerization (Elec,exp) and lattice energies (Elec,lattice) calculated from the multipole refinement, B3LYP-D3(BJ)/def2-QZVP and PIXEL dimerization energies of the intra-and inter-dimer contacts of the triclinic 2ꞏN-MePy and of the antiferromagnetic dimer of the orthorhombic 2ꞏN-MePy. PIXEL contributions to the DEs correspond to electrostatic (Elec), polarization (Pol), dispersion (Disp) and repulsion (Rep) terms. All values in kcal mol -1 .

Table 6

 6 Crystallographic, data collection and charge-density refinement details.

	Compound	1	2•N-MePy,	2•N-MePy,	3
			orthorhombic	triclinic
	Empirical formula	C6Cl4O2	C 12H8Cl4NO2	C12H8Cl4NO2	C6H2Cl4O2
	Formula wt. / g mol -1	245.87	339.99	339.99	247.88
	Crystal dimensions /	0.235x0.152x	0.15 x 0.05 x	0.20 x 0.20 x	0.270x0.162x
	mm	0.020	0.05	0.15	0.078
	Space group	P 21/c	P bnm	P 1	P 21/n
	a / Å	8.5324(1)	3.77667(2)	7.28708(7)	8.23940(10)
	b / Å	5.6636(1)	18.07885(13)	9.22296(8)	4.7740(8)
	c / Å	8.6598(1)	18.60034(12)	10.37403(11)	10.366(2)
	α / °	90	90	73.4641(8)	90
	β / °	105.909(1)	90	72.9593(9)	97.803(8)
	γ / °	90	90	75.6428(8)	90
	Z	2	4	2	4
	V / Å 3	402.449(7)	1269.990(15)	628.660(14)	403.97(10)
	Dcalc / g cm -3	2.030	1.779	1.797	2.039
	 / mm -1	1.414	0.924	0.935	1.410
	Θ range / °	4.35 -45.36	2.25 -59.88	2.34 -51.43	2.97 -45.29
	T / K	104(5)	100.01(11)	90(2)	100(2)
	Radiation	0.71073 (MoKα)	0.71073 (MoKα) 0.71073 (MoKα) 0.71073 (MoKα)
	wavelength
	Diffractometer type XtaLAB Synergy XtaLAB	Rigaku MHF007 Bruker	D8
			Synergy		Venture
	Range of h, k, l	-17 < h < 16;	-9 < h < 9;	-15 < h < 16;	-14 < h < 16;
		-11 < k < 10;	-45 < k < 45;	-19 < k < 20;	-9 < k < 9;

Table S1

 S1

	Table S2 Topology of electron density in the compound 3, derived from electron-density after
	multipole refinement. Symmetry operator: i) -x, 1-y, 1-z.
	Bond	Length (Å)	Electron Density	Laplacian	Ellipticity	Bond order
			(eÅ -3 )  cp	(eÅ -3 )		n topo
	C1-O1	1.3545(8)	2.100	-17.8	0.10	1.06
	C1-C2	1.3982(6)	2.212	-19.6	0.32	1.43
	C2-C3	1.3988(5)	2.108	-17.7	0.25	1.31
	C3-C1 i	1.3996(6)	2.164	-19.3	0.26	1.42
	C2-Cl1	1.7188(5)	1.379	-3.6	0.07
	C3-Cl2	1.7179(5)	1.357	-3.5	0.09
	O1-H1	0.980(2)	0.343	-27.7	0.023	0.51
	Bond	Length (Å)	Electron Density	Laplacian	Ellipticity	Bond order
			(eÅ -3 )  cp	(eÅ -3 )		ntopo
	C1-O1	1.2125(8)	2.862	-22.0	0.10	1.35
	C1-C3	1.4897(6)	1.822	-14.1	0.21	0.94
	C3-C2	1.3467(5)	2.368	-24.4	0.38	1.78
	C2-C1	1.4901(6)	1.831	-14.6	0.20	1.00
	C2-Cl1	1.6984(5)	1.481	-4.2	0.14
	C3-Cl2	1.7000(5)	1.466	-3.5	0.08

Topology of electron density in the compound 1, derived from electron-density after multipole refinement.

Table S3

 S3 Topology of electron density of the tetrachlorosemiquinone radical anion in triclinic 2, derived from electron-density after multipole refinement.

	Bond	Length (Å)	Electron Density	Laplacian	Ellipticity	Bond order
			(eÅ -3 )  cp	(eÅ -3 )		ntopo
	C1-O1	1.2483(3)	2.717	-34.1	0.08	1.50
	C4-O2	1.2510(3)	2.689	-32.2	0.10	1.47
	C1-C2	1.4564(4)	1.939	-16.2	0.20	1.16
	C2-C3	1.3702(3)	2.191	-20.2	0.29	1.50
	C3-C4	1.4563(4)	1.902	-14.8	0.26	1.08
	C4-C5	1.4571(3)	1.897	-15.0	0.22	1.07
	C5-C6	1.3701(3)	2.192	-19.6	0.32	1.45
	C6-C1	1.4552(4)	1.926	-15.5	0.24	1.12
	C2-Cl1	1.7222(3)	1.394	-4.0	0.14
	C3-Cl2	1.7243(2)	1.403	-4.4	0.09
	C5-Cl3	1.7215(3)	1.380	-3.9	0.15
	C6-Cl4	1.7230(3)	1.381	-3.8	0.11

Table S4

 S4 Topology of electron density of the tetrachlorosemiquinone radical anion in orthorhombic 2, derived from electron-density after multipole refinement.

	Bond	Length (Å)	Electron Density	Laplacian	Ellipticity	Bond order
			(eÅ -3 ) cp	(eÅ -3 )		n topo
	C1-O1	1.2480(3)	2.868	-29.6	0.01	1.47
	C1-C2	1.4544(4)	1.953	-13.6	0.13	0.88
	C2-C3	1.3686(3)	2.256	-21.0	0.25	1.50
	C3-C1	1.4558(4)	1.958	-13.5	0.13	0.88
	C2-Cl1	1.7211(3)	1.391	-3.9	0.07
	C3-Cl2	1.7214(2)	1.397	-3.9	0.06
	Bond	Length (Å)	Electron Density	Laplacian	Ellipticity	Bond order
			(eÅ -3 )  cp	(eÅ -3 )		n topo
	N1B-C1B	1.3469(4)	2.27	-27.4	0.17	1.22
	N1B-C5B	1.3525(4)	2.14	-22.3	0.21	1.21
	N1B-C6B	1.4752(4)	1.63	-9.6	0.07	0.97
	C1B-C2B	1.3849(5)	2.21	-21.7	0.31	1.53
	C2B-C3B	1.3915(5)	2.13	-20.0	0.20	1.47
	C3B-C4B	1.3934(5)	2.11	-19.9	0.21	1.49
	C4B-C5B	1.3792(4)	2.22	-22.5	0.24	1.62
	C1B-H1B	0.949(9)	1.79	-19.7	0.07	0.85
	C2B-H2B	0.945(10)	1.72	-18.6	0.05	0.84
	C3B-H3B	0.969(10)	1.72	-18.4	0.06	0.86
	C4B-H4B	0.939(10)	1.76	-20.4	0.04	0.83
	C5B-H5B	0.935(10)	1.75	-20.1	0.06	0.82
	C6B-H61B	0.989(10)	1.75	-17.5	0.11	0.93
	C6B-H62B	0.937(11)	1.73	-17.2	0.14	0.96
	C6B-H63B	0.973(11)	1.74	-16.8	0.14	0.96

Table S5

Topology of electron density of the N-methylpyridinium cation in triclinic 2, derived from electron-density after multipole refinement.

Table S6

 S6 Topology of electron density of the N-methylpyridinium cation in orthorhombic 2, derived from electron-density after multipole refinement.

	Bond	Length (Å)	Electron Density	Laplacian	Ellipticity	Bond order
			(eÅ -3 ) cp	(eÅ -3 )		n topo
	N1-C7	1.4826(4)	1.706	-9.7	0.08	1.02
	N1-C4	1.3498(4)	2.278	-20.8	0.25	1.32
	C4-C5	1.3846(5)	2.221	-21.0	0.24	1.56
	C5-C6	1.3911(5)	2.126	-18.2	0.20	1.38
	C4-H4	1.082(9)	1.793	-19.8	0.02	0.83
	C5-H5	1.082(10)	1.667	-17.5	0.05	0.87
	C6-H6	1.082(10)	1.650	-18.8	0.04	0.76
	C7-H7A	1.076(10)	1.669	-17.0	0.09	0.88
	C7-H7B	1.076(10)	1.545	-19.7	0.08	0.65

Table S7

 S7 Pval derived values are from the Q= Nval -Pval difference between number of valence electrons in neutral and refined multipolar atom. Esd's were obtained after refinement vs.

	all variables.
	Atom	P val derived	Topological DFT/Monomer
	O1	-0.16(6)	-1.000	-1.071
	Cl1	+0.02(8)	-0.087(4)	-0.121
	Cl2	+0.03(8)	-0.086(4)	-0.121
	C1	+0.30(10)	+1.156	1.078
	C2	-0.13(8)	+0.019	0.118
	C3	-0.06(8)	+0.003	0.118

Atomic charges (e) in compound 1 (Cl4Q) derived from Pval, topology of electron density and QTAIM/DFT.

Table S8

 S8 Atomic charges (e) in compound 3 (H2Cl4Q) derived from Pval, topology of electron density and QTAIM/DFT. Pval derived values are from the Q= Nval -Pval difference between number of valence electrons in neutral and refined multipolar atom. Esd's were obtained after refinement vs. all variables.

	Atom	P val derived	Topological DFT/Monomer
	O1	-0.48(9)	-1.093	-1.139
	Cl1	-0.04(18)	-0.12(4)	-0.171
	Cl2	-0.07(18)	-0.15(3)	-0.199
	C1	-0.04(12)	+0.441	0.637
	C2	+0.06(10)	+0.021	0.142
	C3	+0.18(9)	+0.287	0.126
	H1	+0.42(3)	+0.558	0.605

Table S9

 S9 Atomic charges (e) in the semiquinone radical in triclinic 2ꞏN-MePy derived from Pval, topology of electron density and QTAIM/DFT. Pval derived values are from the Q= Nval -Pval difference between number of valence electrons in neutral and refined multipolar atom. Esd's were obtained after refinement vs. all variables.

	Atom	P val derived Topological DFT/Monomer DFT/Dimer	DFT/Dimer	DFT/Dimer
					4	5	6
	O1	-0.12(3)	-0.97	-1.141	-1.088	-1.141	-1.082
	O2	-0.14(3)	-0.94	-1.138	-1.087	-1.073	-1.186
	Cl1	-0.170(12)	-0.243(10)	-0.240	-0.224	-0.199	-0.191
	Cl2	-0.174(12)	-0.249(15)	-0.240	-0.228	-0.183	-0.246
	Cl3	-0.171(12)	-0.232(9)	-0.239	-0.179	-0.184	-0.207
	Cl4	-0.173(5)	-0.236(13)	-0.240	-0.180	-0.216	-0.187
	C1	-0.15(6)	+0.77	0.968	0.987	0.972	0.982
	C2	+0.05(5)	+0.08	0.077	0.085	0.089	0.094
	C3	+0.05(5)	+0.09	0.077	0.085	0.095	0.075
	C4	-0.10(6)	+0.75	0.962	0.980	0.981	0.951
	C5	+0.12(5)	+0.17	0.078	0.095	0.095	0.088
	C6	+0.07(4)	+0.11	0.076	0.094	0.084	0.094
	Total	-0.91	-0.91	-1.000	-0.660	-0.680	-0.815

Table S10

 S10 Atomic charges (e) in the semiquinone radical in orthorhombic 2ꞏN-MePy derived from Pval, topology of electron density and QTAIM/DFT. Pval derived values are from the Q= Nval -Pval difference between number of valence electrons in neutral and refined multipolar atom. Esd's were obtained after refinement vs. all variables.

	Atom	P val derived	Topological DFT/Monomer	DFT/Dimer 1	DFT/Dimer 4
	O1	-0.22(5)	-0.97	-1.141	-1.205	-1.159
	Cl1	-0.12(4)	-0.25(4)	-0.239	-0.228	-0.220
	Cl2	-0.12(4)	-0.25(9)	-0.238	-0.188	-0.186
	C1	+0.30(7)	+0.77	0.964	0.953	0.947
	C2	-0.07(5)	+0.08	0.077	0.083	0.074
	C3	-0.07(5)	+0.09	0.078	0.096	0.092
	Total	-0.96	-1.06	-0.998	-0.978	-0.904

Table S11

 S11 Atomic charges (e) of N-methylpyridinium cation in orthorhombic 2ꞏN-MePy derived from Pval and topology of experimental electron density. Pval derived values are from the Q= Nval -Pval difference between number of valence electrons in neutral and refined multipolar atom.

	S4 Quantum chemical calculations
	Graphical representations of the studied systems are depicted in Figures 1-9, indicating non-
	Table S12 Atomic charges (e) of N-methylpyridinium cation in triclinic 2ꞏN-MePy from Pval and equivalent internuclear distances in green. Values of the Mayer, Fuzzy, Delocalization Index (DI)
	topology of electron density. Pval derived values are from the Q= Nval -Pval difference between
	number of valence electrons in neutral and refined multipolar atom. Esd's were obtained after
	refinement vs. all variables.
		Pval		Pval
	Atom	derived Topological Atom	derived Topological
	C1B	-0.28(7)	0.074 H1B	0.32(4)	0.039
	C2B	0.25(8)	0.085 H2B	0.04(4)	0.040
	C3B	-0.30(9)	0.086 H3B	0.24(5)	0.046
	C4B	0.13(9)	0.088 H4B	0.12(4)	0.044
	C5B	-0.15(7)	0.072 H5B	0.21(4)	0.042
	C6B	-0.03(9)	0.091 H61B	0.20(5)	0.045
	N1B	0.06(4)	0.043 H62B	-0.01(5)	0.050
	Total	+0.91	+0.91 H63B	0.11(5)	0.047
	Esd's were obtained after refinement vs. all variables.
	Atom	P val derived	Topological
	N1	+0.01(8)	-0.251
	C4	+0.02(8)	-0.056
	H4	+0.22(9)	+0.293
	C5	-0.20(12)	-0.138
	H5	+0.05(9)	+0.219
	C6	+0.31(7)	-0.165
	H6	+0.22(10)	+0.137
	C7	-0.03(8)	-0.040
	H7A	+0.02(8)	+0.183
	H7B	+0.02(8)	+0.187
	Total	+0.96	+0.870

Table S15

 S15 Bond orders of benzene calculated with B3LYP.

	Bonds	Mayer	Fuzzy	Delocalization index	Wiberg (NBO)
	C-H	0.91	0.88	0.96	0.92
	C-C	1.51	1.46	1.39	1.45
	Table S16 Bond orders of benzene calculated with M06-2X.
	Bonds	Mayer	Fuzzy	Delocalization index	Wiberg (NBO)
	C-H	0.92	0.88	0.96	0.92
	C-C	1.53	1.46	1.39	1.45

TETRACHLOROQUINONE

Figure S24 Crystallographic structure of chloranil in Cl4Q crystal. Bond distances depicted in green (Å).

Table S17

 S17 Bond orders of chloranil in the Cl4Q crystal calculated with B3LYP.

	Bonds	Mayer	Fuzzy	Delocalization index	Wiberg (NBO)
	C5-C4	1.00	1.00	0.96	1.00
	C4-C6	1.59	1.50	1.55	1.63
	C6-C5	1.00	1.00	0.96	1.00
	C5-O3	2.15	1.97	1.38	1.79
	C4-Cl1	1.20	1.26	1.18	1.12
	C6-Cl2	1.21	1.26	1.18	1.12
	Table S18 Bond orders of chloranil in the Cl4Q crystal calculated with M06-2X.
	Bonds	Mayer	Fuzzy	Delocalization index	Wiberg (NBO)
	C5-C4	1.06	0.99	0.95	0.99
	C4-C6	1.67	1.52	1.58	1.67
	C6-C5	1.06	0.99	0.95	0.99
	C5-O3	1.95	1.99	1.37	1.81
	C4-Cl1	1.33	1.26	1.17	1.12
	C6-Cl2	1.32	1.26	1.17	1.12

TETRACHLOROQYDROQUINONE Figure S25 Crystallographic structure of tetrachlorohydroquinone in H2Cl4Q crystal. Bond distances depicted in green (Å).

Table S19

 S19 Bond orders of tetrachlorohydroquinone in the H2Cl4Q crystal calculated with B3LYP.

	Bonds	Mayer	Fuzzy	Delocalization index	Wiberg (NBO)
	C2-C1	1.35	1.27	1.26	1.32
	C1-C3	1.33	1.27	1.26	1.32
	C3-C2	1.33	1.27	1.30	1.34
	C2-Cl1	1.11	1.23	1.14	1.09
	C1-O1	1.32	1.33	0.93	1.06
	C3-Cl2	1.05	1.22	1.13	1.08
	O1-H1	0.91	0.80	0.59	0.72
	Table S20 Bond orders of tetrachlorohydroquinone in the H2Cl4Q crystal calculated with M06-
	2X.
	Bonds	Mayer	Fuzzy	Delocalization index	Wiberg (NBO)
	C2-C1	1.40	1.27	1.26	1.32
	C1-C3	1.38	1.28	1.27	1.33
	C3-C2	1.37	1.27	1.30	1.35
	C2-Cl1	1.28	1.23	1.14	1.08
	C1-O1	1.14	1.33	0.91	1.05
	C3-Cl2	1.20	1.22	1.13	1.07
	O1-H1	0.84	0.80	0.58	0.72

Table S23

 S23

	Bonds	Mayer	Fuzzy	Delocalization index	Wiberg (NBO)
	N1-C4	1.29	1.40	1.15	1.27
	C4-C5	1.45	1.46	1.37	1.47
	C5-C6	1.38	1.43	1.37	1.42
	N1-C7	0.85	1.11	0.88	0.91
	C4-H4	0.97	0.84	0.91	0.91
	C5H5	0.94	0.86	0.94	0.90
	C6H6	0.94	0.86	0.94	0.91
	C7-H7A	0.96	0.87	0.93	0.93
	C7-H7B	0.96	0.87	0.93	0.92

Bond orders of N-methylpyridium cation in the N-MePyꞏCl4Q (orthorhombic) crystal calculated with B3LYP.

Table S24

 S24 Bond orders of N-methylpyridium cation in the N-MePyꞏCl4Q (orthorhombic) crystal calculated with M06-2X.

	Table S25 Bond orders of tetrachlorosemiquinone radical anion in the N-MePyꞏCl4Q (triclinic) Table S26 Bond orders of tetrachlorosemiquinone radical anion in the N-Me-PyꞏCl4Q (triclinic) Figure S29 Crystallographic
	crystal calculated with B3LYP. crystal calculated with M06-2X. structure of N-methylpyridium
	Bonds N1-C4 Bonds C1A-C2A Bonds cation in (triclinic) crystal. Bond distances Mayer 1.23 Mayer 1.10 Mayer N-MePyꞏCl4Q depicted in green (Å).	Fuzzy 1.40 Fuzzy 1.10 Fuzzy	Delocalization index Wiberg (NBO) 1.14 1.27 Delocalization index Wiberg (NBO) 1.07 1.10 Delocalization Wiberg (NBO) index
	C4-C5 C2A-C3A C1A-C2A	1.40 1.51 1.17	1.46 1.41 1.10	1.37 1.06	1.45	1.47 1.10	1.51
	C5-C6 N1-C7 C3A-C4A C4A-C5A C2A-C3A C4-H4 C5A-C6A C3A-C4A	1.37 0.79 1.10 1.10 1.55 0.83 1.51 1.16	1.43 1.11 1.10 1.10 1.42 0.84 1.40 1.10	1.37 0.88 1.47 0.91 1.06	1.07 1.07 1.45	1.42 1.53 0.91 0.91 1.10	1.10 1.10 1.51
	C5H5 C6A-C1A C4A-C5A	0.80 1.10 1.17	0.86 1.11 1.10	0.94 1.06	1.07	0.90 1.10	1.10
	C6H6 C1A-O1A C5A-C6A	0.80 2.10 1.55	0.85 1.80 1.42	0.94 1.47	1.26	0.90 1.53	1.53
	C7-H7A C2A-Cl1A C7-H7B C3A-Cl2A C6A-C1A C4A-O2A C1A-O1A	0.84 1.08 0.80 1.07 1.17 2.10 1.80	0.87 1.21 0.87 1.21 1.10 1.80 1.81	0.93 0.93 1.06 1.25	1.12 1.12 1.26	0.93 1.10 0.92 1.53	1.06 1.06 1.53
	C5A-Cl3A C2A-Cl1A	1.07 1.23	1.21 1.21	1.12	1.12	1.06	1.07
	C6A-Cl4A C3A-Cl2A	1.08 1.23	1.21 1.21	1.12	1.12	1.06	1.06
	C4A-O2A	1.80	1.81	1.25		1.53
	C5A-Cl3A	1.22	1.21	1.12		1.06
	C6A-Cl4A	1.23	1.21	1.12		1.06

Table S27

 S27 Bond orders of N-methylpyridium cation in the N-MePyꞏCl4Q (triclinic) crystal calculated with B3LYP.

	Table S28 Bond orders of N-methylpyridium cation in the N-MePyꞏCl4Q (triclinic) crystal
	calculated with M06-2X.
	Bonds	Mayer	Fuzzy	Delocalization index	Wiberg (NBO)
	N1B-C1B		1.24	1.41	1.14	1.27
	C1B-C2B		1.40	1.46	1.36	1.46
	C2B-C3B		1.39	1.44	1.37	1.43
	C3B-C4B		1.36	1.43	1.36	1.42
	C4B-C5B		1.41	1.47	1.38	1.48
	C5B-N1B		1.23	1.39	1.14	1.26
	N1B-C6B		0.79	1.12	0.88	0.91
	C1B-H1B		0.83	0.84	0.91	0.91
	C2B-H2B		0.80	0.85	0.94	0.90
	C3B-H3B		0.81	0.85	0.94	0.90
	C4B-H4B	Bonds	Mayer 0.80	Fuzzy 0.85	Delocalization index 0.94	Wiberg (NBO) 0.90
	N1B-C1B C5B-H5B		1.30 0.83	1.40 0.84	1.15 0.91	1.27 0.91
	C1B-C2B C2B-C3B C6B-H61B C3B-C4B C6B-H62B		1.44 1.39 0.84 1.37 0.79	1.46 1.44 0.87 1.42 0.87	1.36 1.37 0.93 1.36 0.93	1.46 0.93 1.43 1.42 0.92
	C4B-C5B C6B-H63B		1.46 0.84	1.47 0.87	1.38 0.93	1.48 0.93
	C5B-N1B		1.29	1.39	1.14	1.26
	N1B-C6B		0.86	1.12	0.88	0.92
	C1B-H1B		0.97	0.84	0.91	0.91
	C2B-H2B		0.95	0.86	0.94	0.90
	C3B-H3B		0.94	0.86	0.94	0.91
	C4B-H4B		0.95	0.86	0.94	0.90
	C5B-H5B		0.97	0.84	0.91	0.91
	C6B-H61B	0.96	0.87	0.93	0.93
	C6B-H62B	0.96	0.87	0.93	0.92
	C6B-H63B	0.96	0.87	0.93	0.93

Table S29

 S29 Decomposition analysis of lattice energies of the Cl4Q, H2Cl4Q and N-MePyꞏCl4Q (triclinic) systems calculated with PIXEL. All values in kcal/mol.

	System	Electrostatic Polarization	Dispersion	Repulsion	Total
	Cl4Q	-12.5	-4.3	-32.5	24.9	-24.4

Table S30

 S30 Configurations with non-negligible weights of the semiquinone dimer taken from the orthohombic systems obtained from CASPT2 calculations.

	Configuration	Occupation	Coefficient	Weight
	1	2222200000	-0.803930	0.646304
	27	2222020000	0.477195	0.227715
	43	222udud000	0.053558	0.002868
	78	2u22du00d0	-0.052513	0.002758
	104	2220202000	0.053388	0.002850
	107	2220200200	0.050254	0.002525
	121	22ud20ud00	0.100880	0.010177
	133	2u2d2ud000	0.070228	0.004932
	150	u22d2u0d00	-0.067819	0.004599
	180	2ud22u0d00	0.066296	0.004395
	193	u2d22ud000	-0.065494	0.004289
	226	ud2220ud00	-0.061943	0.003837
	2003	22ud02ud00	-0.060301	0.003636

Table S31

 S31 Configurations with non-negligible weights of the semiquinone dimer taken from the triclinic systems obtained from CASPT2 calculations.

	Configuration	Occupation	Coefficient	Weight
	1	2222200000	0.865446	0.748997
	27	2222020000	-0.344742	0.118847
	43	222udud000	0.060674	0.003681
	82	2u22du000d	0.051799	0.002683
	104	2220202000	-0.059547	0.003546
	107	2220200200	-0.053769	0.002891
	121	22ud20ud00	0.108331	0.011736
	133	2u2d2ud000	-0.078524	0.006166
	140	2u2d200ud0	0.052956	0.002804
	150	u22d2u0d00	-0.076069	0.005787
	154	u22d20u0d0	0.054455	0.002965
	164	2202202000	-0.051565	0.002659
	167	2202200200	-0.051016	0.002603
	180	2ud22u0d00	0.071029	0.005045
	184	2ud220u0d0	-0.052669	0.002774
	193	u2d22ud000	0.071703	0.005141
	200	u2d2200ud0	-0.053634	0.002877
	226	ud2220ud00	-0.067580	0.004567

Published in Crystal Growth & Design, 19[START_REF] Sies | Methods in Enzymology: Quinones and Quinone Enzymes[END_REF], 391-402. DOI 10.1021/acs.cgd.8b01484

Funding Sources

The work was financed by the Croatian Science Foundation, grant no. IP-2014-09-4079 and French-Croatian bilateral -Hubert Curien grant for years 2015-2016. We thank Gobierno de España MINECO (CTQ2014-56295-R and Severo Ochoa Excellence Accreditation 2014-2018 SEV-2013-031), FEDER funds (Project CTQ2014-56295-R) and the CERCA Programme/Generalitat de Catalunya are acknowledge for funding. B. Landeros-Rivera and J.

AUTHOR INFORMATION

Corresponding Author

*(Word Style "FA_Corresponding_Author_Footnote"). * (Word Style "FA_Corresponding_Author_Footnote"). KM: Department of Physical Chemistry, Rudjer Bošković Institute, Bijenička 54, HR-10000 Zagreb, Croatia, e-mail: kmolcano@irb.hr ; CJ: Cristallographie, Résonance Magnetique et Modélisations, UMR 7036, Institut Jean Barriol, CNRS and Université de Lorraine BP 70239, F54506 Vandoeuvre-les-Nancy CEDEX, France, email: christian.jelsch@univ-lorraine.fr.

Present Addresses †If an author's address is different than the one given in the affiliation line, this information may be included here.

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Supporting Information

N-MePyꞏCl4Q (orthorhombic)

Figure S26 Crystallographic structure of tetrachlorosemiquinone radical anion in N-MePyꞏCl4Q (orthorhombic) crystal. Bond distances depicted in green (Å). DFT tetramerization energies (TE) of the semiquinone species (TE) were computed as the energy difference between the tetramer and four monomers (two anions and two cations, geometries were fixed in both cases to those found in the crystal) at the broken symmetry B3LYP-D3(BJ)/def2-QZVPP level of theory. Three types of tetramers were selected: I) Anion-anion, cation-cation and anion-cation close contacts present, II) Anion-anion and anion-cation close contacts present, and III) cation-cation and anion-cation close contacts present (Scheme 1I). As was expected from the dimerization energies reported in our previous results, the favorable anion-cation interaction compensates for the anion-anion and cation-cation repulsion, therefore the tetramer (hence the crystal structure) is stabilized. Just as in the case of the dimers, the wavefunction stability test revealed an open-shell ground state electronic configuration for these complexes.