Anna Perfetto #

Federica Maschietto #

Ilaria Ciofini
email: ilaria.ciofini@chimie-paristech.fr

Anna Perfetto

Federica Maschietto

Following excited states in molecular systems using density-based indexes: a dual emissive system as a test case

Keywords: Recently, Density-Based Index, Dual Emission, Excited State pathway, Density Functional Theory

Following excited states in molecular systems using density-based indexes: A dual emissive system as a test case

Anna Perfetto, Federica Maschietto, Ilaria

characterized and its dual emission has been ascribed to the presence of two emissive states of different electronic nature and corresponding to two structurally different species.

Nonetheless, the full mechanism ruling the structural interconversion leading to dual emission

has not yet been disclosed.

To this end, in this paper the dual emissive behavior of Phen-PENMe 2 has been unveiled by a combined use of time dependent density functional theory (TD-DFT) and density-based indexes (D CT and ) allowing identifying the radiative and non-radiative decay pathways at work in this system. In particular, the presence of an anti-Kasha emission mechanism as well as the presence of several non-radiative decay channels allowing enhancing either of the two emissions has been proven.

More generally, the results obtained in the present study highlight how this simple and inexpensive computational approach may be of help and general interest for the rational design of new dual emissive systems.

Keywords: 1. Introduction

Dual emission in molecular systems is a phenomenon increasingly reported in the literature and attracting ever-growing interest. [1][2][3][4][5][6] Depending on the mechanism at the origin of dual emission, various classes of compounds may be identified. Indeed, widely documented is dual fluorescence occurring in small organic dyes undergoing excited state intramolecular proton transfer (ESIPT) reactions [7][8][9][10][11][12][13][14] or excited state intramolecular charge transfer processes. 3,15- 21 Such dual emission phenomena have been exploited in the synthesis of various novel chemosensors with different target applications. 7,8,10,[START_REF] Pereira | [END_REF] Dual emission through Thermally Activated Delayed Fluorescence (TADF) deserves of being explicitly mentioned. 1,2,5,6,[23][24][25] These systems are indeed regarded as promising next-generation organic electro-luminescent materials due to their potentially high internal quantum efficiency.

Beside their relevance for applications, molecules displaying dual emission provide a perfect playground to test and validate theoretical approaches aiming to investigate the structural and electronic features of excited states yielding both to radiative [26][27] and non-radiative 9,15,[28][29][30] decay pathways. Indeed, besides molecular systems where dual emission is associated to a change in the chemical nature of the emitting specie (ex. protonation state), 12 native dual emission is usually associated to the presence of two emissive -bright-excited states of different character that can be both populated and that are stabilized by a differential structural reorganization.

In this respect, theoretical approaches aiming at describing this kind of phenomena are of great interest. There are at least two criteria that a method shall fulfill in order to deliver a good understanding of photochemical processes. Firstly, it should reproduce correctly the potential energy surfaces (PES) of the excited states of interest, within and far from the Franck Condon (vertical excitation) region. Next, it should deliver a coherent picture of the photochemical process from the absorption to the emission.

Ab-initio excited state dynamic approaches 26,[30][31][32] can provide this type of information but are often expensive for a routine analysis. By contrast, a static study of the PES as the one proposed in the present study may provide a simplified picture of the possible decay channels in play, delivering a realistic, yet qualitative understanding of the whole process at an affordable computational cost.

In this work we use density-based descriptors to follow the evolution of excited states along a given reaction coordinate, with the aim of proposing a strategy to rationalize the mechanism of the dual emission phenomena in Phen-PENMe 2 (Phen-PENMe 2 = 5-(4dimethylaminophenylenylethylyn)-1,10-phenanthroline).

Indeed, from a theoretical point of view, a large number of studies, 5,14,19,[33][34][35][36] including our previous ones 15,17,27,[37][38][39] has focused on the description of the excited states using densitybased descriptors to analyze the nature of the excited states responsible for the observed absorption and emission, both from a structural and energetic point of view. For a recent and complete review see for instance reference. 40 To this end, in the last years, we introduced some strategies for the description of excited states, coupling Time-Dependent density functional theory (TD-DFT) with descriptors based on electron density. 27,[41][42][43] This type of indexes were primarily aiming at the diagnostic and description of excited states with a charge-transfer character, with the use of the so-called D CT, acronym of Distance of charge transfer and M AC , acronym of Mulliken averaged configuration. [43][44][45] Recently a new index -so called -was also developed enabling to qualitatively identify excited-state potential energy regions where decay channels (both radiative or non-radiative) are highly expected. Unlike previous density descriptors, the index provides an estimate of the probability of different electronic states to interconvert, thus allowing to map the evolution of an excited state along a reaction coordinate. Up to now, this approach has been tested to explore simple photochemical processes, such as ESIPT or to analyze the excited states PES of prototype dual emissive systems such as the 4-N,N-dimethylaminobenzonitrile molecule (DMABN). 45 In the present work, we apply this strategy to study the photophysical behavior of Phen-PENMe 2 here considered as a complex but experimentally well-characterized example of a single dual-emissive molecule. 15,16 To this end, we explored by the mean of the index, all its possible decay pathways thereby providing a deeper understanding of the electronic origins of the observed dual emissive behavior.

The Phen-PENMe 2 can be considered as a typical push-pull system thus similar to many dual emissive molecules relying on a Donor- bridge-Acceptor structure (D--A), 17 starting from the pioneering DMABN 46 system, to more recently synthesized systems possessing stilbene, 47 pyrene, 13 imidazole, 19 or 9-aminoacridine [START_REF] Pereira | [END_REF] or dimethylamino-phenyl-penta-2,4-dienoic acid ethyl ester (DMAPPDE) skeletons. 20 The Phen-PENMe 2 molecule is composed of a 1,10phenanthroline core (Scheme 1) functionalized with a dimethylaminophenyl group acting as an electron donor.

Recent combined experimental and theoretical studies performed by some of us 15,16 clarified that the observed dual emission is associated with the existence of two different emissive states: a planar Intra-Molecular Charge Transfer (ICT) state corresponding to an electronic transition from the donor moiety to the phenanthroline core, and a Locally Excited (LE)state centered on the 1,10-phenanthroline, in which the donor and acceptor are orthogonally oriented. These earlier experimental and theoretical studies also investigated the solvent dependence of the dual emission phenomenon and highlighted the importance of the use of polar-aprotic solution to allow for the formation of both conformations, thus yielding the dual emission.

Scheme 1. Schematic structure of the Phen-PENMe 2 molecule in its planar (=0°) and twisted conformations (=90°).

If the nature of the emissive states has been disclosed, 15,16 the pathways connecting the excited states initially populated in absorption to the ones that actually emit has not yet been thoroughly analyzed. This is the question we aim to answer in this work, using density-based descriptors.

The paper is organized as it follows. In Section 2 we briefly introduce the density descriptors and quantum methods applied. In the Section 3 we provide the reader with a general description of the excited states responsible for the peculiar photochemical behavior of Phen-PENME 2 , through a simple analysis of the energetics, and of the nature of the vertical electronic transitions. These two simple elements are very informative and deliver an approximate -yet coherent-picture of the process, though missing some crucial features.

Further on, we investigate the same process using the index. This descriptor combines the information delivered by the energy and the D CT into a more elaborate function, giving access to additional knowledge on the excited state decay pathway. As a result, we identify a number of decay channels, and rationalize, the photochemical behavior of Phen-PENMe 2 from the vertical absorption to the emission. Finally, in the last section we draw some general conclusions.

Computational details and density-based indexes

In previous experimental and theoretical works 15,16 we showed that two structurally distinct forms, differing by the orientation of the phenyl and phenanthroline rings are responsible for the observed dual emission. The reaction coordinate connecting these two forms is the dihedral angle C 1 C 2 C 3 C 4 (see Scheme 1) which we refer to as  in the following. We performed a relaxed scan starting from the ground state -planar -optimized structure by varying  from 0° to 90° in increments of 10°. The resulting ten geometries encompass the full transformation from the planar to the twisted (perpendicular) structure. Excited states were computed vertically on top of each structure. In line with previous works on the same system, 16 all computations were performed at density functional theory (DFT) and TD-DFT 48- 49 level, respectively for the ground (GS) and excited states (ES), and applying the CAM-B3LYP range-separated hybrid exchange-correlation functional, 50 in combination with the 6-311+G (d,p) basis set. 51 Of note, the CAM-B3LYP functional have proven to provide reliable ES-PES and have been specifically validated in the case of push-pull system giving rise to twisted conformations at the excited state (which is also the present case), see for instance the work of Tozer et al. 52 and Adamo et al. 53 Solvent effects (here acetonitrile) were taken into account employing the polarizable continuum model (PCM), in its conductor-like version (CPCM) 54 using a linear response (LR) scheme. An extensive literature is available on the comparison between State Specific (SS) and LR schemes for the evaluation of solvent effect on both CT and LE states see for instance ref. 55. Nonetheless the computationally less expensive LR scheme has been here applied on the basis of the results obtained in a previous benchmark, showing that the present computational protocol is able to correctly reproduce the experimental absorption and emission profiles -recorded in polar aprotic solvents for the present molecule. 15,16 All calculations were performed with the Gaussian16 software. 56 To characterize the nature and the evolution of the excited states, we computed both the D CT and the indexes all along the reaction coordinate. A detailed description of the indexes mentioned above is provided in the literature. 27,[42][43]45 For ease of reading, here, we briefly recall their basic formulation. The D CT quantifies the length of the hole-electron separation associated with a given electronic transition and therefore provides an estimate of the spatial extent of a given electronic transition, allowing to monitor the changes in the character of the excited states (for instance Locally Excited -LE versus Charge Transfer -CT-). This index is calculated as the module of the distance between the barycenters (R + and R -) of the charge density corresponding to the hole and particle.

.

Positive and negative barycenters are obtained by integration of the associated electron densities, and These last are derived from the difference in total density of the two states S i , S j involved in the electronic transition -where i, j = 1, …, n ∈ R.

The index broadens the information provided by the D CT , by coupling this last both with a charge displacement and an energetic term. It is correlated to the inverse of the work needed to accomplish the charge rearrangement associated to an electronic transition from one electronic state to another. Therefore, it can be used to identify, in a qualitative manner, regions of the excited state potential energy surfaces where decay pathways are more likely to occur. Indeed, in the case of two classical point charges and , with a displacement vector ( pointing from the negative charge to the positive charge, the electric dipole moment is given by Analogously in a molecule, the dipole moment produced in any S i to S j transition is given by the product between the negative -or positive -transferred charge and the sum of all the position operators of all the electrons in the molecule. The norm of the difference in the dipole moment of two electronic states i and j is given by: One can expand as a function of the actual hole-particle transferred charge (hereafter q CT ) and the charge separation length associated with the given electronic transition (D CT ).

. Combining this product with the energy gap , the is readily obtained as, .

High values of will thus define the regions corresponding to the higher decay probability.

Although the energy gap between the two states is generally the most relevant term for many photochemical reactions implying a crossing of states, for a given energy gap, a decay between two states will be more efficient depending on the similarity between the electronic densities of the starting and final states. In other words, the smaller the reorganization of the electronic distributions between the two states, the greater the probability of decay. Therefore, efficient decay pathways are likely to emerge in regions where two states are close together in energy ( → 0), when the electron densities of two states are similar ( → 0), or when both of these criteria occur simultaneously. The index combining both information coming from the dipole moment and the energy difference provides therefore a more complete description with respect to each of its constituting components. and index values have been evaluated using an in-house developed and freely available code. 57 Absorption spectra are simulated by Gaussian convolution of the computed vertical transition energies using a full width at half maximum (fwhm) value of 0.2 eV.

Results and discussion

To investigate the photophysical behavior of the Phen-PENMe 2 molecule we have analyzed the evolution of the ground state and of the first six excited states, along the coordinate of interest (in Scheme 1). This last involves the formation of a planar and an orthogonal conformer, which differ in the orientation of phenyl and phenanthroline rings. Figure 2, showing the normalized Boltzmann distributions of each state, points out to similar conclusions. Indeed, the ground state appears to be equally populated at all reaction steps, while the first excited state S 1 is only accessible in the 0° <  < 20° region. As a remark, conventional DFT functionals tend to overestimate the strength of π -conjugation, with a consequential flattening of the ground state profile, 58 and deprecation of the GS Boltzmann population, though by using a range separated hybrid we mitigate this effect. 1). The energy profile of S 2 increases in energy until it reaches its maximum and approaches the third excited state at about  = 80°. At this point, we have the choice to analyze the energy profiles either according to their placement relative to the ground state curve or according to the nature of each excited state. This duple representation (shown in the upper left and right panels of Figure 1), turns out to be a handful approach, precisely to follow the evolution of the excited states, condensing the information provided by different observables -energy D CT , and oscillator strength (f osc ) -in a unique picture. The Boltzmann population curves (Figure 2) are also labeled according to the nature of the states.

The D CT profile computed for S 2 ranges from 3.913 Å at  = 0° to 1.355 at  = 90°, denoting a change in nature from a charge-transfer state to a locally excited one. Accordingly, the  ES- GS decreases by one order of magnitude, converging towards the ground state value (10 Debye at  = 90°). Besides, S 2 changes from a dark state at  = 0° (f osc = 0.039) to a bright state at  = 90° (f osc = 1.148). S 3 (red curve in the upper-right panel of Figure 1) is only accessed irradiating at energies higher than 4.4 eV (289 nm). Also, this excited state approaches both S 4 and S 2 at  ~ 30° and  ~ 80° respectively. According to Figure 2, the population of S 3 (LE 1 ), decreases considerably, going from 0° to 90°, while the opposite occurs for S 4 .

As a result, one may infer that a crossing involving S 4 and S 3 occurs around  = 30°-40°. This inversion also appears in the D CT profiles, where the S 4 and S 3 curves cross, pointing out a change in nature of the two states. In the  = 0° to  = 40° window, S 4 has a marked CT character, which translates in D CT values ranging from 2.581 to 2.262 Å. S 3 , on the other hand, exhibits small D CT values, synonymous of a localized transition (0.1-0.2 Å).

At  ~ 50°, the picture is inverted. Here, the fourth excited state localizes on the dimethylaminophenyl fragment -the D CT value drops to 0.374 Å while S 3 takes over the CT character (2.388 Å). At this stage, S 4 remains unvaried till the completion of the twist, while S 3 approaches S 2 close to  ~ 80°. The CT length decreases for both S 2 and S 3 states to ~ 1.5 Å for the fully twisted conformation. As we will discuss later on, the S 4 -S 3 inversion is the critical step to access the dual emission.

The photochemical pathway outlined results in the population of the S 4 state. In summary, S 3 acts as a bridge between S 4 -bright CT state in the FC region -and S 2 , LE state -initially dark, and turning into a bright state around 80°. The NTOs, available in Supporting Information, render an orbital picture of the changes in nature of the corresponding electronic transitions.

Finally, the higher excited states, S 5 and S 6 , require respectively excitation energies of 4.60 eV (269 nm) and 4.65 eV (267 nm) to be populated. The corresponding D CT curves cross around  = 55°, suggesting an inversion in their character. S 5 approaches then the trajectory of S 4 at  ~ 90°. The latter, though, lies ~ 0.2 eV above S 3 , limiting the mixing with the lower lying states. S 6 (ICT 4 ), however, appears to be populated between 50° and 90°, suggesting that it may contribute to feeding a non-radiative channel transferring its population to the lower states. It is worth recalling that, due to the very low energetic barrier, at the GS the molecule is able to freely rotate, hence all conformations are accessed. Irradiating the molecule at low energies limits the access to the excited state levels to the sole S 1 . This, in turn, prevents the twisting and with it the formation of the LE state, thereby leading to a single emission from the planar ICT 1 (S 1 ). By contrast, exciting with sufficient energy, all excited states may be reached, leading to a multitude of decay pathways.

Simulation and interpretation of the observed absorption spectrum

Before analyzing in details the decay pathways it is useful to comment on the absorption properties of Phen-PENMe 2 , as such analysis will later be helpful to disclose the mechanism leading to the dual emission.

The simulated absorption spectrum at each internal conversion coordinate (in Figure 3) reflects the vanishing of the ICT 1 state and rising of the LE / state as the molecule twists. In the planar conformation ( = 0°), the absorption is dominated by a single transition at 355 nm (3.49 eV). The resulting broad absorption band is ascribed to the lowest excited state, S 1 (ICT 1 ), of CT character. The band at 270 nm (4.59 eV) arises from two higher ICT states -S 4 and S 6 -and, to a smaller extent, from an LE state of nπ* character (S 3 ). Despite the low oscillator strength of the states involved -they are not exceeding 0.5 a.u. at 0° -the band appears intense, as the three states involved (S 3 , S 4 , and S 6 ) are relatively close in energy. At ( = 90°), the absorption spectrum consists of a single band at 296 nm (4.19 eV) -with a shoulder at higher energy (276 nm / 4.49 eV). This band is ascribed to transitions involving two states: a LE state (S 2 ) of ππ* character centered on the 1,10-phenathroline fragment and an ICT state (S 5 ).

The absorption spectra computed at intermediate values of  smoothly connect these two limiting pictures. The lowest energy band blue-shifts as the molecule twists and disappears entirely at  ~ 90°. At the same time, the highest energy band rises, while increasingly redshifting.

The effect of the solvent in Phen-PENMe 2 was investigated previously. 15,16 Considering the ground state PES of Phen-PENMe 2 computed in acetonitrile we can estimate that the molecule freely twists so that each conformation can contribute to the absorption.

Therefore, it is convenient to estimate an average absorption by pondering each of the spectra calculated at different values of  -using their corresponding GS Boltzmann weights. The outcome is shown in

Interpretation of the dual emission through the index

Up to now, we have used a combination of several observables, each bearing a different physical meaning, to sketch a map of the excited state pathways from the absorption region to the emitting one. Also, we have postulated the existence of several decay channels. However, to reach the correct interpretation, it is essential to assess the relative importance of each. To answer this question, the index will here be used. It is important to mention though that the methodology we are about to discuss is based on static considerations. Therefore, it does not give any indication on the time-scale of the photochemical process. As a result, any consideration on the kinetics of the electronic process remains out of our scope.

As previously mentioned, the index combines energetic arguments -∆E -and a measure for charge rearrangement -D CT •q CT -and can be used as criteria to detect the presence of nonradiative decay channels. It is useful to compare the relative value of the index between electronic transitions that involve a common electronic state. This approach provides a

LE

reasonable estimate of the relative likelihood of the existence of a decay channel, connecting more efficiently an electronic state with one or another state, lower in energy. Intuitively, this information shall be coupled with the vertical absorption, in order to map the excited states all through the pathway that brings to the emission. As for this aspect, a radiative relaxation yielding an emission from any excited state S n necessarily implies that this particular state of interest is populated either directly, by irradiation, or by decay from an energetically higher excited state. The index, combined with the absorption data, provides precisely this information, thereby allowing to estimate the relative efficiency of the relaxation pathways connecting any two states all along a reaction coordinate. The result is a qualitative strategy, which delivers a consonant interpretation of a photochemical process, in an uncomplicated manner. Besides, the index is also computationally inexpensive, which is often not the case when one uses alternative approaches to deal with such questions. Undoubtedly, the global understanding of the physical phenomena will strongly depend on the quality of the ground, and excited states computed PES and thus will be affected by the level of theory (method and basis set) used to calculate densities and energies. This said, the level of theory which we have used to perform our calculations was chosen based on the result of a previous benchmark, which proved to give a good agreement with experimental data, both for absorption and emission. More details are provided in Section 2.

The index curves -in logarithmic scale -are reported in Figure 5 (left panel). We recall that high values of the index correlate with a high probability of interconversion from a state to another.

Two regions of decay result unequivocally. The first is the S 4 to S 3 decay, appearing around  = 40° in the solid olive-green curve. The second connects S 3 and S 2 and is indicated by the marked increment of the index associated with the S 3 -to-S 2 transition between  = 60° and  = 90°. These two curves allow identifying a leading non-radiative decay channel connecting S 4 to S 2 via S 3 . This decay pathway is essentially energy-driven, i.e., it is promoted by the energy nearness of the three states, at specific reaction coordinates. This channel corresponds to the S 4 -to-S 2 decay pathway that we had anticipated earlier through the energetic analysis (refer to Figure 2 and related discussion).

The case of those decay channels that are governed by the product D CT• q CT is subtler. The analysis of Figure 5 suggests the existence of two further decay and emission channels at  = 0° and = 90°. In the right panel of Figure 5, we collected the curves relative to the S n -S 0 transitions, weighted by their corresponding oscillator strength. As the oscillator strength is directly proportional to the transition probability, weighted-values provide a better estimate of the existing emission channels.

The largest weighted-value appears at  = 0° and is associated with the S 3 -S 0 transition (see right side of Figure 5), followed, in the same region by the S 1 -S 0 transition. The observed shapes of the S 3 -S 0 and S 1 -S 0 curves suggest that the LE (ππ*) state, corresponding to S 3 , together with the ICT 1 state (S 1 ) are likely to be primarily responsible for the emission in the Franck-Condon region. Additionally, the computed profiles point out an efficient interconversion between S 2 -S 1 (solid orange curve) and a non-negligible interconversion between S 3 -S 2 (solid red curve) that transfer the electronic population to the lowest excited state. We conclude that the ICT 1 emission is compliant with Kasha's rule. Although both S 3

and S 1 may be populated upon absorption, only the S 1 emits, and the S 3 -S 2 and S 2 -S 1 nonradiative decays enhance this emission channel. These outcomes agree with the experimental data substantiating the existence of an efficient ICT 1 radiative channel. 15,16 The vertical deactivation pathway transferring the electronic population from S 4 to S 1 (through the S 3 -S 2 -S 1 decay channels) and leading to the ICT 1 emission, is poorly efficient compared to the relaxation pathway activated by the torsion. As anticipated earlier in the discussion, if the molecule is irradiated with sufficiently high energy one activates the structural relaxation, which in turn results in populating (LE) S 2 state at 90°. The pathway involves the conversion between state S 4 to state S 3 (at around 50°) followed by the conversion of S 3 to S 2 at ~ 80°.

Furthermore, as the twist approaches 90°, two channels establish, which transfer the electronic population from S 4 to S 2 . By contrast, the oscillator strength of S 4 (0.09 a.u. in the twisted region) is connotative of a poor absorption, suggesting that the existence of an emissive path from S 4 is conditioned to the presence of a higher excited state, transferring its population to S 4 through a non-radiative channel. The steep increase of the index associated with the S 5 to S 4 decay at  = 90° validates this hypothesis. Similar reasoning holds for S 5 , whose population is maintained by S 6 , which absorbs at 0° and approaches S 5 at 60°.

Close to  = 90°, all curves, except that computed for the S 3 -S 1 , S 2 -S 1 and the S 1 -S 0 interconversion visibly rise. This increase again points out the formation of several interconnected decay sub-channels (S 4 -S 3 , S 4 -S 2 , S 3 -S 2 ,) enhancing the transfer of population from S 4 to S 2 . Once more, these sub-channels are not necessarily driven by the energy gap, which ranges between 0.01 a.u. for S 4 -S 2 and 0.003 a.u. for S 3 -S 2 . As such, the formation of these channels is supported by the similar distributions of the electronic densities of the states involved, as witnessed by the small q CT • D CT values -computed values are reported in Supporting Information (Table 4).

Remarkably, the drop in the S 1 -S 0 weighted-curve suggests the absence of the emission from S 1 (ICT 1 ) at 90°. Indeed, the orthogonality of the donor (dimethylaminophenyl) and acceptor (1,10-Phenanthroline) moieties hinders the formation of the ICT 1 state. As a consequence, the lowest emitting state at  = 90° is S 2 (LE). In light of the discussion above, the dual emission mechanism observed in Phen-PENMe 2 can be summarized by the Jablonski diagram shown in Figure 6.

The population of the S1 -ICT 1 planar state in the FC region -leads to the ICT 1 emission experimentally observed at 560 nm 15 . Moreover, irradiation at a higher excitation wavelength allows reaching S 4 . From S 4 a decay channel can open, leading to the population of S 2 , a ππ* state of local character (LE). The relaxation through the vibrational sublevels of S 2 causes the observed fluorescence band observed at 421 nm in the experimental spectrum 15 .

The S 4 -S 0 curve suggests the existence of a further radiative decay at  = 90 °. This channel is connected to S 6 -in the planar conformation. However, further internal deactivation channels between S 4 -S 3 and S 3 -S 2 can intervene, reducing the decay from S 4 and resulting in an enhanced S 2 -S 0 emission. Similarly, S 3 -S 1 and S 3 -S 2 curves hint to the existence of two nonradiative channels which, in the planar conformation, contribute to impoverish the S 3 -S 0 channel. All of the observable evidence leads to the conclusion that the emission from LE violates Kasha's rule. To explain this unusual behavior, it is instructive to examine the energy, and q CT •D CT values of the S 2 -S 1 transition, at  = 0 ° and  = 90 °. At  = 0° ∆E equals 0.021 a.u.. The q CT •D CT product is small (0.83 a.u.), which reflects a high similarity in the character of the two states. On the other hand, at 90°, while the energy gap shrinks to 0.007 a.u., q CT • D CT increases by one order of magnitude (9.07 a.u.). Although S 1 and S 2 are closer in energy at 90° than at 0°, the computed index is higher at 0°, reinforcing the hypothesis that a decay channel transfers the population from S 2 to S 1 at 0°, but not at 90°, allowing S 2 to emit radiatively.

degree S1-S0 S3-S1 S4-S2 S2-S0 S3-S2 S4-S3 S2-S1 S4-S0 S5-S4 S3-S0 S4-S1 S6-S5 0

Conclusions

In summary, we have applied the index to unravel the excited state decay pathway of the Phen-PENMe 2 molecule. We have postulated the existence of different radiative and nonradiative decay pathways, related to structural reorganization occurring at the excited state, which bring to the formation of the observed dual emission.

Two factors are crucial when the interconversion between states is concerned. The closer in energy are the two states, the higher the likelihood that the interconversion occurs. On the other hand, the more similar the electronic densities of the two states, the higher the possibility of decay. The index includes both criteria in a single definition. The energy proximity of the two states is evaluated as the energy difference between two states, while the similarity between their electron densities is recovered through the product q CT •D CTequivalent to the norm of the difference between their dipole moments.

Using the index , we could estimate the relative probabilities of different radiative and nonradiative channels, and infer a coherent picture of the decay pathways of the states involved in this photochemical process.

In particular, we have individuated two main radiative channels, which lead to the formation of two structurally different emissive species, a planar and a 90° twisted one. These findings also agree with the outcomes of previous work. 15,16 Remarkably, our analysis points out the anti-Kasha mechanism of the LE emission. Besides, we have identified several sub-channels that play an essential role, enhancing either of the two emissions.

To conclude, the analysis that we have carried out shows the capability of the index to draw a qualitative map of a photochemical reaction. Although we have focused on one particular system, such analysis could be performed in a similar fashion to unveil the mechanism of other photochemical reactions of interest. Finally, in a more general perspective the present computational strategy may be particularly interesting for the rational design of substituted Phen-PENMe 2 derivatives with a targeted dual emission.

Supporting information

Tables containing optimized Cartesian coordinates of ten structures used, vertical excitation energies, D CT, oscillator strength and dipole moment data computed for each excited state.

NTOs representation. Absorption energies and oscillator strength data used to calculate the UV-visible absorption spectrum. Energy differences, q CT , D CT and data computed for each excited state decay pathway.

  Ground state DFT calculations computed at each reaction step revealed a rather flat ground state potential curve. The planar structure (=0°) is the minimum, though only by 0.04 eV (1.45 Kcal/mol) lower in energy compared to the orthogonal conformation (=90°), the maximum of the ground state curve.Excitation in the 3.5-4.0 eV (354-310 nm) energy regime, populates the first excited state (S 1 ). All along the reaction coordinate, the potential energy curve of S 1 (in yellow in the upper panels of Figure1) increases monotonically, without any crossing over other excited states curves. The absorption is most efficient in the Franck-Condon region -where the oscillator strength is maximal (1.60 a.u.) -and decreases ceaselessly, down to a value of 0.0 a.u. for the twisted conformation (=90°).

Figure 1 S0

 1 Figure1 Upper panels: Ground (S 0 ) and first excited states (S 1 -S 6 ) computed energy profiles (in eV) along the  torsional degree of freedom. Upper-left panel: the excited state labels follow the energy indexing at °; upper-right panel: the excited state labels are assigned according to their nature at = 0°. Lower panels: computed D CT (in Å) and oscillator strength (f osc , in a.u.) associated to each excited state, labelled according to the energy.

3 Figure 2

 32 Figure 2 Computed normalized Boltzmann factors (computed at T=298 K for each state) for the ground state and first six excited states (labelled as a function of their nature, Figure 1 upper-right panel) as a function of  dihedral angle. Each curve is normalized w.r.t. its maximum value.

Figure 3

 3 Figure 3Absorption spectrum of Phen-PENMe 2 at fixed dihedral angles, ranging from 0° to 90°simulated by Gaussian convolution of the computed vertical transition energies using a fwhm value of 0.2 eV. The color-coding highlights the raising and vanishing of the LE and ICT 1 , respectively.

Figure 4 .

 4 The band around 350 nm (3.54 eV) is the result of the ICT 1 (S 0 to S 1 ) transition. The highest energy band at 265-295 nm (4.68-4.20 eV) arises from the convolution of mainly two different states, whose contribution is highlighted with a blue background in the simplified Jablonski diagram reported on the right hand of Figure 4. The transitions lying between 280 and 295 nm (4.43 and 4.20 eV) correspond to the evolution of the ICT 3 ICT 2 state, stemming from the S 0 -S 4 transition in the 0° <  < 40° window. The same state is then populated by S 0 -S 3 transition at dihedral values between 40° and 70°, and by S 0 -S 2 transition at 70° <  < 90°. Slightly higher in energy, at 280-270 nm (4.43-4.59 eV) the S 0 -S 4 (0° <  < 60°) and S 0 -S 5 transition (60° <  < sum up with the other closely lying transitions to contribute to the second band.

Figure 4

 4 Figure 4 Left: Boltzmann weighted simulated absorption spectra of Phen-PENMe 2 Right: Jablonski diagram describing the absorption phenomena occurring in the Phen-PENMe 2 molecule.

Figure 5 (

 5 Figure 5 (Left) Evolution of index (in logarithm scale) along the reaction coordinated (the dihedral angle ). (Right) The evolution of weighted by the oscillator strength (in logarithm scale).

Figure 6

 6 Figure 6 Jablonski Diagram describing the anti-Kasha dual emission of Phen-PENMe 2 molecule.

Acknowledgments

This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 648558, STRIGES CoG grant).

Declaration of interest.

There are no known conflicts of interest associated with this publication.


Karen Davranche
email: karen.davranche@univ-amu.fr

Clément Belletier

Thibault Gajdos

Laurence Carbonnell

Franck Vidal

Pascal Huguet

Thierry Hasbroucq

Deciphering the nature of the joint Simon effect through electromyographic analyses

Keywords: Go/NoGo tasks, Joint Simon Effect, Social facilitation, Increased arousal, Spatial correspondence, Automatic response capture Highlights

This study aimed to apply electromyographic techniques and distributional analyses to test whether an increase in the strength of stimulus-response mapping could explain the mechanisms underlying the joint Simon effect. Within a single protocol, participants performed a Simon task and a Go/NoGo task in isolation, and a joint Go/NoGo task with a co-actor (joint Simon task). Results showed that joint-action impairs cognitive control and shortened reaction time by impacting both pre-motor time and motor time. Jointaction induced a larger facilitation on pre-motor time of ipsilateral than contralateral associations. This potentiation of the spatial correspondence effect plausibly explains the larger Simon-like effect usually observed in the joint Go/NoGo task compared to that observed in the isolated Go/NoGo task. The propensity of making incorrect activations and their concentration among fast responses also increased when working co-actively. Together, these findings indicate that joint-action increases the strength of automatic response capture induced by the stimulus location, promotes the delivery of the stronger association in the behavioral repertoire of the individual, and reduces cognitive control.

Introduction

In the most common version of the standard Simon task, the participants have to choose between a left-and a right-hand key press according to the color of a visual stimulus presented a few degrees either to the left or the right of a fixation point. Mean choice reaction time (RT) is shorter for ipsilateral stimulus-response associations than for contralateral stimulus-response associations [START_REF] Craft | Processing symbolic information from a visual display: interference from an irrelevant directional cue[END_REF]. This effect is termed the Simon effect (SE; see [START_REF] Simon | The effects of an irrelevant directional cue on human information processing[END_REF]). An influential scheme that accounts for the SE has been proposed by [START_REF] Kornblum | Dimensional overlap: cognitive basis for stimulus-response compatibility--a model and taxonomy[END_REF]. Accordingly, the irrelevant stimulus location automatically activates its spatially corresponding response and, because of this activation, ispsilateral (IPS) stimulus-response associations are performed fasterand are less error pronethan controlateral (CNT) stimulus-response associations. In an associationnist stance, this notion amounts to consider that IPS associations are stronger than CNT associations [START_REF] Davranche | A Simon-like effect in Go/No-Go tasks performed in isolation[END_REF]. In support of this interpretation, a small but significant advantage in favor of IPS associations can be found when participants are asked to respond to only one of the two stimuli, the task being thus transformed into a Go/NoGo task [START_REF] Callan | Strength of auditory stimulus-response compatability as a function of task complexity[END_REF]; see [START_REF] Davranche | A Simon-like effect in Go/No-Go tasks performed in isolation[END_REF].

Importantly, this spatial correspondence effect (cSE, in reference to Donders' type c task) is magnified when the Go/NoGo task is performed by two co-actors seated side to side, each of them responding to one of the two possible stimulus colors (Natalie [START_REF] Sebanz | Representing others' actions: just like one's own?[END_REF]. During the last decade, such a potentiation termed the Social Simon effect or Joint Simon effect (JSE) has spawned an important literature (for a review, see [START_REF] Dolk | The joint Simon effect: a review and theoretical integration[END_REF]. Several interpretations of the JSE have been proposed (e.g., [START_REF] Dolk | How "social" is the social Simon effect[END_REF][START_REF] Dolk | The (not so) social Simon effect: A referential coding account[END_REF][START_REF] Sebanz | Joint action: bodies and minds moving together[END_REF], but most of them neglected the small but significant advantage in favor of IPS associations which is also present (all things being equal) when the Go/NoGo task is performed in isolation. The existence of this small advantage can be seen in the frame of [START_REF] Kornblum | Dimensional overlap: cognitive basis for stimulus-response compatibility--a model and taxonomy[END_REF] model as a variation in the strength of automatic response capture between the lateralized stimuli and responses.

Here, we tested the possibility that the JSE results from a potentiation of this preexisting cSE caused by an increase of the strength of the automatic response capture in presence of a coactor. There is indeed evidence from a long-standing literature on social facilitation [START_REF] Zajonc | Social Facilitation[END_REF] that the presence of conspecifics increases the general arousal which, in turn, energizes the emission of the more dominant (for example the most automatic) response [START_REF] Fagot | Using a network of computerized ALDM test systems for the assessment of social cognition in non-human primates[END_REF][START_REF] Huguet | Cognitive control under social influence in baboons[END_REF][START_REF] Zajonc | Social Facilitation[END_REF] for reviews see [START_REF] Bond | Social facilitation: A meta-analysis of 241 studies[END_REF][START_REF] Guerin | Social Facilitation[END_REF][START_REF] Seitchik | Social facilitation: Using the molecular to inform the molar[END_REF]. Testing this hypothesis in the context of the JSE requires quantifying the strength of the automatic response capture by the stimulus location. To this end, we resorted to electromyographic (EMG) techniques and distributional analyses. Many correct response trials contain subthreshold muscle activities that would lead to erroneous responding if their magnitudes were larger. These transient activities are partial errors that are successfully stopped to prevent response errors [START_REF] Hasbroucq | Stimulus-hand correspondence and direct response activation: An electromyographic analysis[END_REF]. Since these partial errors enable to characterize the automatic response capture, we reasoned that if the JSE is due to increased automatic response capture, participants should display more incorrect activations (including both overt errors and partial errors) when performing the task with a co-actor than when performing the task alone. Moreover, in this case we should also observe a higher concentration of incorrect activation among fast responses, which can be measured by the Error Location Index [START_REF] Servant | ELF: A new measure of response capture[END_REF]. Participants went to the laboratory accompanied by a friend for a first session and alone for a second. In the session performed alone, participant completed 10 blocks of 100 trials in a Simon task (Figure 1, panel B) and 10 blocks of 100 trials in an isolated Go/NoGo task (Figure 1, panel C). In the session performed with a friend, participants share a Simon task or in other words complete a joint Go/NoGo task (Figure1, panel A). The order of the sessions and the order of the cognitive tasks in the individual session were counterbalanced across participants.

Figure 1. Illustration of the different cognitive tasks completed by a participant in the experiment: (A) participant A performed a joint Go/NoGo task in co-action with a friend; (B) participant A performed a Simon task and (C) an isolated Go/NoGo task. In the isolated Go/NoGo task, there is only one possible response. If the participant is seating on the left side, the response is given using the left response key with the left hand. Following the same logic when participant is seating on the right side of the device the response is given using the right response key with the right hand. Half participants reply to the lit of the green LED and the other half to the red LED. When participant performed the joint Go/NoGo task, each co-actor did exactly the same task than during the isolated Go/NoGo task. They sat on the same side, replied to the lit of the same colour and pressed the same response key with the same hand.

Participants were seated on chairs positioned side by side which faced a black panel 1.5 metre away. When participants shared the task, they were close but not in contact with each other; when performing the task individually the position was identical and the second chair remained empty (i.e., slightly on the left or right side of the device). Two green/red lightemitting diodes (LEDs), separated by 18 cm, were positioned at both sides of a central blue gaze-fixation LED. The response keys were two 10 cm plastic tubes, separated by 20 cm, equipped with a button on the top and fixed on a table placed in front of the chairs. Regardless of the correctness, the delivery of a response turned off the stimulus and the next trial began after a constant 1500 ms inter-stimulus interval (ISI). If 1 second elapsed without a response, the LED extinguished and the next trial began after the ISI.

Participants were asked to respond as quickly and accurately as possible. The light could be green or red and could be delivered either to the left or to the right side. The response was given by pressing the appropriate response key, according to the colour of the LED (taskrelevant attribute) whatever the location of the LED (the task-irrelevant attribute). Half participants had to exert a press with the left thumb when the LED was red and a press with the right thumb when the LED was green, the other half participants were to perform the reverse stimulus-response mapping. There were two types of trials in each block: ipsilateral trials (50%) and contralateral trials (50%). In ipsilateral trials (IPS), the lateral locations of the stimulus and response are on the same side (e.g., left stimulus/left response). In contrast, in contralateral trials (CNT), the lateral locations of the stimulus and response are on the opposite side (e.g., left stimulus/right response).

Electrophysiological recording

Electromyographic (EMG) activities were recorded with bipolar Ag/AgCl electrodes (BIOSEMI Active-Two electrodes, Amsterdam) glued on the skin over the flexor pollicis brevis). The sampling rate was 1024 Hz (filters: DC to 268 Hz, 3 dB/octave). Electrodes were fixed 2 cm apart on the skin of the thenar eminence. The EMG signal was continuously monitored by the experimenter (that stayed in an adjacent room during the experiment) in order to avoid as much as possible any background activity in order to facilitate the EMG onset detection. If the signal became noisy, the experimenter immediately asked the subject to relax his (her) muscles.

Data analysis and statistics

Reaction time less than 100ms and RT higher than 1000ms, considered as anticipated responses and omissions, were excluded from further analyses (27,23 % of trials in total). The EMG activities recorded during each trial were displayed on a computer screen aligned to the onset of the imperative stimulus, and the onsets of the changes in activity were determined visually and marked with the computer mouse. The experimenter was unaware of the nature of the trial or the task being processed. This method was preferred to an automated one because it allows more precise detection [START_REF] Hasbroucq | Effect of the irrelevant location of the response signal on choice reaction time: an electromyographic study in humans[END_REF][START_REF] Van Boxtel | Detection of EMG onset in ERP research[END_REF]. Reaction time was measured to the closure of the switches located under the response keys and decomposed into premotor-time (PMT, from stimulus onset to the onset of the EMG involved in the response) and motor-time (MT, from the EMG onset to the switch closure). Mean RT, PMT and MT for pure correct trials (trials with no sign of EMG activation associated with the incorrect response) was calculated for each condition. Two subjects did not have enough trials after electrophysiological artifact rejections and the data of one participant were discarded because of technical dysfunction. The incorrect activation trials correspond to two categories of trials: overt errors and partial errors. During the Simon task, partial errors correspond to trials in which a correct activation was preceded by an incorrect activation. The force exerted by the non-required effector was not sufficient to elicit a response error and were followed by a correct activation reaching response threshold. During the joint and isolated Go/NoGo tasks, partial errors correspond to trials in which an activation of the effector was detected on a NoGo trial.

We also relied on the Error Location Function (ELF), which represents the proportion of incorrect activations located below each quantile of the overall PMT distribution, to measure the concentration of incorrect activation among fast responses. The Error Location Index (ELI), which represents the area below ELF, is used as a quantitative measure of automatic response capture [START_REF] Servant | ELF: A new measure of response capture[END_REF]: The more concentrated are the incorrect activations among fastest trials, the higher the ELF, the larger the ELI. It is important to note that the ELI is a relative index. It might thus increase either because incorrect activations are faster, or because overall trials are slower. In the latter case, a larger ELI should not be interpreted as reflecting a stronger automatic response capture.

Response time distributions analyses were conducted to compare the time course of the spatial correspondence effect, the so-called delta plot developed by [START_REF] Jong | Conditional and unconditional automaticity: a dual-process model of effects of spatial stimulus-response correspondence[END_REF], in the individual Simon task, isolated Go/NoGo task and joint Go/NoGo task. Curve density functions were constructed using individual RTs "vincentized" into ten equal-size speed bins (deciles) in each spatial correspondence condition for each task (Figure 4A). Then, the delta plots were computed by plotting the difference between the mean RTs of the two spatial correspondence associations in each bin against the mean RT across both conditions for that bin (Figure 4B). If the presence of a co-actor induces participants to code their unique response in terms of left or right relative to the other's response, we expected that the time course of the spatial correspondence effect in the joint Go/NoGo task should follow a similar qualitative pattern to that of the Simon task. To test this result for statistical significance, the slope of the delta plots was estimated for each of the 38 participants separately by linear regressions [START_REF] Ellinghaus | Delta plots with negative-going slopes as a potential marker of decreasing response activation in masked semantic priming[END_REF].

Repeated-measures canonical analyses of variance (ANOVA) were performed on each dependent variable, with partial eta-squared (ηp 2 ) reported as a measure of effect size. A first series of analyses was conducted on the Simon task, and then a second series was performed on Go/NoGo tasks to focus on the JSE. This latest series involved co-action (joint Go/NoGo vs. isolated Go/NoGo) and spatial correspondence of the trial (IPS vs. CNT) as within-subject factors. Post hoc Newman-Keuls analyses were conducted on all significant interactions. Significance was set at p < .05 for all analyses.

Results

3.1.Simon task

Repeated measures ANOVA conducted on the standard Simon task showed a main effect of Spatial correspondence (F(1,37) = 70.87, p <.001, ηp 2 = 0.66). Reaction time was faster for congruent trials (CO: M=350ms, SE= 6ms) compared to incongruent trials (IN: M=374ms, SE=7ms). Results on PMT mimicked the pattern observed on mean RT with participants displaying faster PMT for CO trials (M=242ms, SE=7ms) than for IN trials (M=266ms, SE=8ms) (F(1,37) = 61.07, p <.001, ηp 2 = 0.62). No main effect of spatial correspondence was observed on mean MT (F(1, 37) = 1.17, p = .28, ηp 2 = 0.03; CO: M=108ms, SE=5ms vs. IN: M=109ms, SE=5ms). A classic effect of spatial correspondence was observed on overt errors (F(1,37) = 16.87, p < .001, ηp 2 = 0.31; CO: M=4%, SE=0.4% vs. IN: M=6%, SE=0.6%) and partial errors (F(1,37) = 20.50, p < .001, ηp 2 = 0.36; CO: M=20%, SE=2.4% vs. IN: M=25%, SE=1.9%).

3.2. Go/NoGo tasks 3.2.1. Reaction time. Results showed main effects of Spatial correspondence (F(1,37) = 16.90, p <.001, ηp 2 = 0.31) and Co-action (F(1,37) = 9.29, p <.01, ηp 2 = 0.20), and a Spatial correspondence x Coaction interaction (F(1,37) = 15.04, p <.001, ηp 2 = 0.29). Reaction time was faster for IPS trials (M=311ms, SE=6ms) compared to CNT trials (M=319ms, SE=7ms). Participants displayed faster RT in joint Go/NoGo (M=307ms, SE=7ms) compared to isolated Go/NoGo (M=323ms, SE=7ms). The Spatial correspondence x Co-action interaction showed that a Simon-like effect was observed in the isolated Go/NoGo task (321ms vs. 326ms, p < .001) and in the joint Go/NoGo task (301ms vs. 312ms, p < .001). The cSE effect was potentiated by the presence of a co-actor, resulting in a larger Simon-like effect in the joint task (isolated: 5ms vs. joint: 11ms, Figure 2).

Premotor time.

Results on PMT mimicked the pattern observed on mean RT. There were main effects of Spatial correspondence (F(1,37) = 18.41, p <.001, ηp 2 = 0.33) and Co-action (F(1,37) = 10.98, p <.01, ηp 2 = 0.23), and a Spatial correspondence x Co-action interaction, F(1,37) = 12.96, p < .001, ηp 2 = 0.26). Premotor time was faster for IPS trials (M=216ms, SE=5ms) than for CNT trials (M=224ms, SE=5ms). Participants displayed faster PMT in joint Go/NoGo (M=213ms, SE=5ms) compared to isolated Go/NoGo (M=227ms, SE=6ms). The Spatial correspondence x Co-action interaction showed that joint-action induced a larger facilitation on IPS trials (joint: M=208ms, SE=5ms vs. isolated: M=224ms, SE=6ms) than on CNT trials (joint: M=219ms, SE=6ms vs. isolated: M=229ms, SE=6ms). The cSE was potentiated by the presence of a coactor, resulting in a larger Simon-like effect in the joint task (joint: 11ms vs. isolated: 5ms).

Motor time.

Results showed main effects of Spatial correspondence (F(1,37) = 8.21, p < .01, ηp 2 = 0.18) and Co-action (F(1,37) = 5.62, p = .02, η p 2 = 0.13). Motor time was faster for CNT trials (M=95ms, SE=4ms) than for IPS trials (M=96ms, SE=4ms). Participants displayed faster MT in joint Go/NoGo (M=93ms, SE=4ms) compared to isolated Go/NoGo (M=98ms, SE=4ms). The Spatial correspondence x Co-action interaction was not significant (F(1,37) = 0.21, p = .65, ηp 2 = 0.005). Joint-action induced an equivalent facilitation on IPS trials (joint: M=94ms, SE=4ms vs. isolated: M=98ms, SE=4ms) and on CNT trials (joint: M=93ms, SE=4ms vs. isolated: M=98ms, SE=4ms).

Overt errors and partial errors.

ANOVA performed on overt errors showed main effects of Spatial correspondence (F(1,37) = 12.44, p < .01, ηp 2 = 0.25) and Co-action (F(1,37) = 10.61, p <.01, ηp 2 = 0.22), and a Spatial correspondence x Co-action interaction (F(1,37) = 4.31, p <.05, ηp 2 = 0.10). Participants committed more overt errors in the joint Go/NoGo (M=1.8%, SE=0.3%) compared to the isolated Go/NoGo (M=1%, SE=0.2%), and IPS errors (M=1.5%, SE=0.2%) were more important than CNT errors (M=1.2%, SE=0.2%). The Spatial correspondence x Co-action interaction showed that the impact of coaction was larger for IPS trials (joint: M=2%, SE=0.3% vs. isolated: M=1%, SE=0.2%) than for CNT trials (joint: M=1.5%, SE=0.2% vs. isolated: M=0.9%, SE=0.2%).

Results on partial errors showed a main effect of Co-action (F(1,36) = 8.86, p <.01, ηp 2 = 0.20). Participants committed more partial errors in the joint Go/NoGo (M=23%, SE=2%) compared to the isolated Go/NoGo (M=16%, SE=2%). The main effect of Spatial correspondence was close to significance (F(1,37) = 4.09, p = .05, ηp 2 = 0.10). IPS partial errors (M=20%, SE=1%) tended to be more numerous than CNT partial errors (M=19%, SE=1%). The Spatial correspondence x Co-action interaction was not significant (F(1,36) = 0.05, p = .83, ηp 2 = 0.01).

3.2.5. Error Location Function (ELF) of incorrect activations. ANOVA was performed on individual ELI which is an index of automatic response capture derived from the PMT distribution of incorrect activations compared to the PMT distribution of all trials (Error Location Function, ELF). The incorrect activations (overt errors + partial errors) committed on the same side than the NoGo signal were considered as ipsilateral incorrect activations, whereas incorrect activations committed on the opposite side than the NoGo signal were considered as contralateral incorrect activations. Results revealed a main effect of Co-action (F(1,34) = 26.44, p <.001, ηp 2 = 0.44) and a Spatial correspondence x Coaction interaction (F(1,34) = 9.39, p <.01, ηp 2 = 0.22). In the joint Go/NoGo, the errors were more concentrated among the faster trials (ELI: M=0.79, SE=0.01) than in the isolated Go/NoGo (ELI: M=0.72, SE=0.01). Given that overall RT were faster in joint Go/NoGo, this can be interpreted as reflecting a stronger automatic response capture. The Spatial correspondence x Co-action interaction showed that in the joint Go/NoGo CNT incorrect activations (ELI: M=0.81, SE=0.01) were more numerous than the IPS incorrect activations (ELI: M=0.78, SE=0.01) among the faster trials (p < .01). Given that RT were slower for CNT trials than for IPS trials, this result cannot be interpreted as reflecting a stronger automatic response capture for CNT trials. This effect was not observed in the isolated Go/NoGo (p = .13, ELI CNT incorrect activations: M=0.71, SE=0.01 vs ELI IPS incorrect activations: M=72, SE=0.01, Figure 3).

Discussion

EMG recordings and RT distributional analyses were used here in a single protocol to quantify the strength of automatic response capture induced by stimulus location when participants performed a standard Simon task, an isolated Go/NoGo task (performed in alone in the cubicle) and completed a joint Go/NoGo task with a co-acting friend.

The results might be interpreted in the light of the double-route model [START_REF] Kornblum | Dimensional overlap: cognitive basis for stimulus-response compatibility--a model and taxonomy[END_REF] for tasks where stimulus-response compatibility is manipulated. This model has two main features: first, automatic responses are triggered by the stimulus-response correspondence. Second, these automatic responses are aborted by control processes. While this model has been designed to account for the S-R effect in the Simon task it can be conceptually useful to understand the present data. Both behavioural and electromyographic data suggest a general increase of arousal, together with an increase of the strength of the stimulus-response association and a degradation of the cognitive control processes when subjects perform the task jointly rather than in isolation.

First, we confirmed the presence of a spatial correspondence effect (cSE) in the Go/NoGo task performed in isolation, replicating previous results [START_REF] Callan | Strength of auditory stimulus-response compatability as a function of task complexity[END_REF][START_REF] Davranche | A Simon-like effect in Go/No-Go tasks performed in isolation[END_REF], and the presence of a JSE in the joint Go/NoGo task. The spatial correspondence effect found in isolation (cSE = 5 ms) was actually twice as large when the Go/NoGo task was performed under coaction (JSE = 11 ms). Note that, as illustrated on Figure 4, the magnitude of the effect of spatial correspondence observed in the Go/NoGo tasks remained much lower than that observed in a Simon task. This might be explained by the fact that in Go/NoGo tasks, the single response is known in advance and so could be fully prepared, which is not the case during the Simon task, for which additional decision stages are required to select one of the two possible alternatives. Moreover, the time course of the spatial correspondence effect in the joint Go/NoGo task did not follow a similar qualitative pattern to that observed in a Simon task. Given these differences in the shapes of observed delta plots, it is worth considering that the interference effect in the Go/NoGo tasks is not of the same nature and may principally be driven by a facilitation of IPS associations. By contrast, it has been proposed that the negative-going slope obtained in the Simon paradigm constitutes a noteworthy phenomenon considered as a signature of some specific cognitive architecture (see [START_REF] Schwarz | Response time models of delta plots with negative-going slopes[END_REF]. This slope is mainly due to the fact that, for CNT associations, the incorrect response triggered by automatic response capture should be interrupted but also corrected [START_REF] Kornblum | Dimensional overlap: cognitive basis for stimulus-response compatibility--a model and taxonomy[END_REF]. These additional processes require an extra time. Hence, even such processes are likely not purely "inserted" (in a Donderian perspective, [START_REF] Donders | La vitesse des actes psychiques[END_REF] ; see also [START_REF] Vidal | An ERP study of cognitive architecture and the insertion of mental processes: Donders revisited: ERPs and the insertion assumption[END_REF], they increase RT and consequently lead to a larger spatial correspondence effect.

Second, the analysis performed on individual ELI suggests a stronger automatic response capture when participants performed the Go/NoGo task in presence of a co-actor than when they performed the task in isolation. These results are in line with a strengthening of ipsilateral stimulus-responses associations, and therefore support the fact that the JSE results from a potentiation of a preexisting cSE due to increased automatic response capture. It is worth noting that these results are difficult to account for in the framework of the referential coding theory (e.g., [START_REF] Dolk | How "social" is the social Simon effect[END_REF][START_REF] Dolk | The (not so) social Simon effect: A referential coding account[END_REF]. According to this theory, the presence of a co-actor, and of a visual and/or auditory irrelevant object (be it social or not) placed nearby single participants would be subjectively coded as an alternative to the required response. The coexistence of these two representations would induce participants to code their unique response in terms of left or right relative to the other's response. This coding would thereby induce a JSE while the participants objectively perform a Go/NoGo task. In other words, the match that drives the JSE would concern the perceptual representations of the stimulus and response events that the participants label "left" and "right" relative to a reference frame. In the course of a trial, the participant would thus have to choose between these two lateralized responses, which would be sufficient to generate a conflict and thereby a Simon-like effect (or a JSE in the case of the presence of a co-actor). The present results are difficult to explain in this framework mainly because it refutes (or at least neglects) the very existence of a cSE when the Go/NoGo task is performed in isolation. Additionally, referential coding theory predicts slower RT and PMT, at least for CNT trials. The current results highlight the opposite effect, showing a speed-up of both RT components (i.e., PMT and MT).

Third, comparing isolated and joint Go/NoGo tasks, we found that joint-action shortened RT by impacting both pre-motor time and motor time. Moreover, participants committed more overt and partial errors in the joint Go/NoGo compared to the isolated Go/NoGo tasks. These observations are compatible with a global increase of arousal that would shorten both fractionated components of reaction time, and a strengthening of the stimulusresponse association that would increase the number of incorrect activations, resulting in more overt and partial errors when the task is performed jointly in comparison to isolation. Finally, we observed that 1) the difference between ipsilateral and contralateral RTs is increased when the task is performed jointly; 2) the difference between ipsilateral and contralateral overt errors is increased when the task is performed jointly (see Figure 2), while this is not the case for partial errors. These results might be also accounted by the conjunction of a general increase of arousal and a strengthening of the ipsilateral stimulus-response association. A general increase of arousal would indeed simultaneously increase ipsilateral and contralateral incorrect activations. A strengthening of the stimulus-response association would specifically increase the number of ipsilateral incorrect activations. As a result, there would be a stronger increase of the number of incorrect activations for ipsilateral than for contralateral trials when the task is performed jointly rather than in isolation. For a given number of incorrect activations, an impairment of the cognitive control processes increases the number of overt errors and decreases the number of partial errors. Thus, a degradation of cognitive control processes when the task is performed jointly would amplify these effects (i.e., increased arousal and strengthening of the association) on overt errors, while reducing them on partial errors. All this would result in a larger increase in the difference between ipsilateral and contralateral overt errors compared to partial errors when the task is performed jointly rather than in isolation.

Importantly, this difference between the patterns of overt and partial errors cannot be explained by [START_REF] Zajonc | Social Facilitation[END_REF] classic view of social facilitation. According to this view, the emission of ipsilateral responses would be facilitated in the joint Go/NoGo task, compared with the Go/NoGo task in isolation. Because ipsilateral responses might be either correct or incorrect, this facilitation effect would speed up correct responses and increase the number of errors, as observed. However, social facilitation theory also predicts that ipsilateral responses should be more facilitated than contralateral ones, inducing a larger increase of the number of both overt and partial responses for ipsilateral trials than for contralateral ones. Thus, the number of both overt and partial errors should increase more for ipsilateral than for contralateral trials when the task is performed jointly. This is actually what we observed for overt errors, but not for partial errors. Therefore, while behavioral results might suggest performing jointly the Go/NoGo task induce a social facilitation effect, electromyographic data reveal a more complex picture. Zajonc's theory accounts for a part of the JSE, as it predicts a facilitation of the ipsilateral stimulus-response association in the joint condition. However, our data indicate that additional processes are at work: (i) the general reduction of RTs and MTs in the joint condition suggest the existence of a global increase of arousal under coaction while (ii) the presence of an ipsilateral facilitation evidenced on overt errors but not on partial errors, when the task is performed jointly, also suggests that coaction impairs cognitive control processes. Importantly, these two last processes could not have been evidenced without EMG analyses. Indeed, overt and partial errors both result from an incorrect activation, which is corrected in the case of partial errors. The fact that only overt errors increase on ipsilateral trials suggests a decreased correction of the incorrect activations, and thus an impairment of cognitive control processes at stake in the joint Go/NoGo compared to the isolated Go/NoGo task. Consistent with the present results, there is evidence of reduced cognitive control in the presence of others [START_REF] Belletier | Choking under monitoring pressure: Being watched by the experimenter reduces executive attention[END_REF][START_REF] Belletier | Chocking under experimenter's presence: Impact on proactive control and practical consequences for psychological science[END_REF][START_REF] Huguet | Cognitive control under social influence in baboons[END_REF][START_REF] Wagstaff | Some cognitive and neuropsychological aspects of social inhibition and facilitation[END_REF][START_REF] Wühr | The impact of social presence on voluntary and involuntary control of spatial attention[END_REF]; for a recent review, see Belletier, Normand, & Huguet, 2019). There is also evidence that socially induced facilitation of dominant responses and reduced cognitive control may occur simultaneously [START_REF] Huguet | Cognitive control under social influence in baboons[END_REF][START_REF] Mazerolle | Stereotype threat strengthens automatic recall and undermines controlled processes in older adults[END_REF].

In conclusion, our findings indicate that joint-action increases the strength of automatic response capture induced by the stimulus location, promotes the delivery of the stronger association in the behavioral repertoire of the individual, and impairs cognitive control.

   yrs; SD = 2.78)] participated in the experiment. They were paid 30€ for taking part. Participants had normal or corrected-to-normal vision. Informed written consent was obtained according to the Declaration of Helsinki.2.2. Design and Cognitive TasksWithin a single protocol, each participant completed a classic Simon task, a joint Go/NoGo task in co-action with a friend, and an isolated Go/NoGo task (performed in isolation). The experiment consisted in two sessions carried out at the same time of day.

Figure 2 .

 2 Figure 2. (Left) Mean RT in millisecond in the joint Go/NoGo (black) and in the isolated Go/NoGo (white) tasks as function of the spatial correspondence of the stimulus relative to the response (ipsilateral vs. contralateral). (Right) Overt error percentage in the joint Go/NoGo (black) and in the isolated Go/NoGo (white) tasks as function of the spatial correspondence of the stimulus relative to the response (ipsilateral vs. contralateral). Errors bars represent standard errors.

Figure 3 .

 3 Figure 3. Error Location function (ELF) derived from the PMT distribution of incorrect activations compared to the PMT distribution of all trials in the joint Go/NoGo (red lines) and in the isolated Go/NoGo (black lines) tasks as function of the spatial correspondence of the stimulus relative to the response (ipsilateral vs. contralateral).3.3. Delta plotsA t-test performed on the individual delta plot slopes suggested that the mean slope in the Simon task (M=-0.035, SE=0.16) was different (t(37) = 2.01, p = .052, Cohen-d = 0.33) from that in the joint Go/NoGo task (M=0.030, SE=0.14).

Figure 4 .

 4 Figure 4. (A) Curve density function (CDF) (in milliseconds) in the individual Simon task, isolated Go/NoGo task and joint Go/NoGo task, from the left to the right, as function of the spatial correspondence. CO: congruent trials, IN: incongruent trials, IPS: ipsilateral trials, CNT: contralateral trials. (B) Delta plot of reaction time illustrating the spatial correspondence effect (in milliseconds) as function of mean reaction time in the individual Simon task, isolated Go/NoGo task and joint Go/NoGo task, from the left to the right.

Funding: This work was part of C.B.'s PhD funded by the "Direction General de l'Armement" under the supervision of P.H. and has also been supported by a public grant overseen by the French National Research Agency (ANR) with P.H. and T.H. as PI [reference: ANR-10- BLAN-1915]