Paola Peluso
email: paola.peluso@cnr.it.

Victor Mamane
email: vmamane@unistra.fr.

Alessandro Dessì

Roberto Dallocchio

Emmanuel Aubert

Carlo Gatti

Debby Mangelings

Sergio Cossu

Halogen bond in separation science: A critical analysis across experimental and theoretical results

Keywords: Chromatography, Enantioseparation, Halogen bond, Molecular modelling, Separation science

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

Introduction

Separation science deals with theory, methods and technologies related to separation of chemical compound mixtures [START_REF] Bowser | Recent developments towards a unified theory for separation science[END_REF][START_REF] Guiochon | Separation science is the key to successful biopharmaceuticals[END_REF][START_REF] Kuehnbaum | New advances in separations for metabolomics: resolving chemical diversity in a post-genomic era[END_REF]. A separation process must be able to discriminate molecules in a multicomponent mixture. Therefore, the knowledge of size, shape, and structure of the molecular components of a mixture is a basic requirement to design a tailored separation system. Indeed, properties of the molecules which are involved in the separation process determine separation mechanisms and noncovalent interactions which underlie mixture formation and separation.

When molecules are at work to carry out a specific function in molecular and supramolecular systems, they relate to each other by means of noncovalent interactions [4,[START_REF] Schneider | Quantification of noncovalent interactions -Promises and problems[END_REF], which represent the essential elements of the code by which molecules are able to transfer the information contained in their structure [START_REF] Lehn | Supramolecular chemistry -Scope and perspectives, molecules, supermolecules, and molecular devices[END_REF]. These molecular relationships underlie mechanisms in several fields [START_REF] Mahadevi | Cooperativity in noncovalent interactions[END_REF], and also makenoncovalent interactions a modern tool for design, preparation and function of advanced processes and materials in separation science [START_REF] Kanao | Separation of halogenated benzenes enabled by investigation of halogen- interactions with carbon materials[END_REF].

Among noncovalent interactions, in the last decades halogen bonds (XBs) have found practical applications in several fields covering catalysis, crystal engineering, functional and soft materials, molecular recognition, supramolecular chemistry and biological, medicinal and pharmaceutical chemistry [START_REF] Cavallo | The halogen bond[END_REF][START_REF] Costa | The halogen bond: nature and applications[END_REF][START_REF] Wilcken | Principles and applications of halogen bonding in medicinal, chemistry and chemical biology[END_REF]. Nevertheless, separation processes promoted by XB are reported in smaller degree [START_REF] Kanao | Separation of halogenated benzenes enabled by investigation of halogen- interactions with carbon materials[END_REF][START_REF] Yan | Halogen bonding: a new retention mechanism for the solid phase extraction of perfluorinated iodoalkanes[END_REF][START_REF] Lara | Halogen bonding for increasing efficiency in liquidliquid microextraction: application to the extraction of hexabromocyclododecane enantiomers in river water[END_REF][START_REF] Zhang | Star-shaped oligothiophene-functionalized truxene materials as stationary phases for capillary gas chromatography[END_REF][START_REF] Yu | Amphiphilic triptycene-based stationary phase for high-resolution gas chromatographic separation[END_REF][START_REF] Takeuchi | Molecularly imprinted polymers with halogen bonding-based molecular recognition sites[END_REF]. In particular, despite the pivotal role of noncovalent interactions in LC enantiomer distinction [START_REF] Lämmerhofer | Chiral recognition by enantioselective liquid chromatography: mechanisms and modern chiral stationary phases[END_REF][START_REF] Scriba | Chiral recognition in separation sciences. Part I: Polysaccharide and cyclodextrin selectors[END_REF], surprisingly, for a long time XBs were unexplored in the enantioseparation science [START_REF] Peluso | Insights into the impact of shape and electronic properties on the enantioseparation of polyhalogenated 4,4'-bipyridines on polysaccharide-type selectors. Evidence of stereoselective halogen bonding interactions[END_REF].

Various reasons have contributed to make the study of XB in separation science challenging. First, halogen substituents can contribute to separation and molecular recognition process by playing multiple roles (hydrophobic site, electron-withdrawing atom, repulsive interaction site, HB acceptor), and the presence of electrophilic regions on bound halogens has to be confirmed theoretically. Indeed, XB comprehension mostly depends on its physical description at theoretical level [START_REF] Kolář | Computer modeling of halogen bonds and other σ-hole interactions[END_REF][START_REF] Nunes | Tackling halogenated species with PBSA: effect of emulating the σ-hole[END_REF][START_REF] Dallocchio | Halogen bond in high-performance liquid chromatography enantioseparations: description, features and modelling[END_REF]. Then, often separation processes occur in solution, and the study of XB in solution [START_REF] Carlsson | Halogen bonding in solution[END_REF] is a more demanding task compared to solid state studies. For example, the chromatography environment is a complex solvated system. Finally, limited availability of brominated and iodinated analytes makes the study of halogen effect on separation processes challenging.

In this perspective, the aim of this paper is to provide a critical analysis of the topic. For this purpose, firstly, XB is profiled by describing its main features. Secondly, the few studies on XB applications in separation science reported so far in the literature are discussed. Then, with the aim to explore and clarify some still open issues, we described herein up-to-date results performed by our laboratories specifically for this purpose and emerging from i) a theoretical re-examination of some literature studies using the density functional theory (DFT) method, and ii) an experimental exploration under supercritical fluid chromatography (SFC) conditions. This multidisciplinary approach is in agreement with recent trends in separation science where theoretical methods are integrating more and more with experiments in order to develop separation systems with high capacity, robustness, and selectivity.

Experimental

Chemicals

Compounds 39i, 39s, and 39v were synthetized as reported [START_REF] Mamane | Chiral hexalogenated 4,4'-bipyridines[END_REF]. Pure enantiomers of compounds 39i, 39s, and 39v were obtained by HPLC enantioseparation and their absolute configuration were assigned on the basis of X-ray diffraction or by comparison of theoretical/experimental electronic circular dicroism spectra, as previously described [START_REF] Peluso | Polysaccharide-based chiral stationary phases as halogen bond acceptors: a novel strategy for detection of stereoselective -hole bonds in solution[END_REF].

Chromatography

For analyses under normal phase (NP) elution conditions, a Merck-Hitachi Lachrom Elite gradient HPLC system with photodiode array detection (Tokyo, Japan) and an Agilent Technologies (Waldbronn, Germany) 1100 Series HPLC system (Agilent Technologies ChemStation Version B.04.03 chromatographic data software) were employed. Analyses under SFC were performed by using a Waters UPC² SFC system with photodiode array detection. The carbon dioxide (CO 2 ) advised by the manufacturer of the SFC equipment was used, i.e. quality 2.7 (purity >99.7%) (Linde Gas, Grimbergen, Belgium). Lux Cellulose-1 (Phenomenex, USA) (cellulose tris-3,5-dimethylphenylcarbamate; 5 m), was used as a chiral column (250 × 4.6 mm). HPLC grade n-hexane, and 2-propanol were purchased from Sigma-Aldrich (Taufkirchen, Germany). Analyses were performed in isocratic mode at 25°C. The flow rate was set at 0.8 and 1 ml/min. The enantiomer elution order (EEO) was determined for compounds 39i, 39s, and 39v by injecting enantiomers of known absolute configuration.

Computationals

Geometry optimization and computation of electrostatic potentials mapped on 0.002 au isosurfaces (V S (r)) and related parameters (V S (r) extrema, maxima (V S,max ) and minima (V S,min ) values, given in kJ/mol or au) were performed and graphically generated by using Spartan' 10 Version 1.1.0 (Wavefunction Inc., Irvine, CA) [START_REF] Shao | Advances in methods and algorithms in a modern quantumchemistry program package[END_REF] (DFT method with the B3LYP functional and the 6-311G* basis set) and Gaussian 09 (Wallingford, CT 06492, USA) [27] (DFT/B3LYP/def2-QZVP and DFT/M06-2X/def2-QZVP). Values of V S (r) were used as an indicator of the molecular charge distribution [START_REF] Riley | Comparative analysis of electrostatic potential maxima and minima on molecular surfaces, as determined by three methods and a variety of basis sets[END_REF]. On the isosurface, colours towards red depict negative mapped potentials, while colours towards blue depict positive potentials and colours in between (orange, yellow, green) depict intermediate values of the mapped potential. Search for the exact location of V S,max and V S,min was made through the Multiwfn code [START_REF] Lu | Multiwfn: a multifunctional wavefunction analyzer[END_REF] and through its module enabling quantitative analyses of molecular surfaces [START_REF] Lu | Quantitative analysis of molecular surface based on improved marching tetrahedra algorithm[END_REF] for several isovalue surface fields and mapped properties thereon. For compounds 39s, 39t, and 39u, electrostatic potential source function decomposition analysis was performed as reported [START_REF] Peluso | Enantioseparation of fluorinated 3-arylthio-4,4'-bipyridines: insights into chalcogen and -hole bonds in high-performance liquid chromatography[END_REF].

Halogen bond

Brief history

The first observed XB-based association was the iodine-ammonia complex (I 2 •••NH 3 ) obtained by Colin in 1814 through the reaction of iodine and gaseous ammonia [START_REF] Colin | Note sur quelques combinaisons de l'iode[END_REF]. Later the same complex was reported by Guthrie upon reaction between iodine and liquid ammonia [START_REF] Guthrie | On the iodide of iodammonium[END_REF]. Then, other theoretical and experimental studies were performed, nevertheless for a long time these data were unable to provide a comprehensive picture of the XB [START_REF] Cavallo | The halogen bond[END_REF].

On the contrary, in the late twentieth century, important observations and experiments brought the great potential of XB to light, and allowed to recognize that the electrophilic behaviour of halogens is a commonplace event rather than exceptional, occurring in the solid, liquid and gas phase [START_REF] Cavallo | The halogen bond[END_REF][START_REF] Costa | The halogen bond: nature and applications[END_REF]. The first use of the term XB can be traced back to the study of Zingaro and Hedges in 1961 [START_REF] Zingaro | Phoshine oxide-halogen complexes: effect on P-O and P-S stretching frequencies[END_REF], the authors describing the complexes formed between halogens and phosphine oxides or phosphine sulphides. In 1968, Bent published a review on the chemistry of donor-acceptor adducts, where he treated about "Organic Molecules with Oxygen Atoms as Electron Donors and Halogen Atoms as Acceptors" and "Molecules with Halogen Atoms as Electron Donors and/or Acceptors". In this paper, the author highlighted the distinctive geometric features of the interactions, evidencing that the distances between the electron donor atom and the halogen atom were shorter than the sum of their respective van der Waals radii [START_REF] Bent | Structural chemistry of donor-acceptor interactions[END_REF]. Later, in his Nobel lecture, Hassel considered that "Particular importance may be attributed to complexes in which direct bonding exists between one atom belonging to the donor molecule and another atom belonging to the acceptor molecule. Complexes of this kind are above all those formed by donor molecules containing atoms possessing "lone pair electrons" and halogen or halide molecules" [START_REF] Hassel | Structural aspects of interatomic charge-transfer bonding[END_REF].

Finally, in 2013 the International Union of Pure and Applied Chemistry issued the "Definition of the halogen bond (IUPAC recommendations 2013)" stating that "a halogen bond occurs when there is evidence of a net attractive interaction between an electrophilic region associated with a halogen atom in a molecular entity and a nucleophilic region in another, or the same, molecular entity" [START_REF] Desiraju | Definition of the halogen bond (IUPAC recommendations 2013)[END_REF].

Halogen bond and -hole bonds

In 1992, Brinck, Murray and Politzer proposed the first theoretical explanation of the XB introducing two basic concepts: the anisotropic charge distribution on bound halogens and the definition of the hole as a region of electronic charge density depletion, which is located on the surface of halogen atoms and usually characterized by a positive electrostatic potential [START_REF] Brinck | Surface electrostatic potentials of halogenated methanes as indicators of directional intermolecular interactions[END_REF]. On this basis, the XB originates from the anisotropic charge distribution which characterizes bound halogens, in particular when they are bound to electron withdrawing groups (EWGs). It means that an area of lower electron density, located on the elongation of the covalent bond, the -hole, coexists with an area of higher electron density, which forms a belt orthogonal to the covalent bond (Fig. 1) [START_REF] Clark | Halogen bonding: the σ-hole[END_REF]. Other atoms were found to interact by means of -hole regions, therefore XBs are a subset of the socalled -hole bonds. This wide family of noncovalent interactions involves an electrophilic region of electronic charge density depletion (the -hole) centred on bound atoms of groups 13-18 (-hole donors), which behave as Lewis acids, and a -hole acceptor, a Lewis base (Table 1) [START_REF] Politzer | Halogen bonding and other -hole interactions: a perspective[END_REF].

Features of the halogen bond

The anisotropic charge distribution explains the amphoteric behaviour of the halogens which behave as Lewis bases, or as XB donors with properties of Lewis acids able to interact with an acceptor through the -hole. The most important feature of the XBs is tunability, the strength of a XB depending on the properties of donor, acceptor and medium, and it increases as the polarizability and the electronegativity of the halogen increases and decreases, respectively. So, XB strength increases following the order F < Cl < Br < I, bromine and iodine being considered as more powerful XB donors. Concerning medium, in general solvents possessing hydrogen bond donor functionalities destabilize the XBs because of XBhydrogen bond competition. Indeed, molecules with properties as Lewis bases can act as acceptors towards both halogen and hydrogen bond donors.

Another distinctive feature of the XB is directionality (Fig. 2), with defined geometrical parameters, ). In this regard, a parameter to measure the strength of the XB is the penetration parameter (p.p.) [START_REF] Mamane | Chiral hexalogenated 4,4'-bipyridines[END_REF] which is calculated as the percentual reduction of the sum of van der Waals radii of the interacting atoms, indicating the penetration degree of the van der Waals spheres. Due to the physical nature of the XBs, computational tools and studies in silico have greatly contributed to their understanding [START_REF] Kolář | Computer modeling of halogen bonds and other σ-hole interactions[END_REF], explaining experimental results and guiding experiment design.

In particular, -hole being a region of electronic charge density depletion, calculated V S (r) has been widely used as an indicator of the anisotropy of the molecular charge distribution. In this regard, the evaluation of the V S,max on the halogen surfaces allows for a quantitative estimation of the -hole depth [START_REF] Brinck | The molecular surface property approach: a guide to chemical interactions in chemistry, medicine, and material science[END_REF] which, in turn, determines the capability of a halogen as XB donor.

Nowadays the nature of XBs still remains matter of hot discussion in order to define the relative importance of electrostatic, dispersion, charge transfer and polarization contributions when XB occurs [START_REF] Cavallo | The halogen bond[END_REF][START_REF] Wang | -Hole bond vs -hole bond: a comparison based on halogen bond[END_REF][START_REF] Andrés | Nine questions on energy decomposition analysis[END_REF]. In this regard, it is worth noting that the studies on the nature of the XB, which have been published so far, tend to be often contradictory in their conclusions. It is likely that this apparent lack of coherence is due to the fact that the relative importance of the different contributions depends on the system, which consists of donor, acceptor and medium [START_REF] Costa | The halogen bond: nature and applications[END_REF].

On the other hand, the general features of the XB are well explained on the basis of its electrostatic nature. In particular, a pure electrostatic model gives reasonable correlations to experimental data gathered in apolar solvents, even if it is unsuitable for the description of XBs in polar systems [START_REF] Carlsson | Halogen bonding in solution[END_REF].

Recently, Clark proposes a protocol consisting of three level of interaction for the analysis of weak intermolecular interactions such as XB: i) a first level containing the classical  + - -electrostatic interactions (permanent electrostatic interactions) that can be evidenced by inspecting the unperturbed V S (r) at the standard isodensity surfaces of an isolated molecule [START_REF] Riley | Comparative analysis of electrostatic potential maxima and minima on molecular surfaces, as determined by three methods and a variety of basis sets[END_REF], ii) the second level improves the previous view by introducing the mutual polarisation of interacting molecules (induced electrostatic interactions), and iii) finally, the third level includes dispersion, which is not is not a real, measurable quantity and can only be observed as a difference between mean-field calculations and those that consider electron correlation [START_REF] Clark | Halogen bonds and -holes[END_REF].

Halogen bond in separation science: a literature survey

Solid-phase extraction of iodoperfluoroalkanes

In 2012, Jin and co-workers described the unprecedented utilization of XB in the solid phase extraction of perfluorinated iodoalkanes (PFIs) from n-hexane. A strong anion-exchange (SAX) sorbent

(1) (Fig. 3) functioning as XB acceptor was used, which forms an associate with PFIs 2 and 3 behaving as XB donors [START_REF] Yan | Halogen bonding: a new retention mechanism for the solid phase extraction of perfluorinated iodoalkanes[END_REF]. PFIs are persistent organic pollutants, being key intermediates for the synthesis of fluorochemicals and fluoropolymers. In this study, following a multidisciplinary approach, nine PFIs, as test probes, were analysed by UV, 19 F NMR and Raman spectroscopies in order to demonstrate the occurrence of C-

I•••Cl -XB interactions.
The results showed that the adsorptivities of SAX for the ,diiodoperfluoroalkanes (DIPFAs) 2 were stronger than those for the monoiodo-PFIs 3. In particular, SAX proved to have no adsorption for hexafluorobenzene, which has no properties as XB donor.

Therefore, the application of XB in solid-phase extraction provides a new retention mechanism in extraction processes. Moreover, this investigation paved the way to the utilization of XB in chromatography and to the idea, which our group will develop later ( § 5), that XBs could also work on chiral sorbents to promote enantiomer distinction.

It is worth mentioning that in 2009 Resnati and co-workers had showed that the organic salts bis(trimethylammonium)alkane diiodides 4 (Fig. 4) could resolve mixtures of DIPFAs 2 by means of crystallization from solution [START_REF] Metrangolo | Nonporous organic solids capable of dynamically resolving mixtures of diiodoperfluoroalkanes[END_REF] promoted by I•••I -XB interactions. Interestingly, the solid-state salts could also selectively bind the DIPFAs from the vapor phase, yielding the same adducts formed from solution. Later, the group of Jin also investigated the adsorption of iodoperfluoroarenes (IPFArs) (Fig. 5) on SAX promoted by XB, using again n-hexane as a solvent [START_REF] Li | Halogen bonding-assisted adsorption of iodoperfluoroarenes on a strong anion exchanger and its potential application in solid-phase extraction[END_REF]. On the basis of 19 F NMR titration experiments, UV spectrometric titrations and theoretical calculations, the authors showed that Cl -, as the XB acceptor, is better than Br -and I -. The adsorption efficiency of IPFArs on SAX followed the order 1,4-DITFB (5) ≈ 1,2-DITFB (6) > IPFB [START_REF] Mahadevi | Cooperativity in noncovalent interactions[END_REF], with no significant adsorption of bromoperfluoroarenes. Interestingly, prominent red shifts of characteristic Raman spectra showed that XB is unambiguously the main driving force of the adsorption process.

Molecularly imprinted polymers

In 2005, a molecularly imprinted polymer (8) (Fig. 6) bearing XB-based binding sites was developed by Takeuchi and co-workers for application in separation science [START_REF] Takeuchi | Molecularly imprinted polymers with halogen bonding-based molecular recognition sites[END_REF]. The formation of this imprinted polymer host was obtained by the polymerization of the functional monomer 2,3,5,6-tetrafluoro-4iodostyrene [START_REF] Cavallo | The halogen bond[END_REF], as the XBdonor, with divinylbenzene and styrene as cross-linking agents, in the presence of 4-(dimethylamino)pyridine [START_REF] Costa | The halogen bond: nature and applications[END_REF] as the XB acceptor templating guest. Indeed, the authors had envisaged that the XB acceptor template could recognize the XB donor sites on the host polymer, imprinting the molecular shape of the guest into the polymer [START_REF] Wilcken | Principles and applications of halogen bonding in medicinal, chemistry and chemical biology[END_REF] and generating specific binding sites selective for 10 and its structural analogues. On this basis, the binding affinity of the imprinted polymer was investigated by using XB acceptors 10 and 12-21 bearing either aliphatic or aromatic nitrogen groups. As expected, the 4-aminopyridine guests 12 and 10 showed the highest affinities for the porous polymer, which exhibited a high affinity for the less bulky 4-aminopyridine [START_REF] Yan | Halogen bonding: a new retention mechanism for the solid phase extraction of perfluorinated iodoalkanes[END_REF], suggesting that nitrogen basicity and steric hindrance may influence the recognition mechanism.

Halogen bond in liquid-liquid microextraction

Recently, Sicilia and co-workers proposed a solubilisation mechanism based on XB and dispersion interactions for increasing the efficiency in the liquid-liquid microextraction of hexabromocyclododecane (HBCD) stereoisomers ( 22) (Fig. 7) in river water, by using a supramolecular solvent (SUPRAS) [START_REF] Carlsson | Halogen bonding in solution[END_REF], which is made up of inverted hexagonal aggregates of decanoic acid in tetrahydrofuran and water [START_REF] Lara | Halogen bonding for increasing efficiency in liquidliquid microextraction: application to the extraction of hexabromocyclododecane enantiomers in river water[END_REF][START_REF] Ballesteros-Gómez | Hyphenating supramolecular solvents and liquid chromatography: tips for efficient extraction and reliable determination of organics[END_REF]. HBCDs are brominated flame retardants used in industry that can be released into the environment. For SUPRAS 23, two types of interactions with 22 were hypothesized: The same XB-based microextraction procedure had been previously proposed by the same group for speeding up the extraction of HBCD in soils and sediments [START_REF] Lara | Speeding up the extraction of hexabromocyclododecane enantiomers in soils and sediments based on halogen bonding[END_REF] and fish [START_REF] Lara | Enantiomer-specific determination of hexabromocyclododecane in fish by supramolecular solvent-based single-step sample treatment and liquid chromatography-tandem mass spectrometry[END_REF]. Unfortunately, these studies suffer from the fact that the proposed mechanism was not supported by spectroscopic analyses or theoretical calculations on both donor (HBCD) and acceptor (SUPRAS).

Halogen bond in gas-chromatography separation of haloarenes

The utilization of XB can open new possibilities for GC separation of halocarbons, a class of industrially relevant compounds. In particular, chlorobenzenes 24 and polychlorobiphenyls (PCBs) 25 (Fig. 8a) are key molecules for chemical industries and environmental analysis.

In the last few years, Qi, Wang and co-workers developed thiophene-functionalized truxene derivatives (TFT 26, TDT 27, TTT 28) [START_REF] Zhang | Star-shaped oligothiophene-functionalized truxene materials as stationary phases for capillary gas chromatography[END_REF][START_REF] Lv | Features of a truxene-based stationary phase in capillary gas chromatography for separation of some challenging isomers[END_REF] as new types of stationary phases for GC separations (Fig. 8b). The separation ability of these supports towards 24 and 25 was explored. A longer retention was observed for 24c, which was attributed by the authors to a strong XB between the chlorines of the again a XB-based retention mechanisms, the authors performed the separation of three trichlorobenzene isomers on 28 with the retention order 24a < 24b < 24c. Later, the same group reported the development of a propeller-like hexaphenylbenzene-based hydrocarbon material (BT) (29) (Fig. 9a) [START_REF] Yang | Selectivity of hexaphenylbenzene-based hydrocarbon stationary phase with propeller-like conformation for aromatic and aliphatic isomers[END_REF] which was used as the stationary phase for capillary GC.

The BT capillary column showed weak polarity and interesting selectivity for aromatic compounds, the stationary phase being characterized by -electron toroidal delocalization and intrinsic microporosity. In particular, the trichlorobenzene isomers were well resolved, the authors hypothesizing combined interactions of XB (Cl•••) (Fig. 9b), - stacking and van der Waals.

Very recently, Qi, Huang and co-workers published a series of papers dealing with the development of triptycene (TP)-based materials 30-33 for capillary GC separations (Fig. 10) [START_REF] Yu | Amphiphilic triptycene-based stationary phase for high-resolution gas chromatographic separation[END_REF][START_REF] Yang | -Extended triptycene-based material for capillary gas chromatographic separations[END_REF][START_REF] He | Triptycene-based stationary phases for gas chromatographic separations of positional isomers[END_REF]. These stationary phases exhibited high-resolution performances for a wide range of analytes, especially substituent of the analyte. The same explanation was used to justify the elution sequence nitrobenzene (34) < 1,3,5-trichlorobenzene (24a) and naphthalene (35) < m-dibromobenzene [START_REF] Hassel | Structural aspects of interatomic charge-transfer bonding[END_REF], which appeared to be against the order of boiling points of the analytes. Despite the fact that no obvious trend related to the identity of the XB emerged from the chromatographic data, the presence of iodine substituents seemed to increase retention on both columns.

Moreover, the three compounds 39i, 39o, and 39q, which were enantioseparated on Hydrodex--PM, contained iodines.

It is worth noting that all XB-based mechanisms proposed until now in GC separation represent working hypotheses which were not supported by focused spectroscopic studies, calculations or analysis in the solid state. Moreover, in these studies the separation of iodinated benzenes is missing, consequently the effect of halogens on separation was only partially evaluated.

With the aim to tackle this unexplored question by means of a case study, we calculated V S,max , V S,min , and related surface parameters for HBipys 39a-r (Table 2) and the presence of structure-GC chromatographic behaviour relationships were verified by linear regression analysis. The results reported in Table 3 show a strong correlation between retention times and molecular weight (MW), area and volume of calculated electrostatic potential surfaces, revealing a leading mechanism controlled by the analyte shapes. On the other hand, two minor statistically significant correlations were derived between retention time on both columns and V S,max values on the halogens (r 2 = 0.4961; 0.4837, P-value = 0.0011; 0.0014) and V S,min on the nitrogen (r 2 = 0.4151; 0.4075, P-value = 0.0039; 0.0044), revealing a possible minor contribution of both XB and hydrogen bond to retention.

Table 2

Retention times on Hydrodex--PM and Chirasil-Val chiral capillary columns [START_REF] Peluso | Insights into halogen bond-driven enantioseparations[END_REF], and calculated molecular properties a of HBipys 39a-r. 48 a Computation of electrostatic potential surfaces and related parameters were performed and graphically generated using the Spartan'10 Version 1.1.0 (Wavefunction Inc., Irvine, CA) program and employing the density functional theory (DFT) method with the B3LYP functional and the 6-311G* basis set.

HBipy 39 Substitution pattern R 2 -R 2' -R 3 -R 3' -R 5 -R 5' MW V S,max (X) [kJ/mol] V S,

Table 3

Linear regression analysis a describing the relationships between retention on Hydrodex--PM and Chirasil-Val chiral capillary columns [START_REF] Peluso | Insights into halogen bond-driven enantioseparations[END_REF] and calculated molecular properties of HBipys 39ar.

Hydrodex--PM

Halogen bond in normal phase liquid chromatography

Very recently, Kubo and co-workers experimentally evaluated the strength of the X- interaction between carbon-materials and a series of halogenated benzenes under NP elution conditions [START_REF] Kanao | Separation of halogenated benzenes enabled by investigation of halogen- interactions with carbon materials[END_REF], assuming that the hydrophobic interaction was completely suppressed in this environment. Under this conditions, higher retentions were observed as the number of Cl, Br, or I substituents on the benzenes increased, especially for the C70-coated column 40 (Fig. 11), which showed higher retention efficiencies than other carbon materials. In particular retention of hexahalobenzenes increased in the order F < Cl < Br < I. The carbon-materials are known to exhibit strong  interactions because of their many  electrons.

By using a multidisciplinary approach based on the combined use of chromatographic analysis, UV-Vis and NMR spectroscopy, and computational calculations, the authors envisaged the existence of bimodal interactions, the - and X- interactions, between the halogenated benzenes and aromatic materials.

Halogen bond in enantioseparation science

So far, XB in chiral systems has been reported in small degree, and few chiral XB donors and enantioselective processes promoted by XBs are known [START_REF] Cavallo | The halogen bond[END_REF].

The first example in enantioseparation science dates back to 1999, when Metrangolo and Resnati used the Lewis base (-)-sparteine hydrobromide (41) (Fig. 12) to resolve the racemic 1,2dibromohexafluoropropane (42) [START_REF] Farina | Resolution of racemic 1,2-dibromohexafluoropropane through halogen-bonded supramolecular helices[END_REF]. The resolution occurred as a result of a highly specific inclusion of only the (S)-enantiomer in a chiral crystal with a helical arrangement formed by XB between the Cbound Br atoms of 42 and the Br -ions of 41. Later, the same group performed the resolution of racemic perfluorocarbons by means of a XB-driven electron donor-acceptor recognition mechanism [START_REF] Messina | Resolution of racemic perfluorocarbons through selfassembly driven by electron donor-acceptor intermolecular recognition[END_REF]. In the field of enantioseparation science, HPLC on chiral stationary phase is widely used. In this environment, the distinction process is based on the ability of this chiral selector to recognize the enantiomers of the analyte by means of stereoselective noncovalent interactions, which are strictly dependent on chiral selector, analyte and mobile phase.

In 1996, Pirkle and co-workers had highlighted an unexpected halogen effect on the HPLC enantioseparation of halogenated amide derivatives of 1-phenylethylamine [START_REF] Pirkle | The enhancement of enantioselectivity by halogen substituents[END_REF]. Nevertheless, in this study, where Pirkle considered that "Unexpectedly, para and meta halogen substituents increase both retention and enantioselectivity when nonaqueous organic mobile phases are used. The more polarizable the halogen, the greater the effect", halogen-dependent effects on enantioseparation were never explicitly related to the XB. The reason was likely due to the fact that, for a long time F, Cl, Br and I substituents in LC enantiorecognition were merely considered as a Lewis base, in the perspective of an isotropic distribution of the electron density [START_REF] Peluso | Liquid chromatography enantioseparations of halogenated compounds on polysaccharide-based chiral stationary phases: role of halogen substituents in molecular recognition[END_REF]. On this basis, it can be expected that XB-driven enantioseparations could be recognized by means of a theoretical re-examination of some published enantioseparation processes.

Enantioseparations involving XB on polysaccharide-based CSPs: a multidisciplinary approach integrating theoretical analysis with experiments

Starting from 2014, XBs being still unexplored in HPLC enantioseparation, our group envisaged that HPLC, as a technical tool, could be successfully used to systematically investigate XBs occurring on the surface of the chiral adsorbent by properly tuning molecular properties of analyte as XB donor, selector as XB acceptor, under NP elution conditions [START_REF] Dallocchio | Halogen bond in high-performance liquid chromatography enantioseparations: description, features and modelling[END_REF][START_REF] Peluso | Polysaccharide-based chiral stationary phases as halogen bond acceptors: a novel strategy for detection of stereoselective -hole bonds in solution[END_REF][START_REF] Peluso | Insights into halogen bond-driven enantioseparations[END_REF]. With this purpose, cellulose dimethylphenylcarbamate (CDMPC) 43 was selected as a chiral stationary phase (CSP) (Fig. 13a) because of a negative V S,min (-173.3 kJ/mol) which makes carbonyl functionality a good halogen -hole acceptor, similar in terms of V S,min and site structure to other typical acceptors like acetone (-177.0 kJ/mol) or N-methylacetamide (-216.3 kJ/mol). As analytes, we have developed halogenated donors based on the electron poor 4,4'-bipyridine core (39a-v) (Fig. 13b) [START_REF] Mamane | Chiral hexalogenated 4,4'-bipyridines[END_REF],

where halogens serve as -hole sites, and inductors of chirality by restricted rotation around the 4,4'bipyridyl bond. The enantioseparation of functionalized 4,4'-bipyridines being dependent on the substituents bearing by the heteroaromatic scaffold [START_REF] Peluso | Insights into the impact of shape and electronic properties on the enantioseparation of polyhalogenated 4,4'-bipyridines on polysaccharide-type selectors. Evidence of stereoselective halogen bonding interactions[END_REF], the chromatographic response of the halogenated analogues is strictly dependent on the -hole depth, XB strength increasing from chlorine to bromine and iodine. Some halogenated bipyridines were studied in the solid state [START_REF] Mamane | Chiral hexalogenated 4,4'-bipyridines[END_REF][START_REF] Peluso | Polysaccharide-based chiral stationary phases as halogen bond acceptors: a novel strategy for detection of stereoselective -hole bonds in solution[END_REF], and nitrogenhalogen contacts, with penetration parameters increasing from chlorine to iodine (-15.1 (N•••I) ≤ p.p. ≤ -2.8 (N•••Cl)), were observed, these results proving the capability of these halogens to act as -hole donors.

To tackle the study of XB in HPLC environment, the use of distinct orthogonal techniques provides complementary information for a more comprehensive picture of XB-based enantiodistinction processes which are the result of a balanced synergy between CSP, analyte, and mobile phase. Therefore, in the last few years we have approached the question by means of a multidisciplinary study involving chromatographic analysis, X-ray diffraction analysis and theoretical calculations [START_REF] Dallocchio | Halogen bond in high-performance liquid chromatography enantioseparations: description, features and modelling[END_REF][START_REF] Mamane | Chiral hexalogenated 4,4'-bipyridines[END_REF][START_REF] Peluso | Insights into halogen bond-driven enantioseparations[END_REF].

Computational tools to design XB donors as test probes and rationalize related recognition mechanisms

The quantitative assessment of V S,max and V S,min have been found to be related to the strengths of noncovalent interactions [START_REF] Kolář | Computer modeling of halogen bonds and other σ-hole interactions[END_REF][START_REF] Riley | Comparative analysis of electrostatic potential maxima and minima on molecular surfaces, as determined by three methods and a variety of basis sets[END_REF]. In particular, the depth of -hole on halogens is related to their XB donor capability. In this regards, Murray and co-workers highlighted the importance of identifying methods and basis sets that are reliable for computing properly V S,max and V S,min [START_REF] Riley | Comparative analysis of electrostatic potential maxima and minima on molecular surfaces, as determined by three methods and a variety of basis sets[END_REF]. In general too large basis sets are not needed for this purpose. Indeed, electrostatic potential values are computed for the unperturbed molecules prior to interaction in order to assess what is likely they do. On this basis, with the aim to demonstrate the concept, herein, the V S,max values of three representative compounds 39s-u are reported comparing different functionals and basis set(Table 4). The relative values of the brominated and iodinated compounds normalized with respect to the chlorinated analogue are reported in parentheses. With all theoretical methods, the -hole on halogens increases as the atomic number of the halogen in a comparable manner, even with the smaller basis set (DFT/B3LYP/6-311G*), which gives slightly more positive V S,max and generates larger variations in -hole magnitude [START_REF] Kolář | Computer modeling of halogen bonds and other σ-hole interactions[END_REF][START_REF] Riley | Comparative analysis of electrostatic potential maxima and minima on molecular surfaces, as determined by three methods and a variety of basis sets[END_REF]. Indeed, M06-2X and def2-QZVP variations of V S,max on the halogen -hole are more contracted.

Table 4

V S,max on halogen -holes for compounds 39s-u. According with calculated V S,max on halogens, the enantioselectivity of compounds 39a-v on the CSP 43 under NP elution conditions increased following the order Cl < Br < I, and V S,max on iodine substituents, ranging from 149 kJ/mol to 154 kJ/mol, were found on compounds enantioseparated with high selectivity values ( > 2.00) [START_REF] Peluso | Insights into halogen bond-driven enantioseparations[END_REF].

Correlating molecular properties and experimental results allows for a better understanding of mechanisms underlying the discrimination process. Taking into account the hydrophobic character of halogenated compounds, two competitive mechanisms are envisaged to contribute to retention and The two P enantiomers of compounds 39i and 39v are eluted with very similar retention times and free energy changes associated with the complex formation. This means that the retention of the P enantiomers is governed by forces which are highly similar in the two enantiomers and related to their molecular shape, thus revealing a mechanism controlled by the steric fit of the P stereoisomers into the polymer groove. Differently, the M enantiomers show different elution times and free energy changes which can be reasonably related to the different -hole depth around the chiral axis. Consequently, the EEO reversal from P,M for 39i to M,P for 39v, is related to the fact that, for 39i, the iodine bond-driven mechanism is more efficient, in terms of enantiomer-CSP complex stability, compared to the mechanisms based on the steric fit. On the contrary, for compound 39v, the chlorine bond-driven mechanism is less efficient, so the M stereoisomer becomes the first eluted.

To examine in depth the origin of the observed V S,max , within a cause-effect view, we calculated the contribution of each atom of the molecule to generate the positive V S,max on the halogen (X) -holes by means of the source function mathematical tool [START_REF] Gatti | Chemical information from the source function[END_REF], on the basis of a theoretical methodology (fruitfully applied by our group to the reconstruction of chalcogen V S,max [START_REF] Peluso | Enantioseparation of fluorinated 3-arylthio-4,4'-bipyridines: insights into chalcogen and -hole bonds in high-performance liquid chromatography[END_REF]. In Table 5, the results of the electrostatic potential source function decomposition applied to the X-centred -holes in compounds 39s-u are summarized. The sign of SF is positive or negative whether the atomic source concurs or opposes to the positive potential of -hole.

Table 5

Electrostatic potential SF decomposition of V S,max at the X-centred -holes in compounds 39s-u. [START_REF] Schneider | Quantification of noncovalent interactions -Promises and problems[END_REF] 90.9 9.1 -0.010 0.006 -0.102 -0.096 0.131 0.0387 a Computation of electrostatic potential surfaces were performed and graphically generated using the Spartan'10 Version 1.1.0 (Wavefunction Inc., Irvine, CA) program and employing the density functional theory (DFT) method with the B3LYP functional and the 6-311G* basis set. Search for the exact location of V S,max was made through the Multiwfn code [START_REF] Lu | Multiwfn: a multifunctional wavefunction analyzer[END_REF] and through its module enabling quantitative analyses of molecular surfaces [START_REF] Lu | Quantitative analysis of molecular surface based on improved marching tetrahedra algorithm[END_REF].

This feature allows us to identify the molecular frameworks which contribute to the electrophilic character of halogens, furnishing valuable information to design properly compounds with properties as XB donors. Considering as reference points the -holes centred on X (n) (n = 2, 3, 5), the contribution of the pyridine ring bearing X (n) is dominant (column 2) compared to the contribution of the other ring (column 3). This response was expected on the basis of the atropisomeric topology of the two orthogonal aryl planes. Moreover, the values reported in Table 5 show that the trend EP (I) > EP (Br) > EP (Cl) for the -holes (column 9) originates from a corresponding trend of the X (column 4), (C X + X) (column 5), and N 6 (column 5) contributions which is only partly compensated by an opposite trend in the remaining ring sources (column 8). This observations highlight the pivotal role that the substituents exert on the stereoelectronic properties of the electrophilic recognition sites, guiding properly analyte design.

Moreover, the different halogen contribution to the -holes of 39s (negative) with respect to 39u (positive) could fully justify the difference in HPLC selectivity of the two compounds (: 1.16 (39s), 2.68 (39u) [START_REF] Peluso | Polysaccharide-based chiral stationary phases as halogen bond acceptors: a novel strategy for detection of stereoselective -hole bonds in solution[END_REF]), enantioseparation being driven by XBs on the cellulose-based CSP 43 under NP elution conditions. Finally, it is worth mentioning that also for the study of XB in HPLC environment molecular dynamics simulations [START_REF] Dallocchio | Halogen bond in high-performance liquid chromatography enantioseparations: description, features and modelling[END_REF][START_REF] Peluso | Recent studies of docking and molecular dynamics simulation for liquid-phase enantioseparations[END_REF] are extremely versatile to reproduce the experimental chromatographic system accounting for solvent effect and mutual conformational adjustment of analyte and selector, and to predict EEO. In particular, good agreement between experimental and simulated data was achieved by using the explicit -hole (ESH) tool [START_REF] Kolář | Computer modeling of halogen bonds and other σ-hole interactions[END_REF][START_REF] Nunes | Tackling halogenated species with PBSA: effect of emulating the σ-hole[END_REF] in order to account for the electrophilic character of the halogen moieties.

HPLC enantioseparations involving XB donors as analytes: a theoretical re-examination

In HPLC, the enantioseparations of fluorinated and chlorinated compounds are more frequent compared to those of brominated or iodinated compounds. In particular, very recently the XB has been proposed as a noncovalent interaction involved in the enantioseparation of some chlorinated compounds on polysaccharide-based CSPs. Okino and co-workers hypothesized that the enantioseparation of Columbamide D [START_REF] Andrés | Nine questions on energy decomposition analysis[END_REF] on Chiralpak AD-H is possibly driven by a XB between chlorine on the analyte and the carbamate carbonyl group of the stationary phase [START_REF] Lopez | chlorinated fatty acid amides from the marine cyanobacterium Moorea bouillonii collected in Malaysia[END_REF]. On the basis of docking results, Wang and co-workers proposed the occurrence of a XB between the chlorine atom on the benzene ring of Cyproconazole [START_REF] Clark | Halogen bonds and -holes[END_REF] and an oxygen atom on the Lux Cellulose-2 CSP [START_REF] He | Separation and detection of cyproconazole enantiomers and its stereospecific recognition with chiral stationary phase by highperformance liquid chromatography[END_REF]. Link and co-workers proposed, on the basis of docking data, the possibility of XB between the chlorine substituent of Ketamine [START_REF] Metrangolo | Nonporous organic solids capable of dynamically resolving mixtures of diiodoperfluoroalkanes[END_REF] as an analyte and the carbonyl group of the i-Amylose-3 CSP [START_REF] Hofstetter | Subcritical fluid chromatography at sub-ambient temperatures for the chiral resolution of ketamine metabolites with rapid-onset antidepressant effects[END_REF].

In this regard, with the aim to evaluate the -hole depth on chlorines in 44-46, we calculated the V S,max on chlorines at DFT level of theory (B3LYP/6-311G*) and the results are reported in Figure 15. Positive V S,max values ranging from 8.8 to 32.9 kJ/mol were found, the V S,max on the primary chlorine of Columbamide D being negative (-21.7 kJ/mol). On this basis, limited involvement is expected for the three compounds 44-46 as XB donors in the HPLC environment, chlorines being characterized by calculated V S,max on -holes lower than 50 kJ/mol [START_REF] Peluso | Insights into halogen bond-driven enantioseparations[END_REF], and functioning in competitive systems, where hydrogen bond centres are also present as recognition sites [START_REF] Dallocchio | Halogen bond in high-performance liquid chromatography enantioseparations: description, features and modelling[END_REF].

The question of the possibility of fluorine to be involved in XB in LC enantiorecognition remains rather undefined [START_REF] Eskandari | Does fluorine participate in halogen bonding?[END_REF]. Indeed, fluorine is less prone to behave as XB donor due to its high electronegativity and low polarizability, and it can act as an electrophile only when attached to strong EWGs like -CN or -F [START_REF] Cavallo | The halogen bond[END_REF].

Exploiting halogen bond in enantioseparation science: open issues and perspectives

In the next subsections we describe a series of new results emerging from experiments and theoretical calculations specifically designed and performed in order to assess open issues perspectives of XB utilization in (enantio)separation science.

Halogen bonds in supercritical fluid chromatography enantioseparations: possible role of CO 2

Non-polar pressurized carbon dioxide is considered a hexane-like solvent with respect to its elution strength [START_REF] Speybrouck | Preparative supercritical fluid chromatography: a powerful tool for chiral separations[END_REF]. Therefore, the replacement of n-hexane to carbon dioxide should cause no important changes in retention and selectivity [START_REF] Khater | Comparison of liquid and supercritical fluid chromatography mobile phases for enantioselective separations on polysaccharide stationary phases[END_REF]. In reality, carbon dioxide is not hexane-like because it is more polarizable, and it has local dipoles (C=O bonds) and partial charges on both carbon and oxygen [START_REF] Khater | Comparison of liquid and supercritical fluid chromatography mobile phases for enantioselective separations on polysaccharide stationary phases[END_REF].

Theoretical calculations and related experimental data proved that carbon dioxide can form XB-based (O=C=O•••X) associations where it acts as XB acceptor [START_REF] Zhu | Halogen bonding interactions between brominated ion pairs and CO 2 molecules: implications for design of new and efficient ionic liquids for CO 2 absorption[END_REF]. In this perspective, with the aim to verify the chromatographic response of halogenated chiral analytes under SFC conditions, we compared retention and selectivity of the enantiomeric pairs of compounds 39i and 39s, used as test probes, under SFC (carbon dioxide/2-propanol 9:1) and NPLC (n-hexane/2-propanol 9:1) on CDMPC as CSP (column: Lux Cellulose-1) in order to explore the effect of changing n-hexane to carbon dioxide on retention and enantioselectivity. Under NPLC conditions, 39i is enantioseparated with good selectivity ( = 2.30, EEO = P,M) through a recognition mechanism based on I•••O contacts, as stereoselective secondary interactions, iodine being a good XBD [START_REF] Peluso | Insights into halogen bond-driven enantioseparations[END_REF]. On the contrary, the selectivity value decreased in the case of 39s ( = 1.22, EEO = M,P), chlorine being a poor XB donor [START_REF] Peluso | Insights into halogen bond-driven enantioseparations[END_REF]. The results of the SFC/NPLC comparative experiments are presented in Table 6. In both cases the flow rate was 1 mL/min. For both racemates 39i and 39s, SFC conditions displayed lower eluotropic power than NPLC conditions, retention factors being from four to seven times higher in SFC than in HPLC, with retention increment higher for 39i compared to 39s. Indeed, for compound 39i, NPLC condition produced baseline resolution within 12 minutes, whereas SFC conditions yielded a longer 50 minutes analysis, at the same T = 25°C. Differently, analysis time increase was not so pronounced for compound 39s (elution time: normal phase, 5 min; SFC, 9 min). On this basis, polyhalogenated analytes as XB donors show stronger retention in SFC. Taking into account that on the CDMPC the carbonyls are acceptors for both XB donors and hydrogen bond donors, our results are consistent with the fact that the interaction ability of CDMPC toward hydrogen bond donors was reported to be stronger in SFC with respect to NPLC [START_REF] Khater | Comparison of liquid and supercritical fluid chromatography mobile phases for enantioselective separations on polysaccharide stationary phases[END_REF].

Both enantiomer pairs 39i and 39s were eluted in SFC keeping unchanged NPLC EEO. However, a decrease of selectivity for both analytes (39i, -37%; 39s, -12%) was observed in SFC compared to NPLC, due to a different effect of carbon dioxide on the retention of the second eluted enantiomers compared to the first eluted. Indeed, for the two second eluted enantiomers, the retention increase, moving from NPLC to SFC conditions, is lower (4.54 and 3.13 times longer for 39i and 39s, respectively) than the retention increase of the first eluted enantiomers (7.01and 3.55 times longer for 39i and 39s, respectively). In particular, for 39i, the effect is higher resulting in a higher decrease of selectivity compared to 39s.

At the molecular level, the same effect on both enantiomers could be expected if the CO 2 acts as nhexane (non-interacting solvent). On the contrary, according with the experimental data, a different effect of CO 2 is foreseeable if it associates with halogens, reasonably forming XB-based solvation clusters. In this context, halogens are less prone to be involved in XB with the CSP, thus the presence of CO 2 is more detrimental for 39i which forms stronger XBs.

On this basis, further investigations are needed to confirm these preliminary observations on the potential role of carbon dioxide in XB-based SFC recognition processes, a question so far unexplored.

2) in the case of chlorine, positive V S,max values ranging from 12.0 kJ/mol to 41.4 kJ/mol revealed the presence of electrophilic -holes on halogens, but small in magnitude. On this basis, the potential of these chlorines to be involved in XB is rather limited, in particular considering that the corresponding N-H moieties (side chains 49-52, 54 and 57), are competitive sites, showing higher positive V S,max (209.5 kJ/mol ≤ EP N-H ≤ 249.5 kJ/mol). Therefore, it is likely that analytes with properties as XB and hydrogen bond acceptors show a preference towards N-H, which is more electrophilic as recognition site;

3) higher positive V S,max were calculated for bromine in side chains 55 and 58, and as expected, the highest positive EP value was found for iodine in the side chain 59; Two pieces of information emerge from this theoretical examination: a) the presence of halogen in CSP structures does not mean that XB underlies enantiomer distinction and the magnitude of the -hole should be always evaluated theoretically; b) the potential function of iodine as XB donor (electrophile) on polysaccharide-based CSPs deserves to be considered in the next future.

Conclusions and perspectives

The studies published so far have shown that XBs can promote separation processes, where halogens behave as electrophilic descriptors. This aspect is of particular relevance in pharmaceutical, environmental and industrial analyses where the separation of halogenated compounds is not unusual.

Nevertheless, the study of XB in separation science is still in its infancy and further investigations are needed in order to find new evidences and make the concept familiar also in this field. For this purpose, a balanced synergy between experimental, theoretical methods and techniques is the best tool to set up appropriate hypotheses and achieve reliable conclusions.

In particular, a growing number of highly directional bromine and iodine-oxygen contacts have been evidenced in biological, medicinal and pharmaceutical chemistry, proving the potential of halogen substituents to contribute to ligand binding through XB [START_REF] Wilcken | Principles and applications of halogen bonding in medicinal, chemistry and chemical biology[END_REF]. On this basis, in the next future an increasing interest towards compounds containing electrophilic halogen -holes is expected in drug discovery and pharmaceutical chemistry. In this perspective, XB as a noncovalent interaction represents a pivotal tool for separation and enantioseparation of pharmaceuticals containing electrophilic holes as recognition sites. Interestingly, the discovery of the first halogen bond-driven self-disproportionation of enantiomers has been recently reported [START_REF] Terada | Possible case of halogen bond-driven self-disproportionation of enantiomers (SDE) via achiral chromatography[END_REF].

On the other hand, other interactions involving electrophilic -holes could function in separation science. In this regards, recent experiments and calculations have also paved the way for chalcogen and -hole bonds application in separation science [START_REF] Peluso | Enantioseparation of fluorinated 3-arylthio-4,4'-bipyridines: insights into chalcogen and -hole bonds in high-performance liquid chromatography[END_REF][START_REF] Yan | The competition of σ-hole•••Cland π-hole•••Clbonds between C 6 F 5 X (X = F, Cl, Br, I) and the chloride anion and its potential application in separation science[END_REF].

Fig. 1 .

 1 Fig. 1. General description of -hole and halogen bond.

  angles and distance (typical values for I•••O contacts: 2.8 Å ≤ d I•••O ≤ 3.4 Å, sum of I,O vdW radii being 3.5 Å [41]

Fig. 2 .

 2 Fig. 2. Geometrical parameters of the halogen bond.

Fig. 3 .

 3 Fig. 3. Interaction models of the PFIs (2,3) and Cl -on the SAX sorbent (1).

Fig. 4 .

 4 Fig. 4. XB adduct between bis(trimethylammonium)alkane diiodides (4) and DIPFAs (2).

Fig. 5 .

 5 Fig. 5. Structures of IPFB, 1,2-and 1,4-DITFB.

Fig. 6 .

 6 Fig. 6. (a) Preparation scheme of the molecularly imprinted polymer developed using 4-(dimethylamino)pyridine as XB acceptor template; (b) affinity order of the XB acceptor guests.

Fig. 7 .

 7 Fig. 7. (a) Structure of HBCD; (b) scheme of the nanostructure of SUPRAS.

Fig. 8 .

 8 Fig. 8. (a) analytes separated on truxene-based stationary phases; (b) Chemical structure of TFT, TDT and TTT.

Fig. 9 .

 9 Fig. 9. (a) Chemical structure of propeller-like hexaphenylbenzene-based stationary phase (BT); (b) halogen bond interaction (Cl•••) of terminal residue of the SP with 1,3,5-trichlorobenzene.

Fig. 10 .

 10 Fig. 10. Structure of TP-base materials used as stationary phase for GC separations, TQPP, TP-2IL, TP-3OB, and TP-3Im.Finally, recently, our group also explored the possibility of XB-based GC separation[START_REF] Peluso | Insights into halogen bond-driven enantioseparations[END_REF], and

Fig. 11 .

 11 Fig. 11. Structure of the C-70 coated column 40.

Fig. 12 .

 12 Fig. 12. Structure of the XB acceptor 41 and XB acceptor 42.

Fig. 13 .

 13 Fig. 13. Chromatographic system developed for the study of XB in HPLC environment: (a) CDMPC polymer as the CSP; (b) polyhalogenated 4,4'-bipyridines as the analytes.

  V S,max [kJ/mol] a program/calculation level CH 3 Cl 39s (X = Cl) 39t (X = Br) 39u (X = I) iodopentafluorobenzene Spartan b /DFT/B3LYP/6c /DFT/M06-2X/def2-QZVP --77.9 (1.00) 93.2 (1.200) 116.1 (1.490) -a In parentheses are given the relative values of the brominated and iodinated analogues normalized with respect to the chlorinated bipyridine 39s. b Spartan '10 Version 1.1.0 (Wavefunction Inc., Irvine, CA). c Gaussian 09 (Wallingford, CT 06492, USA).

Fig. 14 .

 14 Fig. 14. Comparison of enantiorecognition mechanisms of compounds 39i and 39s.

  + C X + X) SF [own ring -(N 6 +C X +X)] V S,max -hole [au]

Fig. 15 .

 15 Fig. 15. EP maxima on chlorine -hole in Columbamide D, Ketamine, and Cyproconazole.

Fig. 16 .

 16 Fig. 16. EP minima on O or N as nucleophilic recognition sites in compounds 60-63.4) from a re-examination of some chromatographic results reported by Okamoto and co-workers[START_REF] Yashima | Enantioseparation on 4-halogen-substituted phenylcarbamates of amylose as chiral stationary phases for high-performance liquid chromatography[END_REF],

Table 1

 1 Noncovalent interactions based on electrophilic -holes.

	Donor 	-hole	Acceptor 
	(Lewis acid)	bond	(Lewis base)
	B, Al, Ga, In, Tl (group 13) Triel bond
	C, Si, Ge, Sn (group 14)	Tetrel bond	O, N, S,
	P, As, Sb, Bi (group 15)	Pnictogen bond	halogen,
	S, Se, Te (group 16)	Chalcogen bond	-donor,
	F, Cl, Br, I (group 17)	Halogen bond	anion
	Kr, Xe (group 18)	Aerogen bond

Table 6

 6 Enantioseparation of HBipys 39i and 39s on CDMPC (FR = 1

	mL/min, T = 25°C) under NP (n-hexane/2-propanol 9:1) and SFC (carbon dioxide/2-propanol 9:1) conditions. a,b
	HBipy MP	k 1	k 2	α
	39i	NP SFC	1.40 (1.00) 9.82 (7.01)	3.22 (1.00) 14.61 (4.54)	2.30 (1.00) 1.49 (0.65)
	39s	NP SFC	0.49 (1.00) 1.74 (3.55)	0.60 (1.00) 1.88 (3.13)	1.22 (1.00) 1.08 (0.88)
	a Column: Phenomenex Lux 5μ Cellulose-1 (CDMPC) 250 x 4.6
	mm. Detection wavelength, 220 nm.
	b In parentheses are given the relative values of SFC
	chromatographic parameters normalized with respect to NPLC
	parameters.

Acknowledgements

This work has been partially supported by Università Ca' Foscari Venezia, Italy (Dipartimento di Scienze Molecolari e Nanosistemi DSMN, ADIR funds). P.P. sincerely thanks Prof. Bezhan Chankvetadze (Tbilisi State University, Georgia) for valuable and stimulating discussions.

Potential function of halogenated polysaccharide-based CSPs as XBDs: a theoretical examination

Polysaccharide carbamates-based CSPs are the most used for HPLC enantioseparations [START_REF] Chankvetadze | Recent development on polysaccharide-based chiral stationary phases for liquidphase separation of enantiomers[END_REF]. The polysaccharide backbone is the essential element of this polymeric system, with the conformational chirality depending on the peculiar helical twist generated by specific glycosidic linkages in cellulose and amylose polymeric chains [START_REF] Chankvetadze | Recent development on polysaccharide-based chiral stationary phases for liquidphase separation of enantiomers[END_REF][START_REF] Okamoto | Polysaccharide derivatives for chromatographic separation of enantiomers[END_REF]. Significantly, the polymer backbone is functionalized with a polar layer containing carbamate moieties able to exert polar interactions and located inside the polymer groove, and a hydrophobic layer containing substituted aromatic rings, located outside the polymer groove and able to activate - interactions (Fig. 13a) with analytes. Nowadays, different types of polysaccharide-based CSPs are commercially available, and the side chains are characterized by distinctive steric and electronic properties which are the key to the different selectivity of the corresponding CSPs. Indeed, the electronic properties of the polar layer and its ability to exert HBs are tuned by changing type and position of both alkyl-and chloro substituents onto the terminal aromatic ring [START_REF] Chankvetadze | Recent development on polysaccharide-based chiral stationary phases for liquidphase separation of enantiomers[END_REF][START_REF] Okamoto | Controlled chiral recognition of cellulose triphenylcarbamate derivatives supported on silica gel[END_REF]. On the other hand, studies on fluorinated, brominated and iodinated CSPs were published [START_REF] Yashima | Enantioseparation on 4-halogen-substituted phenylcarbamates of amylose as chiral stationary phases for high-performance liquid chromatography[END_REF][START_REF] Chankvetadze | 3-Fluoro-, 3-chloro-and 3-bromo-5-methylphenylcarbamates of cellulose and amylose as chiral stationary phases for high-performance liquid chromatographic enantioseparation[END_REF] in the late twentieth century.

Until recently, no systematic study has been performed about the possible electrophilic behaviour of the chlorine located on polysaccharide-based CSPs. However, some authors speculated that XB could underlie recognition mechanisms on chlorinated CSPs. In this regard, West and co-workers stated "Halogen bonds should also be considered as possible contributors to the specific retention and separation behavior of chlorinated CSP" [START_REF] West | Enantioseparation of novel chiral sulfoxides on chlorinated polysaccharide stationary phases in supercritical fluid chromatography[END_REF], and later Jiang and co-workers considered "the halogen bonding occurred as an intermolecular interaction when chlorine atom acted as an electron density acceptor (Lewis acid) and tended to interact with electron donor partners. In this regard, the chlorine atom on CSP phenyl can interact with the C=O group and phenyl ring of the enantiomer by halogencarbonyl oxygen and halogen- interactions, respectively. Based on the above reasons, both the electron-withdrawing inductive effect and the halogen bonding produced by chlorine atoms of CSP appeared to be favorable for the enantioseparation" [START_REF] Zhu | Enantioselective separation of twelve pairs of enantiomers on polysaccharide-based chiral stationary phases and thermodynamic analysis of separation mechanism[END_REF].


N Lamouroux
email: nicolas.lamouroux@cemagref.fr

S Mérigoux

H Capra

S Dolédec

I G Jowett

B Statzner

THE GENERALITY OF ABUNDANCE-ENVIRONMENT RELATIONSHIPS IN MICROHABITATS: A COMMENT ON LANCASTER AND DOWNES (2009)

Keywords: instream habitat models, preference, niche, ecohydraulics

We comment on a criticism of hydraulic preference models and instream habitat models. We provide evidence of the generality of many hydraulic preference models, which supports their use in instream habitat modelling even if the detailed mechanistic causes of the observed preferences are not fully known. We also reply to the assertion that preference models are not based on sound ecological theory. We identify unbalanced use of available knowledge and point out limitations relating to too detailed biological focuses.

INTRODUCTION

In their paper "Linking the hydraulic world of individual organisms to ecological processes: putting ecology into ecohydraulics", [START_REF] Lancaster | Linking the hydraulic world of individual organisms to ecological processes: putting ecology into ecohydraulics[END_REF] (henceforth "L&D ") identify limits of hydraulic "preference" models for aquatic organisms (referred to as abundance-environment relationships AERs) and associated instream habitat models (referred to as habitat-based association models HAMs). In particular, they describe 1) some of the complexity of mechanisms that can lead to observed AERs, 2) potential spurious correlations among the environmental variables under study and others, 3) potential interaction with predation and competition and 4) potential effects of the environment on life history traits and population dynamics.

Though we agree with the need to better understand the complex biophysical interactions underpinning AERs, we disagree with the statement that "what HAMs based on AERs are CemOA : archive ouverte d'Irstea / Cemagref unlikely ever to do well is estimate or predict changes in population density". We do acknowledge that models are always a simplification, based on a compromise among complexity, relevance and realism. They can always be criticized for not being detailed enough or, on the contrary, being too complex to be of general interest. AERs and HAMs certainly follow this rule. They often have been criticised for not explaining all the mechanisms that lead to plastic density-environment association, or on the contrary for being too detailed for practical management applications (e.g. we cannot study hydraulic preferences of any life-stage at any moment in any stream). However, in responding to L&D we aim to illustrate the generality of many AERs, and therefore their usefulness in stream management even if the detailed mechanistic causes of the observed "preferences" are not fully known. We also reply to the criticism that AERs are not based on sound ecological theory and point out that L&D overuse un-representative examples. Finally, we suggest that the criticisms made of AERs also apply to the "good practice" research examples given by L&D.

MANY AERs ARE REMARKABLY GENERAL

L&D state that "agglomerating data" from comparative AER studies involving multiple sites "may result in a blurred, meaningless scatter of points or a very weak average response of questionable utility or ecological sense". We refute this statement and refer to a number of studies that have analysed observed relationships between animal density and microhabitat variables in several sites on repeated occasions (e.g. fish in France, [START_REF] Lamouroux | Fish habitat preferences at the local scale in large streams of southern France[END_REF] invertebrates in small streams in France and Germany, [START_REF] Dolédec | Modelling the hydraulic preferences of benthic macroinvertebrates in small European streams[END_REF]invertebrates and fish in New Zealand, Jowett and D avey, 2007;Jowett et al. 2008; invertebrates in large streams in France, [START_REF] Mérigoux | Invertebrate hydraulic preferences and predicted impacts of changes in discharge in a large river[END_REF]. Concerning macroinvertebrates, the studies of CemOA : archive ouverte d'Irstea / Cemagref [START_REF] Dolédec | Modelling the hydraulic preferences of benthic macroinvertebrates in small European streams[END_REF] and [START_REF] Mérigoux | Invertebrate hydraulic preferences and predicted impacts of changes in discharge in a large river[END_REF] provide a general picture of the degree of variation in AERs among sites and sampling occasions: many taxa, defined at different biological levels, have repeatable AERs at sites on rivers with different size, geology, water quality, community composition and other ecological characteristics; other taxa (examples in L&D and [START_REF] Mérigoux | Invertebrate hydraulic preferences and predicted impacts of changes in discharge in a large river[END_REF] have highly variable AERs. Specifically, of 151 taxa studied by [START_REF] Dolédec | Modelling the hydraulic preferences of benthic macroinvertebrates in small European streams[END_REF], 14 taxa have a generalised (site-averaged) AER that explains >50% of their log-density variations among microhabitats (within sites), and 40 taxa have AERs that explain >30% of their density variations. Two thirds of the variability in density explained by site-specific AERs are accounted for by a site-averaged, generalised AER in small German streams [START_REF] Dolédec | Modelling the hydraulic preferences of benthic macroinvertebrates in small European streams[END_REF], as well as in large French streams [START_REF] Mérigoux | Invertebrate hydraulic preferences and predicted impacts of changes in discharge in a large river[END_REF]. Figure 1 shows an example of a generalised AER for a rheophilic macroinvertebrate taxon that has a high transferability. Note that Figure 1 does not show the best example available, as "only" 37% of the density variation among microhabitats are explained by the generalised Baetis AER (this increases to 80% for some taxa in [START_REF] Dolédec | Modelling the hydraulic preferences of benthic macroinvertebrates in small European streams[END_REF]. Jowett and Davey (2007) also showed that generalised additive models explained about 50% of the abundance variation of benthic invertebrates taxa in 6 New Zealand rivers. Other examples of transferability can be found for fish. For example, [START_REF] Lamouroux | Fish habitat preferences at the local scale in large streams of southern France[END_REF] showed, for 24 species in six streams, that microhabitats with hydraulic conditions corresponding to high fish densities on average (according to generalised AERs) did contain more fish than other microhabitats in about 60% of the streams, and were never avoided in a given stream.

Assemblages at the local scale of microhabitats (e.g., sampled by Surbers) potentially depend on social behaviour, gregarism, predation, competition, physical history of the microhabitat, particle size and many other environmental drivers. In these conditions, the fact that CemOA : archive ouverte d'Irstea / Cemagref hydraulics have been demonstrated to explain >50% of density variations among microhabitats within multiple sites with contrasting characteristics is remarkable, and suggests the existence of strong causal mechanisms even if the details of these mechanisms are not fully known and deserve to be studied.

L&D cite [START_REF] Mérigoux | Hydraulic requirements of stream communities: a case study on invertebrates[END_REF] as an example of a single-stream study (the Ardèche river in France) that assumes a limited tolerance of species and is not supported by empirical data. This assertion is strongly contradicted by another paper they cite [START_REF] Dolédec | Modelling the hydraulic preferences of benthic macroinvertebrates in small European streams[END_REF], where the most remarkable result is the consistency of AERs between the Ardèche river in France (data from Mérigoux and D olédec, 2004) and a group of 12 German rivers, i.e. in streams of different countries independently surveyed by various teams at different seasons (Figure 2). The study of [START_REF] Mérigoux | Invertebrate hydraulic preferences and predicted impacts of changes in discharge in a large river[END_REF] even goes further by showing consistency among preferences in small German and large French streams. Therefore, the study of [START_REF] Mérigoux | Hydraulic requirements of stream communities: a case study on invertebrates[END_REF] is not a study made "over a short gradient" (e.g., it spans nearly the whole range of shear stresses shown in Figure 1) but, on the contrary, a study that generated AERs of general relevance in independent contexts.

It is also surprising that [START_REF] Dolédec | Modelling the hydraulic preferences of benthic macroinvertebrates in small European streams[END_REF] and [START_REF] Statzner | Predicting the abundance of European stream macroinvertebrates using biological attributes[END_REF] are cited as papers that consider AERs as invariant, because the first paper essentially quantifies the variation in AERs across sites and dates, and the second paper does not address the subject at all. More generally, deriving generalised AERs does not imply that species have optimum, non-plastic, invariant AERs. On the contrary, studying the relevance of generalised AERs contributes to quantifying this plasticity. It is a prerequisite for understanding the causes of AERs variability and for identifying which of these models are appropriate for generic predictions.

THEORETICAL BASIS AND PREDICTIVE POWER OF AERs

AERs are firmly rooted in the niche concept that strongly influenced pioneer stream ecologists [START_REF] Statzner | How views about flow adaptations of benthic stream invertebrates changed over the last century[END_REF]. It has long been acknowledged that an ecological niche has multiple, interacting dimensions, and many of L&D's criticisms are merely restating this. For stream organisms, however, we also know that physical constraints typically play a predominant role in comparison to other niche dimensions. Early interest focused on velocity and, combining laboratory experiments and field observations nicely illustrated the ecological response of a blackfly across a velocity gradient (Figure 3). Thanks to ecohydraulics, we know today that the response of a filter-feeding blackfly species could be related to other hydraulic factors such as boundary layer conditions near its body, turbulence near its filter fans, transport rates of fine particles serving as food, lift and drag (e.g. [START_REF] Nikora | Hydrodynamics of aquatic ecosystems: an interface between ecology, biomechanics and environmental fluid mechanics[END_REF]. Finally, we also know that the response pattern of a specific larval blackfly potentially varies with its age/size (i.e. AER assessments at the family level as in L&D's Figure 2 are often scattered).

Consequently, unravelling the "causal basis of the pattern" (L&D ) shown in our Figure 3 would be extremely complex.

Instead of trying to explain all variation, AERs for lotic invertebrates rely on general responses illustrated in our Figure 3: both flow decreases and increases beyond "normal" cause drift of most taxa (D orier and Vaillant, 1953/54;[START_REF] Minshall | The effect of reduction in stream flow on invertebrate drift[END_REF], presumably because of respiratory problems at low flow [START_REF] Ruttner | Bemerkungen über den Sauerstoffgehalt der Gewässer und dessen respiratorischen Wert[END_REF][START_REF] Ambühl | D ie Bedeutung der Strömung als ökologischer Faktor[END_REF] and of unbearable forces at high flow (Dorier and Vaillant, 1953/54). Between this minimum and maximum of the hydraulic niche dimension, specific instars (size groups) should have an optimum that varies across specific size groups and species. However, according to Liebig's "law of the minimum", one would not expect such hydraulic AER patterns when other factors are too extreme. By citing an example from a stream site with extremely low slope and oxygen concentrations (extreme at the sediment surface: <1 mg.l -1 ; see [START_REF] Lancaster | Interacting environmental gradients, trade-offs and reversals in the abundance-environment relationship of stream insects: when flow is unimportant[END_REF] as an example of the limits of AERs, L&D have selected an untypical stream environment for which typically valid AERs must be obviously irrelevant.

Criticizing the predictive power of AERs and HAMs is easy because this criticism applies to most ecological models [START_REF] Peters | A Critique for Ecology[END_REF]. Poor predictability is partly due to the complexity of ecological processes that potentially interfere in the niche of organisms and the difficulty in obtaining sound long-term datasets for testing actual population and community responses to environmental changes. However, there has been some evidence so far of successful predictions of density variations among sites, or before-after flow restoration, based on AERs/HAMs [START_REF] Fuchs | Ökologische Grundlagen zur wasserwirtschaftlichen Planung von Abfluß und Morphologie kleinerer Fließgewässer[END_REF][START_REF] Lamouroux | Intercontinental convergence of stream fish community traits along geomorphic and hydraulic gradients[END_REF][START_REF] Lamouroux | Fish community changes after minimum flow increase: testing quantitative predictions in the Rhône River at Pierre-Bénite, France[END_REF][START_REF] Jowett | Application of the 'natural flow paradigm' in a New Zealand context[END_REF]. For example, [START_REF] Fuchs | Ökologische Grundlagen zur wasserwirtschaftlichen Planung von Abfluß und Morphologie kleinerer Fließgewässer[END_REF] used season-and size-specific AERs of invertebrate species from the nearest sites to predict 49% of the variation (n=15) in observed relative changes of population sizes after increasing the regulated discharge. [START_REF] Lamouroux | Intercontinental convergence of stream fish community traits along geomorphic and hydraulic gradients[END_REF] could partly predict associations between fish community traits and hydraulics in North American reaches from AERs observed at the microhabitat scale in France, i.e. using models built at another scale and in another continent, with distinct fish species.

AERs and HAMs may be correlative but they make sense in terms of biological trait adaptation to flow, e.g. the benefits of being small, streamlined, filter-feeders or attached in stressful habitats are interpretable [START_REF] Lamouroux | Biological traits of stream macroinvertebrate assemblages: effects of microhabitat, reach and basin filters[END_REF][START_REF] Blanck | Relationships between life-history strategies of European freshwater fish species and their habitat preferences[END_REF]). The consistency of niche-based AERs in different contexts, their actual validations and their physically-based interpretations support the idea that they reflect general causal relationships.

Of course, there is some potential for developing more general AERs that are based on robust CemOA : archive ouverte d'Irstea / Cemagref physical principles, such as those suggested by Von [START_REF] Gelei | Zum physiologischen Formproblem der Wasserorganismen[END_REF]. His seminal paper discussed how Reynolds number and body shape (e.g. degree of streamlining) of an aquatic organism affect flow separation from its body and, in turn, the drag it experiences. The use of such variables in AERs has some potential because these variables can explain, similarly for different taxa, variation in flow separation (its location relative to body length; [START_REF] Statzner | Morphological adaptation of shape to flow: microcurrents around lotic macroinvertebrates with known Reynolds numbers at quasi-natural flow conditions[END_REF], fish drag [START_REF] Sagnes | Hydrodynamic abilities of riverine fish: a functional link between morphology and velocity use[END_REF] and drift rates [START_REF] Statzner | Longitudinal patterns and processes along streams: modelling ecological responses to physical gradients[END_REF]. These examples suggest that putting hydraulics into ecohydraulics is at least as important as putting ecology into it.

L&D 'S CRITICISMS OF AERs APPLY ALSO TO THEIR "EXAMPLES OF GOOD PRACTICE"

We support the importance of studying more detailed mechanisms such as the bioenergetics of filter-feeding insects or egg supply and their relations to flow (L&D's "examples of good practice"). These studies can identify key processes influencing population dynamics and biomechanical patterns of general relevance. However, the two examples provided by L&D in support of this point could be criticised, as AERs, for neglecting the complexity of the ecological processes or on the contrary, being too complex for use in management.

In their discussion of flow effects on feeding rate, growth rate and survival of filter-feeders, L&D focus on simuliids and hydropsychids. For the latter, we know that (1) net-building rates (proportion of filter nets to larvae) vary between 0-1 across species, seasons and/or instars; (2) net-building larvae that never build a net generally develop normally; and (3) beyond enabling filter-feeding, the nets have potentially four other functions for its builder (see [START_REF] Statzner | Net-building of a caddis fly (Hydropsyche siltalai) in a French stream: relations with larval density and physical conditions[END_REF]. Increased growth rates can also generate higher drag, higher damage by CemOA : archive ouverte d'Irstea / Cemagref drifting particles and higher predation by fish, i.e. the effects of flow on feeding rate, growth and survival are not as direct as stated by L&D . Furthermore, relations between flow and feeding efficiency are likely highly variable due to additional complications cited by L&D (e.g. intraspecific competition for space, individual phenotypic plasticity of life history traits, behaviour) and others (e.g. thermal regime and its physiological effects, potential barriers to nutriment sources, interspecific predation, bed disturbance frequency and other dynamic hydraulic patterns). In this context, a modelled relationship between flow and feeding efficiency would be necessarily a simplification, partly based on correlation.

We suggest that L&D's discussion of egg supply is also unconvincing. Since the International Biological Programme we know that egg supply is generally not a bottleneck stage for extant riverine invertebrate populations (e.g. [START_REF] Edmondson | A Manual on Methods for the Assessment of Secondary Productivity in Fresh Waters[END_REF]. Providing an example considered by L&D in their Figure 4, the mortality from egg supply to terrestrial adult (i.e. of aquatic stages) was 91% in the Baetis (rhodani) population of a German stream (Wernecke and Zwick, 1992). In addition, L&D's statement that the physical and hydraulic environment is very important to egg supply because egg masses are found on a minority of emergent rocks is not supported by two of the three examples illustrated in their Figure 4, where the relative frequency of velocities available and used by Apsilochorema and Baetis hardly differ.

Finally, assessments of consequences of egg supply for populations would require egg identifications at the species level, which are notoriously difficult (note that the egg data in L&D's Figure 4 are for genera, not for species).

Studies at higher level of detail are useful for identifying the main mechanisms causing the observed preferences. However, ecohydraulics involve such a large variety of biological and physical processes that building predictive models of the effects of e.g., climate change on It is ultimately the predictive power of different models that will decide what is the most useful level of detail for building predictive management tools. In our view, some AERs represent a good compromise between parsimony, generality and ecological relevance for being useful in predictive approaches. For example, some simuliids and hydropsychids have strong, repeated, and interpretable association with high shear stresses, in small and large streams of different countries (e.g. Figure 2), and we cannot see any major reasons why these AERs should not be used to guide flow management in rivers. The test of several predictive approaches will also indicate which details of population dynamics are worth being included in HAMs. Meanwhile, it is incorrect to oppose HAMs and dynamic models, because most HAM applications are interpreted in a dynamic context, and HAMs based on AERs are sometimes explicitly used as part of population dynamic models [START_REF] Statzner | Longitudinal patterns and processes along streams: modelling ecological responses to physical gradients[END_REF][START_REF] Capra | A population dynamics model and habitat simulation as a tool to predict brown trout demography in natural and bypassed stream reaches[END_REF].

CONCLUSIONS

CemOA : archive ouverte d'Irstea / Cemagref

In summary, we think that L&D go much too far in their criticism of AERs. They use counterexamples without describing the general picture concerning the generality of AERs.

They make a subjective use of the papers they cite and a too simplistic presentation of AERs as static, purely correlative models that are disconnected from theory and have little generality. We hope that this comment provides elements that will balance the debate on

  CemOA : archive ouverte d'Irstea / Cemagref

  CemOA : archive ouverte d'Irstea / Cemagref populations (an objective cited by L&D) involving all contributing mechanisms is unrealistic at this time. Moreover, using the conventional tools of hydraulics and fluid mechanics for modelling the local hydraulic history undergone by individuals faces the complexity of both biological and hydraulic processes. In particular, constructing a general model for relating discharge management to the diversity of point hydraulics around individuals remains out of scope of predictive management tools. The 'good practice examples' described by L&D could be interesting pieces of research, but they would need generalisation, replication and validation before being of any use in practical stream management.

  FIGURE LEGENDS

Figure 2 .

 2 Figure 2. The average "preferred" bottom shear stress in the Ardèche river in France (data

Figure 3 .Figure 1 .Figure 2 .

 312 Figure 3. Population loss by drift and density on artificial substrates (all relative to their

CemOA : archive ouverte d'Irstea / Cemagref

ACKNOWLEDGEMENTS

We thank Piotr Parasiewicz and Ton Snelder for their comments. This paper will contribute to the EU project "ERA-Net Forecaster".