# π-mers and π-dimers: Two Radical Supramolecular Interactions – A Tutorial Review

Jean Joseph, Mathilde Berville, Jennifer Wytko, Jean Weiss, Henri-pierre Jacquot de Rouville

► To cite this version:

Jean Joseph, Mathilde Berville, Jennifer Wytko, Jean Weiss, Henri-pierre Jacquot de Rouville. π-mers and π-dimers: Two Radical Supramolecular Interactions – A Tutorial Review. Chemistry - A European Journal, 2024, 31 (2), pp.e202403115. 10.1002/chem.202403115. hal-04866327

HAL Id: hal-04866327

https://hal.science/hal-04866327v1

Submitted on 6 Jan 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>

# π-mers and π-dimers: Two Radical Supramolecular Interactions – A Tutorial Review

Jean Joseph,[a] Mathilde Berville,[a] Jennifer Wytko,[a] Jean Weiss,[a] and Henri-Pierre Jacquot de Rouville*[a]

To Prof. J. Fraser Stoddart, a fantastic mentor

<figure><img src="image_4.png" /></figure>
<figure><img src="image_5.png" /></figure>

In this review, the difference between π-mers (pimers) and π-dimers (pi-dimers) will be discussed. Often interchanged or confused in the literature, these two radical interactions lead to different or even opposite physico-chemical behaviors. This review aims at clarifying the terms π-mers and π-dimers and at

describing their main physico-chemical properties to address their differences. Finally, selected literature examples exhibiting the successive formation of π-mers and π-dimers within the same systems will be detailed to emphasize the physico-chemical changes occurring upon conversion.

# 1. Introduction

Supramolecular chemistry aims at studying molecular assemblies interacting through non-covalent and reversible intermolecular weak interactions (π stacking, hydrophobic interactions, hydrogen bonds, van der Waals interactions, etc.). The formation of π-mer (pimers) and π-dimer (pi-dimers) involving identical conjugated organic radicals has been an efficient addition to the supramolecular toolbox. The first example of a π-dimer dates back to the 1950s.[1] After observing the disappearance of paramagnetism in the EPR spectrum of a tetramethyl-p-phenylene diamine radical cation, Hausser attributed this observation to the association of two radical species and the antiferromagnetic coupling of their respective radicals. These findings were confirmed in 1972 by the resolution of the crystallographic solid-state structure of the corresponding π-dimer.[2] In the meantime, the first extensive investigation of π-dimer formation was performed in 1964 by Kosower et al. on the 1,1'-dimethyl-4,4'-bipyridinium core, also called methylviologen or paraquat.[3] Over the following decades, these radical-radical interactions received growing attention, as they provide both access to topologically interesting structures and are a means of inducing redox-controlled motion in molecules or assemblies.[4] These multi-centered interactions result from an overlapping of the half-empty π-orbitals of the radical motifs.[5] Usually falling into three categories according to the charge state of the chemical species (neutral, cationic, anionic),[6] these interactions lead to relatively weak associations in solution with equilibrium constants (Kₐ) ranging from 10¹ to 10³ L mol⁻¹.[7] The stabilization of π-mers and π-dimers is usually promoted by either i) the use of additional supramolecular forces (including solvophobicity), ii) low temperature of observation, iii) a constrained environment such as the use of a covalent spacer or mechanical bonds, or iv) the use of a confined environment (i.e. the formation of inclusion complexes and micellar environment).

Even though they are part of the most general radical-radical interactions, π-mer and π-dimer were historically and indistinctly referred to as pimerization processes. In 2003, J. K. Kochi clearly defined both terms[8] but they are still sometimes interchanged, misused or confused in literature reports,

especially in the field of viologens.[9,10] Thus, this article will provide neither an overview of π-mer and π-dimer motifs nor an exhaustive list of examples. Instead, the following pages aim at clarifying the differences between π-mers and π-dimers by providing and illustrating clear definitions. After an introductory section defining π-mers and π-dimers (section 2), the differences in their physico-chemical properties will be discussed (section 3). These properties are categorized according to the analytical techniques employed to characterize and observe the species, namely X-ray diffraction (section 3.1), UV/visible/NIR spectroscopy (section 3.2), electrochemistry (section 3.3) and NMR and EPR spectroscopies (section 3.4). In addition, some thermodynamic parameters will be provided for an in-depth comprehension of these interactions (section 4). Finally, selected examples of systems will be provided to illustrate the successive changes occurring in the formation of π-mers and π-dimers (section 5).

# 2. Definition of π-mers and π-dimers

Concepts related to the formation and stabilizing effects present in π-mers and π-dimers are introduced in this section. Simplified orbital diagrams will familiarize the reader with the notions of the stabilizing π-overlap existing between π-radicals[11] and highlight the difference between π-mers and π-dimers. This simple orbital description leads to a rationalization of all physico-chemical properties observed in these systems, thus introducing the notions required for the following sections. We first focus on π-dimers because they are more often encountered in the literature. Even though π-mers are intermediates – sometimes short-lived and/or not observed – in the formation of π-dimers, their case will be introduced last.

## 2.1. π-dimers

A π-dimer corresponds to the association of two radicals, either from acceptors A⁻· or from donors D⁺·, bearing the same charge to form a diamagnetic dimer (A₂)²⁻ or (D₂)²⁺ (Figure 1). The main driving force for π-dimer formation is the pairing of the degenerate semi-occupied orbitals (SOMOs) in a bonding combination to generate a new HOMO stabilized in energy (ΔH<sub>Res</sub>)[11] (Figure 1 bottom). Simultaneously, a new LUMO arises from the corresponding anti-bonding combination, thus leading to a new HOMO-LUMO transition (E<sub>CT</sub>). An essential parameter is the large π-delocalization of each radical species over each subunit. Consequently, the pairing interaction occurs on several atoms of each subunit and thus forms a multi-centered bond that is frequently referred to as a “pancake”

<figure><img src="image_6.png" /></figure>

<footnote>[a] J. Joseph, M. Berville, J. Wytko, J. Weiss, H.-P. Jacquot de Rouville
Institut de Chimie de Strasbourg, UMR 7177 CNRS, Université de Strasbourg
4, rue Blaise Pascal, 67000 Strasbourg, France
E-mail: hpjacquot@unistra.fr</footnote>

<footnote>© 2024 The Author(s). Chemistry - A European Journal published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution Non-Commercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.</footnote>
<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 1.** Top: Simplified reaction scheme describing the formation of π-dimers and simplified orbital diagram (Bottom left: Case of a radical cation generated from an electron donor. Bottom right: case of a radical anion from an electron acceptor).</figcaption></figure>

bond, as coined by Mulliken and Person.[12] The SOMO-SOMO interaction confers a covalent character to the new bond on account of electron pairing in π-dimers.

## 2.2. π-mers

A π-mer results from the association of a π-stabilized radical with its parent compound (Figure 2) to form a new donor-acceptor complex in which either a radical cation acts as an acceptor for a parent species or a radical anion acts as a donor for a parent species.[13] The π-mers are associated by electronic coupling between either the HOMO or the LUMO of the parent compound with the SOMO of the radical species ($ΔH_{Res}$) (Figure 2, bottom). Also called resonant-charge complexes, π-mers differ from classical charge transfer (CT) complexes.[14] Whereas in classical CT complexes only a fraction of the electron density is exchanged between both species, in π-mers an electron contributes to the formation of a new bond. Thus, π-mers can be seen as an extreme case of CT complexes. Despite the formation of this new bond, a π-mer is always in equilibrium with the separated and non-interacting species, thus conferring to the π-mer all the characteristics of a Robin-Day class II mixed valence or class III species. Indeed, the donor and the acceptor are sufficiently bound to display electronic intervalence transitions ($E_{IVCT}$) due to an internal sphere transfer mode. Hence, π-mers can be described as a continuum between a transient CT complex and a mixed valence species.[14] The interpretation of π-mers as mixed valence compounds justifies

<figure><img src="image_9.png" /></figure>

Jean Joseph studied supramolecular chemistry at the University of Strasbourg, where he received his B.Sc. in 2017 and his Master's degree in 2019. In 2019, he started his Ph.D. at the Institut de Chimie de Strasbourg under the supervision of Jennifer Wytko and Jean Weiss. His research has been focused on the topic of 4,4'-bipyridines synthesis and functionalization, their adsorption on a HOPG surface, and the synthesis of boron(III) and titanium(IV) based helicates. He is working as a Team Leader in organic chemistry at Eurofins Villapharma (Spain) since 2023.

<figure><img src="image_10.png" /></figure>

Mathilde Berville obtained her doctorate from l'Université de Strasbourg in 2015 under the direction of Jennifer Wytko and Jean Weiss. Her research has been focused on the topic of 4,4'-bipyridines macrocyclization and functionalization. She has found happiness in motherhood in 2018. She is now Herald in the Dota 2 video game.

<figure><img src="image_11.png" /></figure>

Jennifer Wytko obtained her doctorate from l'Université Louis Pasteur de Strasbourg in 1996 under the direction of Maurice Gross and Jean Weiss. After post-doctoral research with François Diederich at the ETH Zurich, she joined the CNRS in 1998 as a researcher in Strasbourg, first in M. Gross' laboratory and then with Jean Weiss. Her research focuses on self-assembly and redox-active molecules.

<figure><img src="image_12.png" /></figure>

Jean Weiss is a Research Director at the CNRS. He received his Ph.D. in 1986 under the supervision of J.-P. Sauvage. After two post-doctoral positions with Dr. D. J. Cram at UCLA and Prof. Dr. H. A. Staab at the Max Planck Institute in Heidelberg as an Alexander von Humboldt fellow, he joined the CNRS in Strasbourg and became independent in 1998. Since 2007, with his group, he has been interested in porphyrinoids associated with other heterocycles for application as hemoprotein models, redox molecular switches, self-assembling materials and in molecular electronics.

<figure><img src="image_13.png" /></figure>

Henri-Pierre Jacquot de Rouville graduated from the Université Paul Sabatier of Toulouse. In 2007, he joined C. Joachim's Group and obtained a Ph.D. degree for his synthesis of technomimetic molecules under the supervision of Professor G. Rapenne (CEMES-CNRS, Toulouse). From 2010–2012, he joined Professor J. F. Stoddart's Group as a postdoctoral fellow. Then, he moved back to France where he worked as a postdoctoral fellow with N. McClenaghan (ISM, Bordeaux). In 2013, he was appointed as researcher at the CNRS in Paris. In November 2017, he moved at the Institut de Chemistry de Strasbourg.
<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /><figcaption>**Figure 2.** Top: Simplified reaction scheme describing the formation of π-mers and simplified orbital diagram (Bottom left: Case of a radical anion generated from an electron acceptor. Bottom right: case of a cationic radical from a donor).</figcaption></figure>

the use of the term mixed-valence dimer commonly used in the literature.

The simplified orbital diagrams describing π-mer and π-dimer assemblies reflect the clear difference between both interactions, namely the number of electrons occupying the new HOMO formed from the bonding SOMO overlap of the radical partners. Whereas π-dimers correspond to a closed-shell species with the formation of a delocalized bond, π-mers have an open-shell electronic configuration with one electron shared between two partners. The respective intrinsic nature of π-mers and π-dimers consequently leads to a drastic distinction of their physico-chemical properties and, *in fine*, determines the choice of the techniques employed for their characterization.

### 3. Characterization of the Physico-Chemical Properties of π-mers and π-Dimers

Among the techniques used to distinguish π-mers from π-dimers, X-ray diffraction, UV/visible/NIR spectroscopy, electro-chemistry, NMR and EPR spectroscopies are most commonly utilized. Selected data obtained with these methods for π-mers and π-dimers will be briefly described and analyzed. However, only a combination of these techniques can confirm the formation of either π-mers or π-dimers.

#### 3.1. X-Ray Diffraction

Multi-centered interactions between radicals are often observed in the solid state. Hence, π-mers and π-dimers are characterized by interplanar contacts shorter than the usual π-stacking distances (e.g. 3.4–3.5 Å for polycyclic aromatic hydrocarbons). This structural parameter distinguishes the pancake bond from

conventional covalent bonds and π-stacking interactions. In π-mers and π-dimers, the distance separating the two radicals is usually smaller (3.2–3.3 Å) than a van der Waals distance.[15] Contrary to the nature of π-stacking, the multi-centered bond between two radicals in a π-dimer is highly directional. The bonding energy depends on the orientation of each species to maximize the SOMO overlap and simultaneously minimize the intermolecular electrostatic repulsion.[16] The most common arrangement can be rationalized, and therefore predicted, by the “maxmin” principle (see Box 1 and Figure 3)[17] which involves a maximum bonding overlap between interacting π-orbitals. Common π-mer and π-dimer building blocks and their interplanar distances are listed in Table 1.

Ultimately, X-ray diffraction reveals the existence of short contacts in π-mers and π-dimers but does not allow identification of the type of interaction. The main difference between π-

**Box 1: Maxmin Principle**

Interactions in π-mers and π-dimers mainly involve an attractive term where partially occupied frontier orbitals play a dominant role. To maximize the p-overlap of the frontier orbitals, two geometric parameters can be adjusted, namely the rotation angle (θ) of both aromatic rings with respect to each other and the translational shift (x,y) of the center-of-mass of the adjacent molecules.[17] As a consequence, a slight offset of the centers of mass and/or a dihedral angle can be often observed between radicals to maximize their interaction. These offsets also minimize intermolecular repulsions.

<figure><img src="image_16.png" /><figcaption>**Figure 3.** a) Parameters describing the relative positions of the centers-of-mass in π-mers and p-dimers (θ, x and y). b) Example of the naphthalene radical cation and its corresponding π-dimer with a maximum SOMO overlap for θ = 90°, x = 0, y = 0.</figcaption></figure>

The attractive contribution is counterbalanced by a repulsive term resulting from hard-core repulsion of close-lying atoms (number of intermolecular contacts). The repulsive term explains the large barrier to overcome to form the corresponding p-dimers²⁶ and the much longer distance than for a classical covalent bond.

<caption>**Figure 3.** a) Parameters describing the relative positions of the centers-of-mass in π-mers and π-dimers (θ, x and y). b) Example of the naphthalene radical cation and its corresponding π-dimer with a maximum SOMO overlap for θ = 90°, x = 0, y = 0.</caption>
Box 2: Davydov Shift

In addition to the appearance of the red-shifted IVCT and CT bands (e.g. E<sub>CT</sub> transition), the transitions corresponding to the original electronic transitions of the monomeric species are blue-shifted upon formation of π-dimers and π-mers, (Figure 4). This behavior can be rationalized by the stacked arrangement in the assembly leading to a Davydov shift.<sup>30</sup> The following simplified energy diagram for a π-dimer situation explains this tendency that accounts for the formation of both new bonding and anti-bonding orbitals and the larger transition band gaps.<sup>31</sup> When comparing the electronic transitions of the monomers (E<sub>M1</sub> and E<sub>M2</sub>) to the corresponding transitions in the dimers (E<sub>D1</sub> and E<sub>D2</sub>), both dimer transitions are more energetic (E<sub>D1</sub> > E<sub>M1</sub> and E<sub>D2</sub> > E<sub>M2</sub>).

<figure><img src="image_17.png" /><figcaption>Figure 4. Simplified orbital diagram showing the energy of the electronic transitions in p-dimers compared to the isolated monomer.</figcaption></figure>

<caption>Figure 4. Simplified orbital diagram showing the energy of the electronic transitions in π-dimers compared to the isolated monomer.</caption>

the parent counter-part. The solid-state absorbance of the CT complexes has a slightly red-shifted maximum in absorbance compared to their absorption in solution. This trend suggests that the discrete dimers persist in the solid state with an unchanged overall geometry. Finally, for π-mers, the absorption maximum of the IVCT band can be either solvent-dependent or solvent-independent depending on the building blocks. This observation can help distinguish a localized electron from an electron delocalized between two sites, respectively a Robin-Day Class II or Class III compound. Therefore, the electronic coupling parameter (H<sub>AD</sub>) can be estimated by Equation (1) for Class II and Equation (2) for Class III:

$$H_{DA} = \frac{0.0206 (v_{IVCT} \Delta v_{1/2} \varepsilon_{IVCT})^{1/2}}{r_{DA}} \quad (1)$$

$$H_{DA} = \frac{v_{IVCT}}{2} \qquad (2)$$

where v<sub>IVCT</sub> and Δv<sub>1/2</sub> are the spectral maximum and half-maximum width (cm<sup>-1</sup>) of the IVCT band respectively, ε<sub>IVCT</sub> is the corresponding molar extinction coefficient (L mol<sup>-1</sup> cm<sup>-1</sup>) and r<sub>DA</sub> (Å) is the distance between both redox centers in the π-mer.

3.3. Electrochemistry

Cyclic voltammetry is an efficient tool to form π-mers and π-dimers and probe their stability. In the simplest case of electrochemically generating a π-dimer from the corresponding monomer, the variation of the redox potential of the radical species reflects the stabilization of the π-dimer assembly compared to the monomer. For instance, for an oxidizable monomer, the apparent oxidation potential (E<sub>Ox1</sub>) will be cathodically shifted (towards less positive potentials) upon formation of a π-dimer. Conversely, for a reducible monomer, the apparent reduction potential will be anodically shifted (towards less negative potentials).<sup>[32]</sup> More interestingly, this overall stabilization is also observed for monomeric precursors undergoing two consecutive redox processes (Figure 5). The second process is shifted to more positive values if the monomer is oxidizable (E<sub>Ox2</sub> in Figure 5), whereas it is shifted to more negative values if the monomer is reducible. The domain of stability of the π-dimer lies between the E<sub>1/2</sub> potentials of both redox processes.

<figure><img src="image_18.png" /><figcaption>Figure 5. Comparison of the cyclic voltammograms of an oxidizable monomer (red curve) and its corresponding π-dimer (blue curve).</figcaption></figure>
<figure><img src="image_19.png" /></figure>

The redox-triggered formation of π-mers also demonstrates the efficient stabilization of the assembly.[33] Upon formation of a π-mer, the first redox process is split into two consecutive monoelectronic processes respectively corresponding to formation of the π-mer and then the π-dimer (Figure 6). As seen for π-dimers, the redox potential corresponding to π-mer formation will be more facilitated than those of the corresponding π-dimer and the monomeric precursor. Interestingly, the difference in potentials (ΔE<sub>Ox</sub>) of the respective E<sub>1/2</sub> of the redox couples of the π-mer (E<sub>Ox1</sub>) and π-dimer (E'<sub>Ox1</sub>) can lead to an estimate of the dimerization constant (K<sub>π-dimer</sub>) of the π-dimer when not accessible by other techniques.[34] This constant can be assessed by rearrangement of the Nernst equation as follows:

$$ \Delta E_{Ox} = E'_{Ox1} - E_{Ox1} = \frac{RT}{F} \ln \frac{K_{\pi-mer}}{K_{\pi-dimer}} \quad (3) $$

$$ K_{\pi-mer} = \frac{[\pi-mer]}{[X^-][X^+]} \quad (4) $$

$$ \text{and } K_{\pi-dimer} = \frac{[\pi-dimer]}{[X^+]^2} \quad (5) $$

where K<sub>π-mer</sub> is the dimerization constant of the π-mer with [X] and [X<sup>*</sup>] are the concentrations of the diamagnetic precursor and the radical respectively (see Section 4). Therefore, when K<sub>π-mer</sub> equals K<sub>π-dimer</sub>, E<sub>Ox1</sub> and E<sub>Ox1</sub>' are identical (ΔE<sub>Ox</sub>=0). As a consequence, only one wave is detected by electrochemistry. A similar behavior occurs for a weak stabilization of the π-mer

<figure><img src="image_20.png" /><figcaption>Figure 6. Cyclic voltammograms illustrating π-mer formation followed by π-dimer formation from an oxidizable monomer (blue curve) and comparison with the monomer (red curve).</figcaption></figure>

compared to the π-dimer (K<sub>π-mer</sub> < K<sub>π-dimer</sub>, thus ΔE<sub>Ox</sub> < 0). However, when the π-mer is more stable than its corresponding π-dimer (K<sub>π-mer</sub> > K<sub>π-dimer</sub>), two redox processes are observed by electrochemical techniques (ΔE<sub>Ox</sub> > 0).

In addition to standard electrochemical techniques (cyclic voltammetry, square-wave voltammetry, etc.), UV/visible/NIR spectroelectrochemistry is a powerful method to investigate the absorption properties of π-mers and π-dimers. This technique allows the selective electrolysis of each species by carefully choosing the potential. Consequently, the electronic spectra of the π-mer and π-dimer can be monitored cleanly and selectively.

### 3.4. NMR and EPR Spectroscopy

The major difference between π-mers and π-dimers lies in their respective open-shell and closed-shell electronic structures. In solution, EPR spectroscopy is a relevant technique for the characterization of π-mers. The EPR spectra of π-mers display less hyperfine coupling than their isolated monomer, thus resulting in an expected increase of spin exchange rate. In addition, hyperfine coupling constants are generally half those of the monomer due to delocalization of an unpaired electron within the dimer. In contrast, π-dimers are diamagnetic and lead to recovered NMR signals in comparison to their radical monomer. The major limitation of the NMR technique is the difficulty in attaining the concentration of π-dimers. Even if π-dimers are EPR-silent, EPR experiments are relevant to show their formation in addition to NMR spectroscopy. For instance, the observation of the reversible decrease of the EPR signal of a radical upon lowering the temperature can be monitored. The intensity of the signal can be used to quantify the ratio between π-dimerized radicals and their isolated counter-parts. Therefore, the speciation of π-dimer and monomer is known and the K<sub>π-dimer</sub> can be estimated. Interestingly, EPR allows a direct assessment of the dimeric nature of π-dimers since upon dilution a sigmoid shaped curve of the signal intensity should be monitored for l=f([monomer]).

This last section clearly shows that their open- and closed-shell structures differentiate π-mers and π-dimers. As expected, their direct detection can be performed by EPR and NMR spectroscopy respectively (Figure 7). Both interactions show an additional electronic band in the NIR region due to an allowed HOMO/LUMO transition in the newly formed frontier orbitals (see section 2).

### 4. Thermodynamics

The dimerization constant (K<sub>Dim</sub>) of π-mers and π-dimers is the most frequently quantified thermodynamic parameter. Two techniques are used, namely EPR (variation of the signal) and UV/ visible/NIR spectroscopies (increase/decrease of the CT band). The speciation of the dimer can thus be estimated and then K<sub>Dim</sub> of π-mers and π-dimers can be modeled because they correspond to simple association models (Box 3). As in all supramolecular processes, the monomer/π-mer and monomer/π-dimer equilibria are modulated by the temperature. The temperature dependence allows an estimation of the thermodynamic parameters by analysis
<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /><figcaption>**Figure 7.** Summary of differences of the physico-chemical properties of π-mers and π-dimers.</figcaption></figure>

of a van't Hoff plot. The consistency in the $K_{Dimr}$, $\Delta H^0$ and $\Delta S^0$ values determined by both techniques is unquestionable proof of the electron sharing between the building blocks (Table 3).

Examination of the thermodynamic parameters (Table 3) shows that the order of magnitude of the $\Delta H^0$ and $\Delta S^0$ contributions is within the same range for both types of assemblies, thus suggesting no real influence of the charge. Consequently, repulsive forces do not play a major role in destabilizing the assembly. Compared to π-mers, π-dimers are more enthalpically favored but are entropically disfavored. The enthalpic stabilization reflects the stabilization arising from electron pairing in π-dimers. This interpretation is in agreement with $\lambda_{CT}$ (π-dimers) < $\lambda_{IVCT}$ (π-mers). In comparison, the entropic stabilization of π-mers results from the shielding of the solvated charged/uncharged partner in the final assembly. This is in agreement with the lack of influence of the nature of the counter-ion on the thermodynamics of the systems. In other words, π-mers

and π-dimers are well solvated and do not result from a partial shielding by the counter-ion. Consequently, $K_{Dim}$ is affected by the solvent in both types of complexes. In general, the enthalpy of π-mer and π-dimer formation increases with increasing solvent polarity. However, the characteristics of CT bands ($\lambda_{CT}$ and $\varepsilon_{CT}$) are strikingly the same in different solvents. This observation reflects the fact that the geometry of the complexes is not altered.

In conclusion, from a thermodynamic point of view, the formation of a π-dimer is enthalpically favored and entropically disfavored, and thus, mostly observed at low temperature. The free enthalpy contribution to the formation of dimers is low at room temperature (energy in the range of that of van der Waals interactions) hence leading to quite low dimerization constants. Options to increase these constants include using the solvophobicity effect of H₂O, a confined medium, a high concentration or all of the above.

## 5. Selected Examples of the Literature

For the purpose of this review, three literature examples illustrating the formation of π-mers and subsequent formation of π-dimers are presented. It seemed appropriate to focus on the same building block, namely tetrathiafulvalene (TTF), to provide different aspects related to the TTF⁺/TTF π-mer assembly versus the TTF⁺/TTF⁺π-dimer assembly. The tendency of TTF to form radical-radical assemblies was discovered by Torrance *et al.* in 1979 but these assemblies suffer from poor stability in solution.[39] The selected examples reflect most of the various means of stabilizing radical-radical assemblies, including the use of a covalent spacer, a confined environment (here supramolecular cages) and a mechanical bond. These examples also show the physico-chemical changes observed in these different systems upon the successive formation of π-mer and π-dimer. In all cases, the purpose of each approach is to limit the detrimental influence of entropy.

<table><caption>**Table 3.** Thermodynamic parameters ($K_{Dimr}$, $\Delta H^0$, $\Delta S^0$) of π-mers and π-dimers for selected building blocks in CH₂Cl₂.</caption><thead><tr><th rowspan="2">Acronym</th><th colspan="4">π-mers</th><th colspan="4">π-dimers</th><th rowspan="2">Reference</th></tr><tr><th>K<sub>π-mer</sub><br>(L<sup>-1</sup> mol)</th><th>ΔH<sup>0</sup><br>(kcal mol<sup>-1</sup>)</th><th>ΔS<sup>0</sup><br>(eu)</th><th>ΔG<sup>0</sup><sub>298 K</sub><br>(kcal mol<sup>-1</sup>)</th><th>K<sub>π-dimer</sub><br>(L<sup>-1</sup> mol)</th><th>ΔH<sup>0</sup><br>(kcal mol<sup>-1</sup>)</th><th>ΔS<sup>0</sup><br>(eu)</th><th>ΔG<sup>0</sup><sub>298 K</sub><br>(kcal mol<sup>-1</sup>)</th></tr></thead><tbody><tr><td>OMB</td><td>350</td><td>-2.5</td><td>-2</td><td>-3.5</td><td>0.22</td><td>-9.0</td><td>-33</td><td>+0.9</td><td>[14,8]</td></tr><tr><td>TTF</td><td>6</td><td>-5.5</td><td>-16</td><td>-1.1</td><td>0.6</td><td>-8.0</td><td>-28</td><td>+0.3</td><td>[14,27]</td></tr><tr><td>TCNQ</td><td>5</td><td>-3.3</td><td>-7</td><td>-1.0</td><td>0.005</td><td>-9.8</td><td>-42</td><td>+3.1</td><td>[14,8]</td></tr><tr><td>DDQ</td><td>11</td><td>-3.2</td><td>-6</td><td>-1.4</td><td>0.28</td><td>-7.6</td><td>-28</td><td>+0.8</td><td>[14,8]</td></tr><tr><td>TCNE</td><td>4.5</td><td>-3.4</td><td>-8.5</td><td>-0.9</td><td>~7×10<sup>-4</sup></td><td>-8.8</td><td>-41</td><td>+4.3</td><td>[14,8]</td></tr><tr><td>Phen</td><td>90</td><td>-6.5</td><td>-13</td><td>-2.7</td><td>0.16</td><td>-8.8</td><td>-33</td><td>+1.1</td><td>[29,8]</td></tr><tr><td>MV</td><td>-</td><td>-</td><td>-</td><td>-</td><td>600<sup>(a)</sup></td><td>-1.6<sup>(b)</sup></td><td>8<sup>(b)</sup></td><td>-3.8<sup>(b)</sup></td><td>[35<sup>(b)</sup>]</td></tr><tr><td>Zn(II)-OEP<sup>(c)</sup></td><td>-</td><td>-</td><td>-</td><td>-</td><td>25120<sup>(c)</sup></td><td>-17.5<sup>(c)</sup></td><td>-38<sup>(c)</sup></td><td>-6.0</td><td>[36]</td></tr></tbody></table>

[a] Determined in H₂O at 298 K. [b] Determined in CH₃OH. [c] Determined in CH₃OH/CHCl₃ (10:1) at 293 K.
<figure><img src="image_23.png" /><figcaption>**Figure 8.** TTFs on a covalent calix[4]arene platform and their oxidation.[40]
Red = neutral TTF; yellow = TTF⁺.</figcaption></figure>

## 5.1. Covalent Spacer

Linking two redox-active units by covalent bonds offers the advantage of incorporating by design a relatively precise spatial arrangement of the redox-active units. Nevertheless, the structure must also be capable of some internal movement to facilitate the face-to-face arrangement required for π-dimerization or pimerization of the redox-active units. The main drawback of covalently linking the units is the number of synthetic steps often required.

The group of Sallé[40] chose a calix[4]arene (calix) as a somewhat flexible platform to attach two TTF moieties by a simple synthetic strategy. A four-atom spacer linking phenolic oxygen atoms of the calix to the TTFs provides additional flexibility (Figure 8). Each TTF can undergo two reversible one-electron oxidations. In cyclic voltammetry in CH3CN/CH2Cl2, the first oxidation wave of this compound is broad compared to the better-defined second oxidation wave. The broadness of the first wave indicates interactions between the two TTF⁺· whereas the shape of the second oxidation wave is characteristic of isolated dicationic TTF2⁺ moieties due to electrostatic repulsion.

## Box 3: Dimers or Oligomers?

A frequently asked question in the study of π-mers and π-dimers is the number of interacting units. To ensure that no oligomers are formed, the following two equations can be used.

Equation relating the binding constant and the concentration of radical in π-mers:¹³, ³⁷

$$ \frac{[X^-]}{A_{IVCT}} = \frac{1}{\varepsilon_{IVCT}} + \frac{1}{(K_{\pi-dimer} \varepsilon_{IVCT} [X^-])} \quad (6) $$

where [X] and [X⁺] are the concentrations of the diamagnetic precursor and the radical respectively, and AIVCT and εIVCT is the absorbance and molar extinction coefficient of the IVCT band. Therefore, if the plot of [X⁺]/AIVCT = f(1/[X]) gives a straight line, only dimeric species are formed, thus excluding oligomers.

Equation relating the binding constant and the concentration of radical in π-dimers:³⁸

$$ K_{\pi-dimer} = \frac{A_{CT}}{\varepsilon_{CT}(1-\alpha)^2 C_0^2} \quad (7) $$

where C0 is the total radical concentration, a is the degree of dissociation, and ACT and εCT are the absorbance and molar extinction coefficient of the CT band respectively. In an analogous way than p-mers, only dimeric species are formed if the linear relationship ACT = f(1/[C0]²) holds true.

Finally, the thermodynamic parameters can be estimated by analyzing a van't Hoff plot. Plotting R × ln(K) as a function of T⁻¹ leads to the ΔH⁰ and ΔS⁰ values according to the following equation:

$$ R \times \ln(K) = - \frac{\Delta H^{0}}{T} + \Delta S^{0} \quad (8) $$

The nature of the interactions between the TTF moieties after the first oxidation was investigated by UV/visible/NIR spectroscopy. Chemical oxidation with NOSbF₆ in CH3CN led to the appearance of new bands at 1750 and 765 nm that both reached a maximum intensity upon addition of one and two equivalents of oxidant respectively. Based on these observations, the NIR band was attributed to the [(TTF)₂]⁺·π-mer and the band at 765 nm to the (TTF⁺·)₂ π-dimer. Both bands are observed in the presence of one equivalent of oxidant, indicating an equilibrium between the π-mer and π-dimer. The hinge-like nature of the calixarene and the flexibility of the bridges to the TTFs allow favorable interactions at room temperature between two TTFs on opposite edges of the lower rim upon oxidation. This study demonstrates that preorganization and flexibility play key roles in the formation of π-mers and π-dimers in a structure with covalently linked redox-active subunits.

## 5.2. Confined Environment

Among methods promoting intermolecular interactions, the inclusion of the two interacting molecular species within a host or a cavity offers an elegant way to counter the entropy effects. To
<figure><img src="image_24.png" /></figure>

this end, TTF is the most appropriate building block due to its
initial neutral state. Whereas confinement of the initial state is
impossible in the case of dicationic viologens due to electrostatic
repulsion, two neutral TTF moieties are readily able to interact
through van der Waals and hydrophobic interactions within a
suitably designed host. A scholarly example illustrating the
advantages of confinement was reported by Fujita and co-workers
in the case of a self-assembled host accommodating two TTFs in
aqueous medium.[41]

In this work, a cage constructed on a pillared organic
framework organizes two parallel tris(4-pyridyl)triazine moieties
connected by three 2,2',6,6'-tetramethyl-bipyridines and six Pd(II)
ethylene diamine corner pieces as seen in Figure 9. The separation
between the flat aromatic triazine derivatives is approximately
10 Å and the resulting cavity can accommodate two neutral TTF
molecules in aqueous medium. The host-guest interactions result
from hydrophobic interactions within the host cavity and
maximum van der Waals interactions between the TTFs. The
formation of the clathrate complex (Figure 9, structure A) was
confirmed by mass spectrometry and the observation of a charge
transfer band in the UV-visible spectrum (~740 nm) that results
from the interaction between the TTF (electron rich) and the
triazine derivative (electron poor).

Electrochemical studies showed drastic changes in the TTF
behavior when confined in the host cavity. Square-wave voltam-
metry showed two distinct oxidation steps: a one-electron
oxidation of half of the TTF at 152 mV vs. AgCl/Ag and a one-
electron oxidation of the other half of the TTF at 304 mV vs. AgCl/
Ag. Spectroelectrochemical measurements detected a broad
absorption band at λ<sub>max</sub> = ~2000 nm after electrolysis at 180 mV
vs. AgCl/Ag, which confirmed the formation of the [(TTF)<sub>2</sub>]<sup>•</sup>π-mer
(compound B, Figure 9) after oxidation of the first half of TTF. This

species exhibited remarkable stability (t₁/₂ = ~1 day) and its further
oxidation at 400 mV generated an intense absorption band at
758 nm that is characteristic of the formation of a (TTF⁺⁻)₂ π-dimer
(compound C in Figure 9) upon oxidation of the second half of
TTF. These results clearly demonstrate the advantages of confining
radical species to increase their stability and to favor the
observation of otherwise unstable molecular species.

**5.3. Mechanical Bond**

Lastly, employing mechanical bonds to preorganize two TTF units
takes advantage of the above-mentioned approaches. As in the
covalent approach, a restricted number of degrees of freedom can
be achieved. In addition, sophisticated molecular structures can be
obtained in a limited number of steps as in the confined
environment approach.

Stoddart and coworkers reported the synthesis of a
[3]catenane composed of the cyclobis(paraquat-4,4'-biphenylene)
cyclophane as an electron poor central ring accommodating two
electron rich TTF-based cyclophanes (A in Figure 10).<sup>[42]</sup> This
interlocked molecule also possess two additional interacting units
in the structure of the TTF macrocycle, namely a
(1,5)dioxynaphthalene aromatic core. Upon chemical oxidation
with one equivalent of Fe(ClO<sub>4</sub>)<sub>3</sub>, this interlocked system shows
the typical spectral features of the (TTF)<sub>2</sub><sup>•</sup> π-mer (B in Figure 10)
as demonstrated by the increase of its EPR signal and the presence
of an IVCT band at 2040 nm. Addition of a second equivalent of
oxidant led to the formation of the corresponding (TTF<sup>+</sup>)<sub>2</sub> π-dimer
(C in Figure 10). This conversion was confirmed by the drastic
change of the absorbance in the NIR region with the concomitant
decrease of the IVCT band and the increase of a CT band at

<figure><img src="image_25.png" /><figcaption>**Figure 9.** Stepwise oxidation of a bis-TTF chlathrate (A) showing the successive formation of π-mer (B) and π-dimer (C) species within a molecular cage. Only the redox events taking place in the confined space are represented.[41] Red = neutral TTF; yellow = TTF⁺⁻.</figcaption></figure>

<figure><img src="image_26.png" /><figcaption>**Figure 10.** Schematic illustration of the [3]catenane synthesized by Stoddart and coworkers.[42] Red = neutral TTF; yellow = TTF⁺⁻; green = TTF²⁺; blue = - paraquat; grey = (1,5)dioxynaphthalene.</figcaption></figure>
806 nm. In addition, the diamagnetic nature of the [3]catenane was unambiguously established by a well-resolved ¹H NMR spectrum and the quasi disappearance of the EPR signal. Interestingly, this interlocked molecule can be oxidized to its fully oxidized state (8 + state) with only four equivalents of oxidant (D in Figure 10).

Electrochemistry proved to be a powerful tool in understanding the mechanical behavior of the [3]catenane. Compared to the isolated TTF macrocycle that undergoes two reversible oxidation processes at c.a. +0.36 V and +0.75 V (vs AgCl/Ag), the interlocked molecule exhibits a splitting of the first oxidation process into two waves at +0.41 V and +0.63 V. This behavior is explained by the formation of the intermediate π-mer species that stabilizes the neutral TTF, thus rendering more difficult its oxidation and the formation of the π-dimer. After a second monooxidation leading to the π-dimer formation, an additional bi-electronic oxidation (+0.80 V) was observed. The redox potential for the complete oxidation of the catenane is higher than that of the isolated TTF macrocycle. This observation confirms the stabilization induced by the formation of the π-dimer within the cavity of the electron poor ring. After this last oxidation, charge repulsion between the fully oxidized TTFs and the paraquat units leads to rotation of the TTF²⁺-containing macrocycles with respect to the paraquat cyclophane. This interpretation was supported by the reduction of the 8 + state to the 6 + state at +0.71 V, which is also a value higher than that of the free macrocycle. This mechanical behavior involving stabilization of both types of dimers within the macrocycle and ring rotation upon complete oxidation of the TTFs was coined as an affinity *umpolung*. Finally, remarkable solid-state structures of the π-mer and π-dimer states of the [3]rotaxanes reveal short interplanar distances of 3.56 and 3.42 Å between both mono-oxidized TTFs. In this example, the formation of π-mers and π-dimers was exploited to influence the mechanical response in interlocked molecules, thus paving the way to a new generation of molecular machines.

## 6. Summary and Outlook

Under specific conditions, neutral, cationic or anionic radical species can associate in dimers that can be paramagnetic when a radical interacts with a closed-shell parent species or diamagnetic when two radical species interact together. In both cases, the interaction results from the formation of a multi-centered bond called a "pancake bond" in which the bonding orbital contains one electron (π-mer) or two electrons (π-dimer). As shown in this non-exhaustive tutorial, the formation of π-mers and π-dimers can be enforced by design with a careful selection of linkers, platforms, hinges and macrocycles. The large field of applications in the design and synthesis of molecular architectures that utilize these radical interactions has not been evoked and reviews on this subject can be found elsewhere.

## Acknowledgements

This work was supported by the CNRS and the University of Strasbourg. We gratefully acknowledge the Interdisciplinary Thematic Institute SysChem via the IdEx Unistra (ANR-10-IDEX-0002) within the program Investissement d'Avenir and the ANR (APGG 2022, ACROSS, ANR-22-CE07-0014 and PRIMO grant, ANR-12-BS07-0014-01) for financial support.

## Conflict of Interests

The authors declare no conflict of interest.

## Data Availability Statement

No primary research results, software or code have been included and no new data were generated or analyzed as part of this review.

Keywords: Supramolecular chemistry · Radical-radical interaction · Pimer · Pi-dimers

[1] K. H. Hausser, Z. *Naturforsch.* **1956**, *11a*, 20.

[2] M. J. Hove, B. M. Hoffman, J. A. Ibers, *J. Chem. Phys.* **1972**, *56*, 3490–3502.

[3] E. M. Kosower, J. L. Cotter, *J. Am. Chem. Soc.* **1964**, *86*, 5524–5527.

[4] K. Cai, L. Zhang, R. D. Astumian, J. F. Stoddart, *Nat. Rev. 2021*, *5*, 447–465.

[5] J. S. Miller, J. J. Novoa, *Acc. Chem. Res.* **2007**, *40*, 189–196.

[6] a) K. E. Preuss, *Polyhedron* **2014**, *79*, 1–15; b) J. M. Spruell, *Pure Appl. Chem.* **2010**, *82*, 2281–2294.

[7] D.-W. Zhang, J. Tian, L. Chen, L. Zhang, Z. T. Li, *Chem. Asian J.* **2015**, *10*, 56–68.

[8] J.-M. Lü, S. V. Rosokha, J. K. Kochi, *J. Am. Chem. Soc.* **2003**, *125*, 12161–12171.

[9] J. P. Peterson, A. H. Winter, *Org. Lett.* **2020**, *22*, 6072–6076.

[10] M. J. Juetten, A. T. Buck, A. H. Winter, *Chem. Commun.* **2015**, *51*, 5516–5519.

[11] a) T. Bally, K. Roth, R. Straub, *J. Am. Chem. Soc.* **1988**, *110*, 1639–1641; b) M. Kertesz, *Chem. Eur. J.* **2019**, *25*, 400–416.

[12] R. S. Mulliken, W. B. Person, *Molecular Complexes*, Chap. Vol. 16, Wiley, Chichester **1969**, p. 259.

[13] J. K. Kochi, R. Rathore, P. Le Maguères, *J. Org. Chem.* **2000**, *65*, 6826–6836.

[14] S. V. Rosokha, J. K. Kochi, *J. Am. Chem. Soc.* **2007**, *129*, 3683–3697.

[15] K. Goto, T. Kubo, K. Yamamoto, K. Nakasuji, K. Sato, D. Shiomi, T. Takui, M. Kubota, T. Kobayashi, K. Yakusi, J. Ouyang, *J. Am. Chem. Soc.* **1999**, *121*, 1619–1620.

[16] C. Gourlaouen, S. Vela, S. Choua, M. Berville, J. A. Wytko, J. Weiss, V. Robert, *Phys. Chem. Chem. Phys.* **2018**, *20*, 27878–27884.

[17] T. Devic, M. Yuan, J. Adams, D. C. Fredrickson, S. Lee, D. Venkataraman, *J. Am. Chem. Soc.* **2005**, *127*, 14616–14627.

[18] J. Huang, S. Kingsbury, M. Kertesz, *Phys. Chem. Chem. Phys.* **2008**, *10*, 2625–2635.

[19] X. Qu, J. Lu, J. F. Boas, A. M. Bond, L. L. Martin, *Chem. Eur. J.* **2011**, *17*, 9350–9358.

[20] N. Leblanc, N. Mercier, O. Toma, A. Hadi Kassiba, L. Zorina, P. Auban-Senzier, C. Pasquier, *Chem. Commun.* **2013**, *49*, 10272–10274.

[21] T. M. Bockman, J. K. Kochi, *J. Org. Chem.* **1990**, *55*, 4127–4135.

[22] B. A. Scott, S. J. La Placa, J. B. Torrance, B. D. Silverman, B. Welber, *J. Am. Chem. Soc.* **1977**, *99*, 6631–6639.

[23] K. Yakushi, S. Nishimura, T. Sugano, H. Kuroda, *Acta Cryst.* **1980**, *B36*, 358–363.
<figure><img src="image_27.png" /></figure>

[24] W. R. Scheidt, K. E. Brancato-Buentello, H. Song, K. V. Reddy, B. Cheng, *Inorg. Chem.* **1996**, *35*, 7500–7507.

[25] H. Song, C. A. Reed, W. R. Scheidt, *J. Am. Chem. Soc.* **1989**, *111*, 6867–6868.

[26] M. R. Geraskina, A. S. Dutton, M. J. Juetten, S. A. Wood, A. H. Winter, *Angew. Chem. Int. Ed.* **2017**, *56*, 9435–9439.

[27] S. V. Rosokha, J. K. Kochi, *J. Am. Chem. Soc.* **2007**, *129*, 828–838.

[28] V. Ganesan, S. V. Rosokha, J. K. Kochi, *J. Am. Chem. Soc.* **2003**, *125*, 2559–2571.

[29] D. Small, V. Zaitsev, Y. Jung, S. V. Rosokha, M. Head-Gordon, J. K. Kochi, *J. Am. Chem. Soc.* **2004**, *126*, 13850–13858.

[30] J.-F. Penneau, B. J. Stallman, P. H. Kasai, L. L. Miller, *Chem. Mater.* **1991**, *3*, 791–796.

[31] P. Bäuerle, U. Segelbacher, A. Maier, M. Mehring, *J. Am. Chem. Soc.* **1993**, *115*, 10217–10223.

[32] W. Sung Jeon, H.-J. Kim, C. Lee, K. Kim, *Chem. Commun.* **2002**, 1828–1829.

[33] M. Hasegawa, K. Daigoku, K. Hashimoto, H. Nishikawa, M. Iyoda, *Bull. Chem. Soc. Jpn.* **2012**, *85*, 51–60.

[34] a) L. Huchet, S. Akoudad, E. Levillain, J. Roncali, A. Emge, P. Bäuerle, *J. Phys. Chem. B* **1998**, *102*, 7776–7781; b) H. Spanggaard, J. Prehn, M. Brøndsted Nielsen, E. Levillain, M. Allain, J. Becher, *J. Am. Chem. Soc.* **2000**, *122*, 9486–9494.

[35] A. G. Evans, J. C. Evans, M. W. Baker, *J. Chem. Soc., Perkin Trans. 2* **1977**, 1787–1789.

[36] J. H. Fuhrhop, P. Wasser, D. Riesner, D. Mauzerall, *J. Am. Chem. Soc.* **1972**, *94*, 7996–8001.

[37] H. A. Benesi, J. H. Hildebrand, *J. Am. Chem. Soc.* **1949**, *71*, 2703–2707.

[38] A. Yamagishi, *Bull. Chem. Soc. Jpn.* **1975**, *48*, 2440–2447.

[39] J. B. Torrance, B. A. Scott, B. Welber, F. B. Kaufman, P. E. Seiden, *Phys. Rev. B* **1979**, *19*, 730–741.

[40] J. Lyskawa, M. Sallé, J.-Y. Balandier, F. Le Derf, E. Levillain, M. Allain, P. Viel, S. Palacin, *Chem. Commun.* **2006**, 2233–2235.

[41] M. Yoshizawa, K. Kumazawa, M. Fujita, *J. Am. Chem. Soc.* **2005**, *127*, 13456–13457.

[42] J. M. Spruell, A. Coskun, D. C. Friedman, R. S. Forgan, A. A. Sarjeant, A. Trabolsi, A. C. Fahrenbach, G. Barin, W. F. Paxton, S. K. Dey, M. A. Olson, D. Benítez, E. Tkatchouk, M. T. Colvin, R. Carmielli, S. T. Caldwell, G. M. Rosair, S. Gunatilaka Hewage, F. Duclairoir, J. L. Seymour, A. M. Z. Slawin, W. A. Goddard III, M. R. Wasielewski, G. Cooke, J. F. Stoddart, *Nature Chem.* **2010**, *2*, 870–879.

Manuscript received: August 19, 2024

Accepted manuscript online: November 5, 2024

Version of record online: November 27, 2024
π-mers and π-dimers are two radical interactions being easily confused on account of their similarities. This tutorial review introduces i) a clear definition of each interaction, ii) their main physico-chemical differences observable by major analytical techniques (X-Ray, UV/Vis/NIR, EPR, NMR and electrochemistry), iii) some of their thermodynamic features, and iii) examples showing strategies to enhance their stability (using a covalent spacer, a confined environment and mechanical bonds).

<figure><img src="image_28.png" /></figure>

J. Joseph, M. Berville, J. Wytko, J. Weiss, H.-P. Jacquot de Rouville*

1 – 13

π-mers and π-dimers: Two Radical Supramolecular Interactions – A Tutorial Review