Laure De Thieulloy

Clément Barois

Cédric Mongin

Isabelle Leray

Clément Guerrin

Stéphane Aloïse

Guy Buntinx

Aurelie Perrier
email: aurelie.perrier-pineau@u-paris.fr

Aurélie Perrier

Is it possible to

Keywords: cation photoejection, Re(I) complex, TD-DFT, Charge Transfer

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

With the help of CT descriptors (the variation of the electronic density, the so-called D CT index and the variation of natural population analysis NPA charges), we aim to identify the CT states presenting a depletion of electronic density on the complexation site after excitation. If the loss of electronic density is large enough in the cation binding site, the population of such a state should be the first step of the mechanism leading to the cation photorelease.

We test this strategy on ReAZBAP + -M n+ (M n+ = Li + , Na + , Mg 2+ , Ca 2+ , Ba 2+ ) and ReAZAT + -Ba 2+ systems, a series of complexes synthesized and studied by Moore and co-workers [J. Phys. Chem. A 108 (42) (2004) 3852]. We show that our first-order approach that does not take into account the complex excited-state decay routes, is able to correctly predict the photorelease proper-

Introduction

Controlling the chemical, optical and mechanical processes at the nanometer scale constitutes a growing and challenging field of research, and a large variety of molecular devices and machines such as motors or logic gates have already been designed. In these devices, photo-active molecules play an important role in high interest scientific fields such as molecular electronics, molecular machines, advanced materials and biology [1].

The photoswitching reactions are mainly based on elementary photochemical processes that have been extensively studied during the last four decades such as intramolecular charge transfer (ICT) [2], excited state proton transfer (ESPT) [3] or cycloaddition [4]. Another class of photodevices are based on the photocontrol of cation complexation / release [5]. The systems synthesized so far are based on photo-uncaging of the cation after light excitation. More precisely, photoinduced changes in the structure of chelators [6,7,[START_REF] Agarwal | Calcium uncaging with visible light[END_REF] or photocleavage of chelators [START_REF] Ellis-Davies | Nitrophenyl-egta, a photolabile chelator that selectively binds Ca 2 + with high affinity and releases it rapidly upon photolysis[END_REF] or cryptands [START_REF] Warmutha | Photocleavable cryptands: Synthesis and structure[END_REF][START_REF] Grell | Caged cations[END_REF] were shown to efficiently release caged cations (Ca 2+ , K + , Zn 2+ ...).

The main drawback of these approaches is nevertheless irreversibility: upon uncaging the ion the molecules become denaturized. Few systems propose reversible cation ejection and they are, most of the time, based on reversible photochemical reaction (isomerization or electrocyclization) [START_REF] Natali | Molecular switches as photocontrollable 'smart' receptors[END_REF][START_REF] Bianchi | Highlights of metal ion-based photochemical switches[END_REF] . In that vein, Shinkaï et al. were the first to achieve reversibility by proposing a photochromic molecular switches based on an azobenzene derivative functionalized by a crown-ether, "the butterfly effect" was then the first example of Reversibly Photoswitchable Chelators (RPC) [START_REF] Shinkai | Photoresponsive crown ethers. 2. photocontrol of ion extraction and ion transport by a bis(crown ether) with a butterfly-like motion[END_REF]. Other photo-responsive tweezers were then reported with a diarylethene photochromic core connected to a chelator [START_REF] Takeshita | Photoresponsive cesium ion tweezers with a photochromic dithienylethene[END_REF][START_REF] Takeshita | Alkali metal ion effect on the photochromism of 1,2-bis(2,4-dimethylthien-3-yl)-perfluorocyclopentene having benzo-15-crown-5 moieties[END_REF][START_REF] Malval | Photoswitching of cation complexation with a monoaza-crown dithienylethene photochrome[END_REF][START_REF] Dozova | A novel diarylethene-based photoswitchable chelator for reversible release and capture of Ca 2 + in aqueous media[END_REF].

Alternatively, light induced cation ejection can also be observed using photoinduced charge transfer fluorophore as shown for DCM-Crown derivatives [START_REF] Ley | Femtosecond to subnanosecond multistep calcium photoejection from a crown ether-linked merocyanine[END_REF][START_REF] Dozova | Photo-induced cation translocation in a molecular shuttle based on a calix[4]-biscrown including DCM and DMABN chromophores[END_REF] or Metal to Ligand Charge transfer (MLCT) molecules [START_REF] Lewis | Photoinduced Ba 2 + release and thermal rebinding by an azacrown ether linked by an alkynyl pyridine to a (bpy)Re(CO) 3 group[END_REF] thus achieving fast response (picosecond timescale) and reversible photoejection. These systems are generally based on a substituted azacrown ionophore, in which the nitrogen atom is conjugated with an electron-withdrawing group or coordinated to a metal complex. Upon excitation, a photoinduced ICT reduces the electron density on the ionophore: the nitrogen binding site thus becomes positively polarized and repels the cation. Similar systems have also been proposed based on azacrown substituted [(bpy)Re(CO) 3 L] + complex [START_REF] Macqueen | Cation-controlled photophysics in a rhenium(I) fluoroionophore[END_REF][START_REF] Lewis | Picosecond forward electron transfer and nanosecond back electron transfer in an azacrown substituted [(bpy)Re(CO) 3 L] + complex: Direct observation by time resolved UV visible absorption spectroscopy[END_REF][START_REF] Lewis | Photoinduced Ba 2 + release and thermal rebinding by an azacrown ether linked by an alkynyl pyridine to a (bpy)Re(CO) 3 group[END_REF][START_REF] Lewis | Cation sensors containing a (bpy)Re(CO) 3 group linked to an azacrown ether via an alkenyl or alkynyl spacer: synthesis, characterisation, and complexation with metal cations in solution[END_REF][START_REF] Lewis | Light-Controlled Ion Switching: Direct Observation of the Complete Nanosecond Release and Microsecond Recapture Cycle of an Azacrown-Substituted [(bpy)Re(CO) 3 L] + Complex[END_REF], flavonol derivatives [START_REF] Douhal | Stepwise interactions, sodium ion photoejection and proton-transfer inhibition in a crown-ether and protontransfer dye[END_REF] or benzylhydrazone [START_REF] Vantomme | Photo-and thermoresponsive supramolecular assemblies: Reversible photorelease of k+ ions and constitutional dynamics[END_REF]. We have also proposed a novel molecular photoswitch based on a betaine pyridinium chromophore substituted by a 15-aza-5-crown [START_REF] Aloise | Can betaine pyridinium derivatives be used to control the photoejection of cation?[END_REF]. By investigating the photophysics of the complex with ultrafast absorption spectroscopy and subpicosecond temporal resolution, we were able to demonstrate that (i) the imidazole bridge is a better complexant toward Ca 2+ than the azacrown moiety and (ii) the cation was efficiently photoejected from the complexation site but no photorecapture was observed.

In the context of designing efficient RPC, the first requirement is to ensure that the system is capable of photoejecting the cation. Computational chemistry constitutes a powerful tool to participate in this design process thanks to the prediction of the photorelease properties of a large number of molecules, including cyclometalated complexes. Of course, the mechanism leading to the cation release is most often complex and requires the full study of the different excited-state decay routes to decipher the photoejection abilities of the system.

Since our purpose is to study, in the future, a large set of molecules, we propose here a strategy based on the analysis of the properties of the excited states in the Franck-Condon (FC) region. Relying on Density Functional Theory (DFT) and its Time-Dependent counterpart (TD-DFT), the charge-transfer properties (CT) of the low-lying excited states in the FC will be investigated. Indeed, the mechanism of light-controlled cation ejection should be favored if a CT excited state produces a partial positive charge for the complexation site which should lower the cation binding constant [START_REF] Macqueen | Cation-controlled photophysics in a rhenium(I) fluoroionophore[END_REF].

In this work, we propose to test this strategy on a series of Re(I) complexes synthesized and studied by Moore et al. in the early 2000s [START_REF] Lewis | Picosecond forward electron transfer and nanosecond back electron transfer in an azacrown substituted [(bpy)Re(CO) 3 L] + complex: Direct observation by time resolved UV visible absorption spectroscopy[END_REF][START_REF] Lewis | Light-Controlled Ion Switching: Direct Observation of the Complete Nanosecond Release and Microsecond Recapture Cycle of an Azacrown-Substituted [(bpy)Re(CO) 3 L] + Complex[END_REF][START_REF] Lewis | Ground-and Excited-State Infrared Spectra of an Azacrown-Substituted [(bpy)Re(CO) 3 L] + Complex: Structure and Bonding in Ground and Excited States and Effects of Ba 2+ Binding[END_REF][START_REF] Lewis | Cation sensors containing a (bpy)Re(CO) 3 group linked to an azacrown ether via an alkenyl or alkynyl spacer: synthesis, characterisation, and complexation with metal cations in solution[END_REF][START_REF] Lewis | Photoinduced Ba 2 + release and thermal rebinding by an azacrown ether linked by an alkynyl pyridine to a (bpy)Re(CO) 3 group[END_REF][START_REF] Lewis | Infrared and resonance Raman studies of metal cation sensors in which an azacrown ether is linked to (bpy)Re(CO) 3 via an alkenyl or alkynyl spacer[END_REF]. A [(bpy)Re(CO 3 )L] + complex, where bpy is a 2-2' bipyridine ligand and L contains an azacrown ether [START_REF] Macqueen | Cation-controlled photophysics in a rhenium(I) fluoroionophore[END_REF], was shown to act as a light-controlled switch of alkali and alkaline earth cations. This molecule, ReAZBAP + in the following, is represented on Figure 1 and a similar experimental study has been carried out on a similar system, ReAZAT + where the azacrown ether is linked by an alkynyl pyridine to the metal center. Nanosecond time-resolved UV-vis absorption (TRVIS) within the 50-200 ns range have shown that M n+ cations which are initially complexed to the azacrown are released on the nanosecond (ns) time scale for M n+ = Li + , Na + , Ca 2+ , Mg 2+ and Ba 2+ , after irradiation at 355 nm. A photoejection mechanism based on an excitation of the metal-toligand charge transfer (MLCT) state followed by a rapid intramolecular electron transfer creating a ligand-to-ligand charge-transfer (LLCT) state in which the charge separation affects the bpy and azacrown ligands, was proposed. This mechanism is consistent with the one proposed by Schanze and McQueen in the 1990s [START_REF] Macqueen | Cation-controlled photophysics in a rhenium(I) fluoroionophore[END_REF]. Interestingly, the Mg 2+ cation was not released. With TRVIS studies in the 0.2 -500 µs range, the recapture of Li + , Na + , Ca 2+ and Ba 2+ , cations has been observed directly in real time with a characteristic time of a few microseconds (µs).

For these heavy-metal complexes, low-lying singlet excited states are directly excited by photon absorption and then usually undergo intersystem crossing (ISC) to form triplet states [START_REF] Cannizzo | Femtosecond fluorescence and intersystem crossing in Rhenium(i) carbonyl-bipyridine complexes[END_REF][START_REF] Blanco-Rodríguez | 1-(2-pyridyl)-imidazo[1,5-α]pyridine[END_REF]33]. Concerning the series of Re(I) complexes synthesized and studied by Moore, the role of the triplet states in the photoejection mechanism is not specifically mentioned. However, since the excited-state cation release occurs on the ns time scale, these observations are consistent with the involvement of triplet excited states. As previously stated, the mechanism leading to photoejection may thus be particularly complex. It may rely on an excitation of the singlet excited states followed by an ISC to form a triplet MLCT, the latter state being involved in the cation release. The photoejection then certainly occurs when the system is moved away from the FC region. Our purpose is not to study the full photoreaction path leading to the cation release but to investigate if it is possible to correlate the photoreactivity of the system with the singlet-excited state properties in the FC region. We therefore focus our attention on the first step of this complex mechanism: we want to see if there are indicators in this region, on the singlet states, which allow us to predict whether the photoejection will be possible or not.

In this work, we thus propose to study the ReAZBAP + -M n+ and ReAZAT + -M n+ complexes with M n+ = Li + , Na + , Ca 2+ , Mg 2+ and Ba 2+ . By computing the structural and UV-Vis properties of these systems, we will investigate the properties of the low-lying exciting states in the FC region, and compare them with the experimental conclusions concerning the photoejection abilities of these cyclometalated complexes.

After presenting the computational tools and the descriptors based on the charge transfer parameters calculated in the FC region, we will successively discuss the excited-state properties of the ReAZBAP + , ReAZBAP + -M n+ and ReAZAT + -M n+ complexes and compare the photoejection descriptors with their light-controlled cation ejection abilities.

Computational details

All the calculations have been performed using Gaussian 16 package [START_REF] Frisch | Gaussian16 Revision A.03Gaussian Inc[END_REF] relying on (TD-)DFT to determine the ground-state (GS) and excited-state (ES) properties, respectively. We have used (i) the 6-311+G(d) basis set for the H, Li, C, N, O, Na and Ca atoms, (ii) the Def2SVP [START_REF] Weigend | Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy[END_REF] pseudopotential and corresponding basis set for Ba, (iii) the LANL2DZ [START_REF] Wadt | Ab initio effective core potentials for molecular calculations. Potentials for main group elements Na to Bi[END_REF] relativistic pseudopotential and corresponding basis set for Re. The geometry optimizations and the calculation of the excited state properties have been carried out with the PBE0 [START_REF] Adamo | Toward reliable density functional methods without adjustable parameters: The PBE0 model[END_REF][START_REF] Perdew | Rationale for mixing exact exchange with density functional approximations[END_REF] hybrid exchange-correlation functional. We have ensured that we have found true minima on the potential energy surfaces by calculating and analysing the frequency vibrations.

Previous works have demonstrated the performances of global hybrid functionals [START_REF] Mai | Competing ultrafast photoinduced electron transfer and intersystem crossing of [Re(CO) 3 (Dmp)(His124)(Trp122)] + in Pseudomonas aeruginosa azurin: a nonadiabatic dynamics study[END_REF] and more specifically PBE0 [START_REF] Chung | Synthesis, characterization and computational studies of luminescent rhenium(I) tricarbonyl diimine complexes with 8-hydroxyquinoline-containing alkynyl ligands[END_REF][START_REF] Malecka | Towards better understanding of photophysical properties of rhenium(I) tricarbonyl complexes with terpy-like ligands[END_REF][START_REF] Ragone | Photophysics, photochemistry and thermallyinduced redox reactions of a (Pterin)rhenium(I) complex[END_REF], to investigate the nature, dynamics and reactivity of the (charge transfer) excited states of Rhenium(I) complexes. For the interested reader, the excited state properties of ReAZBAP + calculated with PBE0 functional are compared to the range separated hybrid CAM-B3LYP functional [START_REF] Yanai | A new hybrid exchange correlation functional using the coulomb-attenuating method (CAMB3LYP)[END_REF] in Supporting Information and the validity of the PBE0 global functional to describe the CT states of the Re(I) complexes is discussed.

For all TD-DFT calculations, 25 excited states are considered. The computed vertical excitation wavelength λ abs corresponds to the excitation wavelength with the highest f value over the energy range considered and is compared to the experimental maximum absorption λ max . One should note that these values do not necessarily coincide and a more refined computational model should take into account the vibronic structure of the electronic absorption spectra.

All calculations were performed by considering the Polarizable Continuum

Model [START_REF] Tomasi | Quantum mechanical continuum solvation models[END_REF][START_REF] Guido | Excited state gradients for a state-specific continuum solvation approach: The vertical excitation model within a lagrangian TDDFT formulation[END_REF] (IEF-PCM) in the equilibrium limit using the linear-response (LR) PCM scheme to quantify the impact of the acetonitrile solvent (ACN).

To analyze the CT character of the different excited states, we have used three different descriptors. First, the variation of electronic density ∆ρ( r) is calculated on a grid of points using the cubegen utility provided by the Gaussian package:

∆ρ( r) = ρ ES ( r) -ρ GS ( r) (1)
with ρ GS ( r) and ρ ES ( r) the electron density of the ground state and the considered excited states respectively.

Secondly, the density derived indexes namely the D CT index and the norm of the dipole moment corresponding to the CT observed upon excitation µ CT are computed using the DctViaCube [START_REF] Jacquemin | What is the 'best' atomic charge model to describe through-space charge-transfer excitations?[END_REF][START_REF] Bahers | A qualitative index of spatial extent in charge-transfer excitations[END_REF] program. In particular, the gain, ρ + ( r), and the loss, ρ -( r), of electron density are described as :

ρ + ( r) =   ∆ρ( r) if ∆ρ > 0 0 if ∆ρ < 0   ; ρ -( r) =   ∆ρ( r) if ∆ρ < 0 0 if ∆ρ > 0   (2)
These densities are associated with barycentres defined as follows:

R + = rρ + ( r)d r ρ + ( r)d r = (x + , y + , z + ); R -= rρ -( r)d r ρ -( r)d r = (x -, y -, z -) (3)
The distance between these barycenters is known as the D CT index:

D CT = |R + -R -| (4)
The norm of variation of dipole moment between the ground and excited state is:

µ CT = || µ CT || = D CT ρ + ( r)d r = -D CT ρ -( r)d r = D CT .q CT ( 5
)
with q CT the amount of charge transferred.

Finally, for each state (ground state S 0 and excited states), we have calculated the Natural Population Analysis (NPA) charges [START_REF] Reed | Natural population analysis[END_REF]. In order to get a more "localized" information concerning the CT properties of the considered ex-

Results

Absorption properties of ReAZBAP +

For ReAZBAP + , the computed excitation energies and the convoluted absorption spectrum are given in Table 1 and Figure 3. For this system, the computed maximum absorption wavelength λ abs (353 nm) corresponds to the S 4 ← S 0 transition. The convoluted absorption spectrum also shows the existence of a shoulder peaking at 365 nm and corresponding to the S 3 ← S 0 transition. The deviation between the calculated and experimental excitation energy, ∆E, is 0.09 eV for the maximum absorption band (experimental value:

344 nm [START_REF] Lewis | Light-Controlled Ion Switching: Direct Observation of the Complete Nanosecond Release and Microsecond Recapture Cycle of an Azacrown-Substituted [(bpy)Re(CO) 3 L] + Complex[END_REF]) and 0.15 eV for the shoulder (experimental value: 350 nm [START_REF] Macqueen | Cation-controlled photophysics in a rhenium(I) fluoroionophore[END_REF][START_REF] Lewis | Light-Controlled Ion Switching: Direct Observation of the Complete Nanosecond Release and Microsecond Recapture Cycle of an Azacrown-Substituted [(bpy)Re(CO) 3 L] + Complex[END_REF])

demonstrating the good precision provided by our calculation scheme in the simulation of absorption spectra. 2. The position of the different ligands is specified, the same orientation will be used for all the ∆ρ(r) representations.

Experimentally, Moore and coworkers assigned the maximum absorption band to an ILCT (Intra Ligand Charge Transfer) transition [START_REF] Lewis | Light-Controlled Ion Switching: Direct Observation of the Complete Nanosecond Release and Microsecond Recapture Cycle of an Azacrown-Substituted [(bpy)Re(CO) 3 L] + Complex[END_REF]. To confirm this hypothesis, we have calculated the variation of the electronic density, ∆ρ( r), observed upon this transition (Figure 3). ∆ρ( r) shows a CT from the azacrown electron donor group and, to a lesser extent, from the metal center to the amidopyridyl electron acceptor group. Indeed, this transition corresponds to a HOMO → LUMO+1 excitation and the corresponding molecular orbitals are given in Figure S2. This transition is characterized by a large value of the D CT index (4.61 Å, Table 1) and the corresponding CT dipole moment µ CT is depicted in Figure 3. In terms of NPA charges, for this ILCT state, Table 2 mainly shows a CT of 0.565 e from the phenyl azacrown region (region I, Figure 2) to the amidopyridyl (region II). All the CT descriptors (∆ρ( r) , CT vector and NPA charge variations) thus propose a coherent description of the electronic excitation character and are in agreement with the experimental assignment.

Table 2: Charge transfer parameters (D CT in Å, q CT in e, µ CT in D) calculated for the λ abs transition described in Tables 1 and3, for ReAZBAP + and ReAZBAP + -M n+ complexes, respectively. The variations of NPA charges (∆q I to ∆q IV ) upon the corresponding excitation are also given according to the regions defined in Figure 2. A negative (respectively positive) value represents a loss (resp. an increase) of the total electronic charge in the corresponding region.

M Finally, for ReAZBAP + , the S 1 state characterized by λ = 431 nm and a very weak oscillator strength (f = 0.001), corresponds to a LLCT state, with the charge transferred from the phenyl-azacrown to the bpy. For its part, the S 2 state (λ= 369 nm, f = 0.003) is a MLCT state presenting a charge transferred from the metal center to the bpy (see Figure S6).

Absorption properties observed after metal cation binding: ReAZBAP

+ - M n+ complexes
The properties of ReAZBAP + -M n+ complexes in which alkaline cations (Li + and Na + ) and alkaline earth cations (Mg 2+ , Ca 2+ and Ba 2+ ) are bound to the azacrown have then been investigated. Table 3 provides the properties of the λ abs absorption wavelength calculated for the ReAZBAP + -M n+ complexes. The calculated absorption spectra of ReAZBAP + -M 2+ complexes are given in Figure 6 and in Figures S7 andS8 for the alkaline cations. the interaction between M n+ and the azacrown nitrogen atom (N 21 , Figure 1).

An inspection of the structural parameters in

Na + Mg 2+ Ba 2+ Ca 2+ Li + Na + Mg 2+ Ba 2+ Ca 2+ Li + d 11 ⟨d O-M n+⟩ (B) (A) d N-M n+ R 2 = 0.990 R 2 = 0.982

240

More in detail, for all systems, Table 3 shows that the maximum absorption band corresponds to a HOMO → LUMO+1 electronic excitation. As revealed by the comparison of the energy diagram of ReAZBAP + and ReAZBAP + -M n+ in Figure 5, the introduction of the cation in the azacrown leads to a decrease of the energy of the HOMO which is localized on the phenyl-azacrown moiety. The 245 stabilization of this frontier orbital upon complexation is due to the decrease of the antibonding character between the phenyl group and the N atom of the azacrown. Indeed, the stronger the interaction between M n+ and the azacrown nitrogen atom, the more the electronic density of the N atom towards the cation is delocalized. At the same time, the energy of the LUMO+1 is slightly mod-250 ified since the electronic density is much less delocalized on the azacrown. In summary, the modification of these frontier orbital energies leads to a global increase of the excitation energy. |∆λ| can be correlated with the charge-to-radius (z/r) ratios of M n+ [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF][START_REF] Rurack | Chalcone analogue dyes emitting in the near-infrared (NIR) : Influence of donor acceptor substitution and cation complexation on their spectroscopic properties and X-ray structure[END_REF][START_REF] Brzezinski | H + , Li + , and Na + Polarizabilities in 1:1 Crown Ether Cation Complexes. A FTIR Study[END_REF] as shown on Figure 4(C). There is an increase of |∆λ| as (z/r) increases and the calculations reproduce this trend. Experimentally, an anomaly occurs for Li + : despite its large z/r ratio, the |∆λ| value is small. This small value of the λ abs shift was previously reported in the litterature for different azacrown dye. [START_REF] Dix | Ligandstruktur und komplexierung, l. ionenselektive farbstoffkronenether[END_REF][START_REF] Lednev | Benzothiazolium styryl dyes containing a monoazacrown ether: Protonation and complexation with metal and ammonium cations in solution[END_REF] One hypothesis justifying this anomaly is based on the fact that this small cation would bind mainly to the four azacrown O atoms and would stay relatively far from the nitrogen, the other coordination sites of Li + being saturated by counterion and/or solvent molecules [START_REF] Rurack | Chalcone analogue dyes emitting in the near-infrared (NIR) : Influence of donor acceptor substitution and cation complexation on their spectroscopic properties and X-ray structure[END_REF]. Within our PCM-based approach, Li + is bound either to the N and to the O atoms of the azacrown (see Figures 4(A) and(B)) and no anomaly is thus found for this cation. Using an explicit solvent model in presence of counterions may correct this behaviour.

However, this strategy is out of the scope of the present work.

Investigation of the photoejection phenomenon.

Methodology

To investigate the photoejection phenomenon, we propose the following methodology: (1) the excitation energies are calculated with the strategy presented in the previous sections;

(2) we identify the singlet excited states that can be populated with the considered excitation wavelength (λ exc = 355 nm [START_REF] Lewis | Cation sensors containing a (bpy)Re(CO) 3 group linked to an azacrown ether via an alkenyl or alkynyl spacer: synthesis, characterisation, and complexation with metal cations in solution[END_REF] for ReAZBAP + -M n+ ); (3) for these states, we proceed through an analysis of the corresponding CT character with the help of the three different descriptors that we have used and presented before. These three descriptors provide a coherent and complementary vision of the CT character of the excited states: (i) ∆ρ( r)

provides a qualitative and molecular-scale analysis of the CT character; (ii) D CT gives a quantitative evaluation of the CT character that enables a comparison between the different systems; (iii) the variations of the NPA charges allow to obtain more localized information concerning the CT properties; (4) if one of the excited states identified at step (2) presents a strong charge depletion on the cation binding site after excitation, this state is expected to favor the cation release (through an enhanced electrostatic repulsion between positive charges).

We would like to point out that the complete mechanism leading to cation release is indeed much more complex, as indicated in the introduction, and requires the study of the different excited-state decay routes far from the FC region (including the investigation of the properties of the triplet states). Within our methodology, we thus stick to the analysis of the singlet excited states that can be populated at a given irradiation wavelength, that is to say to the first step of the mechanism leading to photoejection.

Our "first-approach" methodology is thus tested to investigate the photoejection abilities of ReAZBAP + -M n+ with M n+ = Li + , Na + , Ca 2+ and Ba 2+ , and ReAZAT + -Ba 2+ . For the latter, the photoejection ability has not been studied for the other cations [START_REF] Lewis | Photoinduced Ba 2 + release and thermal rebinding by an azacrown ether linked by an alkynyl pyridine to a (bpy)Re(CO) 3 group[END_REF].

Analysis of the systems presenting a cation photorelease.

For ReAZBAP + -Ba 2+ , the calculated excitation energies and the convoluted absorption spectrum are given in Figure 6(a). Upon excitation at λ exc = 355 nm, the first three low-lying excited states can be populated and their properties are gathered in Table 4. One can note that the state corresponding to the λ abs excitation (S 5 state, 321 nm) described in the previous section can not be populated. The first excited state S 1 is characterized by a medium range value of both the D CT index (3.24 Å) and the µ CT dipole moment (16.3 D) as shown in Table 4. Considering the variation of the NPA charges (Table 2), there is an overall CT from the AZBAP ligand (regions I and II) and the CO-substituted metal center (region III) to the bpy group (region IV). This is also shown by the variation of the electronic density ∆ρ( r) in Figure 6. In a first and static consideration, the excited state leading to the photoejection should present a strong charge depletion on the phenyl-azacrown in order to favour the cation release. This is not the case for S 1 and we can therefore deduce that this state should not play a role in the photoejection. In the same vein, S 2 does not involve the phenyl-azacrown part as shown by the trifling ∆q I variation (0.013 e) observed upon excitation. Indeed, S 2 corresponds to a MLCT state with a CT towards the bpy group, and this state should not be directly involved in the photejection.

If we focus now on the S 3 state, the CT distance increases up to 6.41 Å and the CT dipole moment value is more than twice as large as the one in the S 1 state. Moreover, the NPA charge variation shows a strong charge depletion from the phenyl-azacrown (∆q I = -0.622 e) to the bpy (∆q IV = 0.816 e). We thus conclude that the CT is strong enough to trigger a photoejection and the population of the S 3 state, which is a LLCT state, should be the first step of mechanism leading to the cation photorelease. Our methodology thus predicts a photoejection, in accordance with experimental observations [START_REF] Lewis | Light-Controlled Ion Switching: Direct Observation of the Complete Nanosecond Release and Microsecond Recapture Cycle of an Azacrown-Substituted [(bpy)Re(CO) 3 L] + Complex[END_REF]. Then, as assumed by Moore et al. from the TRVIS data, a possible route should rely on an ISC and the subsequent population of a 3 MLCT state. A calculation of the triplet excited properties and the spin-orbit coupling (SOC) elements 340 between singlet and excited states [START_REF] Peng | Understanding the efficiency drooping of the deep blue organometallic phosphors: a computational study of radiative and non-radiative decay rates for triplets[END_REF], that play a fundamental role in ISC, should complete our present study to understand the photoejection mechanism. Another important concern is the impact of the flexibility of the system on the singlet excited state properties and thus on our conclusion concerning the photoejection abilities of the complex. To this purpose, we have investigated the impact of the position of the azacrown phenyl amide group with respect to the pyridine (φ 3 torsion angle in Figure 1). It turned out that the rotation barrier along the φ 3 torsion angle reaches 7.0 kcal.mol -1 for the system ReAZBAP + -Ba +2 . The orthogonal orientation corresponds to a transition state and the mode presenting an imaginary frequency corresponds to a rotation along φ 3 .

We have then calculated the absorption properties of ReAZBAP + -Ba +2 with two different orientations ( φ 3 =30 and 60 • ) and compared them with the planar orientation discussed so far (φ 3 =0 • ). The calculated absorption spectra are given in Figures S10 andS11. Indeed, the rotation along this torsion angle decreases the electronic coupling within the system and a blue-shift of the λ abs value is logically observed (321 nm for 0 • , 314 nm for 30 • , 308 nm for 60 • ).

At the same time, for both φ 3 equals 30 • and 60 • , a LLCT state with a strong CT character from the phenyl-azacrown to the bpy, can be populated. Within our framework, we can thus conclude that the flexibility of the system does not impact the cation photoejection abilities of ReAZBAP + -Ba +2 .

Then, we have considered the ReAZAT + complex depicted on Figure 1 that is also known for its ability to photoeject Ba 2+ [START_REF] Lewis | Photoinduced Ba 2 + release and thermal rebinding by an azacrown ether linked by an alkynyl pyridine to a (bpy)Re(CO) 3 group[END_REF]. The calculated convoluted absorption spectrum, shown in Figure 6, is characterized by a maximum absorption wavelength of 380 nm, with a deviation from the experiment of ∆E = 0.28 eV. This transition possesses an ILCT character with a CT from the phenyl-azacrown moiety to amidopyridyl group, with ∆q I = -0.415 e in favor of the region II and a CT dipole moment of 17.7 D (Table S4). It should be noted that the first transition presents the same characteristics with a stronger CT dipole moment (34.8 D) but a much smaller oscillator strength.

For λ exc = 355 nm [START_REF] Lewis | Photoinduced Ba 2 + release and thermal rebinding by an azacrown ether linked by an alkynyl pyridine to a (bpy)Re(CO) 3 group[END_REF], both states can be populated and can thus trigger the photoejection phenomenon, in accordance with experimental features.

The methodology is then tested for other cations, namely Li + and Na + bound to ReAZBAP + . The computed absorption spectrum and the analysis of the excited states can be found in Table 4 and Figures S7-S8. The same analysis 375 revealed that (i) the first three low-lying excited states can be populated, (ii)

the S 1 and S 2 states are MLCT states characterized by a medium-range CT and (iii) The S 3 ← S 0 transition is characterized by a strong LLCT from the phenyl-azacrown to the bpy. The population of the S 3 state can thus trigger the cation photoejection, as experimentally observed [START_REF] Lewis | Light-Controlled Ion Switching: Direct Observation of the Complete Nanosecond Release and Microsecond Recapture Cycle of an Azacrown-Substituted [(bpy)Re(CO) 3 L] + Complex[END_REF].

Analysis of the systems without photoejection properties.

For ReAZBAP + -Mg 2+ , the cation photorelease was not observed [START_REF] Lewis | Light-Controlled Ion Switching: Direct Observation of the Complete Nanosecond Release and Microsecond Recapture Cycle of an Azacrown-Substituted [(bpy)Re(CO) 3 L] + Complex[END_REF]. For this complex, our TD-DFT calculations show that only two states can be populated after excitation as shown on Figure 7. These two states are characterized by a CT from (CO) 3 -Re to the bpy ligand as demonstrated by the NPA charge variations given in Table 4. Thus, there is no charge depletion of the phenylazacrown in any populated state and this should not trigger the photoejection, in accordance with the experimental observations.

As a matter of fact, as shown on Figure 4 and as already discussed, the ionic radius of Mg 2+ is smaller than the other cations. This strengthens the interaction between Mg 2+ and the azacrown, and strongly disturbs the energy levels. From the study of the molecular orbital energy levels, we can see in CT properties is now 259 nm that is to say 1.30 eV more energetic than the irradiation wavelength (see Figure 7(a)).

3.3.4.

The "ReAZBAP + -Ca 2+ " case.

For Ca 2+ , the ionic radius is intermediate between Ba 2+ and Mg 2+ and its optical and photoejection properties can therefore be interpreted by the medium-strength interactions between the azacrown and the cation. Indeed, the excitation energies and the convoluted absorption spectrum of ReAZBAP + -Ca 2+ , with its CT properties are given in Figure 7(b). Upon excitation with λ exc = 355 nm [START_REF] Lewis | Light-Controlled Ion Switching: Direct Observation of the Complete Nanosecond Release and Microsecond Recapture Cycle of an Azacrown-Substituted [(bpy)Re(CO) 3 L] + Complex[END_REF], the first two states can be populated and present a depletion of the electronic density from the (CO) 3 -Re to the bpy as shown by the variation of the electronic density and NPA charges. Hence, the population of these states should not trigger the cation photorelease. This prediction is thus in contradiction with experimental observations since Moore et al. have shown that a cation photorelease was observed for ReAZBAP + -Ca 2+ [START_REF] Lewis | Light-Controlled Ion Switching: Direct Observation of the Complete Nanosecond Release and Microsecond Recapture Cycle of an Azacrown-Substituted [(bpy)Re(CO) 3 L] + Complex[END_REF].

The state presenting a favorable CT character is the S 4 state but the corresponding excitation energy is too high compared to the excitation wavelength (λ = 308 nm) and its oscillator strength is really small. In addition, the maximum absorption wavelength (λ abs = 300 nm) is a MLCT state (see Figure S9).

For this system, compared to ReAZBAP + -Ba 2+ , the interaction between the azacrown nitrogen and the cation is stronger and this leads to a modification of the molecular orbital interaction diagram. Indeed, the phenyl-azacrown localized molecular orbital is now mixed with metal-centered orbitals (see the HOMO and HOMO-2 orbitals on Figure 5). However, the energy variation of these occupied orbitals is smaller than the ReAZBAP + -Mg 2+ system since the cation / azacrown interactions are weaker. Hence, for Ca 2+ , the state able to trigger the photoejection is closer in energy to the excitation wavelength (308 nm, S 4 ← S 0 transition on Figure 7(b) than for Mg 2+ (259 nm). Therefore, the properties of the singlet excited states are not able to capture the fate of the system and it is likely that, after excitation, the role played by the triplet states is crucial to understand the cation photorelease. The ReAZBAP + -Ca 2+ thus shows us that in that case, it is necessary to go beyond the analysis of the CT character in the FC region for the singlet excited-states. Indeed, it is necessary to explore the photophysical/photochemical reaction pathway on both the singlet and triplet excited states, far from the FC region, to investigate the photoejection abilities of this complex.

Is it possible to diagnose cases where our methodology will provide a "false negative" test result (sticking to the analysis of the electronic state properties in the FC region)? A simple tool that can provide such information is the analysis of the electronic structure properties and more particularly the nature of the last occupied molecular orbitals. As shown by Figure 5, when the orbital originally delocalized on the Phenyl-Aza ligand (HOMO for ReAZBAP + ) is mixed with metal-centered orbitals (HOMO and HOMO-2 for ReAZBAP + -Ca 2+ ), one can expect new photophysical routes after the FC region. Then, for these cases ("negative" result and metal/ligand mixed orbitals), the application of our methodology will not be straightforward and further investigation will be required.

Conclusion

In the context of designing photoswitch with cation photorelease properties, we propose a "simple" computational strategy able to predict the cation photoejection. Our strategy is based on the analysis of the CT parameters of the singlet excited states that can be populated for a given excitation wavelength, in the FC region.

To this purpose, we analyze (i) the variation of the electronic density ∆ρ( r) If the loss of electronic density is large enough in the cation binding site, the population of such a state should be the first step of the mechanism leading to the cation photorelease. We therefore focus on this first step, the mechanism leading to the cation release certainly relying on a subsequent ISC leading to a triplet excited state.

We have tested this strategy on the ReAZBAP + -M n+ and ReAZAT + -Ba 2+ systems and we have shown that (i) the photoejection was correctly predicted for Li + , Na + , Ba 2+ bound to ReAZBAP + as well as for Ba 2+ linked to ReAZAT + and (ii) it was possible to understand why Mg 2+ is not photoreleased from ReAZBAP + . For these systems, the state that should trigger the photoejection presents a strong charge depletion on the phenyl-azacrown and is assigned as a LLCT state. There is however a "false negative" for ReAZBAP + -Ca 2+ system.

Indeed, according to our strategy, the photorelease should not be possible since there are no accessible excited states with the desired CT characteristics in the energy range of interest. In that case, our first-order approach that focuses on the FC region and does not take into account the complex excited-state decay routes potentially leading to the photorelease, with the help of triplet excited states, does not provide sufficient information to provide an efficient diagnosis. This theoretical breakdown is related to the static approach that does not account for possible interconversion and inter-system crossing routes, and that does not explore the nature and the role of both singlet and triplet excited states beyond the FC region. However, an analysis of the electronic structure properties of the singlet excited-states in the FC region, through the inspection of the character of the last occupied orbitals, can alert us to the possibility of a "false negative" test result.

In short, for five out of the six systems under investigation, our method was able to correctly predict the photorelease properties. To the question "Is it possible to "simply" predict the photoejection of a cation?", the answer is thus "yes" in approximatively 80 percent of the cases. The success rate reached by this "simple" model is encouraging enough to help us to screen a large number of complexes in the context of the in silico design of Reversible Photoswitchable Chelators.

under the allocations 2020 and 2021-A0010810135 made by GENCI (Grand Equipement National de Calcul Intensif).

Table S1: Comparison of the PBE0 and CAM-B3LYP functional: absorption wavelengths (λ, nm) calculated for the first excited states of ReAZBAP + (S 1 to S 4 ) along with their corresponding oscillator strength (f ) and electronic excitation description (ACN solvent, IEF-PCM model). This is confirmed by the representation of the variation of electronic density upon excitation (∆ρ) computed for this state and represented on Fig. S3. The CT properties of the state corresponding to the maximum absorption are equivalent for both functionals if we focus our attention on (1) the direction of the CT dipole moment and (2) the major NPA charge variation. However, we can note that the computed µ CT value is larger for PBE0 than for CAM-B3LYP. 5 Hence, qualitatively, the excitation energies and the CT parameters calculated with PBE0

and CAM-B3LYP follow the same trends. We have then checked that PBE0 is able to provide a correct description of the transition energies corresponding to a CT excitation.

Indeed, global hybrid functionals may suffer from a failure in the description of throughspace CT excitations due to the quality of the description of the electron-hole interaction at the excited state provided by these functionals. 6 Therefore, we have calculated the socalled t index developed by Le Bahers et al 7 which is a tool that can define the degree of through space character of a transition. It has empirically been shown that if t is larger than 1.6 Å, PBE0 is no more able to provide a correct description of the CT excitation. On the opposite, if t is lower than this threshold value, PBE0 provides a good description of the CT state. Table S2 shows that for the ILCT state, the t value is smaller than 1.6 Å (t = 0.05 Å) We have also checked the value of the t index for ReAZBAP + -M n+ complexes.

S-3

Relative

The t values reported for the first excited states of ReAZBAP + -Ba 2+ in Table S2 shows that this index is never higher than 0.67 Å. Therefore, both ILCT, LLCT and MLCT states are expected to be well reproduced using PBE0.

Consequently, PBE0 has been retained because this functional provides (i) excitation energies in better agreement with experiments and (ii) a good description of CT excitations for the S-5 Table S2: Absorption wavelengths (λ, nm) calculated for ReAZBAP + and ReAZBAP + -Ba 2+ with their corresponding oscillator strength (f ), assignments and charge transfer parameters: D CT and t in Å, q CT in |e| and µ CT in D.

S-9

Table S3: ReAZBAP + -M n+ complexes: key structural parameters defining the position of M n+ cation in the azacrown. See Fig. 1

d 1 :Figure 1 :

 11 Figure 1: Representation of the ReAZBAP + and ReAZAT + and definition of key structural parameters. For ReAZBAP + -M n+ and ReAZAT + -M n+ , the cation M n+ is in the Azacrown.

Figure 2 :

 2 Figure 2: Definition of the different regions used to calculate the variation of NPA charges: I =phenyl-azacrown (blue); II = amidopyridyl (pink); III = (CO) 3 -Re (purple); IV = bipyridine (orange).

S 3 ⟵Figure 3 :

 33 Figure 3: Calculated excitation energies and convoluted absorption spectrum of ReAZBAP + (Convolution: FWHM = 0.25 eV). The variation of the electronic density upon excitation (∆ρ(r)) is shown for selected transitions (Purple: gain of electronic density; Turquoise: depletion of electronic density). The CT vector µ CT is also represented (golden arrow) as well as the major NPA charge variations (see Table 2. The position of the different ligands is

  and the amidopyridyl-phenyl-azacrown ligand (AZBAP) highlights the role of the Re(I) metal center in the CT phenomenon. The excitation energies and the convoluted absorption spectrum of the AZBAP ligand are given in FigureS4.An intense band peaking at λ abs = 321 nm corresponds to a strong CT state from the phenyl-azacrown to the amidopyridyl part. The CT character of the maximum absorption band logically increases when the metal center is added with a D CT value of 3.76 Å for the AZBAP ligand and 4.61 Å for ReAZBAP + .Moreover, the addition of the metal center and the contribution of the Re(I) d orbitals lead to a larger delocalization of the virtual molecular orbitals towards the metal center, and thus to a bathochromic shift of λ abs .For ReAZBAP + , the shoulder at λ = 365 nm, corresponds to a MLCT transition from the metal to the bpy, as shown by the variation of electronic density ∆ρ( r) on Figure3. Moore et al. assigned this MLCT character by comparing the UV-Vis absorption spectra of the ReAZBAP + and tricarbonylchloro-bipyridine rhenium(I) [Re(CO) 3 (bpy)(Cl)] complex[START_REF] Lewis | Light-Controlled Ion Switching: Direct Observation of the Complete Nanosecond Release and Microsecond Recapture Cycle of an Azacrown-Substituted [(bpy)Re(CO) 3 L] + Complex[END_REF][START_REF] Kalyanasundaram | Luminescence and redox reactions of the metal-to-ligand charge-transfer excited-state of tricarbonylchloro-(polypyridyl)rhenium(i) complexes[END_REF]. Indeed, the absorption spectrum of [Re(CO) 3 (bpy)(Cl)] is dominated by a strong absorption band at 370 nm[START_REF] Kalyanasundaram | Luminescence and redox reactions of the metal-to-ligand charge-transfer excited-state of tricarbonylchloro-(polypyridyl)rhenium(i) complexes[END_REF]. For the latter, the calculation of the absorption properties shows that the maximum absorption band (TD-DFT calculated value of 384 nm) has both MLCT (from (CO) 3 -Re to bpy) and LLCT (from Cl to bpy) characteristics as shown in FigureS5. Therefore, this transition, even if it is very close in energy to the band shoulder of ReAZBAP + , does not present exactly the same characteristics and the comparison between ReAZBAP + and [Re(CO) 3 (bpy)(Cl)] is not that straightforward.

  Fig 4 logically shows that for the alkaline cations, the larger the M n+ radius is, the larger the N-M n+ and O-M n+ distances are, and the less M n+ is bound to the azacrown. A same trend for the alkaline earth cations is observed with an increase of the d O-M n+ average distance of 0.81 Å from Mg 2+ to Ba 2+ .

Figure 4 :

 4 Figure 4: ReAZBAP + -M n+ complexes: Evolution of (A) the N-M n+ distance and (B) the average O-M n+ distance ( d O-M n+ ) as a function of the M n+ ionic radius. See Figure 1 for the parameter definitions, d O-M n+ is the d 11 to d 15 average value. The values of the R 2 of the linear regressions are provided. (C) Variation of the λ abs wavelength |∆λ| (isolated versus bound to M n+ ) as a function of the charge-to-radius (z/r) ratios of M n+ .

Figure 5 :

 5 Figure 5: Orbital energy diagram of the ReAZBAP + and ReAZBAP + -M n+ complexes. The color code indicates the major localization of the molecular orbital. Selected frontier orbitals are depicted.

Finally, as shown by Table 2 ,Figure 6 :

 26 Figure 6: Calculated absorption spectrum of (a) ReAZBAP + -Ba 2+ and (b) ReAZAT + -Ba 2+ (b) (Convolution: FWHM = 0.25 eV). Selected CT parameters are shown for selected transitions. See Figure 3 for more details. The experimental excitation wavelength, λexc = 355 nm [24] is represented by a yellow arrow and the shaded area corresponds to the region of the spectrum with excitation energies higher than λexc. The green and red pictograms indicate if the corresponding transition can potentially lead to a cation photoejection (see text).

Figure 7 :

 7 Figure 7: Calculated absorption spectrum of (a) ReAZBAP + -Mg 2+ and (c) ReAZBAP + -Ca 2+ (Convolution: FWHM = 0.25 eV). See Figure 3 for more details.

Figure 5

 5 Figure 5 that in presence of Mg 2+ , the energy of the occupied molecular orbital localized on the phenyl-azacrown decreases in energy by 1.70 eV compared to ReAZBAP + (see the HOMO-4 orbital), while the energies of the virtual orbitals are only slightly modified. The transition that can potentially lead to the photoejection phenomenon, necessarily involves the former occupied orbitals and corresponds, for ReAZBAP + -Mg 2+ , to an ILCT transition (S 19 ← S 0 transition). Consequently, the corresponding excitation energy drastically increases and the excitation wavelength of the first transition presenting the required

  (r), (ii) the D CT index and the charge transfer dipole moment µ CT and (iii) the variation of NPA charges, ∆q N P A observed upon the different accessible S n ← S 0 transitions. With the help of these descriptors, we aim to identify the CT states presenting a depletion of electronic density on the complexation site.

Figure S1 :Figure S2 :

 S1S2 FigureS1: Excitation energies and convoluted absorption spectrum of ReAZBAP + calculated with the PBE0 (A) and CAM-B3LYP (B) functionals. For both calculations, the geometry of the complex has been optimized with the PBE0 functional.

Figure S3 :

 S3 FigureS3: Description of the ILCT state obtained with the PBE0 (A) and CAM-B3LYP (B) functional. The variation of the electronic density upon excitation (∆ρ) is given (Purple: gain of electronic density; Turquoise: depletion of electronic density). The CT vector µ CT is also represented (golden arrow) as well as the major NPA charge variations.

Figure S4 : 8 S 2 ⟵

 S482 Figure S4: Calculated absorption spectrum of the AZBAP ligand (Convolution: FMWH = 0.25 eV). The variation of the electronic density upon excitation (∆ρ) is shown for selected transitions. See Fig. S3 for more details.

Figure S7 :Figure S8 :

 S7S8 Figure S7: Calculated excitation energies and convoluted absorption spectrum of ReAZBAP + -Li + (Convolution: FMWH = 0.25 eV). The charge transfer parameters are shown for selected transitions. See Fig. S3 for more details.

Table 1 :

 1 Absorption wavelengths (λ, nm) calculated for the first fourth excited states of ReAZBAP + with their corresponding oscillator strength (f ), electronic excitation assignments and charge transfer parameters: D CT in Å, q CT in |e| and µ CT in D.

	170
		λ (nm)	f	Electronic excitation Nature D CT	q CT	µ CT
	S 1	431	0.001	HOMO → LUMO	LLCT	7.09 1.458 49.7
	S Relative Absorption	ReAZBAP +
		250		300	Wavelength (nm) 350 400	450	500

2 369 0.003 HOMO -2 → LUMO MLCT 2.19 1.034 10.9 S 3 365 0.092 HOMO -1 → LUMO MLCT 2.24 0.986 10.6 S 4 353 0.750 HOMO → LUMO+1 ILCT 4.61 0.921 20.4

  In addition, the comparison of the excited state properties of ReAZBAP +

	n+	DCT	qCT	µCT	∆qI	∆qII	∆qIII	∆qIV
	-	4.61	0.921	20.4	-0.565	0.500	0.028	0.037
	Li +	3.90	0.845	15.8	-0.454	0.445	-0.001	0.021
	Na +	3.77	0.834	15.1	-0.442	0.440	-0.006	0.020
	Mg 2+	3.89	0.927	17.3	0.614	0.405	-0.478	-0.070
	Ca 2+	1.48	0.777	5.5	-0.072	0.392	-0.286	-0.026
	Ba 2+	3.87	0.823	15.3	-0.453	0.444	-0.001	0.010

Table 3 :

 3 Calculated absorption wavelengths (λ values; (2) for Na + and Ca 2+ , both the f and max values are similar; (3) the largest f and max values are obtained for ReAZBAP + -Ba 2+ .Moreover, when M n+ is bound to the azacrown, λ abs is blue-shifted with, for instance, a value of 353 nm for ReAZBAP + and 321 nm for ReAZBAP + -Ba 2+ . This trend is well described in the literature[START_REF] Bourson | Ion-responsive fluorescent compounds. 4. Effect of cation binding on the photophysical properties of a coumarin linked to monoaza-and diaza-crown ethers[END_REF][START_REF] Loehr | Chromo-and fluoroionophores. A new class of dye reagents[END_REF] 2] and is due to

	M n+	λ abs (f )	∆E (eV) State Electronic excitation	Assignment	λmax ( max) [25]
	Li +	319 (0.813)	0.17	S 5	HOMO→LUMO+1	ILCT	334 (41500) (ILCT)
	Na +	329 (0.830)	0.09	S 5	HOMO→LUMO+1	ILCT	321 (38000) (ILCT)
	Mg 2+	299 (0.518)	0.05	S 4	HOMO→LUMO+1	MLCT	295 (33500) (MLCT)
	Ca 2+	300 (0.835)	0.04	S 5	HOMO→LUMO+1	MLCT/ILCT	303 (38000) (ILCT)
	Ba 2+	321 (1.000)	0.16	S 5	HOMO→LUMO+1	ILCT	309 (39500) (ILCT)
	Except for Li

abs , nm) and oscillator strengths (f ), deviation between calculated and experimental excitation energy ∆E (eV), electronic excitation and assignments for ReAZBAP + -M n+ complexes. The experimental maximum absorption wavelength λmax, the absorption coefficients max in L.mol -1 .cm -1 and the experimental assignments

[START_REF] Lewis | Light-Controlled Ion Switching: Direct Observation of the Complete Nanosecond Release and Microsecond Recapture Cycle of an Azacrown-Substituted [(bpy)Re(CO) 3 L] + Complex[END_REF]

are also given

[START_REF] Lewis | Light-Controlled Ion Switching: Direct Observation of the Complete Nanosecond Release and Microsecond Recapture Cycle of an Azacrown-Substituted [(bpy)Re(CO) 3 L] + Complex[END_REF]

. + , we can note that the calculated excitation energies are in good agreement with experiment. Indeed, the deviation between calculated and experimental excitation energies ∆E ranges from 0.04 eV for Ca 2+ to 0.16 eV for the Ba 2+ with an average deviation of 0.09 eV (the larger deviation obtained for Li + is discussed below). In the same vein, the relative values of the calculated oscillator strengths f reproduce the experimental variations of the absorption coefficients max : (1) the system ReAZBAP + -Mg 2+ presents the smallest f and max

Table 4 :

 4 Absorption wavelengths λ (nm) and oscillator strength f calculated for the first excited states of ReAZBAP + -M n+ and ReAZAT + -M n+ . The CT parameters (D CT in Å, q CT in e, µ CT in D) and the variation of NPA charges are also given. See Table2for more details.

	λ	f	DCT	qCT	µCT	∆qI	∆qII	∆qIII ∆qIV	Assignment
					ReAZBAP + -Li +
	S1 0.016 2.52 1.033 12.5 -0.020 -0.041 -0.630 0.700	MLCT
	S2 0.056 2.16 1.037 10.8 -0.117 -0.131 -0.462 0.719	MLCT
	S3 0.017 6.54 1.289 40.5 -0.695 -0.058 -0.061 0.828	LLCT
					ReAZBAP + -Na +
	S1 0.018 3.72 1.052 18.8 -0.246 -0.080 -0.361 0.740 MLCT/LLCT
	S2 0.002 2.19 1.037 10.9	0.023	-0.014 -0.657 0.698	MLCT
	S3 0.071 6.27 1.226 36.9 -0.588 -0.110 -0.068 0.820	LLCT
					ReAZBAP + -Mg 2+
	S1 0.008 2.18 1.034 10.8 -0.055 -0.055 -0.627 0.687	MLCT
	S2 0.083 2.19 1.000 10.5 -0.090 -0.092 -0.574 0.676	MLCT
					ReAZBAP + -Ca 2+
	S1 0.008 2.18 1.035 10.8 -0.007 -0.058 -0.626 0.699	MLCT
	S2 0.083 2.18 1.007 10.5 -0.014 -0.099 -0.569 0.690	MLCT
	S3 0.002 2.27 1.088 11.8 -0.004 -0.025 -0.683 0.712	MLCT
	S4 0.004 6.98 1.448 48.5 -0.842 -0.094	0.091	0.861	LLCT
					ReAZBAP + -Ba 2+
	S1 0.051 3.24 1.048 16.3 -0.180 -0.148 -0.381 0.736	LLCT
	S2 0.013 2.21 1.035 11.0	0.013	-0.034 -0.652 0.699	MLCT
	S3 0.028 6.41 1.243 38.2 -0.622 -0.069 -0.096 0.816	LLCT
					ReAZAT + -Ba 2+
	S1 0.038 6.28 1.154 34.8 -0.537 -0.179 -0.025 0.751	LLCT
	S2 1.475 4.83 0.764 17.8 -0.415	0.290	0.016	0.105	ILCT
	S4 0.072 1.01 2.594 12.5 -0.127 -0.048 -0.519 0.703	MLCT

  for the parameter definitions. d <O-M n+ > is the average value of O-M n+ distances (d 11 to d 15 ). See also Fig. 4.

		Distance N-M n+			Distance O-M n+
		d 11	d 12	d 13	d 14	d 15	d <O-M n+ >
	Li +	2.55	2.06	2.04	2.18	2.16	2.11
	Na +	2.94	2.43	2.44	2.44	2.41	2.43
	Mg 2+	2.34	2.10	2.07	2.16	2.14	2.12
	Ca 2+	2.83	2.40	2.45	2.47	2.45	2.44
	Ba 2+	3.49	2.94	3.03	2.85	2.89	2.93
				S-10

Acknowledgement

This work was supported by the ANR ExStaCaT project, grant ANR-18-CE29-0014 of the French Agence Nationale de la Recherche". The Chevreul Institute is thanked for its help in the development of this work through the ARCHI-CM project supported by the âĂIJMinistère de l'Enseignement Supérieur de la Recherche et de l'InnovationâĂİ, the region âĂIJHauts-de-FranceâĂİ, the ERDF program of the European Union and the âĂIJMétropole Européenne de Lille. This work was granted access to the HPC resources of CINES and IDRIS

Computational details: comparison of the PBE0 and CAM-B3LYP: excited state properties of ReAZBAP + We compare here the performances of a global hybrid XC functional PBE0 1 and a rangeseparated hybrid CAM-B3LYP 2 with regards to the excited-state properties of ReAZBAP + .

One has to note that our benchmark study is based on the comparison between the experimental maximum absorption λ max with the computed vertical excitation wavelength λ abs , which corresponds to the excitation wavelength with the highest f value over the energy range considered. However, these values do not necessarily coincide and a more refined benchmark model should take into account the vibronic structure of the electronic absorption spectra.

For the S 1 to S 4 excited states, the transition energies along with their oscillator strength and their description in terms of electronic excitation are reported in Table S1. The computed excitation energies as well as the convoluted absorption spectra obtained with the PBE0 and CAM-B3LYP functionals are also provided in Fig. S1.

On the one hand, PBE0 reproduces quite well the absorption maximum of ReAZBAP + with a deviation of -0.09 eV compared to the experimental absorption maximum. 3 On the other hand, CAM-B3LYP provides excitation energies and absorption maxima that are always higher in energy than PBE0 results. 4,5 Indeed, the maximum of absorption is strongly blueshifted with CAM-B3LYP calculations with a deviation between calculated and experimental values of 0.48 eV. The absolute error in the computed absorption maximum is thus much smaller at the PBE0 level. We remind here that we did not take into account vibronic couplings in these calculations.

Concerning the nature of the excited states, the electronic excitations responsible for each transition are given in Table S1 and the representation of the different frontier orbitals is provided in Fig. S2. For both PBE0 and CAM-B3LYP calculations, the maximum absorption wavelength arises from a HOMO → LUMO+1 electronic excitation (S 4 state for PBE0 and S 3 state for CAM-B3LYP). For both XC functionals, this electronic excitation leads to

S-13

Table S4: Calculated absorption wavelengths and oscillator strength associated for the first transitions of ReAZAT + -Ba 2+ complex. The charge transfer parameters (D CT in Å, q CT in e, µ CT in D) and the amount of NPA charge transferred (in e)

Impact of the torsion angle φ 3 on the absorption properties

Table S5: Absorption wavelengths λ (nm) and oscillator strength f calculated for the first excited states of ReAZBAP + -Ba 2+ for different values of φ 3 (see Fig. 1). The CT parameters (D CT in Å, q CT in e, µ CT in D) and the variation of NPA charges are also given. See Table S4 for more details.


Chaoqun Zhang

Hongping He

Xiaorong Qin

Alain Decarreau

Fabien Baron

Fabien Baron b Qi Tao

Jianxi Zhu

Yunfei Xi

Sabine Petit
email: sabine.petit@univ-poitiers.fr

Prof Sabine Petit

The growth process of saponite: A study based on particle size distributions and morphological evolution

Keywords: Crystal growth, particle size distribution (PSD), saponite, particle attachment, smectite morphology

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Introduction

The smectite group of clay minerals, composed of a central octahedral sheet and two tetrahedral sheets, has attracted particular attention due to their geochemical significance [START_REF] Eberl | Clay mineral formation and transformation in rocks and soils[END_REF][START_REF] Tardy | Stability fields of smectites and illites as a function of temperature and chemical composition[END_REF][START_REF] Sposito | Surface geochemistry of the clay minerals[END_REF][START_REF] Merriman | Clay minerals and sedimentary basin history[END_REF][START_REF] Christidis | Geological aspects and genesis of bentonites[END_REF][START_REF] Voigt | Magnesium isotope fractionation during hydrothermal seawater-basalt interaction[END_REF] and wide applications [START_REF] Odom | Smectite clay minerals: properties and uses[END_REF][START_REF] Murray | Overviewclay mineral applications[END_REF]Bergaya and Lagaly, 2013). Its formation processes, including phase transformation and crystal growth, not only affect its applications in industries but also respond to the physicochemical environment where it formed. The alteration of other minerals into smectite has been extensively studied (e.g., [START_REF] Badaut | Authigenic smectite on diatom frustules in Bolivian saline lakes[END_REF][START_REF] Banfield | Direct observation of reactant-product interfaces formed in natural weathering of exsolved, defective amphibole to smectite: Evidence for episodic, isovolumetric reactions involving structural inheritance[END_REF][START_REF] Cuadros | Clay crystal-chemical adaptability and transformation mechanisms[END_REF][START_REF] Tao | Formation of saponite by hydrothermal alteration of metal oxides: Implication for the rarity of hydrotalcite[END_REF]. However, only a few studies on smectite growth have been made available thus far, owing to the limitations of its special properties (e.g., complex compositions, hydrated layers, and small particle size) [START_REF] Christidis | Formation and growth of smectites in bentonites: a case study from Kimolos Island, Aegean, Greece[END_REF][START_REF] Decarreau | Study of Low-Pressure Argon Adsorption on Synthetic Nontronite: Implications for Smectite Crystal Growth[END_REF][START_REF] Zhang | Crystal Growth of Smectite: A Study Based on the Change in Crystal Chemistry and Morphology of Saponites with Synthesis Time[END_REF][START_REF] Besselink | Mechanism of Saponite Crystallization from a Rapidly Formed Amorphous Intermediate[END_REF].

The particle size distribution (PSD) of a mineral has a distinctive shape related to its growth history. It is possible to describe the mineral growth processes based on their measured PSDs [START_REF] Wagner | Theorie der Alterung von Niederschlägen durch Umlösen[END_REF][START_REF] Baronnet | Ostwald ripenning in solution: the case of calcite and mica[END_REF]. [START_REF] Eberl | Deducing growth mechanisms for minerals from the shapes of crystal size distributions[END_REF] simulated PSDs of different crystal growth patterns in closed and open systems. An open system is defined as a system in which matter is supplied to the growing crystals by a source other than the growing phase; whereas a closed system is defined as a system where a single phase is involved, and the less stable crystals dissolve to supply materials for the growth of other crystals. [START_REF] Eberl | Deducing growth mechanisms for minerals from the shapes of crystal size distributions[END_REF] defined surface-controlled growth in open systems when crystals grow with an essentially unlimited supply of nutrients, and the dissolution rate of the "source" is not the limiting factor. Supply-controlled growth in open systems refers to the rate of crystal growth, which is controlled by the rate of nutrients. Ostwald ripening in closed systems is a recrystallisation process in a closed system that is characterized by the simultaneous dissolution and growth of a mineral in a single medium [START_REF] Wagner | Theorie der Alterung von Niederschlägen durch Umlösen[END_REF]. In such a system, large particles grow at the expense of dissolving small particles, resulting in the minimization of surface free energy [START_REF] Lifshitz | The kinetics of precipitation from supersaturated solid solutions[END_REF]. Środoń et al. (2000) measured PSDs of natural illite and illite-smectite using transmission electron microscopy (TEM) and concluded that illite grew through surface-controlled growth in open systems. [START_REF] Christidis | Formation and growth of smectites in bentonites: a case study from Kimolos Island, Aegean, Greece[END_REF] also applied the PSD model of [START_REF] Eberl | Deducing growth mechanisms for minerals from the shapes of crystal size distributions[END_REF] to the investigation of the growth mechanisms of smectite in a natural system. Their results indicated that smectite experiences supply-controlled growth in an open system and random ripening in a closed system. [START_REF] Zhang | Crystal Growth of Smectite: A Study Based on the Change in Crystal Chemistry and Morphology of Saponites with Synthesis Time[END_REF] studied the growth process of synthetic saponite by combining PSDs of particle measurements obtained from scanning transmission electron microscopy (STEM) images, argon adsorption, and crystal chemistry. Obtained results implied that saponite growth proceeds via a lateral extension of layers by surface-controlled growth in an open system.

Natural smectite has complex compositions, and in particular its early stages of growth cannot be reprised. Thus, a synthetic laboratory approach has been extensively used to investigate the crystal growth of smectite (e.g., [START_REF] Kloprogge | Synthesis of smectite clay minerals: a critical review[END_REF][START_REF] Zhang | Synthesis of clay minerals[END_REF][START_REF] Petit | Synthesis of nontronite and other Fe-rich smectites: a critical review[END_REF]. It should be noted that a smectite 'crystal' is more comparable to an assemblage of layers than a true crystal (Lagaly and Dékany, 2013), and smectite growth essentially consists of a two-dimensional lateral extension of layers [START_REF] Decarreau | Study of Low-Pressure Argon Adsorption on Synthetic Nontronite: Implications for Smectite Crystal Growth[END_REF][START_REF] Zhang | Crystal Growth of Smectite: A Study Based on the Change in Crystal Chemistry and Morphology of Saponites with Synthesis Time[END_REF]. Thus, the PSDs obtained by recording the crystal size in the ab-plane of particles are useful for studying smectite growth.

In this study, the growth processes of endmember Mg-saponite and Nisaponite synthesised at 220°C, and two MgNi-saponites synthesised at 400 and 500°C, respectively, were investigated through a combination of PSDs and morphologies. The diameters of numerous synthetic saponite particles were measured from STEM images to obtain a series of PSD models. These PSD models were further used to discuss the growth history of saponite.

Materials and Methods

Synthesis of samples

The synthesis and characterisation of the saponites used in this study have been described in detail by [START_REF] Zhang | The evolution of saponite: An experimental study based on crystal chemistry and crystal growth[END_REF]. Briefly, Mg-saponite and Ni-saponite precursors were synthesised by the hydrothermal treatment (220°C, 1 d) of a coprecipitated gel with a theoretical molar ratio of Si:Al:Mg = 3.7:0.3:3. The Mgsaponite and Ni-saponite precursors were named pMg220 and pNi220, respectively.

The starting material for MgNi-saponite synthesis was prepared by mixing identical molar weights of pMg220 and pNi220, and named pMg220+pNi220. Two samples were obtained by hydrothermal treatment of the starting material at 400 and 500°C, and were named 220-400 and 220-500, respectively.

Characterizations of synthetic saponites

Powder X-ray diffraction (XRD) patterns were obtained using a Bruker D8 advance diffractometer (CuKα radiation, 40 kV and 40 mA) over the range of 2-65° (2θ) with a 0.025° (2θ) step size and 0.6 s per step, while the patterns of the oriented samples and ethylene glycol treated samples were collected over the range of 2-15° (2θ). The randomly oriented samples were prepared by pressing the saponite powder inside a cavity up to the reference level of the sample holders. The oriented samples were prepared by carefully pipetting the clay suspension onto a glass slide and allowing it to dry at ambient temperature. Ethylene glycol treated samples were prepared by treating the oriented samples in a glass desiccator with ethylene glycol at 25°C for 24 h.

High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) observations were performed to investigate the morphology of the saponite particles in the ab-plane. A mixture of 1 mg of sample and 10 ml of deionised water was lightly stirred for one week to obtain a diluted colloidal suspension. The specimens were prepared by dispersing the colloidal suspension in 40 ml of ethanol and treating them ultrasonically for 30 min. A drop of the resultant suspension was placed on a porous carbon film supported by a copper grid, then water and ethanol were evaporated. STEM images were obtained using an FEI Talos F200S high-resolution transmission electron microscope operated at 200 kV.

Measurement of PSDs

The saponite growth studied in this study was based on the two-dimensional extension of the particles in the ab-plane. [START_REF] Zhang | Crystal Growth of Smectite: A Study Based on the Change in Crystal Chemistry and Morphology of Saponites with Synthesis Time[END_REF][START_REF] Zhang | The evolution of saponite: An experimental study based on crystal chemistry and crystal growth[END_REF] successfully observed well-dispersed particles of synthetic saponite by STEM and measured the size of a series of particles to obtain their PSDs by taking the mean value of length plus width in the ab-plane. Because saponite particles are generally irregularly shaped, we have developed a new method to measure the particle size of saponite, which is more accurate than that in [START_REF] Zhang | Crystal Growth of Smectite: A Study Based on the Change in Crystal Chemistry and Morphology of Saponites with Synthesis Time[END_REF] (Fig. 1). After obtaining well-dispersed saponite particles from STEM images, the area of the ab-plane of a particle was calculated using Image-ProPlus 6.0 software package in a manual mode. Then, the obtained area was treated as a circle with a calculable diameter (d) that represents the mean size of the particle. The number of measured saponite particles to obtain PSDs was close to 1500 (1508 for 220-400, 1434 for 220-500, 1325 for pMg220, and 1499 for pNi220). The experimental PSD curves were simulated using a log-normal distribution function. Parameter α describes the mean of natural logarithms of observations d (diameter), with α = ∑(ln𝑑)f (𝑑); while β 2 describes the variance of natural logarithms of observations d, with β 2 = ∑[ln(𝑑)α] 2 f(𝑑); where f(d) is the frequency of d [START_REF] Eberl | Deducing growth mechanisms for minerals from the shapes of crystal size distributions[END_REF].

Results and discussion

Crystal habit

Powder XRD patterns of Mg-saponite (pMg220) and Ni-saponite (pNi220) precursors displayed characteristic reflections of tri-octahedral smectite with the (001) reflection at ~1.25 nm, the (06, 33) at 0.153 nm, and asymmetric (hk) reflections (Fig. 2), as described by [START_REF] Zhang | The evolution of saponite: An experimental study based on crystal chemistry and crystal growth[END_REF]. Compared with that of pMg220, the broader reflections for pNi220 suggested that the coherent scattering domains in the layer plane, as well as the number of stacked layers, are smaller for Ni-saponite than for Mg-saponite. The XRD patterns of the oriented samples display the characteristic reflections of saponites with a basal spacing d(001) at ~1.2 nm, which shifts to 1.72 nm after exposure to ethylene glycol (Fig. 3) [START_REF] Zhang | The evolution of saponite: An experimental study based on crystal chemistry and crystal growth[END_REF]. For 220-500, reflections at 2.58 nm and 3.07 nm are observed before and after ethylene glycol treatment (Fig. 3), respectively. The difference between these two values is ~0.5 nm, comparable to the difference between 1.20 nm and 1.72 nm, presumably due to the occurrence of interstratified non-swelling layers [START_REF] Whitney | Hydrothermal reactivity of saponite[END_REF]. The non-swelling layers are likely low-charge talc-like layers according to the low pre-set layer charge of saponite (0.3) [START_REF] Christidis | A new Ni-rich stevensite from the ophiolite complex of Othrys, Central Greece[END_REF][START_REF] Petit | Transformation of synthetic Zn-stevensite to Zn-talc induced by the hofmann-klemen effect[END_REF][START_REF] Fonteneau | Swelling capacity of mixed talc-like/stevensite layers in white/green clay infillings ("deweylite"/"garnierite") from serpentine veins of faulted peridotites, New Caledonia[END_REF].

The STEM images provided detailed morphological information on the abplane of the particles of all saponites (Figs. 45). The layers of pMg220 were generally irregular in shape (Fig. 4a), whereas those of pNi220 exhibited geometrically hexagonal shapes (Fig. 4b). It was noted that some elongated laths and 120° angles between lateral faces occur in sample pMg220, which were also observed in Kozákov natural saponite (Suquet et al., 1975). The elongated laths were also observed in nontronite and hectorite, and were identified as elongations along the aaxis (Mering and Oberling, 1967). Figure 5 reveals an increase in particle size from the starting materials to obtained samples (220-400 and 220-500), providing evidence of saponite particle growth. At higher temperatures, more euhedral elongated particles were observed.

PSDs of Mg-saponite, Ni-saponite, and Mg-Ni saponite

The shape of the PSDs and the reduced PSD profiles of Mg-saponite, Nisaponite, and Mg-Ni saponite were approximately log-normal (Figs. 678). The diameters of the pMg220 particles were in the range of 10-450 nm, with most of them fell within the range of 10-200 nm (Fig. 6a). In contrast, the diameter of the pNi220 particles varied from 5 to 250 nm, and most of them were in the range of 5-120 nm (Fig. 6c). The mean particle diameter in pNi220 was 36.7 nm, which was far less than that of pMg220 (87.2 nm) (Table 1).

The PSD of sample 220-400 had a log-normal shape with a range of 10-500 nm (Fig. 7a). Meanwhile, from the starting materials to 220-400, the mean diameter of the particles increases from 58.2 to 79.2 nm (Table 1), which indicates the growth of saponite layers. The PSD of sample 220-500 overall displayed a log-normal shape with several secondary maxima in the range of 30-850 nm (Fig. 8a). From the starting material to 220-500, the mean diameter increased from 58.2 to 156.8 nm (Table 1), suggesting a strong growth of saponite particles. [START_REF] Zhang | The evolution of saponite: An experimental study based on crystal chemistry and crystal growth[END_REF] provided a comprehensive FTIR analysis on the evolutionary processes of the starting material (pMg220+pNi220) into the samples (220-400 and 220-500). The results indicated that partial dissolution (~0.59) of the starting material and recrystallisation of Mg-Nisaponite occurred in sample 220-400, whereas a total dissolution of the starting material and recrystallisation of Mg-Ni-saponite occurred in sample 220-500. Thus, saponite growth for both samples proceeded via dissolution of the starting material and the recrystallisation of MgNi-saponite. [START_REF] Eberl | Deducing growth mechanisms for minerals from the shapes of crystal size distributions[END_REF] summarised the crystal growth (ripening) mechanisms based on the dissolution-recrystallisation mechanism. The log-normal shape of PSDs (Figs. 678) and the coordinates of (α, β 2 ) (Fig. 9) can be used to discuss the ripening processes of the saponite [START_REF] Eberl | Deducing growth mechanisms for minerals from the shapes of crystal size distributions[END_REF][START_REF] Środoń | Evolution of Fundamental-Particle Size during Illitization of Smectite and Implications for Reaction Mechanism[END_REF]. Generally, a lognormal shape may imply that crystal growth follows either Ostwald ripening or random ripening in a closed system, and surface-controlled growth or supplycontrolled growth in an open system, according to the α and β 2 values (Fig. 9).

Ripening process

Following the definitions of open or closed systems (see Introduction), the systems discussed in this study are open systems, because the source and the growing crystals are not in the same phase. The source of pMg220 and pNi220 were co-precipitated gels, comprising Mg-saponite and Ni-saponite compositions, respectively; whereas the source of MgNi-saponites (220-400 and 220-500) was the starting material (pMg220+pNi220). Furthermore, the log-normal shape of PSD and reduced PSD profiles for pMg220, pNi220, and 220-400 are heavily skewed to the left (Figs. 67), which indicates supply-controlled growth or surface-controlled growth in open systems [START_REF] Eberl | Deducing growth mechanisms for minerals from the shapes of crystal size distributions[END_REF].

The coordinates of (α, β 2 ) provided more information about the ripening processes. For pMg220 and sample 220-400, the coordinates of (α, β 2 ) (Table 1) in open systems placed them close to the line of surface-controlled growth (Fig. 9). These results are also consistent with the surface-controlled growth of Mg-Nisaponite reported by [START_REF] Zhang | Crystal Growth of Smectite: A Study Based on the Change in Crystal Chemistry and Morphology of Saponites with Synthesis Time[END_REF]. For pMg220, the source refers to the coprecipitated gel and the growing crystals of Mg-saponite, whereas for 220-400, the starting material (pMg220+pNi220) is the source and Mg-Ni-saponite form the growing crystals. Surface-controlled growth proceeds through incorporating the species from the dissolution/disarticulation of the source into the growth surface, and the concentration of the species on the growth surface is the same as that in the source [START_REF] Konak | A new model for surface reaction-controlled growth of crystals from solution[END_REF][START_REF] Eberl | Deducing growth mechanisms for minerals from the shapes of crystal size distributions[END_REF]. Thus, for pMg220 and 220-400, the dissolution/ disarticulation rate of the source is not the limiting factor [START_REF] Eberl | Deducing growth mechanisms for minerals from the shapes of crystal size distributions[END_REF]. In such systems, the surface free energy then tends toward a minimum by the dis-articulation/dissolution of the source and growth of the neoformed saponite. As a result, the mean diameter increases (e.g., from 58.2 nm to 79.2 nm in sample 220-400) (Table 1; Fig. 5), and finally, the level of supersaturation in the solution decreases [START_REF] Lifshitz | The kinetics of precipitation from supersaturated solid solutions[END_REF][START_REF] Wagner | Theorie der Alterung von Niederschlägen durch Umlösen[END_REF].

For pNi220, the point of (α, β 2 ) locates on the line of supply-controlled growth in open systems, near the intersection with the line of surface-controlled growth in open systems (Fig. 9). [START_REF] Decarreau | Partitioning of divalent transition elements between octahedral sheets of trioctahedral smectites and water[END_REF] demonstrated that Ni-smectites are generally less soluble than Mg-smectites in a hydrothermal environment. pMg220 and pNi220 were synthesised from co-precipitated gels containing "embryos" (germs) of saponite [START_REF] Zhang | The evolution of saponite: An experimental study based on crystal chemistry and crystal growth[END_REF]. Consequently, Mg-containing gels dissolved more easily than Ni-containing gels. The mean diameter of the pNi220 particles was half that of pMg220 (Table 1), indicating a less efficient crystal growth process for Ni-saponite.

The low kinetics of pNi220 crystal growth are likely linked to the low solubility of Ni-containing gel, which limits the transformation of the gel into Ni-saponite in the aqueous system and induces a partially supply-controlled growth process.

Non-classical crystal growth of saponite

The PSD and reduced PSD profile of sample 220-500 displayed a mean lognormal shape with several small secondary maxima (Fig. 8). However, the coordinate of (α, β 2 ) for sample 220-500 is placed neither on the surface-controlled line nor the supply-controlled line, suggesting that this sample may undergo complex ripening processes (Fig. 9). [START_REF] Eberl | Deducing growth mechanisms for minerals from the shapes of crystal size distributions[END_REF] proposed that agglomeration growth may occur simultaneously with ripening, leading to multimodal distributions. The STEM observations provided direct evidence for attachments between saponite particles (Fig. 10). As shown in Figure 10a, a smaller particle (marked by 1) attaches to a larger particle (marked by 2) by their edge surfaces (marked by red arrows), where the gap (red dotted line) suggests that the fusion between both particles is likely ongoing. The irregularly shaped particle in Figure 10b is composed of at least three sub-particles, that is, the elongated lath (labelled "3") and two irregular particles (labelled "1" and "2"). In sample 220-500, several secondary maxima resulted from non-classical crystal growth (i.e., particle attachment) (Wang et al., 2014). Thus, both indeterminate ripening and particle attachment were involved in the formation of Mg-Ni-saponite in sample 220-500. Particle attachment was also sporadically observed in the STEM images of sample 220-400 (Fig. S1), where saponite growth proceeded via the fusion of the particle edges (red dotted line). Thus, in sample 220-400, particle attachment occurred simultaneously with surface-controlled ripening but was too imperceptible to be recorded by the PSD model (Fig. 7). For two adjacent particles (Figs. 10 andS1), there is the possibility that one particle is preferentially growing at the expense of the other one, because heterogeneity in composition from one particle to another may drive such preferential dissolution and growth. Such viewpoint could be confirmed by in situ observation during saponite growth processes when the technology is feasible.

It was reported that crystal growth by particle attachment occurs widely in geochemical, biological, and synthetic material systems [START_REF] De Yoreo | Crystallization by particle attachment in synthetic, biogenic, and geologic environments[END_REF].

However, there is little research on the non-traditional growth of clay minerals.

García-romero et al. ( 2018) used a TEM to locate and identify smectite and kaolinite particles that seemed to originate from non-classical crystal growth. Furthermore, the authors proposed for the first time that growth by particle attachment is present in clay minerals, and such growth patterns are related to the depositional environments. [START_REF] Zhang | Crystal Growth of Smectite: A Study Based on the Change in Crystal Chemistry and Morphology of Saponites with Synthesis Time[END_REF] found that the size of Mg-Ni-saponite layers significantly increased with a slight increase in the degree of dissolution in its corresponding precursors, and proposed the existence of non-classical growth during the formation of MgNi-saponite in a hydrothermal synthesis system. [START_REF] He | Evidence for a two-stage particle attachment mechanism for phyllosilicate crystallization in geological processes[END_REF] performed TEM on natural biotite, natural muscovite, and synthetic fluorophlogopite. Their results showed that in addition to the traditional crystal growth mechanism, the oriented attachment of particles is common in the growth process of mica. A nonclassical crystallisation model was proposed for the formation of phyllosilicates at elevated temperatures in magmatic and metamorphic environments, where the oriented attachment of building blocks occurs; frequently along the (001) plane or the [001] direction, or both simultaneously [START_REF] He | Evidence for a two-stage particle attachment mechanism for phyllosilicate crystallization in geological processes[END_REF]. Such a study not only showed that non-classical crystal growth patterns are widespread in phyllosilicates, but also extended the observations of particle attachment to magma and high-grade metamorphic processes. In this study, the combination of PSDs and morphology provided evidence that the non-classical growth of clay minerals may exist in high-temperature hydrothermal environments. These results provide important references for further research on the genesis of complex clay minerals and related geochemical processes. [START_REF] Meunier | Why are clay minerals small?[END_REF] had applied the periodic bond chain (PBC) theory of [START_REF] Hartman | Structure and morphology[END_REF] to the crystal growth in clay minerals, which essentially implied a twodimensional extension of clay minerals within the (001) plane. For smectite, it is not clear whether the extensional crystals are composed of stacked multi-layers or a single layer [START_REF] Meunier | Why are clay minerals small?[END_REF][START_REF] Decarreau | Study of Low-Pressure Argon Adsorption on Synthetic Nontronite: Implications for Smectite Crystal Growth[END_REF].

Crystal growth process

In this study, in the saponite synthesised at 220°C, it appears that the welldispersed particles are single layers (Fig. 4). For saponite, the hydrated interlayer cations could hinder a stack and thus the dominant growth pattern is the twodimensional lateral growth of single layer (or a few layers). These saponite layers stack layer by layer randomly during the process of water loss, leading to heterogeneous saponite particles. In the sample synthesised at 500°C, some observed particles clearly consisted of several stacked layers (Fig. 10), suggesting a different crystal growth process. The XRD patterns of 220-500 indicated the occurrence of talc-like layers (Fig. 3), which have low (no) interlayer charge and easily stack into relatively homogeneous crystals with similar dissolution/growth behaviour.

Consequently, 220-500 can grow following, at least partly, a three-dimensional structure, similar to other clay minerals.

The PBCs present in this study were those within the (001) plane, that is, the PBCs of [100], [110], and [1 ̅ 10]. The growth faces of the crystal were observed lying parallel to one or more continuous PBCs. Al distribution can affect the shape of saponite by controlling the development of PBCs [START_REF] Meunier | Why are clay minerals small?[END_REF]. In this study, saponite with a very low charge (0.3) most likely led to the heterogeneous distribution of tetrahedral Al, which induced defects in the saponite layers. Such defects may hinder the development of PBCs in saponite structures. The occurrence of elongated laths in saponites (pMg220, 220-400, and 220-500) likely suggests that only one PBC is favoured in the saponite structure. For Ni-saponite (pNi220), the small layers with a relatively regular shapes like hexagons may indicate that all PBCs are affected.

Conclusions

The present study combines the PSD model and STEM observations to investigate the growth processes of synthetic saponite. The results have indicated that saponite particle growth proceeds mainly via surface-controlled growth and possibly via supply-controlled growth in closed systems, based on the shape of the PSDs and the plotted coordinates of (α, β 2 ) following [START_REF] Eberl | Deducing growth mechanisms for minerals from the shapes of crystal size distributions[END_REF]'s model. Particle attachment, which leads to a multimodal PSD shape, is probably a corresponding growth mechanism. The heterogeneous Al distribution of the low-charge saponite could lead to the formation of elongated laths, and talc-like layers which favour the "three-dimensional growth" of saponite in high-temperature environments.

Acknowledgment

We appreciate the financial supports by National Natural Science Foundation of China (Grant Nos. 41921003, 41825003, 42072044)

  , Science and Technology Planning of Guangdong Province, China (2020B1212060055), The European Union (ERDF), "Région Nouvelle Aquitaine," French « Ministère de l'Enseignement Supérieur et de la Recherche », The Clay Minerals Society, and China Scholarship Council.

Fig. 1 .

 1 Figures and Tables

Fig. 2 .

 2 Fig. 2. Powder XRD patterns of synthetic Mg-saponite (pMg220) and Ni-saponite (pNi220) precursors.

Fig. 3 .

 3 Fig. 3. XRD patterns of oriented samples (air-driedred dot; after glycolationblack solid).

Fig. 4 .

 4 Fig. 4. STEM images of synthetic precursors: (a) Mg-saponite (pMg220), and (b) Nisaponite (pNi220).

Fig. 5 .

 5 Fig. 5. STEM images of the starting materials (a) (pMg220+pNi220), (b) sample 220-

Fig. 6 .

 6 Fig. 6. Particle size distributions (PSDs) and PSD reduced profiles of synthetic

Fig. 7 .

 7 Fig. 7. PSD (a) and PSD reduced profile (b) of sample 220-400.

Fig. 8 .

 8 Fig. 8. PSD (a) and PSD reduced profile (b) of sample 220-500.

Fig. 9 .

 9 Fig. 9. Simple diagram of variations in α-β 2 of synthetic Mg-saponite (pMg220), Ni-

Fig. 10 .

 10 Fig. 10. STEM images of characteristic particle attachment in sample 220-500.

Table 1 .

 1 Mean diameter in ab-plane of particles, α, β 2 of synthetic saponites. α and β 2 are the mean and variance of the natural logarithms of the observed diameters, respectively.

	Samples	Mean diameter (nm)	α	β 2
	pMg220	87.2	4.24	0.454
	pNi220	36.7	3.40	0.177
	pMg220+pNi220	58.2	/	/
	220-400	79.2	4.20	0.325
	220-500	156.8	4.88	0.312