Mingyue Jiang

Wenjie Zhang

Xu Yang

Fen Xiu

Haoran Xu

Xixiang Ying
email: yingxixiang@163.com

Didier Stien
email: didier.stien@cnrs.fr

Prof Ying Xixiang

Prof Didier Stien

An isoindole alkaloid from Portulaca oleracea L

Keywords: Portulaca oleracea L., alkaloid, NO

A novel isoindole alkaloid named oleraisoindole (1), together with six known compounds, 7'-ethoxy-trans-feruloyltyramine (2), N-trans-feruloyltyramine (3), Ntrans-feruloyl-3-methoxytyramine (4), N-trans-p-coumaroyltyramine (5) aurantiamide (6) and ferulic acid methyl ester (7) were isolated from Portulaca oleracea L.. Compounds 2 and 7 were isolated for the first time from this plant.

Compounds 1 was identified using spectroscopic methods including HR-ESI-TOF-MS, 1D-NMR, 2D-NMR. It was tested in a nitric oxide (NO) inhibition assay and was shown to inhibit NO production in RAW 264.7 cells induced by LPS.

Introduction

Portulaca oleracea L., as a well-known traditional Chinese medicine was recorded in the Chinese Pharmacopoeia (The Pharmacopoeia Commission of PRC. 2015), presents many biological and pharmacological activities such as anticancer [START_REF] Zhao | Antitumor activity of Portulaca oleracea L. polysaccharides against cervical carcinoma in vitro and in vivo[END_REF], anti-inflammatory and anti-oxidation [START_REF] Yang | Protective effects of ethanol extract from Portulaca oleracea L. on dextran sulphate sodium-induced mice ulcerative colitis involving antiinflammatory and antioxidant[END_REF], anti-diabetic (Liang, et al. 2014) and lowering blood lipids [START_REF] Zidan | Portulaca oleracea reduces triglyceridemia, cholesterolemia, and improves lecithin: cholesterol acyltransferase activity in rats fed enriched-cholesterol diet[END_REF]. Thus, many scholars paid more attention on the constituents of P. oleracea such as alkaloids [START_REF] Jiao | Indoline amide glucosides from Portulaca oleracea: isolation, structure, and DPPH radical scavenging activity[END_REF][START_REF] Xiang | Alkaloids from Portulaca oleracea L[END_REF], flavonoids [START_REF] Xu | Determination of flavonoids in Portulaca oleracea L. by capillary electrophoresis with electrochemical detection[END_REF], terpenes [START_REF] Elkhayat | Portulene, a new diterpene from Portulaca oleracea L[END_REF], polysaccharides [START_REF] Zhao | Effects of Portulaca oleracea L. polysaccharides on phenotypic and functional maturation of murine bone marrow derived dendritic cells[END_REF], and so on. Recently, many alkaloids were isolated from P. oleracea, and some were found to have a very good anti-inflammatory effect and other bioactivities (Li, et al. 2016, Li, et al. 2017, Li, et al. 2017, Meng, et al. 2016, Xu, et al. 2016).

As the alkaloids isolated from this plant presented higher activities than the other compounds, we embarked upon finding more alkaloids in P. oleracea. A novel isoindole alkaloid, named oleraisoindole (1) and six known compounds, including 7'ethoxy-trans-feruloyltyramine (2) [START_REF] Maciel | New alcamide and anti-oxidant activity of Pilosocereus gounellei A[END_REF], N-trans-feruloyltyramine (3) [START_REF] Tian | Two new alkaloids from Portulaca oleracea and their cytotoxic activities[END_REF], N-trans-feruloyl-3-methoxytyramine (4) [START_REF] Kokubun | Amides and an alkaloid from Portulaca oleracea[END_REF], N-trans-p-coumaroytyramine (5) [START_REF] Kokubun | Amides and an alkaloid from Portulaca oleracea[END_REF], aurantiamide (6) [START_REF] Xu | Chemical constituents from Viola yedoensis[END_REF], ferulic acid methyl ester (7) [START_REF] Chen | Antioxidant consitituents from Smilax riparia[END_REF] were finally isolated from the water extract from P. oleracea. The structure of compound 1 was determined by HR-ESI-TOF-MS, 1D-NMR, 2D-NMR and other compounds were identified by comparison with literature data (Figure 1). In addition, we also investigated the potential of compound 1 to inhibit the NO production in LPS-stimulated RAW 264.7 cells.

Results and discussion

Compound 1 was a pale yellow powder, which showed a blue fluorescence spot at UV 365 nm, a black spot at UV 254 nm and remained orange when exposed to Dragendorff reagent on a TLC plate. UV (MeOH) λmax: 284 nm (Figure S3). IR (KBr) νmax: 3425,1753,1700,1515,1390,1271, 1216 cm -1 (Figure S4). Its molecular formula C28H23NO8 with 18 degrees of unsaturation was deduced from the 1 H-NMR, 13 C-NMR spectrum data (Table S1) and the HR-ESI --TOF-MS deprotonated molecular ionat m/z 500.1374 (calcd. 500.1351), along with the [M-H2O+H] + ion at m/z 484.1397 in HR-ESI + -TOF-MS (calcd. 484.1391) (Figure S5(a)(b)). At first sight, this compound appeared as a mixture of two very closely related molecules because some signals are doubled both in 1 H and in 13 C NMR spectra (Table S1-S2). We pursued with the structural determination considering each doubled peaks as one signal hoping that the structure would eventually enlighten us on the origin of the doubled signals.

The examination of NMR data allowed to point out two phenyl rings. The HMBC spectrum showed the correlations from H-2', to C-4, C-4', C-6'; from H-5' to C-1', C-3', C-4', C-6'; from H-6' to C-4, C-1', C-4', C-5', together with the 1 H-1 H COSY correlations from H-5' to H-6' suggesting that protons at δ 6.84/6.93, 6.75/6.78, and 6.95 defined a 1,3,4-trisubstituted phenyl moiety, which was linked to carbon C-4 at δ139.6. This phenyl ring bore a methoxy group in C-3' and a hydroxyl in C-4'.The position of the methoxy group could be inferred based on HMBC correlation H-5'/C-3' and was confirmed by the NOE correlation of the methyl with H-2'. The 1 H-1 H COSY spectrum showed the correlation H-2'''/H-6''', H-3'''/H-5''', and in HMBC the equivalent proton H-2'''/ H-6''' correlated to C-2'', C-2'''/C-6''' and C-4'''; H-3'''/H-5''' to C-1''', C-3'''/C-5''', C-4'''. These are typical of a para-disubstituted phenyl ring. A hydroxyl could be placed in 4''' based on C-4''' chemical shift (δ158.2). The H-2'''/C-2'' HMBC correlation indicated that C-2'' was linked to C-1'''. The 1 H and 13 C chemical shifts in position 1'' (δH3.67/3.70 and 3.88, δC46.1/46.2) are typical of a CH2 linked to a nitrogen, while C-2'' bore a hydroxyl (δH4.93, δC71.8/72.0). In HMBC, H-1'' correlated to carbonyl groups C-1 and C-3 at δ170.2 and 169.1/169.3, respectively. In 1 H-NMR, only four signals remained to be attributed. These corresponded to a methyl at δH4.04, δC56.55 and three singlet CH at δH8.17 (H-9), 7.53 (H-8), and 7.15 (H-5), with respective carbons at δC123.30, 110.0, and 112.1. This group also contained nine quaternary carbons. These include C-4 at δ139.6 and carbonyls C-1 and C-3, which are linked to the already established peripheral groups. Protons H-8 and H-9 were not coupled to each other. Nevertheless, they correlated in NOE indicating that they were close to each other but not attached to a single phenyl ring. Also, H-8 correlated to C-9 and H-9 to C-8 in HMBC. Altogether, these indications led to position two peri protons on a naphthalene moiety. In HMBC, H-8 correlated to C-4a, C-6, C-7, and C-9. It was not possible to be sure of the position of the methoxyl and the hydroxyl based on HMBC only. However, strong NOE correlation between the methyl group and H-8 allowed to place the methoxyl substituent in C-7. H-9 correlated to C-8 and C-4a which further confirmed the relative place of H-8 and H-9. H-9 also correlated to C-1 and C-3a. It was therefore possible to link C-1 to C-9a. The C-3-C-3a bond could not be formally detected, but it was reasonable to link these carbons based on chemical shift of quaternary carbon C-3a (δ123.29). Since the last singlet proton H-5 at δ7.15 correlated to both C-6 and C-7, it had to be placed in para-position with respect to H-8. H-5 also correlated to C-8a and C-4. The latter established the position of the tetrasubstituted phenyl ring, which was confirmed by the NOE correlation between H-5 and H-6ʹ. C-9a could be detected neither in 13 C, nor in HMBC. NMR experiments were also conducted in DMSO-d6. In this solvent, the 13 C NMR spectrum was of better quality and the only peak that did not correlate in HMBC was at δ125.20/125.23. This signal was attributed to C-9a. Compound 1 was determined to be the 6-hydroxy-2-( 2 From the MTT assay (Figure S32), compound 1 presented cytotoxicity at the concentration of 100 μM. The concentrations of 1 to 50 μM were therefore selected for the NO assay. Compound 1 significantly inhibited NO production at 20 μM on wards (Figure S33).

Experimental

General Experimental Procedures

NMR spectra were recorded on an AVANCE 500 MHz instrument (Bruker Corporation, Switzerland). UV spectra were detected on a U-3010 spectrophotometer (Hitachi Ltd, Tokyo, Japan). IR spectra were obtained on an IR200 spectrophotometer

Plant materials

The dried plants of P. oleracea were collected in Shijiazhuang, Hebei, China in June 2014 and were identified by Xixiang Ying. A voucher specimen (No. 20140312) was deposited in our laboratory at Liaoning University of Traditional Chinese Medicine.

Extraction and isolation

The dried plants (150 kg) of P. oleracea L. were extracted with 10 fold of hot water twice times, each time for 2 h. The water extract was concentrated and then extracted with 1 fold of ethyl acetate three times. The ethyl acetate extract was concentrated under reduced pressure to obtain crude extract (200 g) and then subjected to chromatography on a silica-gel (200-300 mesh, about 1.5 kg) column (8 × 120 cm)

with ethyl acetate and methanol as the gradient eluent

Biological assays

The RAW 264.7 macrophage cell was incubated in DMEM containing 10% heat inactivated fetal bovine serum and 100 units/ml penicillin and 100 μg/ml streptomycin.

Cells were seeded in 96-well plates at a density of 1 × 10 4 cells per well. Cell viability was performed using MTT assay. The cells were incubated with various concentrations

(1, 10, 20, 50 and 100 μM) of oleraisoindole for 1 h, then 5 mg/ml MTT solution was added after stimulated with LPS (1 μg/mL) for 24 h and incubated for another 4 h at

Conclusion

A novel isoindole alkaloid named oleraisoindole (1) and six known compounds were isolated from P. oleracea. Their structures were determined by spectroscopic analysis techniques and comparison with literature data. The new alkaloid has unique chemical structure and remarkably inhibiting NO production in RAW 264.7 cells induced by LPS.

Disclosure statement

No potential conflict of interest was reported by the authors.

Figure 1 .

 1 Figure 1. Chemical structures of compounds isolated from P. oleracea

  hydroxy-2-(4-hydroxyphenyl)ethyl)-4-(4-hydroxy-3-methoxyphenyl)-7-methoxy-1H-benzo[f]isoindole-1,3(2H)-dione, named oleraisoindole. The optical rotation of 1 was found to be -6 (0.1, MeOH). One center of atropoisomerism (the C-4-C-1ʹ bond) accounts for the duplication of many NMR signals. The relative proportion of the two rotamers as measured on the 3'-OMe proton signals is about 1:1. The structures of six known compounds were identified based on the 1 H and 13 C NMR spectra (Figure S20-31), and comparison with literature data, as 7'-ethoxy-transferuloyltyramine (2), N-trans-feruloyltyramine (3), N-trans-feruloyl-3methoxytyramine (4), N-trans-p-coumaroytyramine (5) aurantiamide (6) and ferulic acid methyl ester (7).

(

  Thermo Electron Corporation, Waltham, MA). MS spectra were measured on an Agilent 6520 quadrupole-time of flight mass spectrometer (Agilent, Waldbronn, Germany). Purification was measured with A Shimadzu Nexera X2 UHPLC LC-30A system (Shimadzu, Kyoto, Japan). Optical rotation was detected on an autopol I antomatic polarmeter (Rudolph Research Analytical, Hackettstown, NJ). Sephadex LH-20 and ODS (40-70 μm mesh, GE Healthcare, Marlborough, MA) were used for Column chromatography (CC). TLC was conducted on silica gel GF254 (Qingdao Marine Chemical Co., Qingdao, China).

  (3:1, 1:1, 1:3, v/v) to obtain 20 fractions (400 mL each). The fractions of 1-2 were combined and repeatedly chromatographed by a 20-40 µm ODS-C18 (100 g) column (3 × 70 cm) with methanol and water as the gradient eluent (40:60, 60:40, 80:20, 100:0, v/v) to obtain 11 fractions (200 mL each). The fractions of 1-2 were separated by a Sephadex LH-20 (100 g) column (2 × 150 cm) with methanol-water (70:30, v/v) as the eluent to obtain 42 fractions (20 mL each). The fractions of 26-30 were purified with UHPLC and eluted with acetonitrile and water (30:70, v/v, 1.0 ml/min), affording oleraisoindole (1) (15 mg, purity > 98% with UHPLC), together with six known compounds, 7'-ethoxytrans-feruloyltyramine (2) (20 mg, purity > 98% with UHPLC), N-transferuloyltyramine (3) (15 mg, purity > 98% with UHPLC), N-trans-feruloyl-3methoxytyramine (4) (10 mg, purity > 98% with UHPLC), N-trans-pcoumaroytyramine (5) (8 mg, purity > 98% with UHPLC), aurantiamide (6) (20 mg, purity > 98% with UHPLC) and ferulic acid methyl ester (7) (30 mg, purity > 98% with UHPLC). Compound 1-6 turned orange when sprayed with Dragendorff reagent on thin-layer chromatography. Oleraisoindole (1): pale yellow powder, [α] 20 D -0.6 (0.1, MeOH

  37C. The formazan was dissolved in 150 μl of DMSO. The absorbance was measured at 570 nm using a Bio-Tek microplate reader, cell viability was expressed as a percentage by comparing with the untreated cells. The production of NO was measured by Griess reaction. An equal volume of Griess reagent (0.1% naphthylethylethylene diamine dihydrochloride in H2O and 1% sulphanilamide in 5% H3PO4) was added to the different concentrations of oleraisoindole cell culture supernatant (100 μl) collected before add MTT solution in MTT assay. The production of NO was detected at 550 nm by a Bio-Tek microplate reader, and was compared with sodium nutrite standard calibration curve.

  C NMR spectral data (in methanol-d4 and DMSO-d6), see TableS1. HR-ESI(+)-

	TOF-/MS m/z 484.1397 [M-H2O+H] + (calcd: C28H22NO7, 484.1391). HR-ESI(-)-
	TOF-/MS m/z 500.1374 [M-H] + (calcd: C28H22NO8, 500.1351).

). UV (MeOH) λmax: 284nm. IR (KBr) νmax:

3425, 1753, 1700, 1515, 1390, 1271, 1216 cm -1

. 1 H NMR and 13

Acknowledgements

We would like to thank to Professor Mingzhe Gao for HR-ESI-TOF-MS analysis in Dalian Institute of Chemical Physics.

Funding

This work was supported by the National Natural Science Foundation of China (Grant 81573546).

Supplementary material

Supplementary material relating to this article is available online, alongside Tables S1-S2 and Figure S1-S33.


L Pillier
email: pillier@cnrs-orleans.fr

S De Persis

G Cabot

R Bounaceur

Y Liu

M Boukhalfa

J M Most

I Gökalp

E Favre

Coupling of oxygen-enriched combustion and CO 2 capture by membrane processes

This study aims to investigate a new technological solution for CO 2 capture from fossil fuel burning power plants. It consists of coupling an oxygen-enriched combustion (typically 30-80% O 2 ) with a CO 2 capture by membrane separation processes. This offers a CO 2 capture process with a greatly reduced energetic cost compared to conventional post-combustion or oxycombustion processes. The overall purpose of the present work is to maximize the energy production by combustion while ensuring a correct operation of the global process in compliance with environmental legislations. First, a feasibility study is performed with numerical simulations of the energy required for this "hybrid" process. In parallel, combustion kinetics simulations are performed in order to determine the best combustion conditions. This numerical approach is now under experimental validation in a counter-flow burner at LCD and in a model gas turbine chamber at CORIA.

Introduction

Carbon dioxide Capture and Storage (CCS) represents a promising option for the reduction of greenhouse gas emissions from fossil fuel-fired power plants [START_REF] Figueroa | Advances in CO 2 capture Technology. The U.S. Department of Energy's Carbon Sequestration Program[END_REF]. Much of the research in this area focuses on minimizing the energy required for CO 2 capture. While pre-combustion capture offers the most promising alternative for integrated coal gasification combined cycle or natural gas combined cycle power plants [START_REF] Wall | Combustion processes for carbon capture[END_REF], post-combustion is usually inescapable for other industrial plants (cement, steel, glass, refineries, chemical plants, etc). The application of this latter technology is still not developed because of high cost (around 40 € per ton of CO 2 captured) for which the capture step dominates, typically 60-80% of the overall cost of the capturetransportation-injection for storage chain. A reduction of this cost is then required. From a practical point of view, CO 2 capture in post-combustion process is currently envisaged through two aspects: i) High purity oxygen supply (oxycombustion) to avoid dilution with nitrogen, leading to the capture of concentrated CO 2 by a simple drying operation; ii) CO 2 capture in the exhaust gas of a conventional process with air supply (CO 2 content is usually between 4 and 15 % depending on the fuel type) using separation process like absorption in liquids (amine washing). The global objective is to ensure a CO 2 capture rate of 80 to 90% while producing a flue gas containing 80% of CO 2 (to allow transportation and sequestration) with a minimal energy consumption (typically less than 2GJ per ton of CO 2 captured) [START_REF] Deschamps | Research and development actions to reduce CO 2 emissions within the European Union[END_REF]. The investigation of a technological solution, allowing minimization of the energy requirement while ensuring high CO 2 concentration, is the major purpose of this study. The basic concept relies on a novel approach based on an association of combustion and capture, which could present an alternative solution between oxycombustion (i.e. combustion with pure oxygen) and the conventional post-combustion capture. In this study we investigate a "hybrid" solution for CO 2 capture based on an oxygen-enriched combustion (typically 30-80% O 2 ) in order to produce a high content of CO 2 in the flue gas (>30% at 1 bar), for which membrane separation processes can provide separation for postcombustion applications at a greatly reduced energetic cost [START_REF] Bounaceur | Membrane processes for post-combustion carbon dioxide capture :a parametric study[END_REF]. The overall purpose of the investigation is to maximize energy production by combustion while ensuring a correct operation in compliance with environmental legislations. A special attention is given to NOx and unburnt compounds emissions. Methane (major constituent of natural gas) is studied here. First, a feasibility study for this "hybrid" process coupling CO 2 capture with oxygen-enriched combustion conditions is performed with numerical simulations of the energy required. In parallel, combustion kinetics simulations (Chemkin/Premix code) are performed in order to determine the best combustion conditions in terms of burning velocity, temperature, and pollutants emissions required for a proper operation of the system. This numerical approach is now undergoing experimental validation in a counter-flow burner at LCD and in a model gas turbine chamber at CORIA. The first results are presented here.

Numerical approach

Numerical validation of the "hybrid" process

The approach starts from the principle that the energy required for the capture of a specific component in a mixture is proportional to the dilution rate of the component to extract and/or the level of enrichment required. The feasibility study consists then of the numerical investigation of a hybrid process associating two technologies for a lesser energy consumption: i) oxygen-enriched air production (typically 30 to 80% of oxygen) for combustion process supply, using a flexible and energetically interesting process (cryogeny for large units, membrane permeation for other units); ii) CO 2 capture in the flue gas using a membrane process particularly well adapted to high CO 2 concentrated mixtures [START_REF] Bounaceur | Membrane processes for post-combustion carbon dioxide capture :a parametric study[END_REF]. A diagram of principle is given in Fig. 1.

Figure 1: Synoptic of the hybrid process including a oxygen-enriched combustion section (oxygen production unit: 1, combustion unit: 2) and a CO 2 capture section in view of sequestration (drying process: 3, capture process: 4). The oxygen mole fraction x is varied between 0.21 and 1, CO 2 purity (y) is fixed to 0.9.

The main purpose of this work is the estimation of the energy required to capture one ton of CO 2 , expressed in GJ per ton. This quantity is associated to the minimal work of concentration W (in Joule per mole of mixture, assuming an ideal gas phase). W depends on the mole fraction (x) of the component to be extracted in the mixture considered, and the level of purity to be attained (y, mole fraction of the component to be extracted after the separation process). A diagram of principle is given in Fig. 2. The oxycombustion strategy, represented by the W2 segment, aims to concentrate oxygen from 21% to more than 99%. The conventional post-combustion process, marked as W1, treats a flue gas containing about 10% CO 2 and must attain a mole fraction higher than 0.9. With a hybrid process strategy, coupling a moderated oxygen enrichment upstream (W'2<W2) and a CO 2 extraction from the exhaust gas containing a high concentration of this compound (represented schematically by the W3 segment for x=0.9), the total work of separation required W'2+W3 can be lower than W2 or W1. This hypothesis has been validated by numerical simulation. For that purpose, the energy E1 (see Fig. 1) required for "oxygen-enriched air" production and the energy E2 required for the capture of one ton of CO 2 with a purity of 90% has been calculated. Results are presented in Fig. 3. They show that coupling an oxygenenriched air production by cryogeny (requiring a specific energy E1) with a CO 2 capture using a membrane process (specific energy E2) leads, for the oxygen content in the oxidizer about 60-70%, to a total energy consumption lower than the one required for oxycombustion or the post-combustion processes. 1). Capture ratio=90%, Purity of 90% is imposed.

Combustion kinetics simulations

This part of the work aims to identify the combustion conditions (initial gas mixtures composition, oxygen content, equivalence ratio, exhaust gas composition,) allowing a correct operation of the entire process in terms of flame velocity, temperature, pollutants emission (NOx, CO, unburnt compounds), CO 2 content in the exhaust gas and oxygen consumption. Simulations have been performed with the PREMIX code [START_REF] Kee | A Fortran Program for Modeling Steady Laminar One-Dimensional Premixed Flames[END_REF] from the Chemkin II package [START_REF] Kee | Chemkin-II: A Fortran Chemical Kinetics Package for the Analysis of Gas Phase Chemical Kinetics[END_REF] and the GRImech3.0 mechanism [START_REF] Smith | [END_REF]. The PREMIX code allows the calculation of flame velocity, temperature profiles and species mole fraction profiles in premixed laminar flames. The present calculations have been performed with the freely propagating flame option. The GRImech3.0 mechanism, containing 53 species involved in 325 reversible reactions, is a reference mechanism largely employed in literature concerning methane combustion. First, the influence of a progressive oxygen enrichment (from 21 to 100% O 2 ) is studied for stoichiometric and slightly rich (φ= 1.1) CH 4 /O 2 /N 2 flames at three different pressures (1, 4 and 8 bar) and for an inlet temperature of 600K. Figure 4 shows the variations of the flame velocity S L and the adiabatic temperature T

Air N 2 + O 2 1 E1 x O 2 N 2 2 Fuel Power CO 2 H 2 O N 2 Flue gas 3 H 2 O CO 2 N 2 x' N 2 + CO 2 4 E2 y CO 2 Compression Transport Storage Air N 2 + O 2 1 1 E1 x O 2 N 2 2 2 Fuel Power CO 2 H 2 O N 2 Flue gas 3 3 H 2 O CO 2 N 2 x' N 2 + CO 2 4 4 E2 y CO 2 Compression Transport Storage
when the O 2 content increases from air (21%) to oxycombustion (100%) conditions for the slightly rich CH 4 /O 2 /N 2 flame (φ= 1.1). Figure 5 shows the calculated NOx (X NO + X NO2 ) emission (in ppm@15%O 2 in the exhaust gas) and the CO 2 final mole fraction for the same conditions. The results show, as expected, an increase of the adiabatic flame temperature and the flame velocity when the O 2 content increases. For the same O 2 content, the adiabatic temperature increases with pressure while the flame velocity decreases. The plot of NOx emissions versus the % O 2 gives a bell-shape profile with a maximum for 60-70% of O 2 . NOx emissions increase drastically as the pressure increases due to an increase in temperature (the thermal-NO mechanism predominates for the present temperatures). As expected, no NOx are formed for oxycombustion (100% O 2 ) condition, however the adiabatic flame temperature is very high (more than 3000K). For a real industrial application, this would require a thermal protection of the combustion chamber walls and of the turbine blades. CO 2 final mole fraction slightly increases with 2 content and pressure but remains too low (about 10% at 1 bar) for an economically favourable application of CO 2 capture by membranes processes. A possible solution consists in diluting the initial mixture by CO 2 (the captured CO 2 for example) in order to decrease the combustion temperature and then NOx emission, as well as to increase the final CO 2 content. The aim is to obtain low NOx emissions that meet current environmental legislations for gas turbines (i.e., ∼15 ppm @15%O 2 ). Figure 6 shows the variations of the laminar flame velocity and the adiabatic temperature when the O 2 (from 50 to 100%) and CO 2 (from 0 to 60%) initial contents increase at a pressure of 4 bar and for the slightly rich CH 4 /O 2 /N 2 flame (φ= 1.1) . Figure 7 shows the NOx emissions and the CO 2 final mole fraction for the same conditions. CO 2 dilution plays its expected role: it decreases the adiabatic temperature (due to its high heat capacity) and increases the final CO 2 content in the burnt gases which is advantageous for the membrane capture process. However, a high CO 2 dilution (60% CO 2 ) is necessary to reach the NOx emissions critical value (∼15 ppm @15%O 2 ). In this case the flame velocity becomes very low (< 20 cm/s for 50 to 80% O 2 ). This numerical study shows therefore that oxygenenriched combustion (60-80 % O 2 ) allows to obtain a high CO 2 content in the exhaust gas while guaranteeing low NOx emissions provided a dilution of the initial gas mixture by high quantities of CO 2 . Future calculations will focus on the effect of Exhaust Gas Recirculation on the oxygen-enriched combustion of methane.

Experimental approach

Experimental study of CO 2 dilution in a counter-flow laminar flame burner

The objective of this part is to enhance the knowledge of the combustion regime generally called MILD (Moderate Intense Low-oxygen Dilution Combustion) or flameless combustion. Experiments were performed in a counter-flow burner. We have investigated the influence of the diluent composition (nitrogen/carbon dioxide), concentration (dilution rate) and preheat temperature of the reactants on the flame stability and on the broadening of the reaction zone. The experimental results are necessary to analyse the thermochemical effects of the flue gas recirculation on the flame stability behaviour.

Experimental set-up and diagnostic

A counter-flow burner is used (Fig. 8

pr c c h T ) T / u ( u ⋅ = ,
where u h is the real exit velocity of the hot reactants, u c is the inlet cold flow velocity, T c is the ambient temperature (T c =  298K), and T pr is the preheat temperature (298-1023K).

Figure 8: Schematic of the counter-flow burner

The non-premixed diluted CH 4 /Air flame is experimentally established in the mixing zone of the reactants diluted in nitrogen and carbon dioxide. The volume fraction of methane X CH4 in the fuel stream varies from 6 to 30%, and the oxygen volume fraction X O2 in the oxidizer stream ranged from 10 to 21%. The volume fraction of carbon dioxide X CO2 varies from 0 to 20% and kept constant on the fuel and oxidizer sides. The remaining part of the diluent is nitrogen:

f N CO CH X X X 2 2 4 1 - - = and o N CO O X X X 2 2 2 1 - - =
where X N2f and X N2o are the volume fraction of nitrogen in the fuel and oxidizer flows respectively. Visualization of the reaction zone is performed by Planar Laser Induced Fluorescence of OH.

Results and discussion

The flame stability diagram is determined by extinction tests as a function of the strain rate S. Fig. 9 presents the flame stability diagram using S versus the oxygen concentration X O2 . The extinction strain rate (linearly dependant of T Pr ) increases with the oxygen concentration X O2 for both nitrogen (X CO2 = 0) and nitrogen/carbon dioxide dilutions, which means that dilution reduces flame stability whatever the diluent composition. The effect of CO 2 content on the flame stability is noticeably increased as the oxygen concentration is low. X O2 (%)

X CO2 =0% (Diluted by pure N 2 )

X CO2 =5% X CO2 =10% X CO2 =20%
T pr = 873K

δ ΟΗ / Η Tpr (K) X CO2 =0% (dilutent is pure N 2 ) X CO2 =5% X CO2 =10% X CH4 =30%, X O2 =18%
Figure 10: Effects of the preheat temperature T pr and CO 2 dilution on the reaction zone thickness δOH/H Figure 10 presents the reaction zone thickness versus the preheat temperature of reactants for different X CO2 content in the diluent. The reaction zone thickness increases with increasing preheat temperature and decreases with increasing CO 2 concentration. This result is attributed to the higher heat capacity of CO 2 compared to N 2 . But, according to some analyses [START_REF] Cavaliere | [END_REF] for a mild combustion model, the CO 2 content in diluents may change the behaviour of the diluted combustion not only because it affects the heat capacity of the system but also because it contributes to the chemical reactions.

Experimental study on premixed combustion with CO 2 dilution in a model gas turbine chamber

In addition, the effect of CO 2 dilution was studied in the case of lean premixed combustion in a gas turbine configuration. The study concerns a composition of 65%CH 4 and 35%CO 2 , typical for biogas [START_REF] Gökalp | Alternative Fuels For Industrial Gas Turbines[END_REF].

Experimental set-up and diagnostic

The injector of the burner is composed of an axial swirl injector with a central bluff-body producing an annular swirling jet; the swirl number is equal to 0.92. This high swirl number produces the Inner Recirculation Zone (IRZ) observed in the figure 11. The combustion chamber is equipped with a full optical access to allow optical diagnostics. The arrangement allows us to mix fuel and air far upstream injection to ensure a fully premixed combustion. Radius R of swirl injector is 10mm. The diameter of the combustion chamber is 80mm and its length is 250mm. A cold air stream is injected along the combustion chamber walls, both for cooling it and for diluting hot gases produced by combustion. Pressure in the combustion chamber can be settled by adjusting a sonic throat placed at the exit. More information concerning burner arrangements is provided in [START_REF] Taupin | Experimental Study Of Lean Premixed Turbulent Combustion, 11th International Symposium On LASER Techniques To Fluid Mechanics[END_REF]. To detect flame structure and to quantify the intensity of the reaction, a CH radicals chemiluminescence system is used [START_REF] Higgins | An experimental study of the effect of pressure and strain rate on CH chemiluminescence of premixed fuellean methane/air flames[END_REF][START_REF] Najm | On the adequacy of certain experimental observables as measurement of flame burning rate[END_REF]. It is composed of a band pass filter centred at 410 nm, and a 16 bits ICCD camera (Princeton 512x512). In order to provide an accurate visualization of the reaction zone, Abel deconvolution is performed from the averaged image obtained. A pressure sensor placed on the injection plane allows us to detect the apparition of unstable flame (i.e. the apparition of low frequencies peaks).

Results and discussion

The studied flames and their corresponding CH* emissions averaged images are reported in figure 12. For all cases, inlet velocity is set to 30m/s (air mass flow rate 7.80g/s), in atmospheric conditions. It shows the modification of flame structure and the modification of CH* emission intensity when the equivalence ratio and the mole fraction of CO 2 are changed. Figure 13 quantifies the global CH* decrease of the flames when equivalence ratio is decreased and when CO 2 is increased. It means that the global reaction intensity [START_REF] Higgins | An experimental study of the effect of pressure and strain rate on CH chemiluminescence of premixed fuellean methane/air flames[END_REF] Concerning the structure of the flame, it is well known that the flame stabilization is difficult in zones with high velocity gradients, especially in the case of low flame velocity. In case A (methane/air flame @ φ=0.75), figure 11 shows the position of the average reaction zone in the average velocity field [START_REF] Lafay | Experimental study of biogas combustion using a gas turbine configuration[END_REF]. It can be observed that the flame is anchored to the burner by a thin reaction zone in the inner annular swirling jet corresponding to the higher radial velocity gradient. Then, the main reaction is produced closed to the wall, where the velocities of the flow are lower. In case B, corresponding to a lower equivalence ratio and then to a lower flame velocity (Fig. 14), it can be observed that the flame anchorage is lower in intensity and area, and the zone of main reaction is larger. Due to a lower flame velocity, the time of combustion increases and then the reaction is convected farther in the flow, one part downstream closed to the wall and the other part in the CRZ (Corner Recirculation Zone). This phenomenon explains all the different structures of the flames observed in figure 12, when CO 2 and equivalence ratio are modified and seem only depend on the laminar flame velocity. Indeed, some similar structures of the flames observed in figure 12, like the couples C1-C2, D1-D2 and E1-E2, always lead to a similar flame velocity as shown in Fig. 14.

Other studies [START_REF] Lafay | Experimental study of biogas combustion using a gas turbine configuration[END_REF] show that this laminar velocity explains also the instability intensity of the flame in case of CO 2 dilution.

Conclusions

This study is a preliminary effort to assess the feasibility of a low cost CO 2 capture process in oxygen-enriched air combustion of fossil fuels. The feasibility study is conducted for methane as fuel. The global objective of the project is to demonstrate that by combining careful analysis of the combustion process and that of oxygen generation and membrane CO 2 capture processes, an optimized hybrid process can be proposed in-between oxyfuel combustion and conventional post-combustion CO 2 capture. The optimisation should confirm reduced oxygen generation and CO 2 capture costs, flame stability and acceptable emission levels in particular for NOx, CO and UHC. Numerical simulations have been conducted to demonstrate the global energetic feasibility of the process and to explore the flame and emission characteristics for various equivalence ratios, pressures, and CO 2 dilution rates relevant for gas turbine applications.

In addition experimental studies have been conducted to determine CO 2 dilution effects on laminar and swirl stabilized turbulent methane/O 2 /N 2 flames. The combined results of this integrated approach indicate that oxygen enriched air combustion of fossil fuels in association with CO 2 capture by membrane processes could be an innovative solution for low cost CCS technologies.

Figure 2 :

 2 Figure 2: Evolution of the minimal work of concentration (W, J.mol -1 ) of a binary gas mixture as a function of the mole fraction in the mixture (x) and the level of purity (y) required.

Figure 3 :

 3 Figure 3: Energy requirement for CO 2 capture versus oxygen content in the feed stream. E1= specific energy for oxygen production, E2= specific energy for capture process by membrane (see Fig.1). Capture ratio=90%, Purity of 90% is imposed.

Figure 4 :Figure 5 :

 45 Figure 4: Adiabatic flame temperature T (K) and laminar flame velocity S L (cm/s) versus the percentage of O 2 in "air" for three different pressures (1, 4 and 8 bar) for a slightly rich CH 4 /O 2 /N 2 flame (φ= 1.1).

Figure 6 :

 6 Figure 6: Adiabatic flame temperature T (K) and laminar flame velocity S L (cm/s) versus the percentage of O 2 in "air" and the CO 2 content in the initial mixture at P= 4 bar for a slightly rich CH 4 /O 2 /N 2 /CO 2 flame (φ= 1.1).

Figure 7 :

 7 Figure 7: CO 2 mole fraction and NOx emissions (X NO +X NO2 ) in the burnt gases of the slightly rich CH 4 /O 2 /N 2 /CO 2 flame (φ= 1.1) versus the percentage of O 2 in "air" and the CO 2 content in the initial mixture at P= 4 bar.

  ), it consists of two identical vertically opposed nozzles. The fuel (mixture of CH 4 /N 2 /CO 2 ) is injected in the top burner and the oxidizer (mixture of O 2 /N 2 /CO 2 ) in the bottom burner. The separation distance (H) between the nozzles and the internal injection diameter D are both fixed to 35mm. An annular concentric co-flow of nitrogen provides a curtain to isolate the flame from reaction of fuel with surrounding air. The two laminar opposed flows are heated electrically up to 700°C. The flow characteristics are kept constant to those of the cold stream velocity of u c = 0.5 m/s, corresponding to a constant volume flow rate of Q c ≈ 4.82×10 -4 m 3 /s. As the two reactant flows are heated up, their effective velocities u h at the exit change the flow strain rate. The average exit velocity after preheating follows the law:

Figure 9 :

 9 Figure 9: Flame stability diagram versus XO 2 for different CO 2 dilutions

Figure 11 :

 11 Figure 11: LDV flow velocity and CH* emission maps of two methane air flames, Case A: φ =0.75 and Case B: φ =0.70

  is decreased by CO 2 or air dilution. This observed decrease of reaction intensity can be related to the decrease of the turbulent flame velocity S T due to the decrease of laminar flame velocity S L as shown in the flame velocity are computed from CANTERA and the GRImech 3.0 mechanism[START_REF] Smith | [END_REF].

Figure 12 :

 12 Figure 12: Abel inversion of CH* emission images from the (CH 4 +aCO 2 ) -air flames. a=0.12;0.2 and 0.3

Figure 13 :Figure 14 :

 1314 Figure 13: Normalized CH* emission for different mole fractions of CO 2 dilution versus equivalence ratio


Julen Munaŕriz

Federico A Rabuffetti

Julia Contreras-García

Building Fluorinated Hybrid Crystals: Understanding the Role of Noncovalent Interactions

22 In the last few years, different computational

■ INTRODUCTION

Noncovalent chemical interactions play a key role in catalysis, biochemistry, and self-assembly of functional materials. Metalorganofluorine (M•••F-C) is an example of donor-acceptor noncovalent interaction (NCI) that determines the structure and reactivity of complexes bearing fluorinated hydrocarbon ligands. The ability of this interaction to electronically and sterically modulate the coordination sphere of metal centers belonging to s, p, d, and f blocks has been exploited to predictively synthesize fluorinated molecules designed to serve as functional units in homogeneous catalysis, 1-3 chemical vapor deposition of thin films, [START_REF] Samuels | Chemical Vapor Deposition of Metal Fluorides Using Sodium and Zirconium Fluoroalkoxides[END_REF][START_REF] Troyanov | Synthesis, Crystal Structure and Properties of Manganese(II) Hexafluoroacetylacetonates Mn(hfa) 2 (H 2 O) 2 and KMn(hfa) 3[END_REF][START_REF] Tahir | Heterobimetallic Copper-Barium Complexes for Deposition of Composite Oxide Thin Films[END_REF][START_REF] Mansoor | Perovskite-Structured PbTiO 3 Thin Films Grown from a Single-Source Precursor[END_REF] and bioactive compounds. [START_REF] O'hagan | Fluorine in Health Care: Organofluorine Containing Blockbuster Drugs[END_REF][START_REF] Paulini | Orthogonal Multipolar Interactions in Structural Chemistry and Biology[END_REF][START_REF] Pollock | Rational Design of Orthogonal Multipolar Interactions with Fluorine in Protein-Ligand Complexes[END_REF] Considerably less effort has been devoted to exploiting synthetic control of those interactions to design fluorinated hybrid crystals that contain multiple metal centers bridged by fluorinated organic ligands. Metal-fluorine contacts present in these crystals provide a low-temperature pathway for their decomposition into the corresponding mixed-metal fluorides or oxifluorides, thereby making fluorinated hybrid crystals ideal single-source precursors for solution-phase routes to compositionally complex functional materials. [START_REF] Samuels | Chemical Vapor Deposition of Metal Fluorides Using Sodium and Zirconium Fluoroalkoxides[END_REF][START_REF] Mishra | Ln) Trifluoroacetate Diglyme Complexes as Novel Single-Source Precursors for Upconverting NaYF4 Nanocrystals Co-Doped with Yb and Er/Tm Ions[END_REF][START_REF] Mishra | Novel Heterometal-Organic Complexes as First Single Source Precursors for Upconverting NaY(Ln)F 4 (Ln = Yb, Er, Tm) Nanomaterials[END_REF][START_REF] Chen | Direct Synthesis of Hexagonal NaGdF 4 Nanocrystals from a Single-Source Precursor: Upconverting NaGd-F 4 :Yb 3+ , Tm 3+ and Its Composites with TiO 2 for Near-IR-Driven Photocatalysis[END_REF][START_REF] Dhanapala | Bimetallic Trifluoroacetates as Single-Source Precursors for Alkali-Manganese Fluoroperovskites[END_REF] One of the main challenges facing the design and predictive synthesis of fluorinated hybrid crystals is the lack of quantitative understanding of the role of metal-fluorine 72 approaches have guided the design of new materials with 73 improved properties by tuning NCIs. [23][24][25][26][27] The recently 74 developed NCI method is uniquely suited to provide a 75 comprehensive and quantitative description of NCIs in 76 fluorinated hybrid crystals. NCI is a topological tool enabling 77 visualization of NCIs in real space. It is based on the analysis of 78 the reduced gradient of the electron density (s(ρ)) 28 and was 79 originally developed to unravel weak interactions in molecular 80 systems. 29 As such, it has been used to describe a broad range 81 of NCIs such as hydrogen 30,[START_REF] Riffet | Alkali Ion Incorporation into V 2 O 5 : a Noncovalent Interactions 711 Analysis[END_REF] and halogen bonds. 32,33 The 82 NCI method has been extended to the study of periodic 83 systems, 34 including molecular crystals, 35,36 layered solids 84 containing metallic atoms, 37,38 and organic-inorganic hybrid 85 materials. [START_REF] Lee | Role of Hydrogen-Bonding and its Interplay with Octahedral Tilting in CH 3 NH 3 PbI 3[END_REF][START_REF] Navas | New Insights Into Organic-Inorganic Hybrid Perovskite CH 3 NH 3 PbI 3 Nanoparticles. An Experimental and Theoretical Study of Doping in Pb 2+ Sites With Sn 2+ , Sr 2+ , Cd 2+ and Ca 2+[END_REF] The method has also proven to be suitable to aid 86 the design novel hybrid functional materials. 41 87 In this article, we demonstrate that the NCI method serves 88 to comprehensively and quantitatively map NCIs in a series of 89 fluorinated hybrid crystals containing alkali-manganese(II) 90 metal pairs and trifluoroacetato ligands. Bimetallic trifluor-91 oacetates of formula Na 2 Mn 2 (tfa) 6 (tfaH), K 2 Mn 2 (tfa) 6 (tfaH) 2 • 92 H 2 O, Rb 2 Mn 2 (tfa) 6 •H 2 O, and CsMn(tfa) 3 (tfa = trifluoroace-93 tato; tfaH = trifluoroacetic acid) have recently been shown to 94 serve as single-source precursors for solution-phase routes to 95 the corresponding mixed-metal fluorides; 14 their crystal f1 96 structures are shown in Figure 1. Using the NCI approach, 97 we establish the nature, strength, and compositional depend-98 ence of the four NCIs present in these hybrid crystals. These 99 interactions are manganese-oxygen, hydrogen bonds, alkali-100 oxygen, and alkali-fluorine. For the latter, their nature (i.e., 101 electrostatic or van der Waals), strength, and spatial local-102 ization are quantitatively determined by combining NCI 103 analysis, search of bond critical points (BCPs), and a simple 104 point charge model. The contribution of dispersive interactions 105 to the total crystal energy is computed for each alkali-106 manganese hybrid, and their significance for crystal packing is 107 discussed. Results presented in this article establish crystallo-108 chemically meaningful criteria to unravel, characterize, and 109 tune NCIs between metal centers and fluorinated organic 110 ligands. These criteria are expected to contribute to the design 111 and predictive synthesis of hybrid crystals featuring organic 112 ligands capable of establishing NCIs with metal centers.

113 ■ COMPUTATIONAL DETAILS 114 DFT Methodology. Spin-polarized DFT calculations were 115 performed using dispersion-corrected revPBE [START_REF] Zhang | Generalized Gradient Approximation Made Simple[END_REF] and optPBE-vdW [START_REF] Dion | van der Waals Density Functional for General Geometries[END_REF] functionals, both as implemented in the VASP 5.4.1 code. [START_REF] Kresse | Ab Initio Molecular Dynamics for Liquid Metals[END_REF][START_REF] Kresse | Ab Initio Molecular-Dynamics Simulation of the Liquid-Metal-Amorphous-Semiconductor Transition in Germanium[END_REF][START_REF] Kresse | Efficient Iterative Schemes for ab initio Total-Energy Calculations Using a Plane-Wave Basis Set[END_REF] D2 47 and D3 [START_REF] Grimme | A Consistent and Accurate ab initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu[END_REF] Grimme dispersion corrections, as well as D3 with Becke-Jonson damping (D3BJ), [START_REF] Grimme | Effect of the Damping Function in Dispersion Corrected Density Functional Theory[END_REF] were added to the revPBE functional in both geometry optimizations and single point calculations. We chose these approaches due to their well-documented ability to accurately reproduce experimental parameters of a broad range of crystals (e.g., molecular, layered structures, and manganese-based materials) while keeping the computational cost reasonable. [START_REF] Zalake | Descriptor-Based Rational Design of Two-Dimensional Self-Assembled Nanoarchitectures Stabilized by Hydrogen Bonds[END_REF][START_REF] Zeinalipour-Yazdi | DFT-D3 Study of Molecular N 2 and H 2 Activation on Co 3 Mo 3 N Surfaces[END_REF][START_REF] Sutton | Noncovalent Intermolecular Interactions in Organic Electronic Materials: Implications for the Molecular Packing vs Electronic Properties of Acenes[END_REF][START_REF] Kim | Carrier Scattering in Quasi-free Standing Graphene on Hexagonal Boron Nitride[END_REF][START_REF] Peralta | Comparison of the Behavior of Metal-Organic Frameworks and Zeolites for Hydrocarbon Separations[END_REF][START_REF] Li | Effect of Amidogen Functionalization on Quantum Spin Hall Effect in Bi/Sb Films[END_REF][START_REF] Sorescu | Assessing the Performances of Dispersion-Corrected Density Functional Methods for Predicting the Crystallographic Properties of High Nitrogen Energetic Salts[END_REF] The Projector Augmented Wave (PAW) [START_REF] Blochl | Projector Augmented-Wave Method[END_REF][START_REF] Kresse | From Ultrasoft Psuedopotentials to the Projector Augmented-Wave Method[END_REF] and that of the isolated layers (E layer ), as shown in eq 1. A vacuum of ∼15 Å was included to ensure that no interlayer interactions occur.

E E E cohesive crystal layer = - (1)
Functional and Dispersion Correction Selection.

Dispersion-corrected revPBE and optPBE-vdW functionals

were screened prior to selecting the most suitable for the study of bimetallic trifluoroacetates. We first tested the ability of these functionals to accurately reproduce experimental lattice constants and Mn/K-O/F distances in K 2 Mn 2 (tfa) 6 (tfaH) 2 • H 2 O. The relative errors for lattice constants (Δ) and the average relative error for Mn/K-O/F distances (Δ d ) were computed using experimental crystallographic data as reference. [START_REF] Dhanapala | Bimetallic Trifluoroacetates as Single-Source Precursors for Alkali-Manganese Fluoroperovskites[END_REF] The revPBE-D2 approach provided the most accurate description of the K 2 Mn 2 (tfa) 6 (tfaH) the significance of van der Waals interactions for crystal cohesion; these interactions will be described in detail later in this article. Finally, we tested the ability of the GGA+U approach 60 to accurately reproduce the crystal structure of K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O. It is well-known that on-site Coulomb interactions in the localized d orbitals of manganese are poorly described by the standard GGA methodology.

Values of the Hubbard parameter (U) between 2.0 and 5.0 eV were employed. 61,62 Structural parameters computed using the GGA+U approach did not show any improvement over those obtained using standard GGA. Therefore, considering we were primarily interested in the crystal chemistry of fluorinated hybrids, the latter approach was utilized. The corresponding t1 results are shown in Table 1 for all four bimetallic trifluoroacetates studied in this work. Results obtained using other approaches, including evaluation of the GGA+U performance, are given in the Supporting Information (Tables S1 andS2).

Noncovalent Interactions Topological Analysis. NCI analysis enables visualization of NCIs in real space, thereby providing an intuitive representation of a broad range of attractive (e.g., van der Waals, electrostatic, and hydrogen bonds) and repulsive interactions (e.g., steric clashes). This approach is based on the reduced electron density gradient (s(ρ)) defined in eq 2.

s( ) 1 2(3 ) 2 1/3 4/3 ρ π ρ ρ = |∇ | (2)
Noncovalent interactions are revealed by plotting s(ρ) as a function of sign(λ 2 )ρ, where the first term of the product corresponds to the sign of the second eigenvalue of the Hessian of the electron density gradient. For noninteracting systems, s(ρ) behaves smoothly. By contrast, zones with low s(ρ) values appear when NCIs are present. An NCI plot is informative of (i) van der Waals interactions, which are characterized by low electron densities and sign(λ 2 )ρ ≈ 0; (ii) attractive interactions, such as hydrogen bonds and strong electrostatic interactions, characterized by sign(λ 2 )ρ < 0; and (iii) repulsive interactions such as steric clashes, for which sign(λ 2 )ρ > 0. An intuitive representation of NCIs is obtained by plotting isosurfaces of s(ρ) and coloring them according to the value of sign(λ 2 )ρ. Strong attractive interactions are depicted in blue, van der Waals in green, and steric clashes in f2 red. Figure 2 illustrates this color coding scheme in an adenine-thymine dimer (Figure 2a), a benzene dimer (Figure 2b), and bicyclo[2.2.2]octane (Figure 2c). The shape of the isosurfaces is informative of the spatial localization of NCIs. Localized interactions such as hydrogen bonds and strong electrostatic interactions appear as blue, disc-shaped surfaces. Weak electrostatic interactions appear as green, disc-shaped surfaces. By contrast, delocalized interactions such as van der Waals interactions appear as diffuse green surfaces (see Figure 2b). In this work, NCI topological analysis [START_REF] Buchanan | Interactions and Heterobimetallics: Furthering the Understanding of Heterobimetallic Stabilization[END_REF] was employed to quantitatively probe the nature, strength, and spatial localization of manganese-oxygen, hydrogen bonds, alkali-oxygen, 241 K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O is the only exception to this trend 242 and will be discussed below. A representative three-dimen-243 sional NCI plot of manganese-oxygen interactions is shown in f4 244 Figure 4 for CsMn(tfa) 3 ; plots for other compositions are 245 provided in the Supporting Information (Figure S1). In all 246 cases, the reduced density gradient isosurface exhibits a well-247 defined, disc-like shape, indicating a highly localized 248 interaction. 66 This observation, in conjunction with the values of sign(λ 2 )ρ, points toward an electrostatic interaction between manganese and oxygen atoms. Further inspection of Table 2 shows that the average values of sign(λ 2 )ρ remain nearly constant for all the trifluoroacetates (ca. -0.055 au), with the exception of K 2 Mn 2 (tfa) 6 (tfaH) ing them according to the nature of the oxygen donor, that is, whether it belongs to a trifluoroacetato, acuo, or protonated trifluoroacetato ligand. Comparison of sign(λ 2 )ρ values for each type of oxygen donor suggests that the strength of these interactions can be ranked as follows: Mn-O(tfa) > Mn-O(H 2 O) > Mn-O(tfaH). This result can be understood noting that the trifluoroacetato ligand is negatively charged, whereas acuo and protonated trifluoroacetato ligands are neutral. The trifluoroacetato ligand is therefore expected to be more nucleophilic and its interaction with manganese stronger. Interactions established between manganese and oxygen donors belonging to the negatively charged trifluoroacetato ligand appear in the same sign(λ 2 )ρ range, indicating that their strength is comparable in all compounds. K 2 Mn 2 (tfa) 6 (tfaH) 2 • H 2 O is the sole exception to this trend. In this compound, a weaker Mn-O(tfa) interaction appears at -0.044 au. This interaction occurs between manganese and a carboxylic oxygen that participates as an acceptor in a hydrogen bond with a protonated trifluoroacetato ligand. The nucleophilicity of the carboxylic oxygen is thus reduced and so is the strength of the corresponding interaction with the manganese cation. Inspection of Table 2 shows that average sign(λ 2 )ρ values for alkali-oxygen interactions decrease upon going from sodium to cesium, and that the amplitude of the range of values remains roughly constant through the series. The relative strength of these interactions is in agreement with their electrostatic nature. As the alkali cation becomes larger, more electropositive, and less polarizing, it establishes increasingly weaker and more diffuse electrostatic interactions with trifluoroacetato and protonated trifluoroacetato ligands. As observed earlier for other NCIs, potassium-oxygen interactions deviate from this trend. These interactions display the lowest average sign(λ 2 )ρ value and the broadest range of values of the entire series. Inspection of Figure 6b sheds light on the origin of the distinct behavior of potassium-oxygen interactions in this compound. The abnormally low sign(λ 2 )ρ value may be attributed to a weak interaction between one of the two nonequivalent potassium cations and an acuo ligand (K2-O1W). The oxygen belonging to the acuo ligand is involved in two hydrogen bonds, and, as a result, its nucleophilicity is weakened and so is the corresponding potassium-oxygen interaction.

Alkali-Fluorine Interactions. Alkali-organofluorine interactions are located in region D of the NCI plots shown in Figure 3. Special emphasis was placed on getting in-depth understanding of these interactions. Three tools were combined to distinguish between electrostatic and van der Waals interactions: (i) sign(λ 2 )ρ values, (ii) the NCI reduced density gradient profile, 67 and (iii) BCPs along the internuclear axis. BCPs are expected in localized interactions but not necessarily in weak delocalized ones. 29 In our case, the absence of BCPs may indicate weak van der Waals interactions. 2 shows that the average value of sign(λ 2 )ρ for electrostatic interactions decreases upon going from sodium to cesium. Accordingly, cesium-fluorine interactions in CsMn(tfa) 3 are more diffuse than in Na 2 Mn 2 (tfa) 6 (tfaH) (see Figure S2a-e). Analysis of alkali-fluorine electrostatic interactions in Na 2 Mn 2 (tfa) 6 (tfaH) reveals sign(λ 2 )ρ values ranging from -0.011 to -0.006 au. These are characterized by disc-shaped isosurfaces (see Figure S2a,b). BCPs were found for interactions Na1-F1A/F3E and Na2-F1C/F2D. By contrast, Na1-F1B/FG van der Waals interactions exhibit sign(λ 2 )ρ values that lie in the -0.004 to -0.002 au range, and, as expected, their corresponding NCI profiles show diffuse surfaces; 37 no BCPs were found for these interactions. In the case of K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O, seven electrostatic interactions are observed; these are K1-F1B/F1C/F1E/F3F and K2-F1D/F2F/F3B. The distinct crystal chemistry of this hybrid is confirmed once again upon inspection of Table 2, as some of these K-F interactions exhibit higher electron densities than K-O interactions. Dispersive interactions in this compound involve K1-F2B and K2-F1G, and, as expected, their corresponding NCI surfaces are diffuse (see Figure 6a,b). Similar to the case of sodium, BCPs were found for electrostatic interactions but not for van der Waals interactions. Analysis of the three-dimensional NCI profiles (see Figure S2c,d) and BCPs in Rb 2 Mn 2 (tfa) 6 •H 2 O demonstrates that Rb1-F1A/F3A/F1D/F3F/F1C and Rb2-F1B/ F2B/F3C/F2D interactions are directional (electrostatic), while Rb1-F1E/F2E/F3E/F2A and Rb2-F3D/F3E/F1F are delocalized (van der Waals). Finally, all alkali-fluorine interactions in CsMn(tfa) 3 appear to be electrostatic, as shown by well-defined, disc-shaped isosurfaces (see Figure S2e). Additionally, all of them present BCPs.

Inspection of Table

In the case of electrostatic alkali-fluorine interactions, a simple charge model was used to identify them and rank their relative strength. In this model, we considered interactions between point charges separated by the equilibrium distance and interacting through a Coulomb-type potential. Charges were computed via Bader analysis. 68 The strengths of electrostatic interactions were linearly normalized to facilitate comparison between bimetallic trifluoroacetates. This was accomplished by using the strongest interaction within each compound as a reference value and calculating a strength coefficient that takes a maximum value of 1.0; additional details are provided in the Supporting Information (see Table S3). Analysis of the electrostatic contributions within this model further supports the distinction between electrostatic and van der Waals interactions. Interactions classified as electrostatic show relative strength coefficients between 0.95 and 1.0 (Na), 0.88 and 1.0 (K), 0.92 and 1.0 (Rb), and 0.91 and 1.0 (Cs). In contrast, values for van der Waals interactions are significantly lower and range from 0.84 to 0.86 (Na), 0.80 (K), and 0.83 to 0.85 (Rb).

Analysis of van der Waals Interactions. van der Waals interactions were quantified using the dispersive term in the total crystal energy, which was calculated using Grimme's D2 scheme. [START_REF] Grimme | Semiempirical GGA-type Density Functional Constructed With a Long-Range Dispersion Correction[END_REF] Dispersive interactions contribute ca. 2% of the total crystal energy in Na 2 Mn 2 (tfa) 6 (tfaH), K 2 Mn 2 (tfa) 6 (tfaH) 2 • H 2 O, and Rb 2 Mn 2 (tfa) 6 •H 2 O; this contribution doubles for CsMn(tfa) 3 (ca. 4%) (see Table S4). The significance of van der Waals interactions for crystal cohesion and packing was further analyzed in the cases of K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O and CsMn(tfa) 3 . These crystals have well-defined building blocks: double layers stacked along the a axis and held together by van der Waals forces (K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O), and a combination of layers stacked along the b axis and threads parallel to the c axis (CsMn(tfa) 3 ). Computation of the cohesive energy between these building blocks yields 0.17 eV/Mn atom (layers in K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O), 1.23 eV/Mn atom (layers in CsMn(tfa) 3 ), and 2.38 eV/Mn atom (threads in CsMn- (Figure 7a) and over the entire structure in CsMn(tfa) 3 (Figure 7b). Even though K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O consists of layers that are held together by dispersive interactions between trifluoroacetato ligands, the dispersive contribution to the total energy is the same as for Na 2 Mn 2 (tfa) 6 (tfaH) and Rb 2 Mn 2 (tfa) 6 •H 2 O, which exhibit a tridimensional mesh of electrostatic interactions between metals and trifluoroacetato ligands. This result, along with the unusually strong hydrogen bonds present in K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O, indicates that this crystal adopts a layered structure in order to maximize the number of hydrogen bonds between protonated trifluoroacetato ligands Major Crystal Chemical Trends. The main crystal chemical trends observed across the series of alkalimanganese(II) bimetallic fluoroacetates are summarized in the following bullet points.

• Manganese-oxygen was the strongest NCI occurring in the series of crystals under study. This interaction was of electrostatic nature. Its strength was independent of the alkali metal present in the structure but strongly dependent on the oxygen donor (Mn-O(tfa) > Mn-O(H 2 O) > Mn-O(tfaH)).

• The strength of hydrogen bonds involving acuo donors did not vary significantly upon changing the alkali metal.

Conversely, those involving protonated trifluoroacetato donors exhibited a pronounced dependence on the alkali metal, being stronger for K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O.

• Alkali-oxygen interactions could be described as weak electrostatic interactions, and, as expected, their strength decreased upon going from sodium to cesium.

• Alkali-fluorine interactions were of electrostatic or van der Waals type. Both types of interactions were observed in sodium-, potassium-, and rubidium-manganese crystals. Only electrostatic interactions were present in CsMn(tfa) 3 .

• The dispersive contribution to the total crystal energy was almost the same for K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O, Na 2 Mn 2 (tfa) 6 (tfaH), and Rb 2 Mn 2 (tfa) 6 •H 2 O.

• The relative strengths of NCIs in the two-dimensional, layered K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O crystal deviated sharply from those observed in the other members of the series. Hydrogen bonds established by protonated trifluoroacetato ligands located in the interlayer space appeared to be as strong as manganese-oxygen electrostatic interactions. Likewise, interactions between potassium and fluorine exhibited higher electron densities than those between potassium and oxygen.

The distinct two-dimensional crystal structure of K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O is therefore attributed to this unique balance of NCIs. By adopting this spatial arrangement, the number of strong hydrogen bonds was maximized. This result illustrates the significance of quantitatively probing NCIs, as these may provide a rational pathway to design anisotropic hybrid functional crystals.

■ CONCLUSIONS

Noncovalent interactions in alkali-manganese(II) bimetallic fluorinated crystals were quantitatively mapped and ranked using the NCI approach. Their strength, spatial localization, and compositional dependence were established. Quantitative chemical principles were outlined to gain insight into the

K 2

 2 method was used to represent interactions between core and valence electrons. A plane wave cutoff of 500 eV was used for all elements. Monkhorst-Pack kpoint meshes of 5 × 4 × 3, 2 × 4 × 2, 5 × 3 × 3, and 3 × 3 × 3 points were employed for Na 2 Mn 2 (tfa) 6 (tfaH), K 2 Mn 2 (tfa) 6 -(tfaH) 2 •H 2 O, Rb 2 Mn 2 (tfa) 6 •H 2 O, and CsMn(tfa) 3 , respectively. Mn 2 (tfa) 6 (tfaH) 2 •H 2 O and CsMn(tfa) 3 exhibit layered structures held together by van der Waals forces. The cohesive energies (E cohesive ) for these crystals were calculated as the difference between the energy of the original structure (E crystal )

K 2 Figure 3 .

 23 Figure 3. Inspection of Figure 3 and Table2shows that the

Figure 2 .

 2 Figure 2. Three-dimensional NCI plots of (a) adenine-thymine dimer (hydrogen bonds depicted in blue), (b) benzene dimer (dispersive interactions depicted in green, and (c) bicyclo[2.2.2]octane (steric clashes depicted in red). Surfaces are colored in the [-0.04, 0.04] au range of sign(λ 2 )ρ (isosurface s = 0.5 au).

Figure 3 .

 3 Figure 3. NCI plots for (a) Na 2 Mn 2 (tfa) 6 (tfaH), (b) K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O, (c) Rb 2 Mn 2 (tfa) 6 •H 2 O, and (d) CsMn(tfa) 3 . Regions A, B, C, and D correspond to manganese-oxygen, hydrogen bonds, alkali-oxygen, and alkali-fluorine interactions, respectively.

  Finally, we note that Mn-O(H 2 O) interactions in K 2 Mn 2 (tfa) 6 -(tfaH) 2 •H 2 O and Rb 2 Mn 2 (tfa) 6 •H 2 O have comparable strengths (-0.048 < sign(λ 2 )ρ < -0.044 au). A similar remark holds for Mn-O(tfaH) interactions in Na 2 Mn 2 (tfa) 6 (tfaH) and K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O (-0.041 < sign(λ 2 )ρ < -0.037 au). Hydrogen Bonds. Hydrogen bonds appear in region B of the NCI plots shown in Figure 3; this region is absent in CsMn(tfa) 3 since it has no hydrogen atoms. Hydrogen bonds are established with acuo (as in K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O and Rb 2 Mn 2 (tfa) 6 •H 2 O) and/or protonated trifluoroacetato ligands as hydrogen donors (as in Na 2 Mn 2 (tfa) 6 (tfaH) and K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O). Three-dimensional NCI plots of hydrogen bonds in Na 2 Mn 2 (tfa) 6 (tfaH), K 2 Mn 2 (tfa) 6 (tfaH) 2 • f5 H 2 O, and Rb 2 Mn 2 (tfa) 6 •H 2 O are shown in Figure 5. A well-293 defined, disc-shaped isosurface is observed in all cases, as 294 expected for hydrogen bonds. 38 Inspection of Table 2 reveals a 295 broad range of sign(λ 2 )ρ values. These values depend on the 296 hydrogen donor involved. Hydrogen bonds involving acuo 297 donors do not vary significantly upon changing the alkali metal. 298 By contrast, those involving protonated trifluoroacetato donors 299 exhibit a large variation upon going from sodium to potassium. 300 Analysis of hydrogen bonds for each compound shows that

Figure 4 .

 4 Figure 4. Three-dimensional NCI plot of manganese-oxygen interactions in CsMn(tfa) 3 . Surfaces are colored in the [-0.07, 0.07] au range of sign(λ 2 )ρ (isosurface s = 0.5 au).

Figure 5 .

 5 Figure 5. Three-dimensional NCI plots of hydrogen bonds in (a) Na 2 Mn 2 (tfa) 6 (tfaH), (b) K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O, and (c) Rb 2 Mn 2 -(tfa) 6 •H 2 O. Surfaces are colored in the [-0.07, 0.07] au range of sign(λ 2 )ρ (isosurface s = 0.5 au).

Figure 6 .

 6 Figure 6. (a, b) Three-dimensional NCI plots of potassium-oxygen and potassium-fluorine interactions in K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O. Plots are shown for the two distinct potassium atoms in the structure. Surfaces are colored in the [-0.04, 0.04] au range of sign(λ 2 )ρ (isosurface s = 0.5 au). Electrostatic K-O/F interactions are characterized by disc-shaped isosurfaces. van der Waals interactions, on the other hand, are depicted by diffuse isosurfaces.

K 2

 2 438(tfa) 3 ).These results further confirm that van der Waals 439 interactions are more significant in CsMn(tfa) 3 than in 440 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O. Unit cells employed in these 441 calculations are given in the Supporting Information (Figure 442 S3). 443 van der Waals interactions in K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O and 444 CsMn(tfa) 3 were further probed by means of three-dimen-445 f7 sional NCI plots; these are shown in Figure 7a,b. The profile of 446 these interactions in K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O displays ex-447 tended green isosurfaces, as expected for dispersive inter-448 actions. Fluorine-fluorine and fluorine-oxygen interactions 449 between atoms belonging to different trifluoroacetato ligands 450 are observed (Figure 7a). In the case of CsMn(tfa) 3 , van der 451 Waals interactions between threads are depicted by a large 452 number of green isosurfaces (Figure 7b). An interesting finding 453 is that alkali-fluorine interactions in CsMn(tfa) 3 are of 454 electrostatic rather than dispersive nature, despite the large 455 number of green isosurfaces and the large contribution of 456 dispersive interactions to crystal cohesion. This contribution 457 can be appreciated by noting that dispersive interactions are 458 present in the interlayer space in K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O

Figure 7 .

 7 Figure 7. Three-dimensional NCI plots of dispersive interactions in (a) K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O and (b) CsMn(tfa) 3 . Surfaces are colored in the [-0.06, 0.06] au range of sign(λ 2 )ρ (isosurface s = 0.5 au). As expected for dispersive interactions, isosurfaces appear extended and diffuse. The interlayer space in K 2 Mn 2 (tfa) 6 (tfaH) 2 • H 2 O and the threads in CsMn(tfa) 3 are indicated with dashed lines. Cesium atoms are shown in turquoise green, manganese in purple, oxygen in red, carbon in brown, and fluorine in gray.

  520 compositional dependence of noncovalent metal-ligand 521 interactions in hybrid fluorinated crystals. These principles 522 should contribute to the design and predictive synthesis of 523 hybrid crystals with tailored dimensionality and crystal packing 524 via compositional tuning of NCIs. From a methodological 525 standpoint, the combination of NCI methodology, BCPs 526 search, a simple charge model, and calculation of the dispersive 527 contribution to the total energy served to identify and 528 quantitatively characterize alkali-organofluorine interactions, 529 which are challenging to probe by other methods. The NCI 530 approach allowed us to go beyond the "sum of radii" 531 approximation routinely used to empirically define metal-532 organohalogen contacts and enabled identification of these 533 contacts based on rigorous quantum-chemical principles. A 534 similar analysis would not have been possible solely on the 535 basis of the total energy or the wave function. 536 ■ ASSOCIATED CONTENT 537 * S Supporting Information 538 The Supporting Information is available free of charge on the 539 ACS Publications website at DOI: 10.1021/acs.cgd.8b01105. 540 (1) Details of DFT methodology selection. (2) Addi-541 tional three-dimensional NCI plots of manganese-542 oxygen and alkali-oxygen/fluorine interactions. (3) 543 Details of the charge model employed for classifying 544 noncovalent alkali-fluorine interactions. (4) Calculation 545 of the dispersion contribution to the total crystal energy 546 of Na 2 Mn 2 (tfa) 6 (tfaH), K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O, 547 Rb 2 Mn 2 (tfa) 6 •H 2 O, and CsMn(tfa) 3 . (5) Unit cells 548 employed in the calculation of the interaction energies 549 between layers and threads in K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 .M.) E-mail: julen@unizar.es. 554 *(J.C.-C.) E-mail: contrera@lct.jussieu.fr. 555 ORCID 556 Julen Munaŕriz: 0000-0001-6089-6126 557 Federico A. Rabuffetti: 0000-0001-8500-3427 558 Julia Contreras-García: 0000-0002-8947-9526 559 Notes 560 The authors declare no competing financial interest. 561 ■ ACKNOWLEDGMENTS 562 J.M. acknowledges the financial support provided by the 563 Spanish MECD (FPU14/06003 and EST16/00466). In 564 addition, the resources from the supercomputer "memento", 565 technical expertise, and assistance provided by BIFI-ZCAM 566 (Universidad de Zaragoza) are acknowledged. F.A.R. would 567 like to acknowledge the financial support of the Department of 568 Chemistry at Wayne State University. J.C.-G. acknowledges 569 CALSIMLAB and the ANR within the Investissements 570 d'Avenir program under reference ANR-11-IDEX-0004-02.

  Crystal structures of (a) Na 2 Mn 2 (tfa) 6 (tfaH) (triclinic P1̅ space-group), (b) K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O (monoclinic P2 1 /c space-group), (c) Rb 2 Mn 2 (tfa) 6 •H 2 O (monoclinic P2 1 /c space-group), and (d) CsMn(tfa) 3 (tetragonal I4 1 /a space-group). Manganese atoms are octahedrally coordinated by oxygen, while alkali atoms are coordinated by both oxygen and fluorine. K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O displays a distinct structure in which double layers are held together by van der Waals forces. Unit cells are depicted with solid lines.

	Figure 1.
	2 •H 2 O structure. A
	maximum error of 0.21% was obtained for lattice constants,
	and average errors in the 0.46-1.32% range were determined
	for interatomic distances. Interestingly, optPBE was the only
	approach that yielded negative errors for lattice constants; this likely resulted from the overestimation of dispersion forces. 59
	Conversely, the nondispersion-corrected revPBE functional
	yielded lattice constants that were significantly larger than
	those observed experimentally, as well as large errors in
	interatomic distances. Altogether, these findings highlighted

Table 1 .

 1 Performance of the revPBE-D2 Methodology

	Na 2 Mn 2 (tfa) 6 (tfaH)	0.01	0.20	0.29	0.61	1.66	2.59
	K 2 Mn 2 (tfa) 6 (tfaH) 2 •H 2 O	0.21	0.17	0.06	0.46	1.28	1.32
	Rb 2 Mn 2 (tfa) 6 •H 2 O	0.22	0.59	0.06	0.50	1.66	2.67
	CsMn(tfa) 3	2.15	n/a	-0.51	1.45	0.77	1.80

Δa (%) Δb (%) Δc (%) Δd Mn-O (%) Δ d alkali-O (%) Δ d alkali-F (%)

  2

Table 2 .

 2

	n/a	n/a	2.157-2.187
	hydrogen bonds
	H 2 O	tfaH

Sign(λ 2 )ρ (in au) for Noncovalent Interactions in Bimetallic Trifluoroacetates manganese-oxygen average range Mn-O(tfa) Mn-O(H 2 O) Mn-O(tfaH) distance range (Å) Na -0.055 [-0.065, -0.037] [-0.065, -0.050] n/a -0.037 2.104-2.354 K -0.051 [-0.063, -0.041] [-0.063, -0.044] -0.048 -0.041 2.100-2.312 Rb -0.055 [-0.062, -0.045] [-0.062, -0.054] [-0.048, -0.045] n/a 2.107-2.283 Cs -0.055 [-0.058, -0.052] [-0.058, -0.052]


Ms Tania Richmond

her PhD thesis in October 2016 on "Secure implementation of cryptographic protocols based on error-correcting codes". Her main results are the invention of novel timing attacks and power consumption analysis against code-based cryptography. Side-channel and fault injection attacks are mainly performed against symmetric cryptography. When it comes to asymmetric cryptography, this is most of the time against elliptic-curve cryptography. Her work is to adapt those techniques to code-based cryptography. Indeed, code-based cryptography is one family of the so-called post-quantum cryptography (with latticebased, multivariate-based, isogeny-based and hash-based cryptography). Side-channel attacks against code-based cryptography were proposed for the rst time ten years ago. With the recent NIST's post-quantum standardization, new schemes need to be analyzed to guarantee security against physical attacks. There are currently eighteen candidates in code-based cryptography.

2.1.2

Prof. Lejla Batina is an expert on side-channel analysis methods, fault attacks and countermeasures for secure embedded devices. She recently has been looking into machine learning for security and privacy and how to use it for side-channel analysis. On the defending side, she is interested in low-cost countermeasures against all kinds of physical attacks. Moreover she is currently supervising a PhD student, M. Pedro Maat C. Massolino, who did this Master's thesis on an hardware implementation of a code-based cryptosystem. These knowledge combined with Tania's research expertise may lead to a promising collaboration, where both partners may contribute from each other. In a so-called Side-Channel Attack (SCA), an attacker can exploit laws of physical phenomena in order to obtain information contained in channels associated to an implementation (software or hardware). The side-channel does not aim at transmitting intentionally some information. It leaks information that an observer can interpret. The rst one was proposed by Kocher in 1996 [START_REF] Paul | Timing attacks on implementations of Die-Hellman, RSA, DSS, and other systems[END_REF]. The most famous attacks are based on time and power, but not limited to these channels. Indeed, an attacker can try for example to exploit electromagnetic or acoustic leakage.

Scientic Mission Details

Then, an attacker can use these additional information to drastically reduce the work factor for a key recovery attack. Indeed, one advantage of SCA over traditional cryptanalysis is that SCA can apply a divide-and-conquer approach to recover the message or more eciently the secret/private key. We give here a brief orverview of machine learning techniques. We do not claim that it is exhaustive. For instance, we are not talking about genetic algorithms in this report.

Neural networks family, or more precisely Articial Neural Networks (ANNs), is a widely used machine learning family of algorithms. ANNs are inspired from Biological Neural Networks to simulate biological learning systems in the human brain. A very simple type of a neural network is called perceptron (i.e. an articial neuron). A perceptron is a linear binary classier applied to the feature vector. Each vector component has an associated weight w i and each perceptron has a threshold value . The output of a perceptron equals "1" if the direct sum between the feature vector and the weight vector is larger than zero and " 1" otherwise. A perceptron is depicted in Figure 1. By adding more layers to a perceptron, we arrive to the Multi Layer Perceptron (MLP) algorithm. A neural network (e.g. MLP algorithm) consists of three or more layers: an input lay, one or more hidden layers, and an output layer. Data is used as the input layer, then is modied in the hidden layer(s) and the result is got from the output layer (see Figure 2). The hidden layers in a MLP algorithm must consist of non-linear activating nodes. Notice that more than one hidden layer is considered as a deep learning architecture. To dene a neural network, we need to know the parameters: the number of hidden layers, the basic multiplication operation, and the activation functions. One can see in Figure 3 dierent architectures of neural networks. MLPs were described above because of their interest in this work. The activation function of a MLP is a linear combination of a given set of inputs. In case of a CNN, the activation function is a convolutional function, and for RNN, a time notion appears because the activation function takes in inputs from previous states.

Related works

Side-channel analysis using machine learning techniques was rst introduced by Hospodar et al. in [START_REF] Hospodar | Machine learning in side-channel analysis: a rst study[END_REF]. They considered a classication algorithm to attack a software implementation of the Advanced Encryption Standard (AES) through the power consumption. They also compared this new approach to template attacks (in the category of proling side-channel analysis).

A comparison between template attacks and machine learning in SCA was proposed by Lerman et al. in [START_REF] Lerman | Template attacks vs. machine learning revisited (and the curse of dimensionality in side-channel analysis)[END_REF]. Then few works followed to demonstrate the eectiveness of machine learning techniques against classical proled side-channel attacks [START_REF] Jap | Support vector regression: Exploiting machine learning techniques for leakage modeling[END_REF][START_REF] Picek | Side-channel analysis and machine learning: A practical perspective[END_REF].

In [START_REF] Maghrebi | Breaking cryptographic implementations using deep learning techniques[END_REF], Maghrebi et al. extended this work to proling techniques based on deep learning. They targeted an unprotected hardware AES and a rst-order masked AES software implementation. They compared their results in deep learning-based attacks to machine learning-based and template attacks. More recently, neural networks have been applied in SCAs to increase the attacker capabilities [START_REF] Gilmore | Neural network based attack on a masked implementation of AES[END_REF][START_REF] Kong | The investigation of neural networks performance in sidechannel attacks[END_REF].

SCAs have been frequently used for cryptanalysis, in particular for key recovery attacks in cryptography and for reverse engineering of cryptographic algorithms. However, usage of side-channel leakage in order to attack machine learning architectures is much less investigated. In [START_REF] Hua | Reverse engineering convolutional neural networks through side-channel information leaks[END_REF], Hua et al. showed how to reverse engineer AlexNet and SqueezeNet, two CNNs, through memory and timing information leakages. Parashar et al. obtained the weight of the neural networks by attacking a specic operation (i.e. the zero pruning) in [START_REF] Parashar | SCNN: An accelerator for compressed-sparse convolutional neural networks[END_REF]. More recently, in [START_REF] Wei | I know what you see: Power side-channel attack on convolutional neural network accelerators[END_REF] Wei et al. recovered the input image from a power consumption analysis on an FPGA-based CNN.

First direction

In [START_REF] Batina | CSI neural network: Using side-channels to recover your articial neural network information[END_REF] Lejla Batina et al. explore the problem of reverse engineering a neural network via a simple power analysis, from a more generic perspective and in a grey to black box setting. Dierential Power Analysis is used to recover secret weights from a pre-trained network. Horizontal Power Analysis is used to perform input recovery attack for a known network where they show that it works very well for medium to large sized networks. They conclude that using an appropriate combination of Simple Power Analysis and Dierential Power Analysis techniques, all sensitive parameters of the network can be recovered. Moreover, a powerful Horizontal Power Analysis method is used to recover secret inputs from a known network in a single shot side-channel analysis. As neural network algorithms are often optimized for performance, the presence of such side-channels is often ignored. The idea is to extend this work by reverse engineering a neural network implemented on a FPGA in order to compare our results with [START_REF] Hua | Reverse engineering convolutional neural networks through side-channel information leaks[END_REF][START_REF] Parashar | SCNN: An accelerator for compressed-sparse convolutional neural networks[END_REF][START_REF] Wei | I know what you see: Power side-channel attack on convolutional neural network accelerators[END_REF].

Code-based cryptography

Cryptography is the art to scramble a message for any undesirable reader. This principle appears in Antiquity. Modern cryptography (also known as public-key cryptography) used in real life is based on number theory, with factorization and discret logarithm problems. But since 1994 [START_REF] Shor | Algorithms for quantum computation: discrete logarithms and factoring[END_REF], the cryptographers' community knows that those problems can be solved in reasonable time with a sucient quantum computer. An ecient quantum computer has not yet been built but progess is constantly made by IBM/Google. Consequently, NIST has begun to prepare for the transition to quantum-resistant cryptography, with a standardization process started in 2017 [START_REF]Post-quantum cryptography standardization[END_REF]. The selection criteria will include security and performance criteria.

Post-quantum cryptography includes any cryptography that is based on hard problems unbroken yet by a quantum algorithm. One solution can be found in coding theory with the so-called syndrome decoding problem [START_REF] Berlekamp | On the inherent intractability of certain coding problems[END_REF]. The rst code-based cryptosystem was proposed by McEliece in 1978 [START_REF] James | A public-key cryptosystem based on algebraic coding theory[END_REF]. Unfortunately, due to large keys, the McEliece cryptosystem did not become as popular as the RSA cryptosystem, based on the facorization problem [START_REF] Rivest | A method for obtaining digital signatures and public-key cryptosystems[END_REF] and proposed the same year. Improvements have been done regarding key sizes. On one hand, dierent families of codes have been proposed, with interesting propoerties. On the other hand, storage capabilities have been increased in forty years.

Error-correcting codes

Error-correcting codes (codes in short) were rst considered, as their name suggests, to correct errors in a message sending through a noisy channel. Since 1978, codes are also considered in cryptography [START_REF] James | A public-key cryptosystem based on algebraic coding theory[END_REF]. Linear codes are the most common because all codewords can be generated thanks to a basis (smaller set), so it is easier to describe them. The most promissing families are Goppa codes (originally proposed, but the large keys, in Hamming metric) [START_REF] Valerii | A new class of linear error-correcting codes[END_REF], QC-MDPC codes (codes with Quasi-Cyclic Moderate Density Parity-Check matrices, in Hamming metric) [START_REF] Misoczki | MDPC-McEliece: New McEliece variants from moderate density parity-check codes[END_REF] and LRPC codes (codes with Low-Rank Parity-Check matrices, equivalent to QC-MDPC codes in Rank metric) [START_REF] Gaborit | Low rank parity check codes and their application to cryptography[END_REF].

Related works

Side-channel analysis against code-based cryptographic protocols using Goppa codes were proposed rst by Falko Strenzke during his PhD [START_REF] Strenzke | Eciency and Implementation Security of Code-based Cryptosystems[END_REF], essentially by timing analysis. This work has been improved by Tania Richmond during her PhD [START_REF] Richmond | Secure implementation of cryptographic protocols based on errorcorrecting codes[END_REF], for timing attacks and power consumption analysis. In the meantime, Ingo von Maurich focused on QC-MDPC codes during his PhD [22], essentially by power consumption analysis.

Second direction

The main issue today for companies is that post-quantum cryptosystems are too big to t in a microcontroller. To show them that they should consider more closely post-quantum cryptography and especially code-based cryptography, the objective is to provide some microcontroller implementations based on the C code of certain NIST submissions. Because of their simple keys' representation, QC-MDPC codes seem to be the best option to start with. NIST submissions based on QC-MDPC codes are BIKE1 and QC-MDPC KEM 2 . Before the NIST standardization process, one implementation was proposed by Tung Chou on a Cortex-M4 microcontroller 3 .

This last implementation is already under analysis by Tania Richmond, in collaboration with Annelie Heuser and Benot G erard4 .

Conclusion and perspectives for this collaboration

During this short term scientic mission, we manage to x ideas about what we could work on together. We explore two possible topics:

1. investigate a neural network implemented in hardware (FPGA) in terms of side-channel resilience:

(a) nd a VHDL implementation of a neural network, in particular a multi layer perceptron; (b) integrate it on a FPGA and adapt the attack proposed by Lejla Batina et al. in [START_REF] Batina | CSI neural network: Using side-channels to recover your articial neural network information[END_REF] to this type of device;

2. side-channel analysis of NIST proposals:

(a) integrate the C implementation of BIKE or QC-MDPC KEM in a microcontroller, using for instance the piñata board5 ; (b) analyze them.

In the future, we expect to solve the debbuging part for the integration in a microcontroller of some code-based submissions to the NIST standardization. More exchanges are expected between our two teams to continue our collaboration.

3. 1

 1 Side-channel attacks and machine learning techniques 3.1.1 Side-channel attacks

ArticialFigure 3 :

 3 Figure 3: Dierent Neural Networks

http://bikesuite.org/

https://csrc.nist.gov/CSRC/media/Projects/Post-Quantum-Cryptography/documents/round-1/ submissions/QC_MDPC_KEM.zip

http://www.win.tue.nl/ ~tchou/qcbits/

https://labh-curien.univ-st-etienne.fr/cryptarchi/workshop18/abstracts/richmond.pdf

https://www.riscure.com/product/pinata-training-target/