Antoine Carof

François-Xavier Coudert

Dario Corradini

Dominika Lesnicki

Elsa Desmaele

Rodolphe Vuilleumier
email: rodolphe.vuilleumier@ens.fr

Carbon species solvated in molten carbonate electrolyser cell from first-principles simulations

Keywords: Molten carbonate, first-principles simulation, solvation properties

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Introduction

Molten carbonates are nowadays used in many applications. [START_REF] Frangini | Molten carbonates for advanced and sustainable energy applications: Part II. Review of recent literature[END_REF] For instance, molten carbonate fuel cells (MCFC) can produce electricity in the MW range with long term stability [START_REF] Cassir | Strategies and new developments in the field of molten carbonates and high-temperature fuel cells in the carbon cycle[END_REF]. Moreover, because MCFC consume CO 2 at the cathode side and release CO 2 at the anode side, they have been proposed to combine this electricity production capability with the capture and the concentration of CO 2 out of exhaust gas from steel mills [START_REF] Campanari | CO 2 capture from combined cycles integrated with Molten Carbonate Fuel Cells[END_REF][START_REF] Chery | Overview on CO 2 valorization: challenge on molten carbonate[END_REF][START_REF] Mastropasqua | Molten Carbonate Fuel Cells retrofits for CO 2 capture and enhanced energy production in the steel industry[END_REF]. Alternatively, the high solubility of CO 2 in molten carbonates is a possible path to perform carbon capture and utilization (CCU) by electroreduction of CO 2 in molten carbonate electrolyser cells (MCEC) [START_REF] Hu | Electrochemical performance of reversible molten carbonate fuel cells[END_REF][START_REF] Chery | Thermodynamic and experimental approach of electrochemical reduction of CO 2 in molten carbonates[END_REF][START_REF] Chery | CO 2 electrochemical reduction into CO and C in molten carbonates: a thermodynamic point of view[END_REF][START_REF] Hu | Electrode kinetics of the NiO porous electrode for oxygen production in the molten carbonate electrolysis cell (MCEC)[END_REF][START_REF] Hu | Performance and Durability of the Molten Carbonate Electrolysis Cell and the Reversible Molten Carbonate Fuel Cell[END_REF]. The reduction of CO 2 in MCEC into amorphous carbon has been well documented and the conversion of CO 2 to CO or even CH 4 has also been evidenced recently [START_REF] Kaplan | Conversion of CO 2 to CO by Electrolysis of Molten Lithium Carbonate[END_REF][START_REF] Chery | Mechanistic approach of the electrochemical reduction of CO 2 into CO at a gold electrode in molten carbonates by cyclic voltammetry[END_REF][START_REF] Meskine | CO 2 electrolysis in a reversible molten carbonate fuell cell: Online chromatographic detection of CO[END_REF], thus adding another opportunity for carbon capture and utilisation using carbonate melts.

Optimizing the conditions for an efficient electroreduction of CO 2 in MCEC, for example by tuning the melt temperature or the composition, calls for a better understanding of the microscopic processes involved. In particular, there is need to better understand the speciation of the carbon species and their solvation properties in the melt. Cyclic voltametry [START_REF] Chery | Mechanistic approach of the electrochemical reduction of CO 2 into CO at a gold electrode in molten carbonates by cyclic voltammetry[END_REF] has shown that the mechanism of electroreduction of CO 2 in CO is complex and involves the formation of several other species during the reaction. However, the exact nature of these species remains unclear and cyclic voltametry provides only limited microscopic information about these species.

Several recent studies have highlighted the power of computational approaches for the understanding of these complex systems, and a number of of molecular dynamics simulation of molten carbonates have been reported [START_REF] Vuilleumier | Structure, equation of state and transport properties of molten calcium carbonate (CaCO 3 ) by atomistic simulations[END_REF][START_REF] Corradini | Carbon dioxide transport in molten calcium carbonate occurs through an oxo-Grotthuss mechanism via a pyrocarbonate anion[END_REF][START_REF] Corradini | Insight into the Li 2 CO 3 -K 2 CO 3 eutectic mixture from classical molecular dynamics: Thermodynamics, structure, and dynamics[END_REF][START_REF] Wilson | Structure and Liquid Fragility in Sodium Carbonate[END_REF][START_REF] Gutiérrez | Theoretical Study on Molten Alkali Carbonate Interfaces[END_REF][START_REF] Desmaele | Atomistic simulations of molten carbonates: Thermodynamic and transport properties of the Li 2 CO 3 -Na 2 CO 3 -K 2 CO 3 system[END_REF][START_REF] Desmaele | The MgCO 3 -CaCO 3 -Li 2 CO 3 -Na 2 CO 3 -K 2 CO 3 melts: Thermodynamics and transport properties by atomistic simulations[END_REF]. Molecular dynamics simulations can provide a picture of molecular mechanisms and can accurately predict physico-chemical properties, especially in high temperature and high pressure conditions where experiments are hard to perform.

Molecular dynamics simulations exist in two different flavours: first-principles molecular dynamics (FPMD) and force field based molecular dynamics (FFMD). In the latter, energy and nuclear forces are calculated at each time step via a force field function. This method is very efficient numerically and can be used to perform molecular dynamics simulation in large systems, but it requires the design and parametrization of a specific force field describing the interactions between the molecular components of the system. On the other hand, FPMD provides an alternative route by computing on the fly the forces acting on the atoms using an explicit description of the electrons via quantum chemistry methods (e.g. DFT). [START_REF] Car | Unified Approach for Molecular Dynamics and Density-Functional Theory[END_REF] FPMD simulations are thus free of force field parametrization and have the further advantage of being able to directly describe chemical phenomena (e.g. bond breaking and forming); however they have a much higher computational cost than classical methods. In the context of modelling molten carbonate, FPMD simulations showed in particular that the solvation of CO 2 within CaCO 3 at geological conditions (T=1773 K and GPa pressure) leads to the formation of a transient species, the pyrocarbonate anion C 2 O 2- 5 . [START_REF] Corradini | Carbon dioxide transport in molten calcium carbonate occurs through an oxo-Grotthuss mechanism via a pyrocarbonate anion[END_REF] This reactivity of CO 2 with the carbonate ions has consequences both on the solubility of CO 2 and on its transport properties; it could not have been observed in a force field-based simulation. FPMD simulations can also be used in combination with FFMD simulations by building new force fields based on the data obtained during the FPMD simulation, and then rely on the efficiency of FFMD to study large systems. This strategy has been successfully applied to the description of alkaline-earth molten carbonates and molten carbonates of lithium, sodium and potassium [START_REF] Corradini | Insight into the Li 2 CO 3 -K 2 CO 3 eutectic mixture from classical molecular dynamics: Thermodynamics, structure, and dynamics[END_REF][START_REF] Desmaele | Atomistic simulations of molten carbonates: Thermodynamic and transport properties of the Li 2 CO 3 -Na 2 CO 3 -K 2 CO 3 system[END_REF][START_REF] Desmaele | The MgCO 3 -CaCO 3 -Li 2 CO 3 -Na 2 CO 3 -K 2 CO 3 melts: Thermodynamics and transport properties by atomistic simulations[END_REF], for instance in order to predict the equation of state of liquid CaCO 3 , its viscosity and its conductivity [START_REF] Vuilleumier | Structure, equation of state and transport properties of molten calcium carbonate (CaCO 3 ) by atomistic simulations[END_REF] in good agreement with available experiments [START_REF] Kono | Ultralow viscosity of carbonate melts at high pressures[END_REF]. However, these first-principles based FFMD do not allow to study the reactivity and the formation/disproportionation of the transient pyrocarbonate anion in CaCO 3 , underlining the necessity to use FPMD to model the solvation of potentially reactive species such as CO 2 or CO in molten carbonates.

We present here a FPMD study of the solvation of species involved during the CO 2 reduction process in the eutectic (62 % :38 %) LiKCO 3 . Among the different melts presently under investigation to operate in a MCEC, we decided to look specifically at the solvation properties in the eutectic (62 % 38 %) LiKCO 3 (simply denoted LiKCO 3 in the following). This binary mixture has a lower eutectic temperature (T = 761 K) than its other alkali-carbonates counterparts (T = 771 K for 42.7 % 57.3 % LiKCO 3 , T = 774 K for 52 % 48 % LiNaCO 3 and T = 983 K for 56 % 44 % NaKCO 3 ). The first species are CO 2 itself and the corresponding pyrocabonate ion C 2 O 2- 5 . Next, we study the end product of the reaction, i.e. CO. It has been proposed in cyclic voltametry experiments that CO can also react with CO 2- 3 to form the oxalate anion according to [START_REF] Chery | Mechanistic approach of the electrochemical reduction of CO 2 into CO at a gold electrode in molten carbonates by cyclic voltammetry[END_REF] CO

+ CO 2- 3 ↔ C 2 O 2- 4 . (1)
The chemical valence of carbon in oxalate is +III, which can then be seen as an intermediate species that can disproportionate into CO and CO 2- 3 . Finally, a crucial parameter in the efficiency of MCFC and MCEC is the oxoacidity of the melt, which can be tuned through the cation composition. Oxoacidity is characterized by the dissociation constant K D of CO 2- 3 :

CO 2- 3 ↔ CO 2 + O 2-. (2)
We therefore studied in detail the solvation of O 2-in the eutectic LiKCO 3 . The paper is organized as follows. In section 2 we present the FPMD setup used in this study. Then we present results in section 3, first discussing the reactivity of CO 2 with CO 2- 3 in section 3.1, then solvation structures in section 3.2 and finally dynamics in section 3.3. We then conclude in section 4.

Methods

We studied four different systems, each one consisting of a single molecule or anion (CO 2 , C 2 O 2- 4 , CO or O 2-) solvated in the eutectic (62 % 38 %) LiKCO 3 at T = 1000 K and P = 1 atm, i.e. close to the operating conditions of MCFC/MCEC. In these conditions, the experimental density of molten carbonate is ρ = 1.88 g.cm -3 [START_REF] Janz | Thermodynamic and transport properties for molten salts: correlation equations for critically evaluated density, surface tension, electrical conductance and viscosity data[END_REF] and we thus placed one solvated species (CO 2 , C 2 O 2- 4 , CO or O 2-), 158 lithium atoms (159 for the system that contains O 2-) , 96 potassium atoms (97 in the case of O 2-) and 127 CO 2- 3 (126 in the case of C 2 O 2- 4 ) in a cubic box of size a = 22.23 Å. Periodic boudary condition are applied in all directions. The initial positions of the atoms were obtained from a classical molecular dynamics simulation of pure LiKCO 3 with a force field developed previously in our lab [START_REF] Corradini | Insight into the Li 2 CO 3 -K 2 CO 3 eutectic mixture from classical molecular dynamics: Thermodynamics, structure, and dynamics[END_REF] and which was tuned using NPT simulations to reproduce the experimental density at P = 1 atm. From a pure LiKCO 3 equilibrated configuration, we built the simulation box for the different solvated species: for CO and CO 2 , we removed one CO 2- 3 anion, one lithium cation and one potassium cation, and we added the solvated molecule (CO or CO 2 instead); for C 2 O 2- 4 we removed two CO 2- 3 anions, one lithium cation and one potassium cation, and we added C 2 O 2- 4 ; and for O 2-we removed one CO 2- 3 and we added the anion O 2-. The electroneutrality is thus ensured for each simulation box.

The molecular dynamics (MD) simulations were run in the NVT ensemble, using a velocity-Verlet integrator (with a timestep ∆t = 0.5 fs) and a canonical sampling/velocity rescaling (CSVR) thermostat [START_REF] Bussi | Canonical sampling through velocity rescaling[END_REF] (with τ CSVR = 1 ps). The length of trajectories for CO 2 , C 2 O 2- 4 , CO, O 2-is 89 ps, 60 ps, 41 ps and 43 ps, respectively. Positions of all atoms are stored at every time step for analysis.

As we aim to study the reactivity and stability of the different solvated molecules in the molten carbonate, we opted for first-principles molecular dynamics where energies and forces are calculated at each time step at a DFT level. We used the software CP2K that employs a hybrid Gaussian plane-wave method (GPW). [START_REF] Lippert | A hybrid Gaussian and plane wave density functional scheme[END_REF][START_REF] Vandevondele | Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach[END_REF][START_REF] Hutter | CP2K: atomistic simulations of condensed matter systems[END_REF] To reduce the number of explicit electrons, core electrons were replaced by Goedecker-Teter-Hutter (GTH) norm-conserving pseudopotentials. [START_REF] Goedecker | Separable dual-space Gaussian pseudopotentials[END_REF][START_REF] Hartwigsen | Relativistic separable dual-space Gaussian pseudopotentials from H to Rn[END_REF][START_REF] Krack | Pseudopotentials for H to Kr optimized for gradient-corrected exchange-correlation functionals[END_REF] The remaining valence electrons were projected into a doublezeta valence plus polarisation (DZVP) basis set optimized for molecules for each atom type (C, O, Li and K). [START_REF] Vandevondele | Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases[END_REF] A cutoff of 700 Ry was used for the electronic density. We chose the BLYP functional to determine the exchange-correlation interactions [START_REF] Becke | Density-functional exchange-energy approximation with correct asymptotic behavior[END_REF][START_REF] Lee | Development of the Colle-Salvetti correlationenergy formula into a functional of the electron density[END_REF] and the DFT-D3 scheme with a cut-off of 40 Å for the dispersive interactions corrections. [START_REF] Grimme | Semiempirical GGA-type density functional constructed with a long-range dispersion correction[END_REF] This combination of BLYP functional and DFT-D3 correction of dispersive interactions was shown to efficiently reproduce the equation of state of different pure molten carbonate (see Ref. [START_REF] Vuilleumier | Structure, equation of state and transport properties of molten calcium carbonate (CaCO 3 ) by atomistic simulations[END_REF][START_REF] Desmaele | Atomistic simulations of molten carbonates: Thermodynamic and transport properties of the Li 2 CO 3 -Na 2 CO 3 -K 2 CO 3 system[END_REF][START_REF] Desmaele | The MgCO 3 -CaCO 3 -Li 2 CO 3 -Na 2 CO 3 -K 2 CO 3 melts: Thermodynamics and transport properties by atomistic simulations[END_REF]).

We complemented these simulations with four simulations of the isolated species CO

2 , C 2 O 2- 5 , C 2 O 2- 4
and CO at T = 1000 K. Each of these isolated species simulations consisted of one molecule in a cubic box of size a = 22.23 Å with periodic boundary conditions, and was run for 20 ps. All parameters for the isolated species simulations (integrator, thermostat, DFT calculations, basis set and pseudopotentials) are the same as for the liquid-phase simulations. For the the isolated anions

(C 2 O 2- 5 , C 2 O 2- 4
), a uniformly background with charge +2 is added in the simulation box to ensure the electroneutrality.

Results

Reactivity

We first investigate the stability and the potential reactivity of CO

2 , C 2 O 2- 5 , C 2 O 2-
4 , CO, and O 2-when they are present in the molten carbonate medium. Different reactions involving these molecules have been suggested in the literature based on indirect experimental evidence (e.g. the presence of peaks in cylic voltammetry experiments [START_REF] Chery | Mechanistic approach of the electrochemical reduction of CO 2 into CO at a gold electrode in molten carbonates by cyclic voltammetry[END_REF]), in particular the following reactions with the carbonate anion:

CO 2 + CO 2- 3 → C 2 O 2- 5 , (3)
CO + CO 2- 3 → C 2 O 2- 4 , (4)
CO 2- 3 → O 2-+ CO 2 . (5)
We thus wanted to determine whether such reactions occur in our firstprinciples MD simulations, but molecules are not intrinsically defined in this kind of simulations. Among different possible criteria to define the molecules from first-principles MD trajectories (i.e. the position of all atoms at a given time), we decided to rely on a simple hysteresis geometrical criterion: a pair of atoms (C-O or C-C) are connected at time t if their interatomic distance is below 1.7 Å or if they were connected at the previous timestep t -∆t and their interatomic distance is still below 1.9 Å. These criteria mean that a bond can form only when the interatomic distance is below 1.7 Å and can break only when the interatomic distance becomes larger than 1.9 Å. The 1.7 Å/1.9 Åvalues were chosen because the radial distribution function of the C-O pair in the bulk LiKCO 3 is close to zero between those distances. [START_REF] Corradini | Insight into the Li 2 CO 3 -K 2 CO 3 eutectic mixture from classical molecular dynamics: Thermodynamics, structure, and dynamics[END_REF] The hysteris approach allows a smoother behaviour than using only a single criterion and were inspired by the criteria used to define hydrogen bonds in water. [START_REF] Laage | A Molecular Jump Mechanism of Water Reorientation[END_REF] Based on these criteria, we built at each time step a N atoms × N atoms connectivity matrix C(t), with C ij (t) = 1 if atoms i and j are connected at time t and C ij (t) = 0 otherwise. We then determined the connected components of connectivity matrix C(t), each of these connected components is a molecule present at time t.

By applying this molecule-search analysis to the four MD trajectories, we found that: (i) the CO 2 molecule reacts with a carbonate to form a pyrocarbonate anion C 2 O 2- 5 (a detailed analysis of this reaction will be given in the next paragraph), (ii) the carbon monoxide CO does not react with carbonate anions to form an oxalate during the 41 ps simulation, while the oxalate C 2 O 2- 4 does not dissociate into CO and CO 2- 3 during the 60 ps of simulation, and (iii) similarly, none of the 507 CO 2- 3 from the four simulation boxes dissociates into O 2-and CO 2 among the 233 ps accumulated from the four simulations, while the anion O 2-remains stable for 41 ps of simulation. The stability of these different solvated species will allow us to present their intra-and intermolecular structure and their dynamical properties in section 3.2 and 3.3, respectively. In the case of the isolated species (CO 2 , C 2 O 2- 5 , C 2 O 2- 4 , CO), we applied the same methodology and found that they are stable for the 20 ps simulation.

The formation of C 2 O 2- 5 was already observed in CaCO 3 at geological condition (high pressure and high temperature T = 1773 K), [START_REF] Corradini | Carbon dioxide transport in molten calcium carbonate occurs through an oxo-Grotthuss mechanism via a pyrocarbonate anion[END_REF] but the present work shows that such a reactivity exists also in the milder conditions of an operating MCFC or MCEC (atmospheric pressure, intermediate temperature T = 1000 K). 5 is at maximum half an order of magnitude shorter than that of CO 2 (2.5 ps vs 12 ps). To extract the characteristic lifetime, both distributions were fitted with an exponential function and we obtained τ CO2 = 2.3 ps and τ C2O 2- 5 = 0.6 ps. These lifetimes are of the same order of magnitude as the one calculated in the geological CaCO 3 (0.88 ps for CO 2 and 0.38 ps for C 2 O 2- 5 ), but the slower kinetics are consistent with the lower temperature. On average, the pyrocarbonate is present about f C2O 2- 5 = 19 % of the time, which means that, even as a transient species, it impacts quantitatively the thermodynamics of the solvated CO 2 (e.g. its solubility and its redox potential). From the fraction of time of presence of the pyrocarbonate f C2O 2-

5

, we estimated the free enthalpy of its formation (eq. 3),

∆G = RT ln(1-f C2O 2- 5 )/f C2O 2- 5 = 12 kJ.mol -1 .
The fraction of time of presence and the free enthalpy of formation are similar as in CaCO 3 at 1773 K: 0.24 % and 16.8 kJ.mol -1 , respectively. We also estimated the enthalpy of formation by considering the difference of average potential energy in presence of pyrocarbonate and in presence of CO 2 ,

∆H = U C2O 2- 5 -U CO2 = 45 kJ.mol -1
, where the bracket • I indicates an average over configurations where the species I is present. The reaction (3) is thus endothermic, meaning the fraction of pyrocarbonate will increase at higher temperature. The entropy of formation, ∆S = (∆H -∆G)/T = 33 J.mol -1 , is positive, which indicates the formation of pyrocarbonate is entropically favoured. This latter observation seems counter-intuitive as the reaction 3 reduced the number of molecules from 2 to 1, i.e. a decrease in the translational entropy. In section 3.2.1 and 3.2.2, we will analyse the solvation of CO 2 and C 2 O 2- 5 and show that the solvation structure of the latter is more disordered, which may explain the positive entropy of formation.

Intramolecular and Intermolecular Structure

We now explore the interactions between the solvated species and the molten carbonate, in particular to understand their differences in stability and reactivity. We consider the intramolecular structure (distances, angles and dihedral angles) as well as the intermolecular solvation structures.

Carbon dioxide

We first focus on the properties of CO 2 , the key molecule in the redox processes occurring within MCFC and MCEC. From the first-principles MD simulations of CO 2 solvated in LiKCO 3 and CO 2 isolated, we extracted the geometrical properties that characterized the CO 2 molecule: the C-O distance and the OCO angle. Table 1 gathers the average value and the standard deviation obtained in both phases at T = 1000 K. The average C-O distance and To understand better the formation of the pyrocarbonate, we explored the solvation structure around CO 2 and its specific interactions with the different ions of the melt. Fig. 3 displays the radial distribution function (RDF) between (a) the carbon atom (C CO2 ) and (b) the oxygen atoms (O CO2 ) and all the solvent atoms (K, Li and C and O atoms of the carbonate, denoted respectively C carb and O carb ). The potassium cations show the strongest affinity with the CO 2 molecule, with a clear intermolecular structure characterized by two peaks, at 4 Å and 6.5 Å for C CO2 and 3.5 Å and 7 Å for O CO2 . The situation is notably different for the lithium cations, for which we observed no peaks in the RDF with C CO2 or O CO2 , meaning that no specific interaction exists between CO 2 and lithium. This absence of interaction may be explained by the competition with the strong lithium-carbonate interactions. The latter is revealed in the RDFs for C carb -Li and O carb -Li pairs shown in the Fig. 4 of Ref. [START_REF] Corradini | Insight into the Li 2 CO 3 -K 2 CO 3 eutectic mixture from classical molecular dynamics: Thermodynamics, structure, and dynamics[END_REF]. The O carb -Li RDF displays in particular a very strong peak at 2.5 Å. The neutral CO 2 molecule cannot interact strongly enough with Li + to counteract the CO 2- 3 -Li + interaction and Li does not form a solvation structure around CO 2 .

Molecule

The RDFs give only access to isotropic information and therefore neglect the particular orientation of the CO 2 with respect to the carbonate, potassium and lithium ions. To better highlight the three-dimensional solvation structure of CO 2 , we built two-dimensional histograms of the probability of the presence of the solvent atoms (C carb , O carb , Li and K) around CO 2 in a cylindrical ρ -ζ coordinate system, where ζ is the projection of an atom position along the O CO2 -O CO2 axis and ρ the distance from the O CO2 -O CO2 axis. The origin of the the cylindrical coordinate system is chosen to be the mid-point of the O CO2 -O CO2 vector, i.e. close to the average position of C CO2 . Fig. 4(a-d) shows these two-dimensional histograms for C carb , O carb , Li and K atoms, respectively. Fig. 4(a-b) reveals a preferential orientation of CO 2- 3 with respect to CO 2 . The highest probability of presence is observed in the region 3 < ρ < 4 Å and -1 < ζ < 1 Å for C carb and in the region 2.5 < ρ < 3.5 Å and -0.5 < ζ < 0.5 Å for O carb . The solvation of the CO 2 molecule by the carbonate anion is thus characterized by a preferential structure where one O of the solvating carbonate is in the plane of symmetry orthogonal to CO 2 . Such a preferential orientation was previously observed for CO 2 solvated in the molten CaCO 3 and participates to the formation of the pyrocarbonate. The solvation structure of K + around CO 2 is also anisotropic, as shown in Fig. 4(d). The presence of K + is the highest within two regions, which are symmetrical with respect to the ζ = 0 axis, which have the shape of an arc of circle with center C CO2 and a radius of 4 Å (that corresponds to the first peak in the RDF between K and C CO2 ) and which extend between the angles 46 • and 65 • with respect to the ζ = 0 axis (maximum around 56 • ). The potassium cation positions preferentially between the carbon and the oxygen atoms and close to the CO 2 molecule. The twodimensional histogram has thus permitted to analyse in details the first peak of the K-C CO2 RDF. Such a double-arc structure in-between C and O atoms was also observed in the case of the probability of presence of Ca atoms around CO 2 in CaCO 3 , which indicates that K + and Ca 2+ play similar role in the solvation of CO 2 . On the other hand, the lithium solvation structure (displayed in Fig. 4(c)) does not show any preferred positions for lithium around CO 2 , which confirms the previous analysis of the Li-C CO2 RDF and corroborates the absence of specific Li-CO 2 interaction, probably due to the strong Li + -CO 2- interaction. The observation of the different solvation structures formed by Li and K around CO 2 is a major step to understand the role of the molten carbonate composition in the solubility or diffusivity of CO 2 .

Pyrocarbonate anion, C 2 O 2- 5

We will now consider the structure and the solvation of the unusual pyrocarbonate cation formed by reaction between the solvated CO 2 molecule and a carbonate CO 2- 3 of the solvent. We first calculated the average and standard deviation of the intramolecular distances, both for a pyrocarbonate solvated within the molten carbonate and isolated. The central oxygen atom of C 2 O 2- 5 will be labelled O * while the four external oxygens and the two carbons will be labelled O and C. Table 1 gathers these distances, that follow on average the trend d CO < d CO * < d CC and whose standard deviations due to thermal fluctuations are relatively low (between 4 % and 7 %). The distances d CO and d CO * are almost identical between the solvated pyrocarbonate and the isolated pyrocarbonate (with difference in average value or standard deviation < 0.02 Å), while d CO is slightly longer for the isolated molecule, with an increase of 0.09 Å compared to the solvated anion. The average intramolecular distances of the pyrocarbonate in LiKCO 3 are also similar to the one in CaCO 3 , whose average value are 1.26 Å, 1.43 Å and 2.53 Å for d CO , d CO * and d CC , respectively. Table 1 also displays the average and standard deviation of the three intramolecular angles of the pyrocarbonate. Like for the distances, the thermal fluctuations are of the order of 5 % to 7 %, the average values are equivalent between the solvated and the isolated molecule (with the maximum difference for CO * C at 4.2 • ). They are also very close between pyrocarbonate ion solvated in LiKCO 3 and ion solvated in CaCO 3 (with the maximum difference for CO * C at 4.0 • ). Finally, we conclude the analysis of the geometry of C 2 O 2- 5 by looking at the dihedral angle OCO * C. Fig. 5 displays the distributions of OCO * C for the solvated and isolated pyrocarbonate. Both distributions peak around 0 • and 180 • which indicates the pyrocarbonate forms preferentially a planar structure. The probability to observe other angles is however far from negligible: the smallest probability is found for dihedral angles of ± 90 • and is only half of the highest probability (planar structure). C 2 O 2- 5 is therefore flexible and it alternates planar and twisted structures.

To understand the formation and relative stability of this transient species, we analyse here its solvation structure. We start with the RDF (shown in Fig. 6(a-c)), between the three types atoms of C 2 O 2- 5 (C pyro , O pyro and O * pyro , respectively) and the four solvent atoms (C carb , O carb , Li and K). The RDFs reveal a different structure of solvation compared to the CO 2 molecule: the closest peak (i.e. intramolecular distance) occur now with Li for all atoms in pyrocarbonate, with distances of 3 Å and 2 Å for C pyro and O pyro respectively. But except for these peaks, the lithium solvation does not present a medium-range structure (RDF close to 1 after 5 Å). The RDFs K-C pyro and K-O pyro are characterized by a double-peak structure, more pronounced for C pyro , a behaviour similar to the one observed around CO 2 . The RDFs between the carbonate atoms and C pyro and O pyro displays almost no solvation-induced structuration, with a small peak (RDF close to 1.3) between C carb and C pyro and O pyro at 4 Å and 6 Å respectively, while no peaks occur for C carb . We conclude the discussion of the RDFs by noting that O * pyro is embedded with the pyrocarbonate molecule and less reachable: its RDFs with solvent atoms (see Fig. 6(c)) does not present any marked solvation structure (except a broad peak for potassium).

As explained in the case of CO 2 , the RDFs only provide isotropic information and we therefore calculated the two-dimensional cylindrical-based histograms to characterize the solvation structure and elucidate the peaks observed in the RDFs with respect to Li and K. Fig. 6(d-e) displays the cylindrical-coordinate density of probability of presence of solvent atoms surrounding the pyrocarbonate. ζ is now the projection along the C pyro -C pyro axis, ρ the distance with this axis and the origin is the midpoint between C pyro atoms. To account for the dissymmetry that might be induced by the formation of pyorcarbonate from the reaction between CO 2 and CO 2- 3 , we always placed the C from the former CO 2 in the region ζ < 0. Fig. 6(c) shows that the lithium atoms surround almost homogeneously the pyrocarbonate, which means the peak in RDF between lithium and pyrocarbonate does not split clearly into different preferential positions. We note nevertheless a slightly higher density of probability in the arc of circle ζ ≥ 0, ρ = 3 Å(and in particular in the place perpendicular to the pyrocarbonate, ζ = 0) which reveals that the lithium cation is closer to the former CO 2- 3 than with the former CO 2 . The same analysis holds for the probability of presence of K + (shown in Fig. 6(d) which also surround homogeneously the pyrocarbonate but with a higher probability of presence both in the perpendicular plane but also in the C pyro -C pyro axis (ρ = 0 Å, ζ = ±4 Å). We note that such homogeneous surrounding was also observed for the presence of calcium atoms around the pyrocarbonate formed in CaCO 3 , which again underlines the similar role played by K + and Ca 2+ in the solvation of CO 2 and C 2 O 2- 5 .

The cylindrical-coordinate density of probability reveals the key difference of the solvation structure around CO 2 and around C 2 O 2- 5 : (i) Li + rarely approach close to CO 2 while it solvates C 2 O 2- 5 homogeneously at 3 Å, and (ii) K + solvates CO 2 anisotropically while it surrounds C 2 O 2- 5 homogeneously. The difference of solvation of Li + may be related to the difference of charges of these molecules (q CO2 = 0, 5 . This result may contribute to the positive sign of the entropy of formation discussed in section 3.1. When the pyrocarbonate anion is formed, the anisotropic solvation structure of K + around CO 2 disappears, leading to a increase of entropy.

q pyro = -2), C 2 O 2-

Oxalate anion, C

2 O 2- 4
Besides CO 2 and pyrocarbonate, the oxalate anion C 2 O 2- 4 may also play a role in the electrochemical properties of MCFC and MCEC. The formation of this species can occur via the reaction between CO and CO 2- 3 (eq. 4), though we did not directly observe this reaction in the system containing a CO molecule or the inverse reaction in the system containing C 2 O 2- 4 (see the discussion on stability in section 3.1). From the 60 ps MD trajectory containing the stable C 2 O 2- 4 solvated in LiKCO 3 , we extracted the intramolecular and solvation structure, in particular to understand its relative stability in comparison with the pyrocarbonate.

The oxalate intramolecular geometry is characterized by two distances (d CC and d CO ), two angles ( OCC and OCO) whose average values and standard deviations in both molten carbonate and vacuum (i.e. for the isolated molecule) are presented in Table 1. The shortest distance is d CO , with an average value (1.28 Å) close to that of pyrocarbonate (1.26 Å) but 8 % longer than in CO 2 (1.18 Å). Similarly to what we observed for CO 2 and the pyrocarbonate anion, the thermal fluctuations for the distances and the angles are small (about 5 %) and solvated oxalate and isolated oxalate ions have almost identical structure (only the CC distance is 5 % higher for the isolated molecule). Finally, Similarly to what was observed for pyrocarbonate, the distribution of dihedral angles is widely spread, the minimum is found at 0 • , with a probability only half of the maximal value. Like the pyrocarbonate ion, the oxalate anion is flexible and alternates twisted and planar structures when solvated in molten carbonate.

The solvation structure of the oxalate is characterized by the RDF (Fig. 8(ab)) and the cylindrical density of probability (Fig. 8(c-d)). The analysis of RDFs between the atoms of the oxalate (O oxa and C oxa ) and the solvent atoms reveal some similarity with the solvation structure of pyrocarbonate, both being anionic species: (i) the RDFs with lithium peak closer than the RDFs with potassium, with a larger Li-O oxa RDF peak than K-C oxa , while Li-C oxa RDF peak is smaller than K-C oxa RDF peak; (ii) the RDF K-C oxa exhibits a two-peak structure; (iii) the RDFs with C carb and O carb display only a very slight structuration, though the RDF C carb -C oxa presents two distinct peaks at 5 Å and 9 Å.

Likewise, the cylindrical densities of probability of presence of Li and K (Fig. 8(c-d)) show some resemblance with the one of pyrocarbonate. Here the cylindrical coordinates are defined with respect to the C oxa -C oxa axis, with ζ the projection onto this axis, ρ the distance to that axis and the origin the midpoint of the C oxa -C oxa bond. Li and K atoms surround homogeneously the oxalate, with a higher density for lithium along the C oxa -C oxa and for potassium in the plane perpendicular to the C oxa -C oxa axis (ζ = 0 Å) and along the C oxa -C oxa axis. This solvation structure, close to that of C 2 O 2- 5 , indicates the existence of different solvation patterns between charged species (pyrocarbonate, oxalate) and neutral species (CO 2 ). The only minor difference between C 2 O 2- 5 . We will confirm the differential solvation patterns between charge and neutral species by looking now into the solvated CO molecules and the oxygen anion O 2-.

Carbon monoxide

The production of carbon monoxide CO is one of the main objectives of molten carbonate electrolyser cells (MCEC) and we therefore present here the solvation properties of CO in the eutectic LiKCO 3 . In particular, the stability of CO discussed in section 3.1 will be analysed by comparing the solvation structures of CO and CO 2 . The dynamical properties, and in particular the diffusion, will be discussed in section 3.3.

From the 41 ps first-principles MD simulation, we measure the average C-O distance and standard deviation in both the molten carbonate and in vacuum (i.e. for the isolated molecule). The average C-O distance is similar in molten carbonate and for the isolated molecule and is the smallest C-O intramolecular distance among the different solvated molecules we investigated (it is 0.02, 0.10 and 0.12 Å smaller than C-O distance in CO 2 , pyrocarbonate and oxalate, respectively), as expected due to its triple-bond nature. The thermal fluctuations are of the order of 5 % in the molten carbonate and 3 % for the isolated molecule.

More interestingly, the solvation around CO is notable for its absence of marked structure. Fig. 9(a-b) shows the RDFs between the two atoms of CO (panel (a) for O CO and panel (b) for C CO ) and the different solvent atoms. These RDFs present some similarity with the ones around CO 2 . First, the highest peak is between potassium and C CO and panel O CO at 3.5 Å and 4 Å, respectively, with a second smaller peak observed between C CO and K at 6.5 Å. The first C CO -K RDF peak reaches however a value of 2 for CO and 3 for CO 2 , that indicates a weaker interaction in the case of CO. Secondly, the RDFs with Li reveal an absence of preferential CO-Li distance, similar to that was already noticed for CO 2 . Finally, the RDFs with the carbonate atoms show a slight solvation structure around O CO : the RDF O carb -O CO peaks at 3.5 Å (with a value of 1.4), while the RDF O CO -C carb peaks at 4 Å (with a value of 1.5). As no peaks are observed for C CO in Fig. 9(b), this shows that the carbonate anion surrounds preferentially the oxygen atom of CO, with one oxygen of CO 2- 3 pointing toward O CO . This specific interaction is explained by the positive charge carried by the O atom of CO (while C carries the opposite negative This particular dipole of CO also impacts the cylindrical-coordinate density of probability for Li and K displayed in Fig. 9(c(d). Here the ζ coordinate is the projection onto the C CO -O CO axis, ρ is the distance to that axis, and the origin of the referential is the midpoint of the C CO -O CO vector. The oxygen O CO is placed in the ζ < 0 portion of the plots. As seen in the RDF, the probability of presence of Li is more diffuse than the one of K, but both Li and K show their highest probability of presence in the vicinity of C CO , along the C CO -O CO axis (ρ = 0 Å, ζ = 3 Å), i.e. the cations of the molten carbonate position preferentially close to the negatively charged C CO .

Overall, CO presents a similar solvation pattern to CO 2 with a strong solvation with K + and an (almost) absence of solvation with Li + . The main differences are (i) the preferential position of Li + close to C CO , which is explained by the negatively charged carbon that can (slightly) compete with the Li + -CO 2- 3 interaction, (ii) the absence of anisotropic potassium solvation structure around CO and (iii) the absence of preferential solvation of carbonate around CO.

Oxygen anion

We conclude our analysis of solvated species in the molten carbonate LiKCO 3 with the oxygen anion O 2-. O 2-may be involved in the electrochemical processes at the interface between molten carbonate and electrodes in MCFC or MCEC. Moreover, in that liquid melt, it also plays the important role of being the strongest oxo-base, an analogue of OH -in water. For this mono-atomic species, the solvation structure is isotropic and thus simply characterized by the RDFs with the different solvent atoms, shown in Fig. 10(a). The Li + -O 2-RDF displays the most notable feature, with a high peak at 2 Å (RDF reaches here a value of 17) followed by a minimum (RDF close to 0) at 3 Å. This peak induces a plateau is the coordination number n(r) between 2 and 3 Å at n(r) = 4, which means that O 2-forms a relatively stable solvation shell with four lithium atoms. Besides the O 2--Li + RDF peak, each RDF between O 2-and the other solvent atoms displays successively a much smaller peak (RDF is around 2) at 3, 3.5 and 4 Å for K, O carb and C carb , respectively.

To prolong the RDFs analysis, we calculate the joint probability of presence of Li + and K + in the first solvation shell of O 2-(Li + and K + are included in the shell if their distance with O 2-is below the first minimum in the respective RDFs, i.e. 3.1 Å and 3.6 Å respectively). This joint probability, displayed in Fig. 10(b), shows that the first shell contains most likely four Li + and no K + , but structures with only three Li + , only five Li + or one K + and three Li + are also significant. Cumulative distribution of residence times for both cations are shown in Fig. 10(c) together with an exponential fit of the long-time tails of the distribution (we disregard the short timescales related to vibrational motions). These distributions reveal different timescales: Li + stays on average 8 ps around O 2-, as given by the exponential decay, and up to tens ps for some ions. On the opposite, the presence of K + is more short-lived with an exponential decay time of 1.5 ps. From the RDFs, the coordination number, the joint distribution and the residence time, a picture emerges of a transient complex OLi 2+ 4 with fast entrance/exit of K + . We explore the internal structure of this complex by looking at the distribution of Li-O-Li, Li-O-K and K-O-K angles (shown in Fig. 10(d)). These angles distributions peak around 90 • and 180 • with minima around 125 • and the ratio between the highest and lowest probability is only a factor 2. These results indicate that (i) tetrahedral configurations are not predominant and (ii) the structure of the complex is flexible with many configurations possible. To summarize our analysis of the solvation of O 2-, we have shown the existence of a transient complex OLi 2+ 4 of electrochemical relevance, rather than the isolated O 2-anion. This complex displays a flexible structure, easily distorted by the fast entrance/exit of K + within the first solvation shell.

Diffusion and Rotation

We now conclude the analysis of these solvated species in LiKCO 3 by investigating two dynamical properties: the translational diffusion in the liquid and the reorientation of these molecules.

The diffusion of these species within the molten carbonate medium -to and from the electrodes-is an essential step in the electrochemical processes of MCFC/MCEC, but the values of diffusion coefficient are often difficult to obtain experimentally. In MD simulations, the diffusion coefficient of a given molecule is obtained by taking the slope of the mean-square displacement (MSD) at long time, D I = lim τ →∞ 4 , CO, O 2-as well as the solvent molecules, but we must take a special care in the case of the reactive CO 2 . We adapt the definition of the MSD to integrate the transient nature of CO 2 and the variable index of its constituent atoms,

MSD CO2 (τ ) = Nsteps t=1 |R(t + τ ) -R(t)| 2 χ t χ t+τ Nsteps t=1 χ t χ t+τ (6)
where the characteristic function χ t = 1 if CO 2 is present at time t and χ t = 0 otherwise. Fig. 11(a) shows the MSDs vs time for the four solvated species and the linear functions fitted on the MSDs to extract the diffusion coefficients. The latter are summarized in Table 2 together with the diffusion coefficient for the three ionic species that composed the solvent. The diffusion coefficient range from 0.5 to 4 •10 -5 cm 2 .s -1 , where the highest diffusion coefficient is found for CO. We explain this feature of CO by noting that CO is a neutral molecule, with a small electrostatic dipole (p CO = 0.11 D), a relatively small size and a near spherical shape. These features indicates that CO interacts only weakly with the surrounding molten carbonate and behaves probably similarly to a noble gas that can diffuse quickly in the liquid. The second highest diffusion coefficient is that of the CO 2 species. The MSD for CO 2 (eq. 6) takes into account its reactivity and the displacement induced by the successive formation and dissociation of pyrocarbonate. If CO 2 shares some similarity with CO (a neutral molecule with a small dipole moment), its interaction with the solvent is stronger, in particular with the carbonate anion CO 2- 3 that forms a preferential structure as discussed in section 3.2.1. The smallest diffusion coefficient is that of the oxygen anion O 2-(0.54•10 -5 cm 2 .s -1 ). As described in section 3.2.5, this divalent anion strongly attracts four lithium ions to form a relatively stable OLi 2+ 4 complex that could explain its slow diffusivity due its larger size and bulkier nature. We also note that the diffusion coefficient of the solvent molecules are three times smaller than the one measured experimentally at 1100 K [START_REF] Janz | Molten Salts Data: Diffusion Coefficients in Single and Multi-Component Salt Systems[END_REF] (3.52•10 -5 cm 2 for CO 2- 3 and 3.81•10 -5 cm 2 for K + ), but they correspond to the calculated diffusion coefficient from MD simulations in the 1100 K to 1200 K temperature range [START_REF] Corradini | Insight into the Li 2 CO 3 -K 2 CO 3 eutectic mixture from classical molecular dynamics: Thermodynamics, structure, and dynamics[END_REF][START_REF] Tissen | Molecular dynamics simulation of binary mixtures of molten alkali carbonates[END_REF][START_REF] Koishi | Computer Simulation of Molten Li 2 CO 3 -K 2 CO 3 Mixtures[END_REF][START_REF] Costa | Molecular dynamics of molten Li 2 CO 3 -K 2 CO 3[END_REF] (0.55-1.9•10 -5 cm 2 , 2.55-5.38•10 -5 cm 2 and 1.55-4.99•10 -5 cm 2 for CO 2- 3 , Li + and K + respectively).

We then analysed our simulations to obtain information on the reorientation of these species in the molten carbonate, a property that could be more easily measured experimentally and may bring information on their diffusion mechanism. We quantified the reorientation process in our MD simulations using the second-order reorientation time-correlation function,

C 2 (t) = P 2 [u(t) • u(0)] (7) = 1 2 3|u(t) • u(0)| 2 -1 (8)
where P 2 is the second-order Legendre polynomial and u is a normalized vector characterizing the orientation of the molecule (we choose the vector between O atoms for CO 2 , between C atoms for C 2 O 2- 5 and C 2 O 2- 4 and between C and O atoms for CO). Fig. 11(b) shows the reorientation time-correlations C 2 (t) for the different solvated molecules, as well as an exponential-fitted decay (of the form A exp (-t/τ reor )) of C 2 (t). The reorientation times obtained from the fit, τ reor , are gathered in table 2 for the different solvated molecules and for the solvent anion CO 2- 3 . Except for the particular case of CO molecule (τ reor = 0.1 ps), the reorientation times range between 1.3 ps and 3.4 ps with the following order:

CO 2- 3 < CO 2 < C 2 O 2- 4 < C 2 O 2- 5 .
The short reorientation time of the CO molecule indicates that it can freely rotate in the molten carbonate and confirms the observation made for the translational diffusion that CO only weakly interacts with the molten carbonate. In contract, the oxalate and pyrocarbonate anions are charged and relatively large molecules whose reorientation is about 30 times slower than CO.

Conclusion

We have investigated in this work the solvation properties of key molecules in the operation of MCFC/MCEC in the eutectic (62 % 38 %) LiKCO 3 using 2.

Table 2: Dynamical properties of the molecules solvated in the eutectic LiKCO 3 . The diffusion coefficient is obtained from a linear fitting of the mean-square displacement, and the reorientation time from an exponential fitting of the time-correlation reorientation function (eq. 8). . The lifetime of the pyrocarbonate anion is however significantly longer in the eutectic LiKCO 3 than in CaCO 3 , possibly because of the lower temperature. In contrast to CO 2 /C 2 O 2- 5 , both CO and the oxalate anion, C 2 O 2- 4 , are found to be stable in the eutectic LiKCO 3 . This confirms the oxalate anion as a putative intermediate in the reduction of CO 2 . Its disproportionation reaction (or inversely its formation) is probably activated as it needs not only the breaking of the C-C bond but also the breaking and formation of a C-O bond. Such activated process are unlikely to be observed during the simulation times accessible to our first-principles simulations, and further studies are needed to describe the formation mechanism and thermodynamics of oxalate. Free energy methods could be employed in combination with first-principles molecular dynamics in order to measure these thermodynamics properties.

Molecule Diffusion coefficient (10

The study of the solvation structures highlights the different behaviour of K + and Li + in the molten carbonate medium. Because of its smaller size, Li + binds more strongly to charged species (C 2 O 2- 5 , C 2 O 2- 4 , O 2-and CO 2- 3 ). O 2- forms in particular a flexible complex with four Li + . K + is found preferentially around neutral molecules (CO 2 and CO). These contrasting behaviour regarding solvation between Li + and K + -and their effects on solubility and transport properties -may contribute to the choice of an optimal molten carbonate composition to operate an MCEC process.

Finally, we have estimated the diffusion coefficients of these solvated species, which are important parameters for the interpretation of experimental data and the modelling of MCEC operation. Of all the species studied, CO diffuses significantly faster consistently with its small size and poor interaction with the melt. In the future, we plan to compute other experimental observables allowing for a direct comparison with in situ experiments, such as Raman spectra or NMR chemical shifts. [START_REF] Morizet | A NMR and molecular dynamics study of CO 2 -bearing basaltic melts and glasses[END_REF] 5. Acknowledgement

  Fig. 1(a) illustrates the presence of C 2 O 2- LiKCO 3 . The kinetics of the formation/dissociation equilibrium of the pyrocarbonate anion affect the diffusion and the electrochemical properties of CO 2 solvated in this molten carbonate and the process of MCFC and MCEC. From the MD trajectory, we quantified the stability of C 2 O 2- 5 and Fig. 1(b) shows the cumulative lifetime distribution of both CO 2 and C 2 O 2- 5 . The lifetime of the transient C 2 O 2-

Figure 1 :

 1 Figure 1: Formation/dissociation of pyrocarbonate C 2 O 2- 5 . (a) Snapshot of C 2 O 2- 5 formed in the eutectic LiKCO 3 . Carbonate molecules in the solvent are represented by cyan/red sticks, O atoms by red spheres, K atoms in blue and Li atoms in orange. (b) Cumulative lifetime distribution of CO 2 and of C 2 O 2- 5 and exponential fit of these distributions (dashed lines).

Table 1 :

 1 Geometry of the different molecules in the eutectic LiKCO 3 and for an isolated species at T = 1000 K. Mean and standard deviation are obtained from the distribution of the geometrical properties (distance and angle) extracted from the MD simulations. The central atom of the C 2 O 2- 5 is labelled O * .

Figure 2 :

 2 Figure 2: Intramolecular properties of CO 2 molecule. (a,c) Snapshots of CO 2 solvated in LiKCO 3 illustrating (a) a bended configuration ( OCO = 124.4 • ) and (c) a linear configuration ( OCO = 179.9 • ). (b) Distribution of O-C-O angle of the CO 2 molecule solvated in the eutectic LiKCO 3 at 1000 K and isolated. For the solvated molecule, angles are measured during the time intervals of existence of CO 2 . The distribution is normalized by dividing by sin θ. Gaussian fits of the form exp A(θ -180 • ) 2 + B are shown as blue and red solid lines for the solvated molecule and isolated molecule cases. Values of the fitted parameters: A = -0.0045, B = 3.33 (solvated molecule) and A = -0.0067, B = 3.81 (isolated molecule).

Figure 3 :

 3 Figure 3: Radial distribution function (RDF) around the (a) oxygen atom of CO 2 molecule O CO 2 and (b) carbon atom of CO 2 molecule C CO 2 . Intermolecular distances are measured during the time of existence of CO 2 as a molecular species. Insets: coordination number n(r) obtained from the integration of the radial distribution functions. The same color code applies for figures (a) and (b).

Figure 4 :

 4 Figure 4: Solvation structure around the CO 2 molecule. Two dimensional colour charts representing the probability of the presence of the following atoms around CO 2 : C carb atom (a); O carb atom (b): Li atom (c) and K atom (d). CO 2 is oriented with its O CO 2 -O CO 2 axis along the ζ direction, where ζ = 0 is the mid-point of the O-O distance. ζ is thus the projection of an atom position along the O CO 2 -O CO 2 axis, and ρ its distance from the O CO 2 -O CO 2 axis.

Figure 5 :

 5 Figure 5: Distribution of O-C-O * -C dihedral angle of pyrocarbonate C 2 O 2- 5 solvated in the eutectic LiKCO 3 at 1000 K and isolated. For the solvated molecule, the dihedral angle is measured during the time intervals of existence of C 2 O 2- 5 .

5

  can compete with CO 2- 3 to interact with the lithium cation, leading to that stronger solvation than between CO 2 and Li. The slight anisotropy of solvation of Li + around C 2 O 2- 5 is another signature of stronger solvation of Li + with the former CO 2- 3 than to the former CO 2 . It indicates that the solvation structure around C 2 O 2- 5 may not reach a fully equilibrated configuration (which would have been symmetrical) during the short lifetime of existence of C 2 O 2- 5 . The potassium plays a role in the solvation of both CO 2 and C 2 O 2- 5 , but it displays a more disordered structure around C 2 O 2-

Figure 6 :

 6 Figure 6: Solvation structure around the pyrocarbonate anion C 2 O 2- 5 . Upper panel: radial distribution function (RDF) for (a) carbon atom (b) external oxygen atoms and (c) internal oxygen atom of C 2 O 2- 5 . Insets: coordination number n(r) obtained from the integration of the radial distribution functions. The same color code applies for figures (a), (b) and (c). Lower panel: two dimensional colour charts representing the probability of the presence of the following atoms around C 2 O 2- 5 : Li atom (d) and K atom (e). C 2 O 2-

Figure 7 :

 7 Figure 7: (a) Distribution of O-C-C-O dihedral angle of oxalate C 2 O 2- 4 solvated in the eutectic LiKCO3 at 1000K and isolated. (b) Snapshot of C 2 O 2- 4 in the eutectic LiKCO 3 . Carbonate molecules in the solvent are represented by cyan/red sticks, O atoms by red spheres, K atoms in blue and Li atoms in orange.

Fig. 7 (

 7 Fig.7(a) shows the distribution of the dihedral angle OCCO for both the solvated molecule and the isolated one. The maxima of distribution are situated at ±100 • , indicating the oxalate is preferentially twisted (as illustrated in Fig.7(b)). Similarly to what was observed for pyrocarbonate, the distribution of dihedral angles is widely spread, the minimum is found at 0 • , with a probability only half of the maximal value. Like the pyrocarbonate ion, the oxalate anion is flexible and alternates twisted and planar structures when solvated in molten carbonate.

4 and C 2

 42 O 2- 5 relates to the lithium solvation structure which displays a slight asymmetry around C 2 O 2- 5 but a perfect symmetry around C 2 O 2- 4 . As discussed in section 3.2.2, this asymmetry originates from the reacting species forming C 2 O 2-

Figure 8 :

 8 Figure 8: Solvation structure around the oxalate C 2 O 2- 4 anion. Upper panel: radial distribution function (RDF) for (a) carbon atom of C 2 O 2- 4 and (b) oxygen atom of C 2 O 2- 4 . Insets: coordination number n(r) obtained from the integration of the radial distribution functions. The same color code applies for figures (a) and (b). Lower panel: two dimensional colour charts representing the probability of the presence of the following atoms around C 2 O 2- 4 : Li atom (c) and K atom (d). C 2 O 2-

Figure 9 :

 9 Figure 9: Solvation structure around the carbon monoxide CO. Upper panel: radial distribution function (RDF) for (a) carbon atom of CO and (b) oxygen atom of CO. Insets: coordination number n(r) obtained from the integration of the radial distribution functions. The same color code applies for figures (a) and (b). Lower panel: two dimensional colour charts representing the probability of the presence of the following atoms around CO: Li atom (c) and K atom (d). CO is oriented with its O CO -C CO axis along the ζ direction, where ζ = 0 is the mid-point of the O CO -C CO distance and O CO is always placed in the negative ζ portion of the plots.

1 6 dMSD

 16 I (τ ) dτ , with MSD I (τ ) = |R I (τ ) -R I (0)| 2 and where R I (t) is the center-of-mass of molecule I at time t and the bracket represents an average over time. We applied this MSD definition for C 2 O 2-

Figure 10 :

 10 Figure 10: (a) Radial distribution function (RDF) for oxygen anion O 2-. Insets: coordination number n(r) obtained from the integration of the radial distribution functions. (b) Distribution of the joint probability of presence of lithium and potassium cations within the first solvation shell of (defined with distance O-Li < 3.1 Å and distance O-K < 3.6 Å). (c) Cumulative residence time τres distribution of lithium and potassium cations and exponential fit for the long-tail of these distributions (dashed lines). (d) Distribution of Li-O-Li angle for lithium cations within the first solvation shell of O 2-. The distribution is normalized by dividing by sin θ.

Figure 11 :

 11 Figure 11: Dynamical properties of the solvated species. (a) Mean-square displacement (MSD) along time. The MSD are fitted to a linear function (dashed lines) to calculate the diffusion coefficient, see Table 2. The MSD for CO 2 molecule is calculated between times where the CO 2 molecule is present. (b) Reorientation time-correlation functions C 2 (t) (eq. 8). The C 2 (t) function are fitted to an exponential decay function to determine the reorientation time, see Table2.

  Figure 11: Dynamical properties of the solvated species. (a) Mean-square displacement (MSD) along time. The MSD are fitted to a linear function (dashed lines) to calculate the diffusion coefficient, see Table 2. The MSD for CO 2 molecule is calculated between times where the CO 2 molecule is present. (b) Reorientation time-correlation functions C 2 (t) (eq. 8). The C 2 (t) function are fitted to an exponential decay function to determine the reorientation time, see Table2.

  In both LiKCO 3 and CaCO 3 , these large OCO distributions indicate that the CO 2 molecules can bend up to 120 • , facilitating the formation of the pyrocarbonate. The larger distribution in LiKCO 3 implies the CO 2 bending is more likely in this molten carbonate rather than in CaCO 3 , but the difference of temperature between the two systems (1000 K in LiKCO 3 and 1773 K in CaCO 3 ) prevents us from discussing further the (small) difference of lifetime of CO 2 (2.3 ps in LiKCO 3 and 0.88 ps in CaCO 3 ).

[START_REF] Cassir | Strategies and new developments in the field of molten carbonates and high-temperature fuel cells in the carbon cycle[END_REF]

. If we had previously noticed a broader distribution of OCO in the case of a CO 2 molecule solvated in CaCO 3 at T = 1773 K compared to the isolated molecule distribution at the same temperature, the OCO distribution in CaCO 3 coincides however with a Gaussian curve, even at small angles ( OCO < 140 • ).

  -5 cm 2 .s -1 ) Reorientation time (ps) first-principles molecular dynamics. Similar to what happens in molten CaCO 3 , we find that the solubilized CO 2 molecule spontaneously reacts with CO 2- 3 to form the transient pyrocarbonate species C 2 O 2- 5

	CO2	1.4	1.4
	C2O 2-5 C2O 2-4	-1.0	2.6 3.4
	CO	3.9	0.1
	O 2-	0.54	-
	CO 2-3 Li +	0.69 2.4	1.3 -
	K +	1.4	-

in the eutectic

is oriented with its Cpyro-Cpyro axis along the ζ direction, where ζ = 0 is the mid-point of the Cpyro-Cpyro distance. ζ is thus the projection of an atom position along the Cpyro-Cpyro axis, and ρ its distance from the Cpyro-Cpyro axis. The C of the former CO 2 molecule is always placed in the negative ζ portion of the plots.

is oriented with its Coxa-Coxa axis along the ζ direction, where ζ = 0 is the mid-point of the Coxa-Coxa distance. ζ is thus the projection of an atom position along the Coxa-Coxa axis, and ρ its distance from the Coxa-Coxa axis.

The authors are grateful to Michel Cassir for discussion on the interesting properties of molten carbonate. We acknowledge funding by PSL Research University (project COOCAR, grant ANR-10-IDEX-0001-02) and from the French Agence Nationale de la Recherche (ANR) under grant ANR-17-CE05-0025 (MCEC) . This work was performed using HPC resources from GENCI (grants A0030802309 and A0050802309).


Yali Wang

Eskander Alhajji

Bernard Rieul

Francis Berthias

Philippe Maitre

Philippe Maître

Infrared isomer-specific fragmentation for the identification of aminobutyric acid isomers separated by differential mobility spectrometry

Keywords: isomer separation, aminobutyric acid, ion mobility spectrometry, differential mobility spectrometry, IRMPD, specific activation Highlights

come

Infrared isomer-specific fragmentation for the identification of aminobutyric acid isomers separated by differential mobility spectrometry

Introduction

Nowadays, the screening of biomarkers allows for an early diagnosis of many diseases, [START_REF] Chen | Differential Mobility Spectrometry-Mass Spectrometry (DMS-MS) in Radiation Biodosimetry: Rapid and High-Throughput Quantitation of Multiple Radiation Biomarkers in Nonhuman Primate Urine[END_REF][START_REF] Chace | Altered metabolism and newborn screening using tandem mass spectrometry: lessons learned from the bench to bedside[END_REF] and can also answer the need for emergency diagnosis. [START_REF] Garganta | Metabolic evaluation of the sick neonate[END_REF] Subtle differences of metabolite abundances in urine or plasma, for example, can be the signature of specific diseases. Small molecules of different classes such as amino acids, acylcarnitines, organic acids are common target molecules of many diseases. [START_REF] Khamis | Mass spectrometric based approaches in urine metabolomics and biomarker discovery[END_REF] The large number of metabolic pathways and corresponding metabolites are at the origin of the analytical challenge.

Metabolomics profiling based on chromatographic separation coupled with tandem mass spectrometry (MS/MS) is considered to be a method of choice for the identification and quantification of metabolites. [START_REF] Khamis | Mass spectrometric based approaches in urine metabolomics and biomarker discovery[END_REF][START_REF] Cui | Challenges and emergent solutions for LC-MS/MS based untargeted metabolomics in diseases[END_REF] Due to the complexity of biological samples, chromatographic separation is routinely used for the separation and identification, but this is not without its drawbacks. Liquid chromatography (LC) requires handling large volumes of solvents most often and difficult to recycle solvents. Diagnosis relies on multiple LC-MS/MS protocols since only a set of molecules with comparable polarities can be isocratically separated under a given set of chromatographic conditions. In addition, while isobar resolution can be achieved with high resolution MS/MS, isomer separation often remains a challenge. [START_REF] Beach | Selective quantitation of the neurotoxin BMAA by use of hydrophilic-interaction liquid chromatography-differential mobility spectrometry-tandem mass spectrometry (HILIC-DMS-MS/MS)[END_REF][START_REF] Ortmayr | Increasing selectivity and coverage in LC-MS based metabolome analysis[END_REF] In this context, ion mobility separation could provide an added value for the separation on its own, or could also be integrated to LC-MS/MS protocols. [START_REF] Chouinard | Improved Sensitivity and Separations for Phosphopeptides using Online Liquid Chromotography Coupled with Structures for Lossless Ion Manipulations Ion Mobility-Mass Spectrometry[END_REF][START_REF] Xu | DMS as an orthogonal separation to LC/ESI/MS/MS for quantifying isomeric cerebrosides in plasma and cerebrospinal fluid[END_REF][START_REF] Fu | Differential Mobility Spectrometry Coupled with Multiple Ion Monitoring in Regulated LC-MS/MS Bioanalysis of a Therapeutic Cyclic Peptide in Human Plasma[END_REF][START_REF] Meng | Differential mobility spectrometry tandem mass spectrometry with multiple ion monitoring for the bioanalysis of liraglutide[END_REF] Additional identification parameters of biomarkers to retention time derived from chromatography and fragmentation mass spectra, which rely on library of standards, would be needed. In this perspective, isomer-selective or even specific fragmentation based upon resonant IR photo-dissociation is particularly interesting. Comparison of gas phase IR spectra with calculated IR absorption spectra allows for structural characterization of the isomeric ions. [START_REF] Macaleese | Infrared spectroscopy of organometallic ions in the gas phase: From model to real world complexes[END_REF] This has been demonstrated for the case of an unknown metabolite where reference compounds are not available. [START_REF] Cismesia | Infrared ion spectroscopy: an analytical tool for the study of metabolites[END_REF][START_REF] Gorlova | Identification and Partial Structural Characterization of Mass Isolated Valsartan and Its Metabolite with Messenger Tagging Vibrational Spectroscopy[END_REF][START_REF] Martens | Molecular identification in metabolomics using infrared ion spectroscopy[END_REF][START_REF] Martens | Combined Liquid Chromatography-Infrared Ion Spectroscopy for Identification of Regioisomeric Drug Metabolites[END_REF] Infrared ion spectroscopy was used to assign the structure of an unknown drug metabolite from a collected chromatographic fraction. [START_REF] Martens | Molecular identification in metabolomics using infrared ion spectroscopy[END_REF][START_REF] Martens | Combined Liquid Chromatography-Infrared Ion Spectroscopy for Identification of Regioisomeric Drug Metabolites[END_REF] Better resolved IR ion spectra can be derived when ions are cryogenically cooled, as demonstrated by the structural characterization of metabolites of the Varsatan drug. [START_REF] Gorlova | Identification and Partial Structural Characterization of Mass Isolated Valsartan and Its Metabolite with Messenger Tagging Vibrational Spectroscopy[END_REF] These recent studies clearly show the promised of IR ion spectroscopy to differentiate isobaric and isomeric variants.

Ion mobility spectrometry (IMS) method could be an alternative and/or a complement to chromatography for the separation step of metabolites. [START_REF] D'atri | Adding a new separation dimension to MS and LC-MS: What is the utility of ion mobility spectrometry?[END_REF][START_REF] Lapthorn | Ion mobility spectrometry-mass spectrometry (IMS-MS) of small molecules: Separating and assigning structures to ions[END_REF] An additional advantage of IMS is that it could provide an additional identification parameter to LC and MS/MS. [START_REF] Barran | Mobilising ion mobility mass spectrometry for metabolomics[END_REF] In a recent identification study of pesticides in standard solutions and in the presence of different matrices, [START_REF] Regueiro | Targeted approach for qualitative screening of pesticides in salmon feed by liquid chromatography coupled to traveling-wave ion mobility/quadrupole time-of-flight mass spectrometry[END_REF][START_REF] Goscinny | Travelling-wave ion mobility time-offlight mass spectrometry as an alternative strategy for screening of multi-class pesticides in fruits and vegetables[END_REF] it had been shown that IMS drift time or better collision cross section (CCS) could be used as identification parameter of ions. Both dispersive and selective, relying on time and space separation, respectively, can be used in an IMS-MS/MS workflow or integrated in an LC-MS/MS workflow. Selective differential mobility spectrometry (DMS) is recognized as being more orthogonal than dispersive drift-tube IMS to MS, which is an important aspect for improving the resolving power of the analytical method. [START_REF] D'atri | Adding a new separation dimension to MS and LC-MS: What is the utility of ion mobility spectrometry?[END_REF] DMS has been successfully used for resolving various sets of molecules featuring isomers in pure solution or in uncomplicated matrices. [START_REF] Campbell | Differential mobility spectrometry: a valuable technology for analyzing challenging biological samples[END_REF][START_REF] Schneider | Differential Mobility Spectrometry/Mass Spectrometry History, Theory, Design Optimization, Simulations, and Applications[END_REF][START_REF] Porta | Gas-Phase Separation of Drugs and Metabolites Using Modifier-Assisted Differential Ion Mobility Spectrometry Hyphenated to Liquid Extraction Surface Analysis and Mass Spectrometry[END_REF][START_REF] Varesio | Real-time 2D separation by LC x differential ion mobility hyphenated to mass spectrometry[END_REF] It has also been shown to be effective in particular in cleaning the baseline and rising up the signal-to-noise ratio in complex matrices to improve the detection and quantification of analytes of interest. [START_REF] Fu | Differential Mobility Spectrometry Coupled with Multiple Ion Monitoring in Regulated LC-MS/MS Bioanalysis of a Therapeutic Cyclic Peptide in Human Plasma[END_REF][START_REF] Winter | Differential Ion Mobility-Mass Spectrometry for Detailed Analysis of the Proteome[END_REF] In this paper, two DMS-MS/MS(IR) workflows combining three orthogonal techniques are presented for the separation, identification, and structural characterization of isomers of aminobutyric acid (ABA). Separation of ABA isomers is an important issue for their quantification. [START_REF] Vemula | Gaussian and linear deconvolution of LC-MS/MS chromatograms of the eight aminobutyric acid isomers[END_REF] For instance, -aminobutyric acid (GABA) is known for being an inhibitor of neurotransmission in the nervous system of animals, 28 whereas β-aminobutyric acid (BABA) can act as a partial agonist of the glycine receptor. [START_REF] Ton | beta-amino-butyric acid-induced resistance against necrotrophic pathogens is based on ABA-dependent priming for callose[END_REF] -aminobutyric acid (AABA) has been investigated as biomarker for liver toxicity and alcohol abuse. [START_REF] Dello | Systematic review of ophthalmate as a novel biomarker of hepatic glutathione depletion[END_REF] In a recent study, LC-MS/MS performance for the separation of these derivatized species (with Marfrey's reagent) has been evaluated. [START_REF] Vemula | Gaussian and linear deconvolution of LC-MS/MS chromatograms of the eight aminobutyric acid isomers[END_REF] In the present study, a chromatography free DMS-MS/MS(IR) approach is used. This is the first application of the coupling of DMS and isomer-selective infrared induced fragmentation with high resolution MS/MS Fourier transform ion cyclotron resonance (FT-ICR). DMS-and mass-selected ions are subjected to infrared (IR) irradiation of the CLIO Free Electron Laser [START_REF] Prazeres | Two-colour operation of a Free-Electron Laser and applications in the mid-infrared[END_REF] allowing for infrared multiple photo-dissociation (IRMPD). Isomer-selective fragmentation of each isomer at a selected wavelength allows for the structural characterization. This is exploited for the identification of modifier-assisted DMS peaks in a workflow where the IR wavelength is fixed and while the DMS parameter is scanned (DMS(scan)-MS/MS(IR fixed)). Alternatively, structural characterization of the DMS peaks can be achieved through the comparison of IRMPD spectra of DMS-and mass-selected ions with IR absorption spectra predicted by density functional theory.

Methods

Sample preparation

The solutions of AABA, BABA, and GABA isomers were prepared by diluting from high concentration of 10 -2 to 10 -4 M using methanol/water (50/50, v/v) and 5% acetic acid. Similarly, the mixture solution of three isomers was formulated at the final concentration of 10 -4 M for each of them. Protonated ABA ([C 4 H 10 NO 2 ] + , m/z 104.071) were generated by electrospray ionization (ESI). The sample was pumped into the ESI emitter at a flow rate of 70 μL.h -1 by a syringe pump.

Mass spectrometry instrumentation

All the experiments were performed on a 7 Tesla APEX-Qe (Bruker Daltonics), a hybrid Fourier transform ion cyclotron resonance (FT-ICR) tandem mass spectrometer (MS/MS). Infrared Multiple Photon Dissociation (IRMPD) experiments were carry out using the IR beam delivered by the CLIO infrared free electron laser (IR FEL). [START_REF] Prazeres | Two-colour operation of a Free-Electron Laser and applications in the mid-infrared[END_REF] The coupling of the IR FEL with the FT-ICR has already been described in details elsewhere. [START_REF] Bakker | Gas-phase structure of a -allylpalladium complex: Efficient infrared Spectroscopy in a 7 T Fourier transform mass spectrometer[END_REF] The FT-ICR was equipped with an Apollo II ESI ion source, on which a homebuilt differential mobility spectrometry (DMS) device has been mounted. The conception of this DMS device is based on the one developed by G.L. Glish, [START_REF] Isenberg | Optimization of peptide separations by differential ion mobility spectrometry[END_REF] which was designed for the coupling with the ESI source of a quadrupole ion trap ESQUIRE 3000+ (Bruker Daltonics). The coupling of such DMS device and IRMPD activation with our quadrupole ion-trap has already been described. [START_REF] Berthias | Resolution and Assignment of Differential Ion Mobility Spectra of Sarcosine and Isomers[END_REF][START_REF] Hernandez | Probing Mobility-Selected Saccharide Isomers: Selective Ion-Molecule Reactions and Wavelength-Specific IR Activation[END_REF] The DMS cell is integrated between the ESI emitter and the capillary transfer. Positive ions are generated by setting the ESI emitter at 4 kV, and the DMS housing to the ground.

Electrosprayed ions are transported at atmospheric pressure by a carrier gas stream (N 2 ) between two parallel electrodes (dimensions 0.7 × 6 × 20 mm for gap height, width and length, respectively) towards the glass capillary transfer. The carrier gas flow is a part of the N 2 desolvation gas, originally implemented on the mass spectrometer, partially redirected through the electrodes gap due to the pressure difference between the ESI source and the mass spectrometer vacuum. The temperature and flow rate of the desolvation gas are set using the Bruker control software at 150 °C and 6 L.min -1 , respectively. A custom built ESI chamber allows for a better control of the composition of the carrier gas flow. This ESI chamber allows for the adjustment of the position of the electrospray emitter next to the two DMS electrodes.

Upstream the ESI-DMS part, polar modifier molecules can be introduced in the desolvation gas using a NanoHPLC (LC-20AD nano, Shimadzu). A liquid flow rate of methanol set at 1.5 µL.min -1 was used. The gas line is also heated at ~80-100 °C to ensure homogeneous distribution of the small liquid amount in the N 2 gas before reaching the ion source. The molar percentage of the methanol vapor in the N 2 carrier gas was on the order of ~0.01%.

Considering the gap between the electrodes (0.7 mm), and assuming that the carrier gas is near atmospheric pressure and a temperature around 70°C (measured temperature of the electrodes using a thermal camera), the reduced electric field value corresponding to a voltage of 1800 V can be estimated to ~120 Td. In the following, the DMS spectra correspond to Alternatively, when the DMS is used in scanning mode (fixed 𝜈 ̃, scanned CV), identification can also be achieved based on specific depletion of DMS peaks at selected IR wavelength.

Quantum chemical calculations

IRMPD spectra were compared to calculated IR absorption to provide a guide for selecting IR signature of each isomer to be used for selective fragmentation of specific isomers. Hybrid density function calculations were carried out with the Gaussian package of programs [START_REF] Berthias | Resolution and Assignment of Differential Ion Mobility Spectra of Sarcosine and Isomers[END_REF] at the B3LYP/6-311+G** level of theory. A manual search using different starting guess structures featuring a hydrogen bonding motif were optimized using the gradient minimization algorithm of Gaussian and the B3LYP/6-311+G** level. Vibrational frequency values were determined within the harmonic approximation, and the corresponding values were scaled by 0.98.

Result and discussion

DMS peak capacity and resolution can be significantly improved by introducing dopant molecules, also called modifier gas, into the N 2 carrier gas. [START_REF] Eiceman | Separation of ions from explosives in differential mobility spectrometry by vapor-modified drift gas[END_REF][START_REF] Krylova | Effect of moisture on the field dependence of mobility for gas-phase ions of organophosphorus compounds at atmospheric pressure with field asymmetric ion mobility spectrometry[END_REF] The term modifier-assisted DMS-MS/MS method for detection and quantification of metabolites in complex samples has been coined recently. [START_REF] Chen | Modifierassisted differential mobility-tandem mass spectrometry method for detection and quantification of amphetamine-type stimulants in urine[END_REF] By seeding polar molecules in the carrier gas, differential mobility between low and high electric field change. During each cycle of the waveform applied to the DMS electrodes, clustering and declustering phenomena is assumed to occur at low and high electric field, respectively. The drawback of this modifier-assisted DMS-MS/MS method is that the peak ordering is difficult to predict, although some recent correlation between DMS peak shifts and ion-molecule binding energy [START_REF] Liu | Using differential mobility spectrometry to measure ion solvation: an examination of the roles of solvents and ionic structures in separating quinoline-based drugs[END_REF] have been proposed. Identification of the modifierassisted DMS-MS/MS peaks through MS/MS is thus important.

Separation of protonated ABA isomers with modifier-assisted DMS is investigated with methanol. The DMS spectra of an equimolar mixture of protonated AABA, BABA and GABA isomers is shown on Figure 1 with only N 2 desolvation gas flow (Figure 1a) and with methanol when injected at 1.5 L.min -1 (Figure 1b). Fig 1a displays two peaks, one centered at -7.0 V, and another, broader, centered at -5.5 V. By adding methanol in the N 2 flow, the DMS spectrum exhibits three baseline separated peaks shifted towards more negative CV values and centered at -24.6, -20 and -16.9 V. This allows in particular for the resolution of the broadband observed near -5.5 V in the absence of modifier. Identification of the DMS peaks is presented in the following using IR isomer-specific fragmentation. The three peaks observed using methanol can be assigned by recording the IRMPD spectrum of the DMS-and mass-selected m/z 104 ions. Then, a second operation mode of the DMS-MS/MS(IRMPD) is for the identification of the peaks when no modifier is added to the carrier case. In this case, a special emphasis is made on the resolution of the broadband (Figure 1a).

Isomer-specific IR-activation is used for the identification of the three DMS peaks in Figure 1b.

For this purpose, DMS-MS 2 (IRMPD) experiments are performed with the DMS device used in a selective mode, i.e. at a fixed CV value. The IRMPD spectrum of the DMS-and massselected m/z 104 ions is thus recorded at three fixed CV values (-24.6, -20 and -16.9 V) corresponding to the maximum transmission of protonated ABA isomers with using methanol as modifier. Identification of each DMS peak can then be done by comparing experimental IRMPD spectra with calculated IR absorption spectra of the three protonated isomers (Figure 2). For this purpose, quantum chemical calculations were performed. The lowest energy optimized structure of the three isomers are given in Figure 2. For the three isomers, the lowest structure has a hydrogen bond (HB) between the ammonium and the carboxylic C=O group. This type of intramolecular HB allows for charge solvation and is observed for protonated aminoacids, [START_REF] Berthias | Resolution and Assignment of Differential Ion Mobility Spectra of Sarcosine and Isomers[END_REF] for example. In the present case, the HB gives rise to the formation of a five-, six-, and seven-membered ring for protonated AABA, BABA, and GABA, respectively. As expected, the (ammonium)H … (carbonyl)O distance varies from one isomer to another: 1.95, 1.77, and 1.71 Å for AABA, BABA, and GABA, respectively. The carbonyl C=O bond distance is also sensitive to the HB distance. One can thus expect the vibrational modes associated with the carbonyl C=O and the ammonium to be different from one isomer to the other.

IRMPD of the DMS-and mass-selected ions are shown in Figure 2. The C=O stretching region is the most structurally diagnostic region, and only this region is shown in this Figure . The experimental IRMPD spectra of the individual standards were also recorded for comparison and presented in Figure S1, along with the calculated IR absorption spectra. Identification of the three DMS peaks and structural identification of the isomeric forms can be done based on the relative position of the C=O stretching band. The corresponding IRMPD band observed when the CV value is fixed at -24.6, -20 and -16.9 V are centered at 1775, 1730, and 1710 cm - 1 , respectively. This trend nicely reflects the one predicted for the protonated AABA, BABA, and GABA for which the C=O stretching band predicted at 1769, 1722, and 1703 cm -1 .

Identification of the DMS peaks using a methanol flow rate (Figure 1b) can be made based on the MS/MS(CID) spectra of the DMS-selected ions, i.e. using an approach similar to the socalled Single Reaction Monitoring (SRM) employed in LC-MS/MS protocols. Indeed, each ion has a specific fragment at m/z 44.05, 58.07, and 87.05 for protonated AABA, BABA, and GABA respectively. In addition, peak identification can also be made based on the DMS spectra of the individual standards (Figure S2). These results support the assignments made based on the IRMPD spectra of the DMS-and mass-selected m/z 104 isomers (Figure 2).

The lower energy part of the IR spectra seems to be less diagnostic (Figure S1), although some subtle differences can be observed. In the 1350-1550 cm -1 range, a broadband is observed for the three protonated isomers. These bands correspond to C-H and N-H bending modes, and in particular the ammonium umbrella mode. As can be seen in Table 1, the latter mode is sensitive to the nature of the isomer. Finally, the third cluster band is observed between 1050 and 1250 cm -1 . As can be seen in Table 1, this band can be assigned to the C-O stretching and C-O-H bending modes. It can thus be concluded that the C=O stretching range is the most structurally diagnostic region. In particular, the protonated AABA and GABA isomers are likely to be selectively fragmented if the IR laser is tuned to 1780 and 1690 cm -1 , respectively (vide infra).

In the following, we will turn our attention to the assignment of the DMS peaks obtained in the absence of modifier gas (Figure 1a) using the DMS in scanning mode by recording DMS-MS 2 (IRMPD) at a selected wavelength. DMS-MS 2 (IRMPD) spectra recorded at four selected IR FEL wavenumbers are given in Figure 3 along with the DMS-MS spectrum, i.e.

without IR activation. In the left part of the figure, the intensity of the m/z 104 parent is given as a function of the CV. In the right-hand part of the figure, the abundances of the fragments ions, i.e. m/z 44, 58, 86, and 87 are given.

Based on the IR spectra of the protonated isomers previously shown, the C=O stretching region appears to be highly diagnostic. The corresponding IRMPD band is found to be the least red-shifted in the case of protonated AABA, with a maximum near 1780 cm -1 . The DMS-MS 2 (IRMPD@1780 cm -1 ) spectra are given in Fig. 3e. As can be seen in the right-hand part, only the m/z 58 fragment is obaserved, and the Gaussian fit is centered at -7.0 V, which is a clear signature of the specific fragmentation of the protonated AABA isomer. A depletion of the m/z 104 parent ion is also observed at -7.0 V (Fig. 3e, left).

Specific depletion of the protonated GABA isomer can be observed when the laser wavenumber is fixed at 1690 cm -1 . The corresponding DMS-MS 2 (IRMPD@1690 cm -1 ) spectra are given in Figure 3c. Both the m/z 86 and 87 fragment ions were observed, and the two Gaussian fits are centred at -5.6 V (Figure 3c, right). Inspection of the DMS spectrum in the m/z 104 parent channel reveals that the Gaussian fit of the broad band reveals a depletion of the component centered at -5.5 V. By tuning the laser wavenumber in the C=O stretching region, selective fragmentation of the BABA isomer could not be observed. As illustrated in Figure 3d with the DMS-MS 2 (IRMPD@1730 cm -1 ) spectra, simultaneous fragmentation of both protonated BABA and GABA isomers was observed at wavenumber values between 1690 and 1780 cm -1 . Specific depletion of the protonated BABA isomer could however be obtained at 1372 cm -1 (Figure 3b). At this laser wavenumber, the fit of the broadband centered near -5.5 V reveals a depletion of the BABA contribution, which is consistent with the Gaussian fit of the m/z 44 and 86 fragments (Figure 3b, right).

Overall, DMS-MS 2 (IRMPD) at three selected laser wavenumbers allows for the identification of the three isomers, and in particular for the resolution of two overlapping components. These results are consistent with those which can be drawn from the comparison of the DMS spectrum of the equimolecular mixture with those of the individual standard DMS spectra given in Figure S3. The broad peak in Figure 1a results from the overlap of two contributions centered at -5.6 and -5.5 V associated with protonated BABA and GABA isomer, respectively. The -7.0 V peak can be assigned to the protonated AABA isomer. The width of the DMS peaks is ~0.80

V for the individual standards.

Conclusion

Wavelength-selective IR activation is integrated in two workflows for the separation and identification of isomers of small molecules such as metabolites using tandem mass spectrometry. Separation is performed using a homebuilt DMS device which has been specifically designed for the coupling with our high resolution FT-ICR MS/MS. Performance of the two workflows is illustrated on the separation of aminobutyric acid isomers.

Our objectives here range from fundamental understanding of the DMS separation process to developing complementary methodology for improving the identification of isomeric species in the context of targeted metabolomics analyses. From a fundamental point of view, IRMPD spectroscopy is a particularly interesting tool since it does not only offer identification but also structural information on DMS-selected ions. This is particularly useful since the ordering of DMS peaks is not easily a priori predictable, especially when modifier gases are seeded in the carrier gas. The first IRMPD spectra of modifier-assisted DMS separated isomers have been recorded. They match well with the IR absorption spectra predicted by DFT. In particular, a clear trend is observed in the C=O stretching region, which is consistent with isomer-specific hydrogen bonding motifs predicted for the lowest energy isomers.

A second operation mode of the DMS-MS/MS(IRMPD) instrument consists selective or even specific depletion of DMS peaks. At each step of the DMS scan, DMS-and mass-selected ions are irradiated by the IR beam at a selected wavelength. This second workflow would be particularly well suited for a rapid screening of target compounds within complex mixture, as in targeted metabolomics. Indeed, with the CV parameter set for the optimal transmission of a targeted ion to the ion trap, high ion count can be obtained allowing for subsequent infrared interogation.

  extracted ion chromatogram plotted as a function of the CV value, where a 1 V value correspond to ~0.7 Td. A LabView program (v12.0.1f5, National Instrument) has been developed in order to control the radiofrequency field and the data acquisition, which is synchronized with the Bruker acquisition software under chromatogram mode. Space separation of ions through the DMS device is obtained by applying a high frequency bisinusoidal waveform, alternating phase of high and low electric field, on the DMS electrodes. The dispersion voltage (DV), which corresponds to the maximum amplitude of the radiofrequency waveform, can be adjusted in the 0-2 kV range and has been set at 1.8 kV in this study. The maximum electric field between the two DMS electrodes is thus on the order of ~2.6 10 6 V.m -1 . Selection of the ions to be transmitted based on their differential ion mobility is made by applying a DC offset called compensation voltage (CV) to one electrode. DMS-selected ions can be mass-selected in a quadrupole, and accumulated in a hexapole ion trap. Typical accumulation time is 500 ms. DMS-and mass-selected ions are then pulseextracted toward the ICR cell, where they are irradiated by IR light for a fixed time period. The energy of the IR FEL electron accelerator was set to 42 MeV. A fairly stable power was maintained in the 900-1900 cm -1 wavenumber (𝜈 ̃) range. Typical irradiation time for these experiments was 250-500 ms. DMS spectra are recorded by scanning the CV value by steps of 0.1 V. The DMS spectrum is derived from the ion chromatogram. The centroid of each peak and its full width at half maximum (FWHM) are obtained from Gaussian fits of the experimental DMS spectra. Uncertainties on the CV and FWHM values, estimated with the standard deviation over several experiments, are on the order of magnitude of the bin width of the DMS spectra, i.e. 0.1 V. Two operation modes of the DMS-MS/MS(IRMPD) experiment are possible, a selective and scanning mode. DMS selective mode (fixed CV, scanned 𝜈 ̃) allows for structural identification of DMS-and mass-selected ions based on the comparison of IRMPD spectra with IR absorption spectra of candidate structures derived from quantum chemical calculations.

Figure 1 :

 1 Figure 1: DMS spectra of an equimolecular mixture of AABA, BABA, and GABA. All spectra were recorded with a dispersion voltage value of 1.8 kV. The DMS spectrum recorded in the absence of modifier is shown in panel a). Modifier-assisted DMS spectrum recorded with a methanol at a 1.5 L.min -1 flow rate and DV=1.8 kV is given in panel b).

Figure 2 :

 2 Figure 2: IR spectra of DMS-and mass-selected m/z 104 ions separated by modifier-assisted DMS (methanol at a 1.5 L.min -1 flow rate). IRMPD spectra corresponding to CV= -24.6, -20.0, and -16.9 V are shown in panels a), b), and c), respectively. All the extracted ion chromatograms are normalized to the maximum. The spectra are given in black as stick bars. Optimized structures of protonated AABA, BABA, and GABA. Selected bond lengths are given in Angstrom unit.

Figure 3 :

 3 Figure 3: DMS-MS 2 (IRMPD) spectra of an equimolecular mixture of AABA, BABA, and GABA. In each panel (a-e), in addition to the extracted ion chromatograms (EIC) of the parent m/z 104 ion (left), the EICs of the four fragments are shown on the right. Specific fragments of protonated AABA, BABA, and GABA are shown in red (m/z 58.07), green (m/z 44.05), and blue (m/z 87.05). All data were fitted with a single Gaussian, except for the EIC corresponding to the m/z 86.06 for which a two Gaussian fit was used.

Table 1 :

 1 Experimental and calculated vibrational frequencies for protonated AABA, BABA, and GABA.Vibrational frequencies are given in units of cm -1 . Calculated intensities units of km.mol -1 ) are given

	in parentheses.
			AABA	BABA	GABA
	description	exp	theory	exp	theory	exp	Theory
	C-O st.	1130-	1166 (124)		1099 (97)	1177 1176 (213)
	C-O-H	1195	1174 (87)	1177 1182 (155)
	bend
	CH bend	1385-	1393 (109) 1380-	1412 (186) 1400-	1419 (99)
	-NH 3 + umb	1480	1447 (169)	1495	1462 (181)	1545	1464 (118)
	C=O st.	1780 1769 (279) 1740 1722 (273) 1725 1703 (353)

Acknowledgments

This work is supported by a public grant from the "Laboratoire d'Excellence Physics Atom Light Mater" (LabEx PALM) overseen by the French National Research Agency (ANR) as part of the "Investissements d'Avenir" program (ANR-10-LABX-0039). Financial support from the European Community's Horizon 2020 Programme (CALIPSOplus and EU_FT-ICR_MS, undergrant number 730872 and 731077, respectively) is gratefully acknowledged. YW would also like to acknowledge the China Scholarship Council (CSC) program for a full scholarship. EA is for the support of the "Programme national d'aide à l'Accueil en Urgence des Scientifiques en Exil" (PAUSE) the Collège de France.