domain: spi chim phys

text:
Austin Hubley

Amina Bensalah-Ledoux

Bruno Baguenard

Stephan Guy

Benjamin Abécassis
email: benjamin.abecassis@ens-lyon.fr

Benoit Mahler
email: benoit.mahler@univ-lyon1.fr

Chiral Perovskite Nanoplatelets Exhibiting Circularly Polarized Luminescence through Ligand Optimization

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Chiral perovskite nanoplatelets exhibiting circularly polarized luminescence through ligand optimization

Austin Hubley 1,2 , Amina Bensalah-Ledoux 1 , Bruno Baguenard 1 , Stephan Guy Chiral halide perovskite nanocrystals have many applications in next-generation optoelectronic devices due to their interaction with circularly polarized light. Through the careful selection of chiral organic surface ligands, control over the circular dichroism (CD) and circularly polarized luminescence (CPL) of these materials can be achieved. However, while recent developments of CD-active perovskites have seen significant advances, effective CPL remains a challenge. Here, we synthesize colloidal perovskite nanoplatelets exhibiting room temperature CPL with dissymmetry factors up to g lum = 4.3 × 10 -3 and g abs = 8.4 × 10 -3 . Methylammonium lead bromide nanoplatelets are synthesized with a mixture of chiral dimethyl benzyl ammonium ligands and achiral octylammonium ligands, the precise ratio of which is shown to be critical to achieving high g-factors. We investigate the competitive binding of these surface ligands using 1 H NMR, and use an equilibrium model to demonstrate the ligand affinity. The magnitude of CPL and CD is quantitatively shown to exhibit a linear correlation, such that g lum = 0.40 × g abs . Lastly, by screening several amines with close structures, we show that subtle differences in ligand structure have significant impact on the resulting CD signal of the nanoplatelets. Our findings provide new insights for the effective design of perovskites exhibiting CPL and can facilitate the development of high-performance devices based on circularly polarized luminescence.

Introduction

Chiral materials exhibit preferential interactions with lefthanded or right-handed circularly polarized light. The unequal absorption or emission of circularly polarized light is referred to as circular dichroism (CD) or circularly polarized luminescence (CPL), and leads to many practical technologies such as 3D displays, spintronics, quantum computing, drug screening, anti-counterfeiting, and photoelectric devices [START_REF] Zinna | Highly Circularly Polarized Electroluminescence from a Chiral Europium Complex[END_REF][START_REF] Wang | Spin-optoelectronic devices based on hybrid organic-inorganic trihalide perovskites[END_REF][START_REF] Liu | 3D chiral color prints for anti-counterfeiting[END_REF][START_REF] Yang | Circularly polarized light detection by a chiral organic semiconductor transistor[END_REF][START_REF] Finn Purcell Milton | The chiral nanoworld: chiroptically active quantum nanostructures[END_REF][START_REF] Chen | Circularly polarized light detection using chiral hybrid perovskite[END_REF]. However, realizing such technologies requires the development of sources of circularly polarized light. Conventionally this involves filtering unpolarized light using an optical polarizer, the drawbacks of which include both a decrease in intensity, and the need for additional optical elements. Current methods seek to circumvent these issues by producing direct sources of CPL, leading to device miniaturization, lower production costs, lower energy consumption, and faster data processing rates [START_REF] Wang | Polarization-Sensitive Halide Perovskites for Polarized Luminescence and Detection: Recent Advances and Perspectives[END_REF]. Small organic chiral fluorophores can be used for this purpose, but typically suffer from weak CPL with luminescence dissymmetry values on the order of g lum = 10 -4 to g lum = 10 -2 (8, 9). Additionally, many of these organic molecules show optical activity in the UV-range, whereas applications often require emission in the visible spectrum. One of the solutions is to couple chiral organic molecules with semiconductor nanocrystals (NCs), consequently achieving direct CPL in the visible spectrum [START_REF] Tohgha | Ligand Induced Circular Dichroism and Circularly Polarized Luminescence in CdSe Quantum Dots[END_REF]. Doing so, it is possible to achieve much stronger chiroptical signals [START_REF] Ben-Moshe | Chirality and chiroptical effects in inorganic nanocrystal systems with plasmon and exciton resonances[END_REF][START_REF] Im | Chiral Surface and Geometry of Metal Nanocrystals[END_REF].

Ligand-induced chirality has been shown to induce optical activity in semiconductor nanocrystals [START_REF] Mícheál | Chiral highly luminescent CdS quantum dots[END_REF]. This involves the incorporation of chiral ligands either directly in the synthesis of colloidal nanocrystals, or through post-synthetic surface treatment [START_REF] Kuznetsova | Ligand-induced chirality and optical activity in semiconductor nanocrystals: theory and applications[END_REF]. This can result in new optical activity at the characteristic wavelengths corresponding to excitonic transitions of the NC, and both circular dichroism and circularly polarized luminescence can be observed [START_REF] Gao | Perspective of Chiral Colloidal Semiconductor Nanocrystals: Opportunity and Challenge[END_REF]. However, materials showing CPL are less common than those exhibiting CD [START_REF] Ma | Chiral Perovskites for Next-Generation Photonics: From Chirality Transfer to Chiroptical Activity[END_REF]. Furthermore, to produce high-performance CPL emitters through ligand-induced chirality requires both a chiral molecule compatible with the NC surface, and a NC with superior optoelectronic properties including narrow emission line width, high photoluminescence quantum yield, and a wide range of color tunability.

Hybrid organic-inorganic perovskite nanocrystals meet these optoelectronic prerequisites, making them ideal candidates for the development of next-generation chiroptical devices [START_REF] Dang | Chiral halide perovskite crystals for optoelectronic applications[END_REF]. In addition to excellent optoelectronic properties, these materials have the advantages of affordability, flexibility, and solution processability [START_REF] Dey | State of the Art and Prospects for Halide Perovskite Nanocrystals[END_REF][START_REF] Manser | Intriguing Optoelectronic Properties of Metal Halide Perovskites[END_REF][START_REF] Shamsi | Metal Halide Perovskite Nanocrystals: Synthesis, Post-Synthesis Modifications, and Their Optical Properties[END_REF]. Furthermore, organic-inorganic perovskites are a good foundation for designing optically active NCs due to the wide variety of compatible chiral organic ligands available. Typically, these molecules consist of a chiral centre adjacent to a primary ammonium moiety which can be inserted into the perovskite framework [START_REF] Long | Chiral-perovskite optoelectronics[END_REF]. A number of reports have shown that perovskites can be prepared directly in the presence of chiral ligands, resulting in optically active nanocrystals [START_REF] Ahn | A new class of chiral semiconductors: chiral-organic-molecule-incorporating organic-inorganic hybrid perovskites[END_REF][START_REF] Yuan | Chiral Lead Halide Perovskite Nanowires for Second-Order Nonlinear Optics[END_REF][START_REF] Ma | Recent Progress of Chiral Perovskites: Materials, Synthesis, and Properties[END_REF]. However, while significant progress has been made in the

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field of chiral perovskite materials, CPL in these materials has received few reports, particularly in the case of colloidal nanocrystals [START_REF] Kim | Strategies to Achieve High Circularly Polarized Luminescence from Colloidal Organic-Inorganic Hybrid Perovskite Nanocrystals[END_REF][START_REF] Chen | Two-Photon Absorption-Based Upconverted Circularly Polarized Luminescence Generated in Chiral Perovskite Nanocrystals[END_REF]. This is because the optical properties of these nanocrystals are strongly dependent on the surface chemistry, and the impact of chiral ligands remains poorly understood. Hence, this work aims to provide insight into the relationship between chiral organic surface ligands, and the resulting chiroptical properties in hybrid organic-inorganic perovskite nanocrystals.

Here, we report colloidal perovskite nanoplatelets exhibiting room-temperature CPL. Using a nonsolvent recrystallization process, we show that a precise ratio of chiral and achiral ligands is crucial for achieving high chiroptical responses. We develop an 1 H NMR method to establish a relationship between chiroptical properties and the ratio of chiral and achiral ligands, finding that an equilibrium model can be used to understand the competitive binding of chiral ligands on the NPL surface. The correlation between the absorption and luminescence dissymmetry factors is quantitatively investigated to elucidate a linear relationship between g lum and g abs . The effects of small differences in ligand structure on the CD signal at the NC excitonic transition are compared. These results lead to a better understanding of ligand-induced chirality in perovskite nanoplatelets, and help in the strategic design of tunable sources of circularly polarized light.

Results and discussion

Methylammonium lead bromide perovskite nanoplatelets (NPLs) were prepared using a ligand-assisted re-precipitation (LARP) approach (see Methods section for details). NPLs were synthesized with a stoichiometric ratio of precursors corresponding to the thickness of a single unit cell. This is denoted as n=2 in terms of the number of leadbromide octahedra n, in the form L 2 [MAPbBr 3 ] n -1 PbBr 4 , whereby L represents the organic ligands. In this work, chiral perovskites were prepared using a ligand mixture of octylammonium (OctAm) bromide and either (R)-(+)-α,4dimethylbenzylammonium (R-DMBA) bromide or (S)-(-)α,4-dimethylbenzylammonium (S-DMBA) bromide. Typically, a molar fraction of [DMBA]/[OctAm]= 0.825 was used unless denoted otherwise. For simplicity, these chiral NPL enantiomers are hereby denoted as Ror S-DMBA NPLs. The achiral perovskites were prepared using only OctAm ligands. Fourier Transform Infrared Spectroscopy (FTIR) confirms the immobilization of alkylammonium moieties on the surface of the nanoplatelets (Figure S1). Scanning transmission electron microscopy (STEM) images of the R-DMBA NPLs show well-dispersed nanoplatelets of roughly circular morphology and a mean diameter of 65 ± 12 nm, with contrast homogeneity indicating a uniform thickness (Figure 1a). Additional STEM images of Rand S-DMBA NPLs and achiral NPLs are shown in supplementary information (Figure S2), including images showing the sample degradation which can occur as a result of radiolysis induced by the electron beam (Figure S3). The corresponding powder X-ray diffraction (PXRD) pattern of this sample is shown in Figure 1b. No apparent differences are observed between PXRD patterns of the Sand R-DMBA NPLs (Figure S4). Peaks resulting from periodic reflections of stacked nanoplatelets in the powder are indicated, corresponding to a stacking periodicity of 2.6 nm. A single MAPbBr 3 perovskite layer has a thickness of 1.2 nm [START_REF] Tyagi | Colloidal Organohalide Perovskite Nanoplatelets Exhibiting Quantum Confinement[END_REF]. Thus, the remaining 1.4 nm can be attributed to interdigitated OctAm and DMBA ligands which have respective lengths of 1.1 nm and 0.8 nm (Figure 1c). This is consistent with values reported previously in literature for n=2 methylammonium lead bromide nanoplatelets and for bulk perovskites [START_REF] Mark | Highly Tunable Colloidal Perovskite Nanoplatelets through Variable Cation, Metal, and Halide Composition[END_REF][START_REF] Wang | Structural and Photophysical Properties of Methylammonium Lead Tribromide (MAPbBr3) Single Crystals[END_REF].

We systematically changed the molar ratio between chiral and achiral ligands in the synthesis, and observed that the magnitude of the CD signal strongly depends on this ratio, in accordance with previous reports for perovskite NCs [START_REF] Kim | Strategies to Achieve High Circularly Polarized Luminescence from Colloidal Organic-Inorganic Hybrid Perovskite Nanocrystals[END_REF][START_REF] He Ren | 2D Perovskite Nanosheets with Intrinsic Chirality[END_REF].

We observed that the maximum CD signal was obtained at a molar fraction of [DMBA]/[OctAm]= 0.825. This is the composition that was chosen for optical and structural characterization. The circular dichroism and circularly polarized luminescence are shown alongside the corresponding absorption and fluorescence spectra of the chiral NPLs (Figure 2a,b). The exciton absorption maximum at 430 nm with fluorescence emission maximum at 438 nm indicate a NPL thickness of n=2 [START_REF] Mark | Highly Tunable Colloidal Perovskite Nanoplatelets through Variable Cation, Metal, and Halide Composition[END_REF]. The photoluminescence quantum efficiency (PLQE) of these chiral NPLs is 0.27%, with a Full Width at Half maximum (FWHM) of 14 nm. Comparatively, a PLQE of 3.63% and a FWHM of 11 nm is exhibited for the achiral samples synthesized with purely OctAm ligands, consistent with previous literature [START_REF] Mark | Highly Tunable Colloidal Perovskite Nanoplatelets through Variable Cation, Metal, and Halide Composition[END_REF]. The chiral samples show a luminescence dissymmetry g-factor, g lum of 4.0 × 10 -3 calculated as:

g lum = 2 × (I L -I R )/(I L + I R )
, where I L and I R are the intensities of the left-and right-handed components of the emitted light at the 438 nm emission maximum. The corresponding g abs at the 430 nm absorption maximum is 8.4 × 10 -3 , defined as g abs = CD (mdeg) /(32980 × A), where CD mdeg is the circular dichroism signal in millidegrees, and A is the absorbance at the given wavelength. To the best of our knowledge, these g-values are the highest reported for colloidal perovskite NPLs to date. Figure 2c shows g abs over the full spectrum, with the corresponding absorbance. The feature observed in the region near 300 nm can be attributed to a ligand-NC charge transfer band, with the bisignate peak in the region of 400-450 nm corresponding to the perovskite excitonic transition [START_REF] Bloom | Spin Selective Charge Transport through Cysteine Capped CdSe Quantum Dots[END_REF][START_REF] Zheni | Imprinting Chirality onto the Electronic States of Colloidal Perovskite Nanoplatelets[END_REF]. Spectra for the Rand S-DMBA NPLs appear as mirror images of one another for both CD and CPL. As expected, no chiroptical features are observed in the visible spectrum for either the Ror S-DMBA-Br ligands alone, or for the achiral NPLs synthesized with purely OctAm ligands (Figures S5 andS6).

It follows that the optical properties are highly dependent on the surface chemistry of the nanoplatelets, as ligand binding alters the electronic energy levels of surface atoms [START_REF] Lim | Quantum dot surface engineering: Toward inert fluorophores with compact size and bright, stable emission[END_REF]. Therefore, to understand the role of the different ligands involved, a better understanding of the surface chemistry must be developed. Due to the structural differences between the ligands, it is expected that they would have different binding affinities for the surface of the nanoplatelets [START_REF] Anderson | Ligand Exchange and the Stoichiometry of Metal Chalcogenide Nanocrystals: Spectroscopic Observation of Facile Metal-Carboxylate Displacement and Binding[END_REF]. Furthermore, only a small portion of the total ligands present are re- quired to passivate the surface because the NPLs are synthesized in the presence of an excess of ligands. Therefore, the ligand composition at the surface of the nanoplatelets is not necessarily equal to the initial composition in solution. Thus, 1 H NMR was used to compare the relative concentration of free ligands to that of ligands bound to the nanoplatelet surface.

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A detailed procedure for the relative concentration determination of ligands through 1 H NMR is described under Experimental Methods. In short, this involved centrifuging the platelets to remove unbound ligands before dissolving the precipitate in a polar deuterated solvent. When the NPLs are dispersed in a polar solvent, they dissolve into their constituent precursors because the initial formation of the platelets occurs as a result of a nonsolvent crystallization process. This allows for sharp signals from free ligands to be resolved in the 1 H NMR spectrum, as there is no peak broadening resulting from bound ligands [START_REF] Anderson | Stereoelectronic Effects on the Binding of Neutral Lewis Bases to CdSe Nanocrystals[END_REF]. Figure S7 compares the 1 H NMR spectra of bound and free ligands. Additionally, because excess ligands were removed during washing, an accurate quantification of only the ligands which were previously bound to the surface can be deduced. To do so, peaks from the 1 H NMR spectrum with no overlapping signals were used for relative concentration determination with the following equation:

M = I OctAm I DMBA × N DMBA N OctAm + 1 -1
Where I is the integral of the signal, N is the number of nuclei giving rise to the signal, and M is the molar fraction of DMBA ranging between 0 and 1. The signals used for comparison were the alpha proton of DMBA (δ = 4.38 ppm) and the methyl protons of OctAm (δ = 0.87 ppm), as indicated in Figure 3. This procedure was repeated for samples syn-thesized with different molar fractions of chiral and achiral ligands, ranging from 100% (purely chiral DMBA, M = 1) down to 0% (purely OctAm, M = 0). From this, an equilibrium of the ligands with the NPL surface was thus established and correlated with the magnitude of g abs (Figure 4a,b). The binding equilibrium between the different ligands and nanoplatelet surface can be expressed as follows:

[DMBA] + [NPL OctAm ] [OctAm] + [NPL DMBA ]
The equilibrium constant K can then be written as:

K = [NPL OctAm ][DMBA] [NPL DMBA ][OctAm] = (1 -M ) M × x (1 -x)
Where x is the molar fraction of DMBA in solution, and again M is equivalent to the molar fraction of DMBA on the surface of the nanoplatelet. Therefore, K = 1 would be indicative of equal affinity of the ligands for the NPL surface. Fitting the experimental values using this equilibrium model results in K = 7.3 ± 3.2 and reveals the competitive binding between the ligands and the NPL surface, showing that OctAm has a much higher affinity than DMBA for the NPL surface, to such an extent that when 82.5% of ligands in solution consist of DMBA at the beginning of the synthesis, the percentage on the surface after the synthesis is only 33%. This composition corresponds to the ratio at which the maximum CD signal is observed. A chiral ligand fraction of 0.88 corresponds to equal amounts of both ligands on the surface of the NPLs, and this composition was used to evaluate the reproducibility of chiral signals (Figure S8). The dependence of g abs on the fraction of chiral ligands at the 430 nm absorption maximum can be rationalized in a number of ways when considering both the ligand affinity to the nanoplatelet surface and the absorption spectra of samples synthesized with different ligand fractions (Figure 4c). As the ratio of chiral to achiral ligands is changed, the formation of different species is favoured. However, the equilibrium of ammonium ligands to the lead bromide surface is independent of the platelet morphology, and thus intercomparison of the different species is possible. In the presence of purely chiral ligands, an absorption maximum at 380 nm occurs, resulting from the formation of distorted lead-halide octahedra which can be attributed to a (110) perovskite with layered corrugated inorganic sheets [START_REF] Smith | White-Light Emission from Layered Halide Perovskites[END_REF]. Profile plot STEM images of stacked platelets show the presence of multiple thicknesses including n=1, which is confirmed by PXRD indicating the majority population has a stacking periodicity of 1.6 nm (Figure S9). After accounting for the 0.6 nm lead-bromide octahedra, the remaining 1.0 nm can be attributed to interdigitated ligands. A CD signal on the order of g abs = 10 -4 is observed in this region of 380 nm, as well as a smaller signal at 430 nm, resulting from the n=1 and n=2 layers, respectively (Figure S10a). This preferential formation of distorted n=1 species at high chiral ligand fraction is a result of the bulkyness of DMBA, because flexibility of the single lead bromide octahedra layers allows for a larger degree of distortion in the system, thus accommodating more ligands on the surface. Additionally, the absence of OctAm allows for increased π-π stacking of interdigitated DMBA, further favouring the formation of a layered Ruddlesden-Popper phase structure instead of well-dispersed individual NPLs [START_REF] Gao | Ruddlesden-Popper Perovskites: Synthesis and Optical Properties for Optoelectronic Applications[END_REF].

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The simultaneous formation of both the n=1 thickness (absorption at 398 nm) and the n=2 thickness (absorption at 430 nm) can result in the low magnitude of g abs due to competing CD signals from the different species. The preferential absorption of left or right circularly polarized light coincides with the redistribution of helical electron clouds for a specific excitonic transition. The CD spectrum is then constructed as differential spectra of the absorption values of the leftand right-handed components of polarized light as a function of the wavelength. Thus, for different excitonic transitions which occur at nearby wavelengths, opposite-signed CD signals can overlap and partially eliminate one-another. Figure S10b shows the absorption and g abs spectra for NPLs synthesized with a chiral ligand fraction of 0.6, in which both n=1 and n=2 species are present. Comparison of the CD bands between these two populations shows interfering signals. That is, the Cotton effect for S-DMBA NPLs in the direction of increasing wavelength is positive to negative at the n=1 transition, and negative to positive at the n=2 transi-tion. Additionally, a correlation is seen between a decrease in the relative concentration of n=2 platelets and a decrease in g abs when comparing the NPLs synthesized with the opposite enantiomers. The simultaneous presence of multiple species in solution will result in a CD spectrum that is the sum of all individual signals from each population. Furthermore, the CD spectrum of one species is the the sum of the differential absorption of left and right circularly polarized light. Hence, when excitonic transitions of two different species are close, the overlapping CD peaks can have cancelling effects since a positive CD signal of one population can be partially canceled by a negative signal of another thickness thus resulting in low overall signals for samples of polydisperse thickness. The monodisperse populations of n=2 platelets at low molar fractions of chiral ligands (approaching 0%) exhibit low g abs -factors. In this case, it simply results from an insufficient amount of chiral molecules on the surface, as the small portion of DMBA is out-competed by OctAm, which has a much higher affinity for the surface. Of interest is the composition for which the largest g abs magnitude is exhibited, corresponding to M=0.33. Assuming full passivation of the surface by the mixture of OctAm and D R A F T DMBA, this means 1/3 of surface sites are passivated by chiral ligands. At this ratio, a single species of monodisperse n=2 platelets are formed. The dramatic increase in CD at this specific ratio of chiral and achiral ligands can possibly result from chiral amplification due to the "sergeants-and-soldiers" effect on the nanoplatelet surface. Such a phenomenon can arise at precise ratios of chiral and achiral units when a small number of chiral units ("sergeants") control a larger portion of achiral units ("soldiers") [START_REF] Im | Chiral Surface and Geometry of Metal Nanocrystals[END_REF][START_REF] Mark | Macromolecular stereochemistry: the out-of-proportion influence of optically active comonomers on the conformational characteristics of polyisocyanates. The sergeants and soldiers experiment[END_REF]. This collective arrangement of molecules on the surface can result in long-range ordering, and chirality can be amplified beyond what is observed for ratios at which no collective interactions occur. Chiral amplification is observed when the increase of CD is non-linear in chiral molecule concentration, as can be seen in Figure S11 showing the g abs maxima as a function of the fraction of chiral ligands on the nanoplatelet surface. Furthermore, the ligand concentration has influence over the geometry of the chiral molecules on the NPL surface, which can consequently affect the magnitude of the CD signal [START_REF] Vera | Effect of Chiral Ligand Concentration and Binding Mode on Chiroptical Activity of CdSe/CdS Quantum Dots[END_REF]. This cooperative ligand effect can result in the order of magnitude increase in g abs which is observed at the optimal ligand fraction. The large error associated with measurements of samples prepared near this optimal ligand fraction is a consequence of the small energetic barrier separating the formation of these different species and the different conformations of the ligands on the NC surface.

Previous reports for colloidal perovskites prepared with other chiral ligands theorize that incorporation of a small amount of achiral ligands is required because the chiral molecules cannot passivate the surface alone due to their large steric profiles [START_REF] He Ren | 2D Perovskite Nanosheets with Intrinsic Chirality[END_REF][START_REF] Zheni | Imprinting Chirality onto the Electronic States of Colloidal Perovskite Nanoplatelets[END_REF]. However, approximate calculations indicate that the packing density of chiral ligands is much greater than the density of available surface sites. The number of available surface sites for a MAPbBr 3 crystal is 2.8 nm -2 . The packing density of DMBA can be compared to similar aromatic chiral molecules by calculating the large-area coverage of single monolayers, arriving at an approximate density of 3.3 to 4.4 ligands nm -2 [START_REF] Wang | Structural and Photophysical Properties of Methylammonium Lead Tribromide (MAPbBr3) Single Crystals[END_REF][START_REF] De | R,S)-1-Phenylethylammonium (R,S)-Mandelate[END_REF][START_REF] Turkington | Supramolecular structures of 1-phenylethylammonium tartrates[END_REF][START_REF] Rademeyer | 2-Phenylethylammonium bromide[END_REF]. Comparatively, a packing density of ∼4.9 ligands nm -2 is typically exhibited for crystalline alkane chains, or a density of 4.6 nm -2 for self-assembled monolayers (SAMs) on an Au(111) surface [START_REF] Lim | Quantum dot surface engineering: Toward inert fluorophores with compact size and bright, stable emission[END_REF][START_REF] Anderson | Stereoelectronic Effects on the Binding of Neutral Lewis Bases to CdSe Nanocrystals[END_REF]. From this, we see that bulky chiral ligands alone are sufficient to achieve complete passivation, suggesting that the achiral ligands have a role beyond simple surface passivation, but may contribute to long-range ordering.

To elucidate the relationship between CD and CPL, the g lum value at the emission maximum was plotted against the g abs value at the absorption maximum for nanoplatelets prepared with different chiral ligand fractions (Figure 5). The plot gives a regression line of g lum = 0.4 × g abs (r 2 = 0.84). Negative CD and CPL signals are observed for R-DMBA NPLs, while the S-DMBA NPLs exhibit positive signals. A slight deviation to higher g lum values for R-DMBA NPLs in comparison to the S-enantiomer can be attributed to the enantiomeric purity of the ligand salts, which were synthesized using precursors obtained from different suppliers. The linear correlation between the g-factor magnitudes is consistent with previous reports showing that g lum is proportional to, and smaller than, g abs [START_REF] Tanaka | Circularly Polarized Luminescence and Circular Dichroisms in Small Organic Molecules: Correlation between Excitation and Emission Dissymmetry Factors[END_REF]. Evaluation of the chiral sensitivity of the experimental setup is shown in Figure S12, showing the g lum values for samples synthesized at different dilution factors. Nanoplatelets exhibiting high g lum values will consequently also exhibit high g abs values. Thus, to screen for potential NPL compositions with high dissymmetry values, the CD signals were recorded for perovskites synthesized with a number of different chiral amines. We observed a dependence of g abs on the chiral to achiral ligand ratio for these NPLs prepared with different ligands, including (S)-and (R)methylbenzylamine (MBA), (S)-and (R)-ethylbenzylamine (EBA), and (S)-and (R)-cyclohexylethylamine (CHEA). In all cases, n=2 methylammonium lead bromide nanoplatelets exhibited an increased CD response when a small amount of OctAm ligands were included. The chiral ligand fraction was varied in increments of 0.02 to arrive at the optimal CD signal for each nanoplatelet, with the precise amount of Oc-tAm required being unique to each ligand. Figure 6 compares the CD spectra of nanoplatelets synthesized with the R-enantiomer of each ligand. The NPL absorption spectra, the corresponding CD spectra of S-enantiomers, and the calculated g abs values are shown in Figure S13. Interestingly, despite the structural similarities between each molecule and identical NC composition and thickness, significant differences are observed in the CD spectra. Simply removing the methyl group from DMBA to yield the structure of MBA results in a decrease of g abs by more than an order of magnitude, but preserves the sign of the CD signal. However, altering the ligand structure between DMBA and the isomer EBA results in both a decrease in g abs , and an inversion in the CD signal. Replacing the aromatic ring with cyclohexane results in a CD band with a more pronounced Cotton effect, unlike that of the previous ligands. Instead of a single positive (or negative) band, the CD response becomes bisignate and changes sign at the wavelength where it was maximum for amines bearing an aromatic moiety. Different ligands, depending on chemical structure and composition, can split the excitonic levels of the perovskite NC with different efficiency, resulting in different shape and intensity of the induced CD signal [START_REF] Puri | Circular Dichroism of CdSe Nanocrystals Bound by Chiral Carboxylic Acids[END_REF]. Even the same ligand can induce different CD spectra as a result of different geometrical configurations on the NC surface [START_REF] Kuznetsova | Ligand-induced chirality and optical activity in semiconductor nanocrystals: theory and applications[END_REF]. The chirality is dependent not only on the chemistry of the ligand involved, but also on the exact geometry of binding [START_REF] Li | Fluorescence and Optical Activity of Chiral CdTe Quantum Dots in Their Interaction with Amino Acids[END_REF]. Thus, small differences in ligand structure can induce significant changes in the CD spectra, even for nanoplatelets of the same thickness and composition. The extent to which subtle differences in ligand structure and orientation result in significant changes in CD shape and magnitude indicates that the mechanism of the optical activity observed is likely a result of chiral molecular dipole and transition dipole coupling [START_REF] Forde | Induced Chirality in Halide Perovskite Clusters through Surface Chemistry[END_REF]. Such chirality transfer originates from coupling of the static dipole of the chiral surface ligand to the transition dipole moment of the perovskite nanocrystal, and the resulting CD spectrum is dependent on the specific binding configuration of the ligand. [START_REF] Forde | Induced Chirality in Halide Perovskite Clusters through Surface Chemistry[END_REF]. Changes to the electronic structure of the NPLs by altering either the A-site cation or halide composition resulted in a decreased CD signal intensity, supporting this theory (Figures S15,S16). The drastic difference in the magnitude of g abs between DMBA and other chiral ligands suggests that longrange ordering may be present for this ligand, resulting in a chiral amplification which is not observed for MBA, EBA, or CHEA. Each of these ligands requires a small portion of OctAm to improve the signal, suggesting that the methods used here are a generic approach applicable to a wide range of perovskite systems. However, these results also indicate that OctAm is not required simply to help passivate the surface alongside the bulky ligands, but that inter-ligand interactions play an additional role in the orientation of the chiral molecules, and inhibit the formation of layered Ruddlesden-Popper phases. Furthermore, dipole-dipole coupling between the chiral ligand to the nanocrystal show that the specific choice of chiral ligand is also important to achieve optimal signals. Thus, future studies may seek to further investigate subtle structural differences between ligands to optimize chiroptical responses.

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Conclusions

In conclusion, we report chiral colloidal perovskite nanoplatelets exhibiting room temperature circularly polarized luminescence. A combination of chiral and achiral molecules containing a primary ammonium moiety are incorporated as surface ligands directly in the NPL synthesis. We show that the ratio of these ligands strongly affects the chiroptical properties of the nanoplatelets, and that the competitive binding of these ligands to the nanoplatelet surface follows an equilibrium model. When the molar fraction of chiral to achiral ligands is too high or too low, formation of polydisperse thicknesses and different ligand binding orientations result in a decrease in the chiroptical signals. This approach is demonstrated to be applicable for a number of different chiral molecules. We further show that in order to optimize the magnitude of the signal, careful consideration must be given to the choice of ligand because minute structural differences result in significant changes in the magnitude and sign of the induced CD. We believe the insights provided here will help the systematic and rational development of perovskite NCs with strong chirality, leading to applications in chiroptical devices.

Methods

Reagents and Materials Used. Lead (II) bromide (PbBr 2 , 99.999%), methylammonium bromide (MABr, anhydrous, ≥99%), n-octylammonium bromide (OctAm-Br, ≥99%), hydrobromic acid (HBr, 48 wt% in water), (R)-(+)-α,4-Dimethylbenzylamine (R-DMBA, 99%), (S)-(-)-α-Methylbenzylamine (S-MBA, 98%), (R)-(+)-α-Methylbenzylamine (R-MBA, 98%), (S)-(+)-1-Cyclohexylethylamine (S-CHEA, 98%), N,Ndimethylformamide (DMF, anhydrous, 99.8%), dimethyl sulfoxide-d 6 (DMSO, 99.9 atom% D), toluene (anhydrous, 99.8%), ethanol (anhydrous), and diethyl ether (anhydrous, ≥99%) were purchased from Sigma-Aldrich and used as received. Oleic acid (OA, technical grade 90%) was purchased from Sigma-Aldrich and was dried for 1 hour at 120 • C under vacuum before storage and use in a glovebox. (S)-(-)-α,4-Dimethylbenzylamine (S-DMBA, 98% ee 99+%), (S)-(-)-α-Ethylbenzylamine (S-EBA, 99+%, ee 99%), (R)-(+)-α-Ethylbenzylamine (R-EBA, 99+%, ee 98%), and (R)-(-)-1-Cyclohexylethylamine (R-CHEA, 98%, ee 94+%) were purchased from Alfa Aesar and used as D R A F T received. Precursor preparation. Precursor salts of Sand R-DMBA-Br were synthesized as follows. The desired enantiomer of DMBA (37 mmol, 5 g) was dissolved in ethanol (anhydrous, 25 mL) in a round bottom flask. A water bath was placed around the flask for heat dissipation and HBr (38 mmol, 4.3 mL, 48wt%) was added dropwise under vigorous stirring. After 2 hours, the flask was transferred to a rotary evaporator and dried at 70 • C to remove volatile solvents. The resulting white crystals were transferred to a Büchner funnel and washed with cold diethyl ether (6 washing cycles) before being placed in an oven at 80 • C for 1 hour. The products were transferred to an oxygen and water-free glovebox for storage. The other chiral ammonium halide salts were synthesized in a similar manner. Nanoplatelet synthesis. All synthesis was performed in an oxygen and water-free glovebox. Stock solutions were prepared by dissolving precursor salts (PbBr 2 , MABr, OctAm-Br, S-DMBA-Br, R-DMBA-Br) in DMF to produce 0.5 M solutions. A portion of these stock solutions were combined into a precursor solution, consisting of 20 µL MABr, 40 µL PbBr2, 100 µL OA, and 200 µL of ammonium ligands (for instance 165 µL of S-DMBA-Br and 35 µL of OctAm-Br). This corresponds to a stoichiometric ratio for n=2 nanoplatelets, with an excess of ligands for added stability. A small amount of this precursor solution (20 µL) was rapidly injected into 10 mL of toluene under vigorous stirring, resulting in instantaneous NPL formation. For purification, platelets were centrifuged at 6000 rpm for 5 minutes before being redispersed in 10 mL of toluene. Circular Dichroism Spectroscopy. CD was measured using a Jasco J-1700 Spectrometer. Samples were measured in toluene using a 1 cm quartz cuvette, a 2 second integration time, and a 1 nm bandwidth. Background was subtracted with a toluene blank, and all g abs -factors were calculated from absorbance data measured simultaneously. Circularly Polarized Luminescence. CPL was performed at room temperature using a home-built spectrometer described elsewhere [START_REF] Guy | Modulation of Chiroptical Properties in a Series of Helicene-like Compounds[END_REF]. All g lum -factors were calculated from fluorescence data measured simultaneously. Samples were excited at a 45 degree angle using a 365 nm diode at 20 mA, with a 2100 ms integration time, a 2 mm slit width and 4 nm resolution. Photoluminescence Quantum Efficiency. PLQEs were measured using an Edinburgh Instruments Spectrofluorometer FS5 equipped with an SC-30 integrating sphere. Samples were excited at 365 nm with a Xe lamp. Powder X-Ray Diffraction. Samples prepared under inert atmosphere were centrifuged and redispersed in a minimal amount of toluene before being drop-cast onto an air-free sample holder. PXRD measurements were performed using an Malvern Panalytical Aeris X-ray diffractometer operating at 30 kV and 15 mA with a copper radiation source. Fourier Transform Infrared Spectroscopy. FTIR was performed using a PerkinElmer Spectrum 65 FTIR Spectrometer. NPLs were centrifuged into a pellet and dropcast onto a Universal ATR Sampling Accessory.

Transmission Electron Microscopy. Samples were prepared by dropcasting solutions onto an Ultrathin C film on lacey carbon support, 400 mesh, Cu. (Ted Pella, Inc.) Highangle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images were obtained using a Jeol microscope (JEM-ARM200F Cold FEG NeoARM) at an operating voltage of 200 kV. 1 H NMR Spectroscopy. To prepare samples, the typical synthesis was scaled up to involve the injection of 120 µL of precursor solution into 20 mL of toluene. After 5 minutes, samples were centrifuged at 6000 rpm for 5 minutes. The supernatant was discarded, and samples were left uncovered to evaporate any residual solvent overnight. The pellet was dissolved in dimethyl sulfoxide-d 6 (600 µL) and sonicated for 10 minutes before being transferred to a 5 mm NMR tube. Measurements were taken on a Bruker 300 MHz spectrometer using a standard proton pulse, 16 scans, and a 2.7 second acquisition time. The signals used for relative concentration determination were the alpha proton of DMBA (δ = 4.38 ppm) and the methyl protons of OctAm (δ = 0.87 ppm).

D R A F T

Fig. 1 .

 1 Fig. 1. (a) HAADF-STEM image of R-DMBA NPLs, (b) PXRD pattern of R-DMBA NPLs with diamonds at repeating intervals of 3.4 • indicating stacking periodicity of 2.6 nm, (c) schematic illustration of corresponding NPL composition with chemical structure of (R)-(+)-α,4-dimethylbenzylammonium ligand.

Fig. 2 .Fig. 3 .

 23 Fig. 2. (a) CD and CPL in region of NPL excitonic transition, (b) corresponding absorption and fluorescence spectra, (c) g abs -factors and absorbance over full spectrum.

Fig. 4 .

 4 Fig. 4. (a) g abs at the 430 nm absorption maximum for S-and R-DMBA NPLs, (b) equilibrium curve showing competitive binding of chiral and achiral ligands to NPL surface considering K = 7.3 (solid) and K = 1 (dashed), (c) absorption spectra for NPLs synthesized with increasing fraction of chiral ligands in solution, with pure DMBA NPLs indicated in yellow, pure OctAm NPLs in purple, and the ligand fraction used for primary optical and structural characterization indicated in red.

Fig. 5 .

 5 Fig. 5. Correlation of the luminescence versus absorption dissymmetry factors for NPLs prepared with different chiral ligand fractions.

Fig. 6 .

 6 Fig. 6. CD spectra of n=2 methylammonium lead bromide nanoplatelets synthesized with the (R)-enantiomer of different chiral ligands including (a) (R)-(+)-α,4dimethylbenzylamine (DMBA), (b) (R)-(+)-α-methylbenzylamine (MBA), (c) (R)-(+)-α-ethylbenzylamine (EBA), and (d) (R)-(-)-1-cyclohexylethylamine (CHEA). Nanoplatelet absorption maxima are indicated by dashed lines. The chiral ligand fractions which gave the optimal responses are, respectively, 0.825, 0.75, 0.92, and 0.80, from top to bottom.

  Univ Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622, Villeurbanne, France 2 Univ Lyon, ENS de Lyon, CNRS, Laboratoire de Chimie, UMR 5182, F-69342, Lyon, France

1 , Benjamin Abécassis 2, , and Benoit Mahler 1, 1

Hubley et al. | Chiral perovskite nanoplatelets exhibiting circularly polarized luminescence through ligand optimization

ACKNOWLEDGEMENTS

This article is part of a project that has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant agreement No. 865995, ERC CoG SENECA). B.M. thanks the Université de Lyon PALSE program under the framework "Investissements d'avenir" (ANR-11-IDEX-0007). We thank the Consortium Lyon St-Etienne de Microscopie (CLYM) for access to the microscope platform TEM characterization and we thank Sandrine Denis-Quanquin for access to the NMR facility.


Oscar Corcho
email: ocorcho@fi.upm.es

Catherine Roussey
email: catherine.roussey@liris.cnrs.fr

Luis Manuel Vilches Blazquez

Catalogue of Anti-Patterns for formal Ontology debugging

Keywords: Ontologies, OWL, Correction d'Erreurs, AntiPattern, Debugger. 1. Cano comunica.(Albufera Mar Marisma

Debugging of inconsistent OWL ontologies is normally a tedious and time-consuming task where a combination of ontology engineers and domain expert is often required to understand whether the changes to be performed in order to make the OWL ontology consistent are actually changing the intended meaning of the original knowledge model. This task is aided by existing ontology debugging systems, incorporated in existing reasoners and ontology engineering tools, which ameliorate this problem but in complex cases are still far from providing adequate support to ontology engineers, due to lack of efficiency or lack of precision in determining the main causes for inconsistencies. In this paper we describe a set of anti-patterns commonly found in OWL ontologies, which can be useful in the task of ontology debugging in combination with those debugging tools.

HydrOntonlogy

The Spanish National Geographic Institute (IGN-E) developed a common reference model by means of a domain ontology, called hydrOntology. IGN-E wants to build this ontology in order to facilitate the semantic harmonization of hydrographic information among data producers at different levels (national, regional and local).

The statistical data (metrics) and its different taxonomic relations appearing below provide an overview of the hydrOntology characteristics.

HydrOntology is saved in the OWL format; it has 150 classes, 34 object properties, 66 data properties and 256 axioms. Some examples of the four taxonomic relations defined in the Frame Ontology [START_REF] Farquhar A | The Ontolingua Server: A Tool for Collaborative Ontology Construction[END_REF] and the OKBC Ontology [START_REF] Vk | Open Knowledge Base Connectivity 2.0.3[END_REF], namely, Subclasses, Disjoint-Decomposition, Exhaustive-Decomposition and Partitions, have been implemented in the ontology. Further details are shown in [START_REF] Lm | Towntology & hydrOntology: Relationship between Urban and Hydrographic Features in the Geographic Information Domain[END_REF]. The ontology documentation is exhaustive, thus, definitions and their definition sources can be found in each concept (class). The ontology has an important amount of labels with alternative names (synonyms) as well as concept and synonym provenances.

A domain expert about geographical information was trained to build an ontology in Description Logics using Protégé tools (Protégé-OWL version 4). He built the ontology following METHONTOLOGY, a widely-used ontology building methodology. A detailed description of this methodology can be found in [START_REF]Ontological Engineering[END_REF].

HydrOntology has been developed according to the ontology design principles proposed by [START_REF] Gruber Tr | Toward principles for the design of ontologies used for knowledge sharing[END_REF] and [START_REF] Arpírez | ONTO)2Agent: An ontology-based WWW broker to select ontologies[END_REF]. Some of its most important characteristics are that the concept names (classes) are sufficiently explanatory and rightly written. According to some naming conventions, each class is written with a capital letter at the beginning of each word, while object and data properties are written with lower case letters. At the end of the development process 102 concepts were classified as incoherent by the classifier.

When implementing this ontology in OWL several issues arose with respect to its consistency, given its complexity. In the first iteration of implementation, where the domain expert took the conceptualization following Methontology's intermediate representations and encoded it with Protégé 4, all the classes in the ontology were considered inconsistent. Then the process of refinement started, using the OWL ontology debugging facilities of Protégé. Indeed, the debugging systems used did not provide enough information about root unsatisfiable classes or adequate (e.g., understandable by domain experts) justifications of the reasons for their unsatisfiability. Thus, we made an effort to understand inconsistency-leading patterns used by domain experts when implementing OWL ontology. Moreover in several occasions during the debugging process the generation of justifications for inconsistencies took several hours, what made these tools hard to use.

Ontology developer needs more recommendation for debugging than those provided by actual tools. We found out that in several occasions domain experts were just changing axioms from the original ontology in a somehow random manner, even changing the intended meaning of the real definitions instead of correcting errors in their formalisations.

After several iterations, which resulted in a large number of changes to the original implementation, the final consistent ontology could be delivered.

In this paper we propose a detailed list of such anti-patterns, compiling all the relevant cases that we came across when helping ontology developers to debug their ontologies.

Anti-patterns

We have identified a set of patterns that are commonly used by domain experts in their OWL implementations and that normally result in inconsistencies that may be easy or difficult to solve by them. This set of patterns is what we call anti-patterns, and we have categorized them in three groups:

• Logical Anti-Patterns (LAP). They represent errors that DL reasoners detect. These are the ones for which tool support is easier to provide and hence some support already exists.

• Non-Logical (aka Cognitive) Anti-patterns (NLAP). They represent possible modelling errors that are not detected by reasoners (they are not logical but model-Il ne faut pas numéroter les pages -3 ling errors, which may be due to a misunderstanding of the logical consequences of the used expression).

• Guidelines (G). They represent complex expressions used in an ontology component definition that are correct from a logical point of view, but in which the ontology developer could have used other simpler alternatives for encoding the same knowledge.

In the rest of this section we describe each of the anti-patterns identified in each group, providing their name and acronym, their template logical expressions and a brief explanation of why this anti-pattern can appear. As aforementioned, it is important to note that LAP are identified by existing ontology debugging tools, although the information that is provided back to the user explaining the reason for the inconsistency is not described according to such a pattern, what makes it difficult for ontology developers to find out where the inconsistencies are coming from. With respect to NLAP and G, they are not currently detected by these tools as such, although in some cases their combination may lead into inconsistencies that are detected (although not appropriately explained) by tools. We think that tool support for them could be a major step forward in this task.

Finally, all these anti-patterns should be seen as elementary units that cause ontology inconsistencies. That is, they can be combined into more complex ones.

Logical Anti-Patterns

AntiPattern AndIsOr (AIO)

C1 R.C2 C3), Disj(C2,C3) 1
This is a common modelling error that appears due to the fact that in common linguistic usage, "and" and "or" do not correspond consistently to logical conjunction and disjunction respectively [START_REF] Wang | OWL Pizzas: Practical Experience of Teaching OWL-DL: Common Errors & Common Patterns[END_REF]. For example, I want a cake with milk and chocolate is ambiguous. Does the recipe of cake contain some chocolate plus some milk? (Cake_Recipe ( contain.Chocolate) ( contain.Milk). Does the recipe of cake contain chocolate-flavoured milk? (Cake_Recipe contain.(Chocolate Milk)). Does the recipe of cake contain some chocolate or some milk? (Cake_Recipe contain.(Chocolate Milk)). The domain expert makes a confusion between the linguistic "and" and the logical "or". Notice that the position of the logical "and" has an importance in the semantic of an axiom.

This anti-pattern appeared 2 times in HydrOntology debugging process2 .

Ponor comunica.(Aguas_Subterráneas Aguas_Superficiales)

AntiPattern EquivalenceIsDifference (EID)

C1 C2, Disj(C1,C2)
This inconsistency comes from the fact that the ontology developer wants to say that C1 is a subclass of C2 (that is, that C1 is a C2, but at the same time it is different from C2 since he has more information). This anti-pattern is only common for ontology developers with no previous training in OWL modelling, since after a short training session they would discover that they really want to express C1 C2. This inconsistency can hide also a terminological synonymy relation between classes like in SOE.

This anti-pattern appeared 5 times in HydrOntology debugging process.

AntiPattern OnlynessIsLoneliness (OIL) C1 R.C2, C1 R.C3, Disj(C2,C3)
The ontology developer has created an universal restriction to say that C1 can only be linked with a R role to C2. Next, a new universal restriction is added saying that C1 can only be linked with R to C3, disjoint with C2. In general, this means that the ontology developer forgot the previous axiom This anti-pattern appeared 2 times in HydrOntology debugging process. The ontology developer has added a universal restriction for class C1 without remembering that he had already defined another universal restriction with the same property in a parent class. This anti-pattern is a specialization of OIL.

This anti-pattern appeared 2 times in HydrOntology debugging process. The ontology developer misunderstands the subproperty relation between roles, thinking that it is similar to a part-of relation. This anti-pattern is a specialization of OIL because C1 R1.C2, R1 R2 ╞ C1 R2.C2

This anti-pattern did not appear in HydrOntology, we derived it from others.

AntiPattern UniversalExistence (UE)

C1 R.C2, C1 R.C3, Disj(C2,C3)
The ontology developer has added an existential restriction for a concept without remembering the existence of an inconsistency-leading universal restriction for that concept.

This anti-pattern did appear in HydrOntology, we derived it from others.

AntiPattern UniversalExistenceWithInheritance1 (UEWI_1)

C1 C2, C1 R.C3, C2 R.C4, Disj(C3,C4)
The ontology developer has added an existential/universal restriction in a concept without remembering that there was already an inconsistency-leading universal/existential restriction in a parent class, respectively. This anti-pattern is a specialization of UE.

This anti-pattern appeared 1 time in HydrOntology debugging process. The ontology developer misunderstands the subproperty relation between roles, thinking that it is similar to a part-of relation. This anti-pattern is a specialization of UE because C1 R1.C2, R1 R2 ╞ C1 R2.C2 This anti-pattern appeared 1 time in HydrOntology debugging process. The ontology developer has added restrictions about C2 and C1 using a role and its inverse. This antipattern is a specialization of UE because: C2 R -1 .C1 ╞ C1.1 R.C2, C1.1 C1

This anti-pattern appeared 1 time in HydrOntology debugging process. This anti-pattern can also be written like this C1 R.C2, C1 R.C3, C1 =1R.T, Disj(C2,C3)

The ontology developer has added a new existential restriction without remembering that he has already defined another existential and a cardinality restriction for the same concept and role. This pattern is not an elementary one because it contains the NLAP SOS and the G DCC (presented latter), none of these elementary antipattern cause inconsistency; nevertheless it is a good example that a combination of NLAP and G cause inconsistencies.

This complex anti-pattern appeared 1 time in HydrOntology debugging process.

1. Agua_de_transicion sometida_a_influencia.Aguas_Dulces sometida_a_influencia.Aguas_Saladas sometida_a_influencia.(Aguas_Dulces Aguas_Saladas) =1sometida_a_influencia.T

Non Logical Anti-Patterns

As aforementioned, these anti-patterns are not necessarily errors, but describe common templates that ontology developers use erroneously trying to represent a different piece of knowledge.

AntiPattern SynonymeOfEquivalence (SOE)

C1 C2

The ontology developer wants to express that two concepts C1 and C2 are identical. This is not useful at all in a single ontology. This is not very useful in a single ontology that does not import others. Indeed, what the ontology developer generally wants to represent is a terminological synonymy relation: the class C1 has two labels: C1 and C2. Usually one of the classes is not used anywhere else in the axioms defined in the ontology.

This anti-pattern appeared 6 times in HydrOntology debugging process. The ontology developer has added a new existential restriction without remembering that he has already defined another existential restriction for the same concept and role. Although this could be ok in some cases (e.g., a child has at least one mother and at least one father), in many cases it represents a modelling error.

This anti-pattern appeared 4 times in HydrOntology debugging process.

C1 C2, C1 R.C3, C2 R.C4, Disj(C3,C4)
The ontology developer has added an existential restriction in a concept without remembering that he had already defined another existential restriction with the same role in a parent class. This Anti-Pattern is a specialization of SOS.

This anti-pattern appeared 3 times in HydrOntology debugging process.

R1 R2, C1 R1.C2, C1 R2.C3, Disj(C2,C3)
The ontology developer misunderstands the subproperty relation between roles, thinking that it is similar to a part-of relation. This Anti-Pattern is a specialization of SOS because C1 R1.C2, R1 R2 ╞ C1 R2.C2

This anti-pattern did not appear in HydrOntology, we derived it from others.

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AntiPattern SumOfSomWithInverseProperty (SOSWIP) C2 R -1 .C1, C1 R.C3, Disj(C2,C3)

The ontology developer has created two existential restrictions using a role and its inverse. This anti-pattern specializes SOS because:

C2  R -1 .C1 ╞ C1.1 C1, C1.1  R.C2.
This anti-pattern did not appear in HydrOntology, we derived it from others.

AntiPattern SomeMeansAtLeastOne (SMALO)

C1 R.C2, C1 ≥1R.T
The cardinality restriction is superfluous, because if there is an existential restriction that means that the cardinality restriction using the same role is at least equal to 1. The ontology developer had created the axiom C1 ≥1R.T first, to say that C1 should be defined by the R role. Next, he specialized his definition and forgot to remove the first restriction.

This anti-pattern appeared 2 times in HydrOntology debugging process.

1. Rambla es_originado.Torrente, Rambla ≥1es_originado.T 2. Estero está_proxima.Desembocadura ≥1está_proxima.T

Guidelines

As aforementioned, guidelines represent complex expressions used in an ontology component definition that are correct from a logical point of view, but in which the ontology developer could have used other simpler alternatives for encoding the same knowledge.

Guideline DisjointnessOfComplement (DOC)

C1 not C2

The ontology developer wants to say that C1 and C2 can not share instances. Even if the axiom is correct for a logical point of view, it is more appropriate to state that C1 and C2 are disjoint.

This anti-pattern appeared 3 times in HydrOntology debugging process.

Aguas_Marinas not Aguas_Dulces 2. Albufera not Aguas_Dulces 3. Laguna_Salada not Aguas_Dulces

Guideline Domain&CardinalityConstraints (DCC) C1 R.C2, C1 (≥2R.T) (for example)

Ontology developers with little background in formal logic find difficult to understand that universal restriction does not imply existential one [START_REF] Wang | OWL Pizzas: Practical Experience of Teaching OWL-DL: Common Errors & Common Patterns[END_REF]. This antipattern is a counterpart of that fact. Developers may forget that existential restrictions contain a cardinality constraint: C1 R.C2 ╞ C1 (≥1R.C2). Thus, when they combine existential and cardinality restrictions, they may be actually thinking about universal restrictions with those cardinality constraints. This anti-pattern appeared several times in HydrOntology debugging process, we only provide some examples. In order to facilitate the comprehension of complex class definition, we recommend grouping all the restrictions of a concept that use the same role R in a single restriction. The previous restriction becomes C1 ( R.C2) (≥2R.T)

Because the development of an ontology is an iterative process, most part of the class definition using the same R role are split in several expressions. Have a look to previous examples.

Guideline MinIsZero (MIZ)

C1 (≥0R.T)

The ontology developer wants to say that C1 can be the domain of the R role. This restriction has no impact on the logical model being defined and can be removed.

This anti-pattern appeared 1 time in HydrOntology debugging process.

1. Laguna_Salada 0≥ es_alimentada.T

Related works

As far as we know there exist only two works about anti-pattern in formal ontology development. In [START_REF]LABORATORY FOR APPLIED ONTOLOGY[END_REF], the authors present four Logical Anti Pattern but all of them focus on the domain and range of Role. In our case all the domain and range of role are been remove before consistency checking. Due to the fact that we are in the development process of the ontology, class hierarchy is not valid enough to save the domain and range of role. Our proposition differs from [START_REF] Wang | OWL Pizzas: Practical Experience of Teaching OWL-DL: Common Errors & Common Patterns[END_REF] even if we use also the protégé tools in our experiment. In [START_REF] Wang | OWL Pizzas: Practical Experience of Teaching OWL-DL: Common Errors & Common Patterns[END_REF], the authors describe common difficulties for newcomers to Description Logics in understanding the logical meaning of expressions. Their use case examples are very small. In our case the ontology is bigger thus the ontology developer builds his ontology in several times. Moreover our ontology developer is not a DL expert but he has already learnt DL primitives.

Automated OWL ontology debugging features have been described, connected to reasoners and ontology engineering tools, in several recent works ( [START_REF] Horridge | BIJAN PARSIA AND ULRIKE SATTLER for Laconic and Precise Justifications in OWL[END_REF][START_REF] Kalyanpur | Repairing Unsatisfiable Concepts in OWL Ontologies[END_REF]). These features are very useful to debug ontologies, and allow identifying the main root unsatisfiable classes with different approaches, so that the debugging process can be

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Il ne faut pas numéroter les pages -10 guided by them and can be optimized. However, these features are very focused on the logical consequences that can be extracted from the logical theory of an OWL ontology, and are not so focused on the ontology engineering side, hence the explanations are still sometimes difficult to understand for ontology developers.

Conclusion and future works

In this paper, we have described a detailed list of anti-patterns commonly used by domain experts when implementing ontologies in OWL. This list is aimed at complementing the work that is done by automated ontology debugging tools when detecting inconsistencies in this type of ontologies, so that we can provide better explanations of the reasons why a specific class or set of classes of the ontology are inconsistent, and hence improve the efficiency of the ontology debugging process.

All these anti-patterns should be seen as elementary units that cause ontology inconsistencies. That is, they can be combined into more complex ones. However, providing a solution for the individual ones will be a good advance to the current state of the art, and our future work will be also devoted to finding the most common combinations and providing recommendations for them.

We have applied this list of anti-patterns to the development of an ontology in the hydrology domain (HydrOntology [START_REF] Lm | Towntology & hydrOntology: Relationship between Urban and Hydrographic Features in the Geographic Information Domain[END_REF]), resulting in an improvement in the efficiency of the debugging process that we have not actually measured. However, our intuition suggests that the process has been much faster than what it would have been without the use of such anti-patterns, that is, with the use of debugging tools alone.

Our next steps towards providing effective tools to help domain experts in their ontology building tasks are making formal experiments with a set of inconsistent ontologies, built by domain experts that we have been collecting in the past year. The aim of these experiments would be to compare the time needed to complete the debugging process with and without the use of our anti-patterns, and the quality of the final models generated after debugging, in case that there are differences. Finally, another piece of work that we are planning to do in the future is to organize this list of anti-patterns into a set of debugging guidelines for the creation of a better-specified method for ontology debugging that can be more effective.

  se_extrae.Acuífero =1se_extrae.T, Fuente_Artificiale es_alimentada.(Tubería) =1es_alimentada.T AntiPattern UniversalExistenceWithInverseProperty (UEWIP) C2 R -1 .C1, C1 R.C3, Disj(C2,C3) IC 2009 Il ne faut pas numéroter les pages -6

  C2, C1 R.C3, C1 ≤1R.T, Disj(C2,C3)

This does not mean that the ontology developer has explicitly expressed that C2 and C3 are disjoint, but that these two concepts are determined as disjoint from each other by a reasoner. We use this notation as a shorthand for C2 C3 .

All the examples from HydrOntology are in Spanish. Indeed, we cannot translate the examples without changing the meaning of terms, because the conceptualization depends of the language used.

For convenient purpose, we do not add the disjointness relation between classes when the reasoner deduces this relation. Thus notice that all the classes used in our example are found disjoint by the reasoner.

Acknowledgements

This work is a result of collaboration between the OEG and LIRIS lab. It has been done under the context of the project GeoBuddies, funded by the Spanish Ministry of Science and Technology and it was also partially funded by the COST Action C21 sponsored by the European Commission under the grant number STSM-C21-04241.