# The Structronic Concept: Harnessing Carbon-Carbon Chemical Bonding for Electron Storage and Related Applications

Éric Brémond,[a] Magdaléna Hromadová,[b] and Philippe P. Lainé*[a]

[a] Dr. É. Brémond, Dr. P. P. Lainé
Université Paris Cité, CNRS, ITODYS,
15 rue J-A de Baif, F-75013 Paris (France)
E-mail: philippe.laine@u-paris.fr

[b] Dr. M. Hromadová
Department of Electrochemistry at the Nanoscale
J. Heyrovský Institute of Physical Chemistry of the Czech Academy of Sciences
Dolejškova 3, 182 23 Prague (Czech Republic)

**Abstract:** While the concept of storing electrons in chemical bonds is not new, innovative approaches to achieve it continue to emerge. This applies to the structronic electrochemical paradigm. Typically, when strategically positioned in space, electrophoric components within structronic functional assemblies –featuring potent electrophilic centers (i.e., atomic orbitals with a significant contribution to the LUMO of their redox-active components)– can engage in direct electronic interactions through sigma-type orbital overlap, creating a set of so-called supra-molecular orbitals (supra-MOs). The core idea is to fill the potentially bonding supra-LUMO with electrons, thereby storing them in the form of a weakened (elongated) reservoir bond. This approach bypasses electrostatic limitations by leveraging the quantum behavior of electrons within covalent bonds. Structronic assemblies are bistable systems that can be electrochemically cycled, allowing for the charging and discharging of stored electrons. This Concept Article aims to define the conditions necessary for generating these supra-MOs, explore their electrochemical characteristics (such as hysteretic electrochemical behaviors and inversion of redox potentials), and highlight potential applications in advanced energy storage and other fields within the dynamic scope of electrochemistry.

## 1. Introduction

Electrical energy from sustainable sources like solar and wind is inherently intermittent, making energy storage essential for reliable on-demand use. In the realm of electrochemical energy storage and conversion devices such as batteries,[1] two key trends are emerging in the pursuit of sustainability. On the one hand, there is a shift in the choice of functional materials, moving from inorganic to transition-metal-free (organic) storage systems. This shift is evident in the growing development of redox-flow batteries for large-scale applications and organic solid-state batteries for mobile uses, often in place of traditional lithium-ion batteries (for example). On the other hand, there is a shift in engineering focus from macroscopic manufacturing toward precise molecular-level tuning.[2] Interestingly, one of the simplest and oldest alternatives to conventional batteries is renewable electricity storage through electrolysis (water electrolysis to dihydrogen and dioxygen is an archetypal example).[3] The point we want to emphasize is that our approach differs from traditional

methods, which use *catalysts* to recombine bonds and store solar-generated electrical energy as "solar fuels" in the gas phase, ultimately producing high-energy-density liquid fuels with energy densities often exceeding those of batteries.[4] Instead, we focus on a *non-catalyzed* process involving the filling of empty bonding orbitals with "sustainable electrons" (e.g., from a photovoltaic source) to create "reservoir" bonds. This strategy aligns with the concept of "orbital engineering," which highlights that a chemical bond provides the smallest known volume for storing electrons.[4] The concept discussed here, termed "structronic" –a neologism combining "structure" and "electronics"–[5] is based on the idea that electron storage forms a covalent "reservoir" bond that is fully integrated into the structure of a functional covalent assembly called a *superelectrophore*. In particular, redox (reduction/oxidation) activity is centered on this reservoir bond, which is weakened (stretched) by local steric constraints and lowered electron density (see below). Although certain coordination and organometallic compounds are known for their ability to store electron pairs in C-C bonds,[6] this article focuses specifically on purely organic species capable of such storage, aligning with sustainability goals that prioritize avoiding metals potentially associated with resource scarcity and toxicity concerns. Special attention will be given to the *pyridinium platform*, a prototypical structure that appears to be particularly well suited for this purpose.

Éric BRÉMOND was born in Le Brusc, France, in 1986. He graduated from École Nationale Supérieure de Chimie de Montpellier (France) in 2009 and completed his Ph.D. in Theoretical Chemistry at Chimie ParisTech (France) in 2012. After two years as a postdoctoral fellow at École Polytechnique Fédérale de Lausanne (Switzerland), he undertook a second postdoctoral position at Istituto Italiano di Tecnologia in Genoa (Italy), which lasted three years. In September 2017, he secured a tenure position and joined University Paris Cité (France) as an Associate Professor. His primary research

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interests include developments and applications of DFT and TDDFT.

Dr. Magdaléna Hromadová is a Senior Researcher at the J. Heyrovský Institute of Physical Chemistry in Prague, Czech Republic heading the

Department of Electrochemistry at the Nanoscale. She holds an Associate Professorship in Physical Chemistry. She received her Ph.D. in 1998 from Georgetown University, Washington, D.C., USA under the supervision of Prof. R. de Levie. Later she joined the group of Prof. W.R. Fawcett at the University of California, Davis as a postdoctoral fellow. Her main interest is in the field of the mechanistic aspects of charge transfer and charge

transport for various applications including electron storage and molecular electronics.

Dr. Philippe P. Lainé is currently a CNRS Senior Researcher (Research Director) at the ITODYS laboratory, University Paris Cité, France. He

graduated from Sorbonne University (P. & M. Curie campus, Paris) and obtained his Ph.D. in 1993 from Paul Sabatier University, Toulouse (France) under the supervision of Prof. J.-P. Launay. He then worked as a postdoctoral fellow in the groups of Prof. A. von Zelewsky / P. Belser (University of Fribourg) and Prof. G. Calzaferri (University of Bern) in Switzerland. As a molecular chemist, his main interests lie in the field of molecular

and supramolecular transduction for energy and information

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## 2. Methods for creating organic reservoir bonds for electron storage

There is first the pathway of photo-(electro)-chemical storage, that can be illustrated by looking at natural oxygenic photosynthesis. In this complex process, electrons extracted from water molecules, the primary electron donors, serve as energy carriers, or vectors, that acquire energy from sunlight as they pass through photosystems II and I. These energized electrons are ultimately stored at the end of the electron transport chain as reducing equivalents within chemical bonds in bio-relevant molecules, such as NADPH. Acting as a carrier of two electrons and one proton (a formal "hydride donor"), NADPH then plays a vital role in anabolic reductive biochemical processes, where it donates its stored energy to drive various reduction reactions (Figure 1).[7] However, while NADPH serves as a valuable cofactor in plant and human physiology, functioning as "biochemical/biological hydrogen", it has limited utility in sustainable technological applications. Artificial photosynthesis (AP), on the other hand, draws inspiration from the most effective aspects, i.e., the early events, of natural photosynthesis,[8] with the ultimate goal of producing solar fuels,

as is the case for dihydrogen typically obtained from archetypal water splitting (Figure 1), among a few other key reactions. AP systems are categorized into (i) challenging homogeneous AP (based on molecular and supramolecular assemblies), which have seen limited success due to difficulties in integrating all functional elements into a single entity, and (ii) the hybrid photoelectrochemical synthesis cells and heterogeneous AP (involving electrodes, semiconductors, and nanoparticulate materials), which are operational but require further optimization for industrial-scale production.[9] Finally, fuel cells enable energy recovery in the form of electricity from solar fuels (H₂ and O₂), although they are constrained in particular by the undesirable reliance on platinum in their composition.[1] The key point, however, is that the energized electrons stored in the chemical bonds of organic solar fuels can be converted into electricity when needed.

<figure><img src="image_4.png" /><figcaption>**Figure 1.** Photo-electro-chemical pathway (NADPH and H₂ formation).</figcaption></figure>

Second, drawing on a purely chemical approach to electron storage, there are ground-state neutral organic super-electron-donors (SEDs), pioneered and developed by Murphy's group.[10] SEDs are designed for organic synthesis and are typically used as single-use reagents, occasionally being synthesized in situ. These compounds can facilitate either single or double electron transfers (SET or DET, respectively). Notably, the prototypical bis-2-pyridinylidene platform, typically synthesized by reacting a base (e.g., NaH) with the 2-position (α) of tethered pyridinium rings (Figure 2),[11] can store two electrons within its interannular carbon-carbon (double) bond. Hansmann's group has further developed this platform with pyridinium-carbene hybrids capable of storing up to four electrons, but shifting their focus away from applications in organic synthesis.[12]

The driving forces for electron storage and release stem from differential electronic energy gains, which underpin the reversible, apparent one-step two-electron uptake and release observed via cyclic voltammetry (CV). This also highlights phenomena such as compression (including coalescence) or inversion of redox potentials.[11a,11b,13] These SEDs find applications in reductive chemistry[14] and energy storage technologies, such as redox flow batteries, provided that the electron transfer (ET) processes remain electrochemically reversible.[15,16]
<figure><img src="image_5.png" /><figcaption>**Figure 2.** Chemical pathway: formation of bis-2-pyridinylidene as a potent SED.</figcaption></figure>

Third, there is the electrochemical approach represented by the *structronic paradigm*. As an initial framework for describing covalent assemblies relevant to the structronic concept, we identify concave (U-shaped) architectures characterized by “islanded” LUMOs, i.e. disjoint electronic domains where these empty frontier MOs are localized, leading to the partitioning of electrophoric activity (multisite redox behavior). These features are exemplified by constructs composed of multiple electrophoric components connected by scaffolds to which they are not π-conjugated (further explanation of this specificity is provided below). The structronic paradigm involves the formation of an empty bonding orbital, referred to as the "supra-LUMO", which is subsequently filled with electrons to establish a "reservoir bond" (corresponding to the supra-HOMO). This orbital engineering is defined by a structure-property relationship that links specific structural and electronic characteristics, particularly the presence of close contacts between highly electrophilic atomic centers.[5] This unique electrochemical behavior involves the formation of a carbon-carbon bond upon a two-electron reduction (charging), referred to as the "reservoir bond," which can be cleaved through a two-electron oxidation (discharging) to release the stored electrons. It is important to note that the process of bond formation fundamentally differs from bimolecular σ-dimerization of radicals, despite their superficial similarities.[17,18] The defining criterion for the existence of this bond is a through-space distance between electrophilic centers that is shorter than the van der Waals contact distance (typically 3.40 Å for carbon atoms). These centers significantly contribute to the LUMO of the electrophoric components they belong to. A prototypical example is the local topology arising from interannular steric hindrance between two tilted, nearly cofacial pyridinium rings ("askew stacking"). This arrangement enables close contact between the C(γ) atoms at the 4-position of the pyridinium rings and a sigma-type overlap of their 2p<sub>z</sub> atomic orbitals (AOs), which extend out of the electrophoric planes. This results in a transannular interplay with the formation of a supra-LUMO (see Figure 3). In essence, the 2p<sub>z</sub> AOs of the C(γ) atoms contribute both to the LUMO of their respective pyridiniums and to the through-space interaction that creates the so-called "supra-LUMO" i.e., the proto "reservoir bond".

<figure><img src="image_6.png" /><figcaption>**Figure 3.** Electrochemical pathway: the structronic paradigm (PI refers to "potential inversion").</figcaption></figure>

**3. Characteristics of structronic (STR) systems as functional assemblies**

This section, dedicated to the electrochemical behavior of the STR paradigm with references to bispyridinylidene type SEDs and "expanded bipyridinium" (EBP) case study,[19] focuses exclusively on factors intrinsic to molecular entities. The competing or supportive influences of extrinsic factors, such as environmental effects like solvation energy, are not considered here, even though they may play a crucial role.[13,20]

From an electrochemical perspective, when bispyridinylidene-type SEDs are not employed as reducing agents in chemical reactions that permit single-electron transfers (SETs) –that is, when they are treated as independent systems– their operation of reversible single-step two-electron donation/acceptance[11a,11b] is primarily governed by the transition between two states associated with two distinct types of electronic energy gains. On one side, the formation of an extended π-conjugated (pseudo-quinoidal) structure enables π-type[21] electron storage, resulting in an essentially coplanar conformation of the bipartite platform of SEDs in their native form (SED�0). On the other side, electron release occurs through the recovery of stabilization energy arising from the aromaticity of the electrophoric components in their native cationic state within SED²⁺ oxidized form.[11b] Notably, this SED⁰-to-SED²⁺ transition, accompanied by a configuration change, is achieved with minimal structural reorganization, involving only a localized interannular torsional relaxation of about 53 degrees (a conformational adjustment that reduces unfavorable electrostatic repulsion between cations), along with a corresponding change in the overall electronic structure of the assembly. Taken together, these findings account for the mechanistic reversibility of the electrochemical process and explain the single-step two-electron transfer in bis-2-pyridinylidene derivatives, whether linker-free or equipped with suitable tethers (e.g., a propylene linker), which would otherwise exhibit reversible stepwise ETs.[11b] It remains an open question whether the one-step two-electron transfer arises from potential compression (up to coalescence) or potential inversion. However, the significant electronic energy gains associated with the two states of the redox-active assemblies (SED²⁺/SED⁰) likely serve as sufficient driving forces for the potential inversion (PI) phenomenon to occur,[22] unlike the relatively modest structural reorganization triggered by redox events.[20] In PI processes, the addition (reduction) or removal (oxidation) of the second electron
requires less energy than the first. As a result, CV shows a single reduction and/or oxidation peak corresponding to the transfer of two electrons, even though the electron transfers occur sequentially (the radical intermediate is unstable).[20]

We are now transitioning from chemically derived SEDs, which are potentially reusable stand-alone redox-active entities but have traditionally been used as disposable reagents in reductive organic chemistry, to specifically designed, reusable, electrochemically rechargeable STR assemblies.[5]

A significant difference in the electrochemistry of STR assemblies compared to this type of SED is the emergence of an *electrochemical hysteresis*, with its boundary peaks attributed to the distinct processes of reductive formation (*E*<sub>Red-1</sub>) and oxidative cleavage (*E*<sub>Ox-2</sub>) of the reservoir bond.[5,18,23] This hysteresis indicates processes that are electrochemically irreversible but chemically reversible, a key feature for cyclability (electron charging and discharging) and bistability. Beyond their differing operating principles, STR assemblies (natively dicationic) must be distinguished from bispyridinylidene-type SEDs (natively neutral), as the former undergo a *pronounced* redox-induced structural relaxation, as demonstrated by molecular modeling.[5,18,23] Like in SEDs, this relaxation occurs during both two-electron reduction and two-electron oxidation (donation).

These observations indicate that the formation and cleavage of a covalent σ bond, as operated in STR systems, involve a significant configurational change in the assembly, with consequences extending far beyond the simple transformation of an unsaturated bond (e.g., a carbon-carbon double bond) into a single saturated σ-type linkage, as seen in SEDs. In other words, this process has a profound impact on structure-property relationships. Specifically, it entails the creation of a covalent σ bond (supra-HOMO) at a close-contact site where no pre-existing chemical bond exists, only the empty *supra-LUMO* to be filled. This site is situated outside the scaffold (bond network) of the native dicationic STR assembly but remains within its inner space.[5,18,23] This type of "molecular expansion" may also give rise to specific properties, such as atropisomerism,[23] a temperature-dependent conformational isomerism characterized by the formation of rotamers, i.e., isomers resulting from hindered rotation around a single bond, in this case, the elongated reservoir bond.

Of particular importance is the finding that electrochemical hysteresis depends on cooperative ETs, specifically PI processes. This hysteresis is characterized by the reduction peak corresponding to the filling of the *supra-LUMOs* with two σ electrons[21] in a single step (reductive formation of the reservoir bond) and the oxidation peak observed during the return scan in CV, which also involves a single-step, two-electron process but represents the oxidative cleavage of the reservoir bond (release of the two stored electrons).[5]

In addition to classical characterization methods (e.g., X-ray diffraction, NMR), the combination of electrochemical investigations (including steady-state CV, AC voltammetry, electrochemical impedance spectroscopy (EIS), exhaustive electrolysis, log-plot analysis, semi-integration treatment, digital simulation, and both UV-vis-NIR and FTIR

spectroelectrochemistry) with molecular modeling at DFT level[5,23] has revealed that the PI processes in this context are driven by significant redox-triggered structural relaxation during both reductive bond formation and oxidative bond cleavage. In the reduction regime, this relaxation involves the tetrahedralization of the two C(γ) atoms participating in reservoir bond formation, specifically a hybridization change from sp² to sp³ (spiro), resulting in an increased outward tilt of the N-methyl-1,4-dihydropyridine fragments (see Figure 3), the formation of which corresponds to the adjustment of the electronic configuration adopted by the pyridinium units that accommodate part of the injected electron density. Despite this electro-structural relaxation, which also involves a "leakage" of the injected electrons into the two electrophoric components, the C-C reservoir bond that forms is therefore elongated (approximately 1.65 Å) compared to the standard C-C bond length of 1.54 Å, indicating its weakened nature. During the oxidative cleavage of the reservoir bond, the STR assembly reverts to its native structure, restoring the aromaticity of the pyridinium units. Notably, the PI mechanism underlying STR functioning fundamentally differs from that of the previously described type of SED, which is believed to be most likely governed by differences in electronic energy gains.

To summarize, within the STR paradigm, we established that the mechanism underlying the two-way PI, along with the electrochemical hysteresis, follows an EEC-type reaction scheme involving two-electron reduction and re-oxidation coupled with a chemical reaction, which governs both the formation and cleavage of the reservoir bond.[5,18,23]

*At this point, it is worth recalling the foundational principles of the STR paradigm, which harnesses the quantum behavior of electrons within covalent bonds to counteract the unfavorable electrostatic repulsion between like-charged electrons, thereby enabling their "concentrated" storage (confinement). The notion of "storage", closely related to that of a "reservoir", is evidenced by the presence of hysteresis, the magnitude of which (related to the level of intramolecular steric strain, including both the strain within the holder and inter-electrophoric hindrance) determines the stability range of the reservoir bond in terms of electrochemical potential.*

In addition, the formation and cleavage of the scissile reservoir bond act as the chemical trigger (or tipping event) that drives the concerted two-electron storage and release observed in PI processes. These electrons are not confined solely to the newly formed, elongated C–C sigma bond—which, strictly speaking, does not fully contain them—but are also delocalized over synergistically interacting parent electrophoric units (see Figure 3, along with the spatial expanse of supra-LUMOs and *supra-HOMOs* in references 5 and 23). The distribution of spin density between the sigma reservoir bond and electrophoric anchors is influenced by two key factors: the structural strain applied to the reservoir bond and the electrophilicity of the electrophoric units. This electrophilicity can be tuned by electronic effects from substituents, such as electron-withdrawing or electron-donating groups, which modify the characteristics of electrophilic centers at the close-contact site. *In fact, and correspondingly, the two above-mentioned key factors allow for tuning the magnitude of the electrochemical hysteresis, and thus the amount of energy lost by stored electrons when released.*
To highlight the differences in two-electron storage mechanisms between a supra-LUMO, which is specific to a proto-"reservoir bond" within a molecule, and a LUMO, commonly encountered at the molecular level, it is valuable to examine (bi)pyridinium-based assemblies. A particularly illustrative example involves the contrasting cases of "expanded pyridiniums" (EPs)[¹⁹b] and "expanded bipyridiniums" (EBPs).[¹⁹a,¹⁹c] These systems can undergo processes of potential compression (EPs) or potential inversion (EBPs), both driven by significant redox-triggered structural reorganizations, provided that steric crowding does not excessively hinder the linkage between the "core" pyridinium and its N-pyridinio group, which can also be redox-active, as is the case for EBPs. These rearrangements eventually lead to charge localization, as shown in the Figure 4.

<figure><img src="image_7.png" /><figcaption>**Figure 4.** Mechanisms of single-step two-electron reduction with potential compression (up to coalescence) for EPs (top) and with potential inversion, PI, for EBPs (bottom).</figcaption></figure>

EPs are monocationic single pyridinium nuclei featuring aryl substituents at the 1-, 2-, 4-, and 6-positions. Upon two-electron reduction, the electrochemical behavior varies depending on the

nature of the pendant N-pyridinio group, exhibiting different degrees of reversibility. This behavior ranges from stepwise reduction with redox potentials separation (in the case of a highly sterically hindered N-pyridinio atom) to redox potentials coalescence (in the case of a pyridyl N-pyridinio group). These processes are accompanied by varying degrees of pyramidalization at the N-pyridinio atom, driven by a *hybridization* change and influenced by local steric hindrance. In all cases, the two-electron reduction ultimately results in the formation of a carbanionic species at the C(γ) position (Figure 4).[¹⁹b]

For EBPs, which are essentially "head-to-tail" positional isomers of the archetypal "tail-to-tail" methyl viologen (a representative of the Weitz-type electrochemical paradigm characterized by reversible stepwise two-electron processes), the electron storage mechanisms at the molecular level differs from that of EPs. In EBPs, the intrinsic dissymmetry of the bis-electrophoric assemblies causes the LUMO to localize initially on the pendant pyridinium (N-pyridinio group), which is weakly coupled to the core pyridinium due to substantial interannular steric hindrance (Figure 4).[¹⁹a] Interestingly, the two-electron reduction is not restricted to the pendant entry site, where the first heterogeneous electron transfer occurs. Instead, it extends across the entire bis-pyridinium system, mediated by the interfering electromers (axial/pyramidal redox isomers) of the *elusive* radical cation intermediate. This results in a large redox-triggered structural reorganization involving the entire superelectrophore. Unlike EPs, where global pyramidalization originates from a hybridization change at the N-pyridinio atom of the pyridinium cores, the reorganization in EBPs arises from a *competing interplay* between the π-conjugation of electrophoric components and interannular steric hindrance.[¹⁸,¹⁹c]

In summary, dicationic EBPs represent a distinct electrochemical paradigm, characterized by electrochemically reversible PI processes. These systems transition, after a single-step (though fundamentally sequential) two-electron reduction, to a zwitterionic state comprising a cationic N-pyridinio atom and a carbanionic C(γ) atom, both located within the electrophoric core.

Interestingly, the C(γ) carbanionic center formed following the two-electron reduction of EPs and EBPs resembles the functional core of NAD(P)H, a biological two-electron-plus-one-proton symporter, but in its proton-deprived analogue form (see Figures 1 and 5).[¹⁹] However, the reactivity of these E(B)P systems with protons, which could determine their relevance as artificial functional analogues of NAD(P)H, remains an unexplored area of study.

<figure><img src="image_8.png" /><figcaption>**Figure 5.** Case study of 2e-reduced EPs: Are they functional models for NAD(P)H?</figcaption></figure>
## 4. On the role of U-shaped spacers as π-decoupling holders in STR systems

STR assemblies are multicomponent systems that are fundamentally distinct from SEDs in terms of the role of π-conjugation in coupling electrophoric moieties. In bispyridinylidene-type SEDs, the two electrophoric units are not only strongly coupled but are also typically tethered by an oligomethylene (saturated) linker, which serves both a synthetic role (facilitating SED formation) and influences the SED's electrochemical behavior.

In contrast, the spacer units in U-shaped STR assemblies play a different role. These spacers ensure a precise 3D topology around the inter-electrophoric close contact site and are more accurately described as "electrophoric pre-organizing holders" (see Figure 3). The (semi-)rigid nature of these spacers is preferred, as it allows for precise control over the molecular geometry, particularly the location of the close contact for through-space interaction.

However, this design choice often comes at the expense of introducing potential intramolecular π interactions between electrophoric units, mediated by the bonding network of the holder component. Such interactions must be avoided, as they could lead to undesired π delocalization (e.g., quinoid electronic structures) that would compromise the STR functional assembly's effectiveness. This point is further illustrated below.

It is important to emphasize that the deliberate absence of inter-electrophoric π-conjugation mediated by the holder moiety in STR systems does not imply a lack of interaction between the electrophoric components. On the contrary, the close contact site precisely facilitates the coupling of redox-active pyridiniums via a through-space sigma-type orbital overlap of C(γ) 2p<sub>Z</sub> AOs, leading to the emergence of the supra-LUMO as the only operative interaction channel.

Adverse effects of inter-electrophoric π-conjugation, mediated by the holder component, are demonstrated in the case study of "helquats". In these systems, the bielectronic reduction occurs stepwise (Weitz type electrochemical paradigm),[24] resulting in an *ortho*-quinodimethane (o-QDM)[25] electronic structure in the two-electron reduced species. This electronic pattern prevents the pyridiniums from direct (through-space) interaction necessary for reservoir bond formation (Figure 6).

<figure><img src="image_9.png" /><figcaption>**Figure 6.** Stepwise redox activity of Helquats (top) and o-QDM resonance forms of Kekulé-type delocalized diradicals (bottom).</figcaption></figure>

So far, the required suppression of π conjugation has been achieved through careful design, either by incorporating a cross-conjugated rigid holder (as in the case of 1,8-disubstituted naphthalene)[5] or by geometrically decoupling the π system within a semi-rigid spacer using intramolecular steric hindrance (as in the case of 2,2'-disubstituted-1,1'-biphenyl).[23] Finally, while the use of a saturated backbone that also provides (semi)rigidity as a holder component is often synthetically challenging and, therefore, underexplored, there are examples of simple saturated linkers that, despite their flexibility, meet the STR criteria, as discussed in the next section (cyclomer formation).

## 5. Extending the Structronic concept: Revisiting the mechanism of intramolecular sigma bond formation in Dyrex systems and during cyclomer formation

Sigma dimerization of radical species is typically a diffusion-controlled process that occurs intermolecularly (as a bimolecular reaction involving the formation of encounter pairs of radicals) rather than intramolecularly. The two case studies discussed in this section –namely the "Dyrex" (dynamic redox) systems and the cyclomer reductive formation– implicitly and fundamentally assume that radicals behave independently. This assumption, based on the independence of radical centers, contrasts with the structronic approach. The structronic approach emphasizes a pre-existing specific supra-LUMO, which can be understood as the result of a structurally promoted formation of an "encounter pair" of C(γ) 2p<sub>Z</sub> AOs undergoing sigma-type overlap. This is subsequently followed by the spin pairing of the injected electrons under PI conditions, resulting in supra-HOMO formation that corresponds to the new elongated sigma bond ("reservoir bond").

### 5.1. Case study of the Dyrex systems

The development of "Dyrex" (dynamic redox) systems is linked to both the pursuit of "ultralong" C–C bonds[26,27] and the design of molecular platforms exhibiting electrochromism.[28] The chosen approach to achieve these interrelated goals involves the reduction –either chemical or electrochemical– of parent dicationic assemblies to trigger sigma-dimerization of geminate radicals under structurally constrained conditions. It is worth noting, however, that while considerable focus has been placed on the bond length of the switchable (scissile) newly formed elongated bonds, relatively little attention has been given to the mechanism(s) underlying their reductive formation.

It is noteworthy that Dyrex systems fulfill the criterion of an absence of inter-electrophoric π conjugation, despite potential interactions between electrophilic centers. Their holder units are virtually identical to those used in the STR paradigm, typically based on 1,8-disubstituted naphthalene (and associated constrained derivatives such as acenaphthene, pyracene, etc.) or 2,2'-disubstituted-1,1'-biphenyl and its constrained derivatives,
which may or may not be chemically restricted to a favorable conformation to meet the close-contact criterion (Figure 7).

<figure><img src="image_10.png" /><figcaption>**Figure 7.** Illustrative examples of basic Dyrex systems.</figcaption></figure>

In Dyrex systems, the electrophilic centers are no longer the C(γ) atoms of pyridinium groups but rather the related C(9) atoms of acridiniums or, alternatively, the carbocationic centers of tritylium derivatives (i.e., bis-triarylmethylions; Figure 7B) bearing electron-donating substituents. Beyond facilitating ultralong C–C bond formation through reductive processes, the primary goal is to design electrochromic covalent assemblies. The working principle of these assemblies is based on a change in the status of the electrophilic centers upon reduction (and internal σ bond formation), switching from cationic (electron-withdrawing) to neutral. This transition effectively eliminates the intramolecular charge transfer within each of the two electrophoric components, thereby producing the electrochromic activity. Dyrex systems are characterized by hysteretic electrochemical behaviors, as expected for bistable assemblies.[28a,28c]

As a caveat, while Dyrex systems are formally composed of the same functional ingredients as STR systems, this section focuses exclusively on case studies involving assemblies based on the (semi)rigid holder components, where the pre-organization of electrophilic centers is ensured. In contrast, for unrestricted biphenyl-type holders combined with bulky diarylcarbenium derivatives (a kind of “tritylium dimers”, see Figure 7B), the critical pre-organization of the methylium centers appears less reliable due to significant intramolecular steric hindrance. Notably, in several of these systems, the radical cation intermediate can be isolated,[29] which is incompatible with the occurrence of PI processes associated with the presence of supra-LUMOs. In such cases, "intramolecular sigma dimerization of radical centers" is a more plausible explanation.

Conversely, semirigid biphenyl-2,2'-diylbis(10-methylacridinium) derivatives, which are chemically locked (pre-organized) into a

conformation that promotes close contact between C(9) electrophilic centers, exhibit notable behaviors. Similarly, functional assemblies based on peri-substituted naphthalene backbone derivatives act as effective holder components. This is particularly true for those associated with the acridinium/acridan redox couple, as shown in Figure 7A. The hysteretic electrochemical behaviors observed in these systems are influenced by intramolecular steric constraints, specifically the "stretchability/expandability" of the scissile sigma bond. Additionally, UV-vis-NIR spectroelectrochemical studies indicate the absence of a radical cation intermediate. These findings reported in the literature align well with the STR paradigm. This paradigm relies on both the existence of supra-LUMOs (Figure 8-top) and PI processes to account for the observed single-step two-electron reductive bond formation, along with the transient and elusive nature of the radical cation within the one-electron loaded systems. Regarding the methylium centers, their synergy, resulting from the enforced transannular interplay of their p<sub>z</sub> AOs and reflected by enhanced electrophilicity (and Lewis acidity), has already been demonstrated by Gabbaï et al. in the case study of the 1,8-bis(bis(*p*-methoxyphenyl)methylium)-naphthalenediyl dication[30] (X = OMe in Figure 8-bottom; see also ref. [31] for X = H), which is characterized by electrochemical hysteresis,[30] as expected.

<figure><img src="image_11.png" /></figure>
**Figure 8.** Calculated frontier supra-LUMOs and supra-HOMOs (σ-bonded species) in acetonitrile implicit solvent model were obtained at DFT level using the PBE0-D3(BJ) exchange-correlation functional (see ref. [23]), plotted with an iso-contour value of 0.05 unless otherwise specified. **Top:** Case study of 1,8-bis(10-methylacridinium)naphthalenediyl dication (see Figure 7A). **Bottom:** Case study of 1,8-bis(diarylmethylium)naphthalenediyl dication (with X = NMe₂ para substituents), not yet reported but synthetically attainable (iso-contour value of supra-HOMO is 0.015).

**5.2. Case study of the reductive formation of pyridinium-based cyclomers.**

As far as the reductive formation of cyclomers is concerned, new light can also be shed on this rather old reaction mechanism.[32] With the aim of studying spin-spin interactions at the molecular level, and considering that one-electron reduced pyridiniums yield reactive (possibly stable, depending on their substituents, but certainly not persistent) pyridinyl radicals, a series of 4,4'-oligo[n]methylene-bipyridinium covalent assemblies (with n = 2 to 5) has been synthesized. Upon two-electron reduction, these assemblies form so-called cyclomers,[32] which have been extensively studied by Muramatsu et al.[33,34] Cyclomers of this type serve as model compounds and have long been of interest due to their formation mechanism. Until now, the reductive formation of the interannular σ bond between C(γ) atoms –i.e., cyclomer closure– was believed to result from "intramolecular σ bond dimerization".[32,33]

Our study complements Japanese research based on the chemical reduction (using Na) of the dications and EPR monitoring of the reactions, which revealed the intriguing absence of paramagnetism in most cases and a very weak detection signal associated with the limited presence of radical cations at the initial stages of the reduction of the bis-electrophore with a pentylene bridge.[33e] This, along with other techniques such as NMR spectroscopy and UV-vis electronic absorption (recorded on purified/isolated reduction products), was used to confirm the effective formation of cyclomers.

To reach our conclusions on the relevance of the structronic paradigm in this case study and to revisit the mechanism of cyclomer reductive formation, we undertook an in-depth study of the entire series of dications. This was achieved by changing the methodology, specifically by combining advanced electrochemistry –allowing precise control over the energy of the injected electrons as well as kinetic control of heterogeneous electron transfers (ETs)– with molecular modeling, all while continuing to rely on valuable experimental insights gained by Muramatsu et al.

Our approach allowed us to uncover several important and meaningful features, outlined as follows:

(i) While free-standing short flexible *n*-alkane molecules typically adopt an extended "all-trans" conformation in solution, molecular modeling revealed that when terminated with "large surface area" groups such as pyridinium end groups –i.e., when incorporated into dicationic bis-electrophoric assemblies as linkers– these oligomethylene bridges adopt a critical U-shaped conformation under the influence of London Dispersion (LD) forces (Figure 9). This conformation facilitates the emergence of supra-MOs (and particularly supra-LUMOs), which drive cyclomer formation (see

Figure 3).[34] In fact, these 4,4'-oligo[n]methylene bis-electrophores were found to meet the criteria for close contact between strong electrophilic centers (C(γ) and even C(α) atoms), as defined by the structronic concept, thanks to the involvement of so-called weak (van der Waals) forces –typically at work in supramolecular assemblies (according to Lehn's conceptual framework)– but here operating at the intramolecular level.
(ii) From electrochemistry, a characteristic hysteresis was observed for each bis-electrophore (except for n = 2),[34] with the reduction peak corresponding to a single-step, two-electron process based on a (modest) PI. This is incompatible with a mechanism of sigma-dimerization of pyridinyl radicals but fully consistent with the structronic mechanism. Last but not least, the structronic mechanism also accounts for the elusive nature of radical cations (due to PI processes) and the almost quantitative formation of various cyclomers, i.e., the absence of (linear) oligomers resulting from intermolecular couplings.[34]

<figure><img src="image_12.png" /><figcaption>**Figure 9.** Revised mechanism for the reductive formation of pyridinium-based cyclomers according to the STR concept.</figcaption></figure>

**6. Summary and Outlook**

The structronic paradigm, based on purely organic assemblies, enables electron storage in specifically designed C–C elongated (strained) sigma bonds, referred to as "reservoir bonds." This concept relies on the through-space formation of a bonding supra-LUMO between properly arranged electrophilic centers. This supra-LUMO can be electrochemically filled with electrons, characterized by a potential inversion mechanism (a one-step, two-electron reduction process), creating the "reservoir bond". This scissile bond can be selectively cleaved to release the stored electrons, which proceeds according to another potential inversion process, returning the STR assembly to its native dicationic state. Superelectrophores based on the STR paradigm are characterized by electrochemical hysteresis, which reflects their bistability and the cyclability of the charging/discharging of electrons. Notably, while the STR paradigm aims to provide an innovative and sustainable approach to ultimately achieving electricity storage, it does not directly target redox catalysis, such
as solar fuel production (e.g., dihydrogen formation for energy storage and dioxygen as the oxidizer), even though such processes can be achieved using electricity, as in water electrolysis.

Whether this concept can be adapted to store holes in electron-
rich assemblies –mechanistically involving, for example, the
elusive formation of distonic radicals– remains to be explored.[³⁵]
Interestingly, the STR concept sheds new light on the
mechanisms and provides new insights into both the operation of
the previously introduced Dyrex concept and the reductive
formation of pyridinium-based cyclomers.

So far, structronic assemblies are multicomponent systems covalently linked by (semi-)rigid holders, fitting a localized description of functional ingredients similar to that adopted in the framework of supramolecular photochemistry for the design of photochemical molecular devices (PMDs),[³⁶] but implemented for electrochemistry. In principle, non-covalent assemblies typical of supramolecular chemistry[³⁷] could also be operative for the STR paradigm, provided that a close contact with proper 3D arrangement is available between relevant electrophilic centers. This could be achieved by implementing host-guest interactions or molecular recognition between ancillary elements attached to electrophoric units, which are to be assembled to form STR-based superelectrophores. These approaches could also lead to redox-switchable STR-based building blocks forming electrochemically responsive covalent organic frameworks (COFs) as "bistable materials" for electron (energy) storage, which could reversibly change their state (phase) upon electron loading (storage) and release.

Furthermore, considering that what can be achieved electrochemically can also be achieved photochemically, provided the appropriate photosensitizers (acting as electron donors in the photoexcited state) are involved, the STR paradigm could be implemented as a new functional element in PMDs. This approach aims at light-driven multielectron storage (photo-electro-chemical transduction), which could represent a noteworthy advancement in the field of (homogeneous) artificial photosynthesis.[³⁸]

Last, in the context of molecular electronics research, the
hysteretic electrochemical behavior of STR systems, also referred
to as the "memory effect," opens up possibilities for information
storage at the molecular level, as exemplified by the
electrochromism of Dyrex systems.

**Supporting Information**

The few new data presented (calculated frontier supra-MOs in
Figure 8) do not require any additional information (see the figure
caption).

**Acknowledgements**

Financial support by the Grant Agency of the Czech Republic (21-13458S), and the Academy of Sciences of the Czech Republic (RVO: 61388955), the Ministry of Education of the Czech Republic (Barrande Project 8J21FR016), the French Ministries of

Europe and Foreign Affairs (MAE) and of Advanced Education, Research and Innovation (MESRI) (PHC Barrande, Project No. 46775VG), and the French National Research Agency, ANR (ANR-14-CE05-0002, ANR-20-CE05-0041 and ANR-21-CE29-0003), is gratefully acknowledged. EB acknowledges the TGCC center for HPC resources (Project AD010810359R1). MH also acknowledges the assistance provided by the Advanced Multiscale Materials for Key Enabling Technologies project, supported by the Ministry of Education, Youth, and Sports of the Czech Republic. Project No. CZ.02.01.01/00/22_008/0004558.

**Keywords:** Molecular electrochemistry • Structure-activity relationships • Structronics • Electron storage • Electrochemical hysteresis

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Entry for the Table of Contents

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

This concept outlines the mechanism of molecular-level multi-electron storage, leveraging the quantum properties of electrons in sigma bonds. Effective through-space interactions between the 2p<sub>z</sub> atomic orbitals of electrophilic centers in organic superelectrophores enable the formation of supra-LUMOs with bonding character, capable of hosting electrons. The formation and cleavage of elongated C-C "reservoir bonds" impart hysteretic behavior to the systems.