Dr Damien Bissessar

Dr Julien Egly

Dr Thierry Achard

Dr Pascal Steffanut

Dr Matteo Mauro

Dr Stéphane Bellemin-Laponnaz

A stable and photoreactive copper-iodide

Introduction

Being able to generate molecular diversity in a simple and rapid way by chemical synthesis is essential to identify and optimize new properties of interest. For example, high-throughput screening and combinatorial chemistry are two representative examples of strategies that can rapidly lead to the discovery of new drugs. These approaches are proving to be very effective in this field but are not necessarily applicable to other areas, such as transition metal materials for example. An approach more adapted to molecular materials, especially with transition metal complexes, may be divergent synthesis, since it allows for rapid generation of libraries of compounds, which is in contrast to traditional target-driven linear or convergent synthesis. [1] However, divergent synthesis involves post-functionalization steps, which is a challenging route because metal complexes are potentially reactive molecules that generally do not tolerate further manipulation.

In the field of photoactive materials, there is a growing interest in systems based on earth-abundant and non-expensive transition metals, also owing to their potential applications in different fields of photochemistry. [2,3] In this regard, copper has rapidly emerged as a metal of choice motivated by its low toxicity, low cost and abundancy. [4,5] In particular, tetranuclear copper-iodide clusters of general formula [Cu(µ3-X)L]4 consisting of a {Cu4X4} cubane core (X = halogen) and ligands (L = nitrogen or phosphorus-based ligand) located apically are attractive entities because of their intriguing photophysics combined with their extensive stimuli responsive properties. [6] Light-emitting devices based on coppercubane derivatives have also been reported recently. [7] They also have been successfully applied for the development of low cost highly luminescent inks with different colors that cover the whole visible spectrum range. [8] Since these systems constitute an unprecedented family of luminescent stimuli-responsive compounds and materials, the control and modulation of their physical and photophysical properties is highly sought. The properties of such particular polynuclear complexes are associated with the four apical ligands that influence both the metallophilic interactions within the cubane and the inter-cluster interactions (aggregation-induced emission properties for example). [9,10 ] Little chemical modification on the ligand may greatly influence the overall behavior of the material (Scheme 1a). In this context, the development of modular approaches aiming at introducing chemical diversity straightforwardly onto a luminescent scaffold is of great importance for their further application as photofunctional material. In particular, strategies enabling the direct chemoselective functionalization onto preformed metal complexes are attractive for an easy access to a large library of luminescent compounds and it would be a strong asset to facilitate the development of such emerging materials. Indeed, post-functionalization of coordination compounds has long been understudied because it was thought that complexes were incompatible with chemical transformations by nature. [11] Herein, a highly stable copper cubane featuring photoreactive P-H bonds can react with various alkenes to produce a large range of interesting copper complexes. The proposed postfunctionalization strategy offers easy access to molecular diversity in future developments of potentially luminescent materials.

Results and Discussion

The synthesis of the cubane [Cu(µ3-I)(PPh2H)]4 1 is depicted in Scheme 1b. Copper iodide was heated in presence of diphenyl phosphine in toluene which gave the tetranuclear species in 96% yield. Interestingly, whereas diphenylphosphine PPh2H is highly reactive and should be stored under N2, the resulting Cu complex displays exceptional stability under air (up to 250 °C as deduced from thermogravimetric analysis). Crystals suitable for X-ray diffraction analysis were grown and Fig. 1 displays the molecular structure of the cubane. The bond distances and angle mean values for 1 are within the range of reported values for this type of clusters coordinated by phosphine ligands. The mean Cu-Cu distance is 2.87 Å which is greater than the sum of the van der Waals (2.80 Å). [START_REF] Hammoud | Compound 1 has been investigated as a co-initiator for the free radical polymerization of acrylates monomers[END_REF] Figure 1. Molecular structure of tetranuclear copper complex [Cu(I)(PPh2H)]4 1. Selected bond lengths (Å): P(1)-H(1), 1.29(3); P(2)-H(2), 1.26(4). Average bond lengths (Å) Cu-I, 2.682; Cu-Cu, 2.884; Cu-P, 2.251.

Although exceptionally stable, we anticipated that the P-H functions could be activated to allow a direct hydrophosphination reaction onto alkene substrates. Hydrophosphination of methyl vinyl ketone was examined first (Scheme 2) to generate the functionalized cubane 2, a complex that we recently synthesized starting from CuI and the corresponding tertiary phosphine. [13] Interestingly, traces of cubane 2 were observed when dissolving compound 1 in methyl vinyl ketone at room temperature for 12 hours, demonstrating its reactivity (entry 1). The conversion could be improved by heating and 18% of conversion were observed after 12 h in refluxing acetonitrile (entry 2). Finally, the mixture was irradiated with a UV lamp at lexc = 365 nm for 1 hour at ambient temperature (entry 3), resulting in complete conversion of methyl vinyl ketone as deduced from 1 H NMR analysis. The fully functionalized cubane could be isolated in 97% by precipitation in cyclohexane. [START_REF] Interestingly | it has been recently shown that under UV light Cu(acac)2 is an active catalyst for the hydrophosphination of alkenes[END_REF] Scheme 2. Reactivity of tetranuclear copper complex [Cu(µ3-I)(PPh2H)]4 1 toward methyl vinyl ketone (Entry 3: lexc = 365 nm).

In order to demonstrate the utility of this method, we have applied the procedure to a variety of alkene substrates as shown in Scheme 3. Methyl vinyl ketone (2), styrene (3a-b), acrylamide (4), acrylate (5a-f) and methacrylate derivatives (6a-c) were tested with success, giving the corresponding products with isolated yields ranging from 47% (6c) to 97% (3). Interestingly, it is possible to functionalize 1 with acrylates bearing alkyne or inactivated alkene: compounds 5d and 5e were obtained in 73% and 79% yield, respectively. Thiophene-based compounds are widely studied in materials science and technology: cubane 1 could be functionalized with acrylate 5f bearing a thiophene moieties. Poly(ethylene glycol) methyl ether acrylate is used to create biocompatible homopolymer used as material for biomedical applications. The post-functionalization with such a type of monomer is also possible (5g) thus providing the possibility of creating potentially biocompatible materials. Therefore, a whole molecular diversity is offered which will make it possible to quickly identify some molecules of interest for various potential applications. In recent decades, developments in molecular biology and microscopy techniques have made it possible to visually detect molecules in living systems. [15] Among the variety of reactions, alkyne-azide "click" chemistry has been identified as a conjugation reaction of choice and the identification of new tools for potential biological targets remains topical. [16] In this direction, the cubane 5d is of interest since the alkyne-containing acrylate may be post-functionalized using click-strategy, thus offering potential easy fluorescence labeling. [ 17 ] We found that the complex reacts rapidly within minutes in the presence of 4 equiv. of benzyl azide with no need of additional catalyst, as deduced from NMR and mass spectrometry experiments (Eq. 1, see SI for details). Although more work is needed to identify the exact mechanism of the reaction, it seems most likely that the system undergoes an autocatalytic mechanism, with cubane being the catalyst of the reaction. [18,19] Among examples displayed in Scheme 3, complex 5g decorated with poly(ethylene glycol) (PEG) chains constitutes novel family of cubane, since it exhibits unprecedented solubility in water.

The peculiar photoluminescence properties of this class of cupper-iodine clusters and the remarkable solubility in aqueous environment of derivative 5g prompted us to investigate the photophysical properties of this latter, as a proof of principle of the proposed straightforward post-functionalization strategy. At a first stage, compound 5g was investigated in diluted aqueous solution . The electronic absorption and emission are displayed in Figure 2b and the corresponding data are listed in the ESI (Table S1). Upon excitation at lexc = 300 nm, diluted H2O solution of 5g display an intense, broad and featureless photoluminescence band with emission maxima centered at lem = 595 nm. This emission is attributable to a radiative process from a triplet excited state with admixed cluster-centered ( 3 CC) and halogen-to-ligand charge transfer ( 3 XLCT) nature, in comparison with related copper-iodine cubane clusters of {Cu(µ3-I)(phosphane)}4 general structure. 11 An irreversible and slow photodegradation of the sample was observed upon cycling photoluminescence spectra, which hampered deeper investigation by means of time-resolved techniques. Nevertheless, observation of photoluminescence in solution is surprising and unprecedented for copper-iodide cubane, to the best of our knowledge. Lack of solution photoluminescence is typically attributed to the reduced chemical stability of the cluster due to the flexible nature of the metal-iodine scaffold and ligand dissociation in fluid solution. [ 20 ] These processes appeared to be favorably suppressed in solution samples of 5g most likely due to the shielding effect imparted by the multiple oligo-ethyleneglycol chains onto the luminescent tetra-metallic core that also provide an amphiphilic character to the compound. As consequence, radiative de-excitation becomes now competitive over non-radiative intra-and inter-molecular (dissociative) processes. This finding of switching-on effect on the luminescence in amphiphilic metal complexes is in agreement with other systems reported in the literature. [21] Interestingly, the neat PEG-cubane cluster 5g obtained as a colorless oil after synthesis, displays stable photoluminescence centered at 595 nm with moderate intensity (photoluminescence quantum yield = 6%) with long-lived excited-state lifetime (tav = 1.88 µs) as typical of formally spin-forbidden triplet emission from 3 CC/ 3 XLCT band (see Table SI in SI) Dynamic light scattering (DLS) was also used for studying sizes of nanoparticle in water (Figure 2c). The signal was monodisperse and the particle size was found to be around 9 nm which is consistent with single cubane clusters. [START_REF] Utrera-Melero | Aggregation-induced emission properties were recently observed with copper iodide cubanes in THF/water or acetone/water mixtures[END_REF] Increasing the concentration in solution did not affect the results suggesting no aggregation under these conditions. Replacing water by organic solvent such as CH2Cl2 leads to loss of signal by DLS measurement and loss of luminescence, suggesting a dynamic intermolecular exchange process of the copper atoms. [19a]

Conclusion

In summary, copper-iodide diphenylphosphine cubane is a highly stable precursor, which can be activated under UV light to generate molecular diversity in the field of cubane copper chemistry. The post-functionalization occurs under smooth conditions at room temperature and the corresponding products were isolated in high yields. We envisage that this study can open up an avenue to use copper cubanes in emissive devices.

Cubane [Cu(µ3-I)(PPh2H)]4 1. Copper(I) Iodide (500 mg, 2.62 mmol), diphenylphosphine (500 mg, 2.68 mmol) and dry toluene (8 mL) were placed in a flame-dried Schlenk tube under argon. The solution was heated at 100 °C during 12 hours. Then the mixture was cool down to room temperature and the solvent was removed under vacuum. The solid residue was dissolved in CH2Cl2 and the solution was poured into Et2O. The complex precipitated instantaneously and was filtered and washed several times with Et2O. The product was dried under vacuum. White powder (947 mg), yield 96%. ). Four equivalents of the acrylate derivative was added and the solution was irradiated at l = 365 nm with a LED lamp for 4 hours (except for compound 3: 1 hour). Then the mixture was cooled down to the room temperature and the solvent was removed under vacuum. The solid residue was dissolved in CH2Cl2 and the solution was poured into Et2O or n-Hexane. The complex precipitated instantaneously and was filtrated and washed several times with Et2O and n-hexane. The product was then dried under vacuum. For analytical data of all compounds, see Supporting Information.

Scheme 1 .

 1 Scheme 1. (a) General molecular structure of [Cu4I4L4] copper iodide cubanes. Modulation of the physical and photophysical properties by varying the nature of the ligand; (b) Synthesis of copper(I) cubane 1.

Scheme 3 .

 3 Scheme 3. Scope of the direct hydrophosphination of tetranuclear copper complex [Cu(µ-I)(PPh2H)]4 1 (Isolated yield). Reaction conditions: dichloromethane as solvent, r.t., lexc = 365 nm, reaction time: 1 h for compound 3 and 4 h for all other compounds listed.

Figure 2 .

 2 Figure 2. (a) Complex 5g in pure form (on a glass plate, left) and in water at 10 - 3 M and 10 -4 M (right) under UV radiation. (b) Emission spectra as neat oil (red solid trace) and in air-equilibrated aqueous solution at 2.10 -4 M upon excitation at 300 nm (black solid trace). Excitation spectra (300 nm, black dotted trace) at 2.10 -4 M and UV-Vis spectra (black dashed trace) at 2.10 -5 M in air-equilibrated aqueous solution. (c) DLS analysis of complex 5g in water or in dichloromethane as solvent.

  1 H NMR (400 MHz, CDCl3) δ 7.50-7.46 (m, 16H), 7.31 (br t, J = 7.4 Hz, 8H), 7.28 (br td, J = 7.5, 1.3 Hz, 16H), 5.83 (d, JP-H = 255 Hz, 4H) ppm;13 C NMR (101 MHz, CDCl3) δ 134.2 (d, JC-P = 13 Hz, CH), 130.4 (d, JC-P = 29 Hz, C), 129.7 (CH), 128.7 (d, JC-P = 9 Hz, CH). ppm; 31 P { 1 H} NMR (202 MHz, CDCl3): δ: -40.2 (br) ppm; FTIR: νmax (pure, diamond orbit) = 2975, 1476, 1437, 1089, 887, 819, 725, 686 cm -1 ; ATG: 5% weight loss at 257 °C HRMS (ESI): m/z calcd for [C48H43Cu4I4P4] + : 1502.5672, Found: 1502.5672. CCDC Deposition Number 2063316 for copper complex 1. Direct hydrophosphination of tetranuclear copper complex [Cu(µ-I)(PPh2H)]4 1. General Procedure: Complex 1 was placed in a flamedried Schlenk tube under argon and was dissolved in dry dichloromethane and (concentration 50 mg.mL -1

Acknowledgements

Financial support for this project was provided by the Région Grand Est (France) and Clariant (Muttenz, Switzerland). Dr. Lydia Brelot and Corinne Bailly are gratefully acknowledged for X-ray crystallographic analyses.

Keywords: copper complexes • coordination chemistry • luminescence • phosphine • reactivity


Thibault Thierry
email: thibault.thierry@ipcms.unistra.fr

Yannick Geiger
email: y.geiger@rug.nl

Stéphane Bellemin-Laponnaz

Observation of Hyperpositive Non-Linear Effect in Asymmetric Organozinc Alkylation in

Keywords: asymmetric catalysis, nonlinear effect, chiral amplification

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

Asymmetric synthesis and catalysis are of paramount importance for obtaining enantiopure molecules, especially in the development of chiral drugs that are almost exclusively applied in the form of single enantiomers [START_REF] Jacobsen | Comprehensive Asymmetric Catalysis[END_REF]. In asymmetric catalysis, a chiral auxiliary (most often a chiral ligand attached to a metal) is used ideally in its enantiomerically pure form to maximize the enantiomeric excess of the desired product (eeP). When the chiral auxiliary is not enantiopure, in most cases a linearity is observed between the optical purity of the product (eeP) and the reagent (eeL), as shown in Figure 1a. However, deviations from linearity between eeP and eeL can occur and are referred to as non-linear effects (NLEs) [START_REF] Puchot | Nonlinear effects in asymmetric synthesis. Examples in asymmetric oxidations and aldolization reactions[END_REF][START_REF] Guillaneux | Nonlinear effects in asymmetric catalysis[END_REF]. In the case of a positive non-linear effect (often called (+)-NLE), the eeP can be much higher than the eeL, resulting in asymmetric amplification (Figure 1b). The opposite is also possible, called negative non-linear effect ((-)-NLE) (Figure 1c). Recently, we observed that a chiral catalyst, when not enantiopure, can be more enantioselective than its enantiopure counterpart (Figure 1d) [START_REF] Geiger | Hyperpositive nonlinear effects in asymmetric catalysis[END_REF].Such unusual, "hyperpositive" NLE was first suggested by Kagan in the mid-90's [START_REF] Puchot | Nonlinear effects in asymmetric synthesis. Examples in asymmetric oxidations and aldolization reactions[END_REF][START_REF] Girard | Nonlinear Effects in Asymmetric Synthesis and Stereoselective Reactions: Ten Years of Investigation[END_REF][START_REF] Satyanarayana | Nonlinear Effects in Asymmetric Catalysis[END_REF]. This was observed in the zinc-catalyzed alkylation of aldehyde in the presence of N-benzyl ephedrine and we rationalized the hyperpositive NLE by introducing a monomer-dimer competition model where both monomers and dimers are catalytically active [START_REF] Geiger | Hyperpositive nonlinear effects in asymmetric catalysis[END_REF][START_REF] Geiger | Observation of hyperpositive non-linear effect in catalytic asymmetric organozinc additions to aldehydes[END_REF][START_REF] Geiger | Absence of Non-Linear Effects despite evidence for catalyst aggregation[END_REF][START_REF] Noble-Terán | Nonlinear Effects in Asymmetric Synthesis: A Practical Tool for the Discrimination between Monomer and Dimer Catalysis[END_REF]. Such model also allows to describe enantiodivergent NLEs, that is when a catalyst can generate one enantiomer or its opposite by simply varying the ligand ee (see Figure 1e) which was observed with N-methyl ephedrine as ligand [START_REF] Geiger | Hyperpositive non-linear effects: enantiodivergence and modelling[END_REF]. Since chiral ligands based on ephedrine or norephedrine have been and still are widely used in asymmetric catalysis, it appeared important to study other derivatives of this family in the context of non-linear effect. Among all the derivatives, N-pyrrolidinyl norephedrine (NPNE) attracted our attention [START_REF] Soai | Asymmetric synthesis of optically active β-substituted ketones by highly enantioselective catalytic conjugate addition of dialkylzinc reagents to enones using a catalyst system of nickel(II)-chiral ligand-achiral ligand in acetonitrile/toluene[END_REF][START_REF] Niwa | Catalytic asymmetric synthesis of optically active alkynyl alcohols by enantioselective alkynylation of aldehydes and by enantioselective alkylation of alkynyl aldehydes[END_REF] in part because it is one of the most enantioselective ligands in ephedrine-based catalytic organozinc additions.

Herein, we wish to report our investigations in the enantioselective zinc-catalyzed alkylation of benzaldehyde with NPNE as partially resolved chiral ligand. A hyperpositive non-linear effect was observed with diethylzinc or dimethylzinc as reagent, which was found to be more pronounced at low temperatures. The results were rationalized by studying the effect of temperature and concentration and also on the basis of our previous studies with N-benzyl ephedrine. Overall, this system concords with the previously proposed monomer-dimer competition model, where a monomeric species is in equilibrium with a dimeric species, both being active and competing to generate the product albeit with different enantioselectivity.

Results

Non-linear studies

The zinc-catalyzed alkylation of benzaldehyde was investigated with partially resolved chiral N-pyrrolidinyl norephedrine ligand (NPNE). Figure 2 displays the results with diethylzinc (a) or dimethylzinc (b) as reagent. The catalyst loading was fixed at 20 mol% and toluene was used as solvent. The reactions were carried out at 20 °C, 0 °C and -20 °C. In case (a), at room temperature the product was isolated in 81.4% ee when the enantiopure ligand was used (green curve). A strong positive non-linear effect occurred with essentially no change of the product enantiopurity up to eeL of 25%. The lowering of the reaction temperature induced a slight increase in the optical purity of the product and the appearance of a hyperpositive effect that is more significant at -20 °C than 0 °C (Dee of 4.2% and 3.2%, respectively). In contrast, in case (b) the best enantioselectivity in presence of the enantiopure ligand was observed at room temperature (68.2% ee), since the lowering of the reaction temperature caused an opposite result than before. The three curves showed a hyperpositive effect that intensified with decreasing temperature. Here, the highest Dee was found to be 10.6%. During the catalytic investigations, we detected that, when the partially resolved ligand was used, upon addition of the dialkylzinc reagent a precipitate was observed. This was in contrast to the use of the enantiopure ligand which gave a clear solution. Figure 3 displays three selected catalytic samples at 20%, 50% and 100% eeL (from left to right) that clearly illustrates the differences. Additional experiments were carried out to identify the nature of the precipitate. Analyses of the hydrolyzed precipitate obtained from 20% ee NPNE ligand sample revealed the free ligand in its racemic form, as deduced from the measurement of the optical rotatory power.

Impact of catalyst loading

The enantioselective reaction was evaluated by varying the catalyst loading of the enantiopure NPNE ligand with diethylzinc (Figure 4, a) or dimethylzinc (Figure 4, b) as reagent. In both cases, the results showed that a decrease in catalyst loading resulted in an increase in the enantiomeric excess of the product.

All curves show the same trend, the major difference between the two reagents lies in the temperature effect as already observed in the previous NLE studies. The reaction conditions and experimental procedure are described in the Supplementary Methods. Each point is the mean of three different experiments. The vertical error bars depict standard deviations. The dotted trendlines are second-order polynomial fits, which serve as guidelines.

Impact of temperature

The impact of the reaction temperature on the product enantioselectivity was investigated. Figure 5 displays the results ranging from -20 °C to 40 °C with diethylzinc (yellow triangle) or with dimethylzinc (blue square) as reagent. With diethylzinc, the product ee went down from 84.4% at -20 °C to 77.8% at 40 °C. In contrast, the product ee increased from 54.4% at -20 °C to 72.4% at 40 °C with dimethylzinc.

Discussion

The norephedrine skeleton has been used extensively for the development of efficient chiral auxiliaries in asymmetric synthesis and asymmetric catalysis, mostly with zinc as active metal [START_REF] Pu | For a review on zinc-catalyzed alkylation of carbonyl compounds[END_REF]. Enantioselectivities greater than 90% ee were often reported in the alkylation (or alkynylation) of carbonyl or imine compounds [START_REF] Cruz | N-Substituted Ephedrines as Chiral Auxiliaries in Enantioselective Alkylation Reactions of Carbonyl Compounds[END_REF][START_REF] Patel | Synthesis of Islatravir Enabled by a Catalytic, Enantioselective Alkynylation of a Ketone[END_REF][START_REF] Sekiguchi | Enantioselective Conjugate Addition of Catalytically Generated Zinc Homoenolate[END_REF]. Additionally, Efavirenz, an industrially produced drug for the treatment of Human Immunodeficiency Virus (HIV), includes an enantioselective transformation mediated by N-pyrrolidinyl norephedrine (NPNE) [START_REF] Griffiths | Proposed Mechanism for the Enantioselective Alkynylation of an Aryl Trifluoromethyl Ketone, the Key Step in the Synthesis of Efavirenz[END_REF]. We therefore decided to focus NLE studies with NPNE ligand to better understand the nature of the catalytically active species.

Investigations of the product ee (eeP) as function of ligand ee (eeL) with NPNE revealed a hyperpositive NLE in the zinc-catalyzed alkylation reaction (Figure 2). Such behavior is similar to what was observed previously with the N-benzyl ephedrine ligand [START_REF] Geiger | Hyperpositive nonlinear effects in asymmetric catalysis[END_REF]. Interestingly, using ZnMe2 as reagent the enantioselectivities are more pronounced than with the NBE ligand. The hyperpositive NLE effects (i. e. the difference between the highest eeP obtained and the eeP with enantiopure ligand) with NPNE ligand are relatively small at room temperature and more pronounced at lower temperature (0 and -20 °C).

Similar to what was observed with the NBE system, a zinc aggregate precipitated when the ligand was not enantiopure, as shown in Figure 3 [START_REF] Geiger | Non-linear effects in asymmetric catalysis: impact of catalyst precipitation[END_REF]. A measurement of the rotatory power of the ligand contained in the aggregate revealed that the ligand was in its racemic form. Therefore, the precipitate is an overall racemic mixture of NPNE-complexes, as previously observed with NBE as ligand, most likely as a heterochiral dimer or co-precipitated RRS•RSS trimer adduct (trimeric adducts were observed in solution with the parent ligand N-methyl ephedrine) [START_REF] Geiger | Absence of Non-Linear Effects despite evidence for catalyst aggregation[END_REF]. Such precipitation of racemic ligand causes a strong positive non-linear effect to emerge, as it enantioenriches the zinc species left in solution (i.e. Kagan's reservoir effect) [START_REF] Guillaneux | Nonlinear effects in asymmetric catalysis[END_REF]. Trapping the ligand in a racemic form implies that when decreasing the enantiomeric excess of the ligand, we generate more racemic inactive aggregates and thus less catalytically active species. Figure 4 displays the evolution of product ee as function of the catalyst loading of the enantiopure NPNE. In all cases, a decrease of the catalyst loading led to an increase of the product ee.

The catalytic loading effect with the enantiopure ligand and the non-linear effects were correlated. Considering that the reservoir effect on the racemic species is optimal in these systems, we could correlate the data points from the catalyst loading effect with a virtual enantiomeric excess if a scalemic ligand was used. The plots were superimposed with the NLE curves and are displayed in Figure 7 below [START_REF] Geiger | Hyperpositive nonlinear effects in asymmetric catalysis[END_REF]. At -20 °C and 0 °C, good agreement was observed but not at room temperature. 2). Black dots: Superimposition of eeP as function of catalyst loading, which was previously converted to eeP vs. simulated ligand ee assuming a complete trapping of the racemic ligand (from Figure 4).

Altogether, these results indicate a monomer-dimer mechanism as proposed in Figure 8 [START_REF] Kitamura | Quantitative Analysis of the Chiral Amplification in the Amino Alcohol-Promoted Asymmetric Alkylation of Aldehydes with Dialkylzincs[END_REF]. Two different enantiodivergent pathways are present in the system: a monomeric (-)-NPNE-ZnR-catalyzed mechanism and a dimeric (-)-NPNE-ZnR-catalyzed mechanism that operate at a steady state. Since the overall ee (and yield) of the product is the combination of the two catalysts, if (i) the monomeric catalyst is more enantioselective than the dimeric catalyst (i.e. ee1 > ee2), (ii) the two chiral catalysts are in dynamic equilibrium, and (iii) the minor enantiomer is trapped in the form of an inactive species such as a solid heterochiral dimer, then a hyperpositive non-linear effect is possible. Indeed, decreasing eeL leads to an increase of eeP because the equilibrium should be shifted to the monomeric catalyst. Decreasing the catalyst loading should have the same effect. However, this hyperpositive non-linear effect will only be possible if the reservoir effect is highly efficient, trapping the minor enantiomer. This is the case at low temperatures (0°C and -20 °C). On the other hand, at room temperature we observe essentially a "classical" positive non-linear effect although the study of the catalysis revealed an increase of eeP as function of the catalyst loading (Figure 4). This suggest that at room temperature a portion of the heterochiral dimer is soluble and lowers the overall eeP by allowing for the formation of the minor enantiomer catalyst, or by being catalytically active itself and generating racemic product.

In asymmetric catalysis, the enantioselectivity is determined by the relative rates of the enantiodifferentiating step (i.e. DDG*), which is temperature-dependent. As a result, the enantioselectivity is greater at lower temperature. Here, we also investigated the effect of the temperature on the overall product ee of the reaction (Figure 5). With diethylzinc as reagent, eeP goes from 84.2% at -20 °C to 77.8% at 40°C, a variation that is very little given the temperature range. With dimethylzinc, the enantiomeric excess of the product was significantly increased (from 54.4% to 75.1%) which is an unusual inverse temperature dependence. Altogether, this is consistent with an equilibrium between a monomeric species and a dimeric species, which is shifted towards the more enantioselective monomer at higher temperature.

Materials and Methods

Synthetic procedures as well as additional data for experimental catalytic runs can be found in the supplementary information section. Detailed experimental data (reactant quantities, reaction conditions, raw and treated results for all catalytic runs).

Conclusions

In asymmetric synthesis or catalysis, the NPNE ligand is one of the most used in the family of ephedrine-based ligands usually generating products with high enantiocontrol. The study of the ee of the product versus the ee with this ligand in the asymmetric organozinc alkylation demonstrated that the chiral catalyst, when not enantiopure, is more enantioselective than its enantiopure counterpart. Mechanistic studies show that the system follows the same pattern as that with N-benzyl ephedrine or N-methyl ephedrine ligands: with NPNE ligand, we noticed the presence of an insoluble racemic aggregate that allowed to trap the minor enantiomer catalyst. The remaining enantioenriched active species consist in a two-component system, where a monomeric catalyst is in equilibrium with a dimeric catalyst. The equilibrium between the catalytic species is dependent on the total concentration of species in solution which depends on the enantiomeric excess of the ligand used in the reaction. Evidence for this model has been found by varying the catalyst loading, or the reaction temperature. A correlation between the catalytic loading effect with the enantiopure ligand and the non-linear effects suggested that part of the racemic aggregate could catalyze the reaction and reduce the magnitude of the observed hyperpositive non-linear effect at higher temperature.

Figure 1 .

 1 Figure 1. Product ee vs ligand ee-graphs of catalytic asymmetric reactions showing examples for a) no NLE, b) a positive NLE [(+)-NLE)], c) a negative NLE [(-)-NLE)] d) a hyperpositive NLE and e) a enantiodivergent NLE.

Figure 1 .

 1 Figure 1. Catalytic enantioselective addition of dialkylzincs to benzaldehyde, catalyzed by N-pyrrolidinyl norephedrine.

Figure 2 .

 2 Figure 2. Optical purity of the product as a function of the enantiomeric excess of NPNE ligand (20 mol%) at different temperatures. (a) with ZnEt2 as reagent; (b) with ZnMe2 as reagent. The reaction conditions and experimental procedure are described in the Supplementary Methods. Each point is the mean of three different experiments. The vertical error bars depict standard deviations. The dashed line represents the product e.e. of the enantiopure compound; the full line is a free-hand drawing, which serves as a guideline.

Figure 3 .

 3 Figure 3. Reaction medium (Ligand, substrate, diethylzinc, toluene) as function of the optical purity of the NPNE ligand. From left to right: 20%eeL ; 50%eeL; 100% eeL.

Figure 4 .

 4 Figure 4. Optical purity of the product as a function of the catalyst loading of NPNE ligand (enantiopure 1S-2R form) at different temperatures. (a) with ZnEt2 as reagent; (b) with ZnMe2 as reagent. The reaction conditions and experimental procedure are described in the Supplementary Methods. Each point is the mean of three different experiments. The vertical error bars depict standard deviations. The dotted trendlines are second-order polynomial fits, which serve as guidelines.

Figure 5 .

 5 Figure 5. Optical purity of the product as a function of the temperature. Orange triangles correspond to the reaction with ZnEt2 as reagent; Blue squares correspond to the reaction with ZnMe2 as reagent. The reaction conditions and experimental procedure are described in the Supplementary Methods. Each point is the mean of three different experiments. The horizontal error bars depict temperature variation during the reaction. The vertical error bars depict standard deviations. The dotted trendlines are second-order polynomial fits, which serve as guidelines.

Figure 7 .

 7 Figure 7. Colored dots: Non-linear studies (from Figure2). Black dots: Superimposition of eeP as function of catalyst loading, which was previously converted to eeP vs. simulated ligand ee assuming a complete trapping of the racemic ligand (from Figure4).

Figure 8 .

 8 Figure 8. Proposed enantiodivergent model with (-)-NPNE as major enantiomer.

Acknowledgments:

We thank A. Maisse-François, T. Achard and E. Couzigné. Dedicated to Henri B. Kagan for his outstanding contribution to asymmetric catalysis and organometallic chemistry.

Funding: This research was supported by the Interdisciplinary Thematic Institute ITI-CSC via the IdEx Unistra (ANR-10-IDEX-0002) within the program Investissement d'Avenir.

Data Availability Statement: Data is contained within the article and Supplementary Materials.

Supplementary Materials: Additional information of this research is included in Tables S1-S13, which are available online. Synthetic procedures are also included.

Conflicts of Interest:

The authors declare no conflict of interest.


Oussama Messai

Aladine Chetouani

END-TO-END DEEP MULTI-SCORE MODEL FOR NO-REFERENCE STEREOSCOPIC IMAGE QUALITY ASSESSMENT

Keywords: stereoscopic image quality assessment, Convolutional Neural Network (CNN), Multiscore deep learning

Deep learning-based quality metrics have recently given significant improvement in Image Quality Assessment (IQA). In the field of stereoscopic vision, information is evenly distributed with slight disparity to the left and right eyes. However, due to asymmetric distortion, the objective quality ratings for the left and right images would differ, necessitating the learning of unique quality indicators for each view. Unlike existing stereoscopic IQA measures which focus mainly on estimating a global human score, we suggest incorporating left, right, and stereoscopic objective scores to extract the corresponding properties of each view, and so forth estimating stereoscopic image quality without reference. Therefore, we use a deep multi-score Convolutional Neural Network (CNN). Our model has been trained to perform four tasks: First, predict the left view's quality. Second, predict the quality of the left view. Third and fourth, predict the quality of the stereo view and global quality, respectively, with the global score serving as the ultimate quality. Experiments are conducted on Waterloo IVC 3D Phase 1 and Phase 2 databases. The results obtained show the superiority of our method when comparing with those of the state-of-the-art. The implementation code can be found at: https://github.com/o-messai/multiscore-SIQA

INTRODUCTION

Stereoscopic images are now widely used in a variety of applications including 3D medical imaging, virtual reality, and 3D video games [START_REF] Messai | Adaboost neural network and cyclopean view for no-reference stereoscopic image quality assessment[END_REF]. Several processes are typically conducted to such images (compression, transmission, restoration, etc.), each of which can impact the perceived quality [START_REF] Chetouani | Convolutional neural network and saliency selection for blind image quality assessment[END_REF][START_REF] Chetouani | A blind image quality metric using a selection of relevant patches based on convolutional neural network[END_REF]. This problem has prompted the computer vision field to develop sophisticated quality measurements that forecast the perceived impact of these distortions, known as Stereoscopic Image Quality Assessment (SIQA). There are two types of SIQA methods: subjective SIQA and objective SIQA. The former approaches are costly and time consuming because they rely on human score opinion to judge quality, whereas the latter are inexpensive and quick since they rely on machine algorithmic score. However, because humans are the final recipients of 3D content, it is important to validate the metric output with a subjective evaluation, namely human visual quality assessment. It is mostly expressed in terms of Mean Opinion Score (MOS) or Difference Mean Opinion Score (DMOS).

The need for SIQA development first gained traction in 2009, when Benoit et al. [START_REF] Benoit | Quality assessment of stereoscopic images[END_REF] suggested a methodology that combines two metrics. They begin by calculating the difference between the left and right reference images and the corresponding distorted images. The difference between the pure stereo image disparity map and the distorted ones is then computed. Another remarkable FR-SIQA [START_REF] Chen | Fullreference quality assessment of stereopairs accounting for rivalry[END_REF] metric has been presented that outperforms the latter. The authors used a linear formulation of cyclopean view that is impacted by binocular competition between left and right views. Ma et al. [START_REF] Ma | Fullreference quality assessment of stereoscopic images by learning binocular visual properties[END_REF] also presented NR-SIQA, which employs binocular combination idea to conduct Human Visual System (HVS) simulation.

Due to the general benefits they provide, SIQA researchers are increasingly relying on NR measures. Therefore, most present SIQA approaches are dedicated to NR-SIQA to satisfy the requirements of most modern applications. Machine learning approaches, in particular Deep Learning (DL) [START_REF] Mahmoudi | Kernelized dense layers for facial expression recognition[END_REF][START_REF] Mahmoudi | Learnable pooling weights for facial expression recognition[END_REF], enabled the automatic extraction of the best features, allowing them to outperform handwritten characteristics. However, in the SIQA domain, the learning techniques may differ from one measure to another, but the success is strongly dependent on the derived quality characteristics. Simulating the HVS's quality assessment behavior during binocular vision is another key aspect. The latter, on the other hand, is still in its early phases. In the following, we briefly address the recent suggested NR-SIQA metrics: In [START_REF] Sun | Learning local quality-aware structures of salient regions for stereoscopic images via deep neural networks[END_REF], saliency information [START_REF] Abouelaziz | 3D visual saliency and convolutional neural network for blind mesh quality assessment[END_REF][START_REF] Abouelaziz | No-reference mesh visual quality assessment via ensemble of convolutional neural networks and compact multi-linear pooling[END_REF] was used to select salient and non-salient patches for local feature extraction. The authors used reference stereo images to build local quality maps, which were then used as labels to train deep CNN as a local quality-aware structures predictor. The latter are then combined into a final quality score. Image segmentation techniques have also been used in NR-SIQA methods. In [START_REF] Liu | No-reference stereoscopic image quality evaluator with segmented monocular features and perceptual binocular features[END_REF] a superpixel segmentation based on the K-mean clustering technique is used. Then, using a regression model, spatial entropy and Natural Scene Statistics (NSS) features are retrieved from these superpixel regions to generate quality scores. CNNs can be applied to a variety of topics, for instance, authors in [START_REF] Yang | A blind stereoscopic image quality evaluator with segmented stacked autoencoders considering the whole visual perception route[END_REF] have modeled the human visual cortex using the deep CNN auto-encoder. The CNN-based autoencoder is also used in [START_REF] Yang | Predicting stereoscopic image quality via stacked autoencoders based on stereopsis formation[END_REF] to achieve high-level features, where the authors first compute a gray level cyclopean image, difference and summation image from the input stereoscopic view. Then, series of feature extraction have been conducted from these images. Recently in [START_REF] Wang | No-reference stereoscopic image quality assessment using quaternion wavelet transform and heterogeneous ensemble learning[END_REF], monocular and binocular quality features, including texture and energy features, are first retrieved, and then ensemble learning is utilized to map the quality score. Meanwhile, in [START_REF] Bourbia | A multi-task convolutional neural network for blind stereoscopic image quality assessment using naturalness analysis[END_REF] a multi-task CNN model is proposed to extract NSS features as an auxiliary task, and to produce quality score as primary task. Besides auto-encoders, multi-task models are increasingly being deployed in SIQA domain, but none of them explore the concept of multi-score predictions (e.g., right, left and stereo score). Because binocular quality attributes differ from left to right, especially in the situation of asymmetric distortion, that yield binocular rivalry. An independent quality-aware indicator must then be learned from the stereoscopic view. Moreover, many of NR-SIQA approaches require a fixed resolution for the input image. Therefore, in this paper, we propose an NR-SIQA measure that addresses these drawbacks.

The remainder of this paper is organized as follows. In Section 2, we describe the proposed method. Then, we present the experimental results in the Section 3. Finally, we give some concluding remarks in Section 4.

PROPOSED MULTI-SCORE METHOD

Fig. 1 presents the flowchart of the proposed model which combines three sub-networks: for the stereoscopic image input, each view corresponds to sub-network. These two sub-networks are distinct in order to accommodate for independent binocular information and aim to mimic binocular vision. Then, to simulate the pathway of optic nerve in HVS, the left and right views are concatenated as input for the third sub-network. It is worth noting that the proposed metric scheme takes the input RGB (Red, Green, Blue) stereo image without any pre-processing and provides four output scores (e.i., left, right, stereo and global score), whereas most SIQA metrics convert the input images to a typical gray tone as a pre-treatment step for the CNN model and give a single score. As demonstrated in our recent work [START_REF] Messai | 3d saliency guided deep quality predictor for noreference stereoscopic images[END_REF], using three channels as input rather than a single gray scale tends to increase the performance by preserving the perceived original distortion effects and judged by the human during the evaluation process.

Extraction of Independent Features

Independent binocular features are retrieved through the proposed multi-score prediction model. The left sub-network seeks to extract features from the left view, while the right one seeks to extract features from the right view using left and right objective score, respectively. However, using just left and right sub-networks, we may extract features individually from the left and right images, and then weight-average the score to determine final quality. However, as previously stated, binocular rivalry occurs when the two views of a stereo pair exhibit different types or degrees of distortion. As a result, the average quality of the left and right views cannot predict the objective quality of the most often viewed stereo image. To illustrate this point, we take 55 distorted stereoscopic images. We then compute the average of M OS lef t and M OS right , and compare it to the corresponding M OS stereo . The comparison is carried out by simply computing the absolute value of difference D as follows:

D = | (M OS lef t + M OS right ) 2 -M OS stereo | (1)
The result is illustrated in Fig. 2. As can be seen, there is always a mismatch between the stereo quality score and the average left and right score, particularly with asymmetric distortion, where we note up to a 25-point difference in term of MOS. This basic analysis prompted us further more to propose the multi-score prediction system described in the following subsection. The model uses 32 × 32 patches from each view without normalization, clipped consecutively without overlapping from distorted stereoscopic images with a stride of 32 pixels, where each patch has the same score as its associated source. The predicted quality score Q of the whole input stereo image is finally reported by computing the mean of patches scores.

Model training

In order to minimize the error during the training of the designed end-to-end CNN model, we use the Loss function which is a linear combination of four L 1 loss functions as described in the following:

Loss = 2 × |Q g -M s | + |Q s -M s |+ |Q l -M l | + |Q r -M r | (2)
where Q g , Q s , Q l , and Q r are the predicted quality score of the global, stereo, left and right image, respectively. The M s , M l and M r refer to the MOS of the stereo, left, and right image, respectively.

To update the weights of the whole network, we used the Stochastic Gradient Descent (SGD) with a momentum factor equals to 0.9, a weight decay factor sets to 0.0001, a mini batch size equals to 128 and a learning rate initialized to 10-3. The Pytorch framework was used to implement our approach.

EXPERIMENTAL RESULTS

Dataset and training protocol

A database of images with quality scores for each image is required for training and evaluating SIQA measures. The quality score is often obtained by subjective scoring and shown as MOS/DMOS According to ITU-T P.910 [START_REF] Recommendation | Subjective video quality assessment methods for multimedia applications[END_REF] recommendations. For the SIQA domain, a variety of databases are publicly available for the implementation and evaluation of the proposed metrics [START_REF] Moorthy | Subjective evaluation of stereoscopic image quality[END_REF][START_REF] Chen | Fullreference quality assessment of stereopairs accounting for rivalry[END_REF][START_REF] Wang | Quality prediction of asymmetrically distorted stereoscopic images from single views[END_REF][START_REF] Wang | Quality prediction of asymmetrically distorted stereoscopic 3d images[END_REF]. However, only Waterloo IVC 3D Phase 1 and Waterloo IVC 3D Phase 2 provide MOS scores for each view, in addition to stereo MOS scores. Moreover, the asymmetric degradations in the Waterloo P-1 and P-2 databases are different from those in the LIVE-II database [START_REF] Chen | Fullreference quality assessment of stereopairs accounting for rivalry[END_REF]. LIVE-II uses only one type of distortion to perform the asymmetry, while the two Waterloo databases consider the possibility of multiple types of degradation in which the left and the right images are affected by different distortions. Therefore, in our validation experiments, Waterloo-P1 and P2 have been used, described as: Waterloo IVC 3D Phase 1 (P1) [START_REF] Wang | Quality prediction of asymmetrically distorted stereoscopic images from single views[END_REF] includes 330 full HD (1920 x 1080 pixel) distorted stereo images generated from six pristine stereo pictures through three types of distortion: additive white Gaussian noise, Gaussian blur and JPEG compression. Subjective evaluation scores are expressed in terms of MOS and are distributed in the range [START_REF] Abouelaziz | 3D visual saliency and convolutional neural network for blind mesh quality assessment[END_REF]100], where 100 indicates the best quality score. Waterloo IVC 3D Phase 2 (P2) [START_REF] Wang | Quality prediction of asymmetrically distorted stereoscopic 3d images[END_REF] includes 460 full HD stereo images made up of 10 pristine stereo image pairs by considering the same distortion types. Both datasets comprise symmetric and asymmetric distortions. Subjective assessment scores are in terms of MOS, with the same range as Waterloo-P1 ( [START_REF] Abouelaziz | 3D visual saliency and convolutional neural network for blind mesh quality assessment[END_REF]100]).

The performance of our method was quantified using the two databases. To guarantee that our model evaluates the image quality rather than focusing on the content, we divide each database into 80% for training and rest 20% for test based on reference images. So the training images scene are independent from those used in test phase. We repeat the same process 10 times and report the average performance. During the training, we do not consider data augmentation because the noted subjective score may differ if data augmentation techniques are used (e.g., rotation, flipping, etc.) [START_REF] Messai | 3d saliency guided deep quality predictor for noreference stereoscopic images[END_REF].

Comparison with the State-of-the-Art

The performance has been measured across three metrics: The RMSE, Pearson linear correlation coefficient (PLCC), Spearman's rank order correlation coefficient (SROCC) between the machine quality judgments (objective scores) and the human ratings (subjective scores). High values for PLCC and SROCC (close to 1) and low values for RMSE (close to 0) indicate a better prediction performance.

Overall, the statistical association between human quality scores and our method ratings exhibited outstanding performance and consistency. The obtained results were compared to many FR and NR-SIQA. Among them, there are recent reference-less metrics based on the use of CNN models, namely Chen [START_REF] Chen | Blind stereo image quality assessment based on binocular visual characteristics and depth perception[END_REF] and Sun [START_REF] Sun | Learning local quality-aware structures of salient regions for stereoscopic images via deep neural networks[END_REF]. Table 1 shows the results of these methods on both Waterloo-P1 and P2 datasets. Best metric of each category (FR and NR) is represented on bold and the best one whatever the category is with a gray background. As can be seen, our metric outperforms all the state-of-the-art NR and FR metrics on both databases. Furthermore, we report the performance of our method according to the size of the training set. Table 2 shows the correlations achieved for a training set of size 50%, 70% and 80%. The partition ratio has a slight impact on the performance. And it does not suffer from an over-fitting problem. The diminution is similar for both datasets. Metrics Waterloo-P1/Waterloo-P2 Waterloo-P2/Waterloo-P1 Liu [START_REF] Liu | No-reference stereoscopic image quality evaluator with segmented monocular features and perceptual binocular features[END_REF] 0.696 0.701 Yang [START_REF] Yang | Predicting stereoscopic image quality via stacked autoencoders based on stereopsis formation[END_REF] 0.781 0.864 Chen [START_REF] Chen | Blind stereo image quality assessment based on binocular visual characteristics and depth perception[END_REF] 0.806 0.846 Saliency-SIQA [START_REF] Messai | 3d saliency guided deep quality predictor for noreference stereoscopic images[END_REF] 0.826 0.848 DECOSINE [START_REF] Yang | A blind stereoscopic image quality evaluator with segmented stacked autoencoders considering the whole visual perception route[END_REF] 0.842 0.873 Wang [START_REF] Wang | No-reference stereoscopic image quality assessment using quaternion wavelet transform and heterogeneous ensemble learning[END_REF] 0.856 0.881 Proposed 0.944 0.940 0.9. Compared to the second best metric (i.e., Wang), the improvement accuracy of quality assessment was found to be 10% in terms of PLCC.

Ablation study and run-time

In the ablation test case, we simply erase the loss of left and right views. As a result, the model is entirely trained on stereo MOS loss. Table 4 shows the performance without using left and right human ratings versus using them. Furthermore, we investigated the advantage of utilizing the global score as the final quality score rather than the stereo score. The results show that our concept improves performance and support the idea of a multi-score model. We measured less than 2 seconds of run-time (1.485 s) using a single Full-HD stereoscopic image (1920 x 1080 pixels), including patch cropping and loading using a Dell Precision 7550 laptop equipped with an Intel i9-10885H CPU @ 2.40GHz processor and an NVIDIA Quadro RTX 3000 GPU. In terms of run-time speed, the proposed metric has the potential to be used on stereoscopic videos.

CONCLUSION

In this paper, we introduced a new NR-SIQA approach based on a multi-score convolutional neural network model for evaluating the quality of left, right and global stereoscopic images. We used the corresponding MOS for each view to learn the best quality indicators task to improve the quality prediction. Based on a comparative examination using two public databases, Waterloo-P1 and Waterloo-P2, our model outperforms state-of-the-art approaches, especially in crossvalidation tests. The ablation study demonstrates that using a multi-score task is a promising path for improving the accuracy of quality score prediction. In addition, we employ RGB color channels rather than gray ones to maintain the same spatial domain being viewed by the observer. As future work, we will undertake a detailed examination and consider extending the model to handle auxiliary tasks such as distortion type recognition and degree of deformations.

Fig. 1 .

 1 Fig. 1. The proposed multi-score CNN based model. The network outputs are: left, right, stereo, and global quality scores.

Fig. 2 .

 2 Fig. 2. Difference values of M OS stereo with M OS mean mean of 55 distorted views produced from a pristine stereoscopic image called Art from Waterloo IVC Phase 1[START_REF] Wang | Quality prediction of asymmetrically distorted stereoscopic images from single views[END_REF]

Table 1 .

 1 Overall performance comparison on Waterloo-P1 and Waterloo-P2.

				Waterloo-P1			Waterloo-P2
	Type	Metrics	SROCC	PLCC	RMSE SROCC	PLCC	RMSE
		Benoit [4]	0.332	0.332	-	0.165	0.320	-
	FR	Chen [5]	0.457	0.631	-	0.272	0.442	-
		Ma [6]	0.911	0.925	5.876	-	-	-
		DECOSINE [13]	0.924	0.943	-	0.914	0.933	-
		Yang [14]	0.911	0.940	-	0.866	0.899	-
		Chen [22]	0.923	0.931	5.989	0.922	0.925	7.119
	NR	Sun [9]	-	-	-	0.835	0.840	-
		Liu [12]	0.928	0.945	5.268	0.901	0.913	7.658
		Wang [15]	0.950	0.959	4.089	0.953	0.965	4.498
		Proposed	0.967	0.972	3.635	0.966	0.971	4.161

Table 2 .

 2 Performance of the proposed metric under different train-test partitions on Waterloo-P1 and Waterloo-P2.

			Waterloo-P1			Waterloo-P2
	Partition	SROCC	PLCC	RMSE SROCC	PLCC	RMSE
	80%-20%	0.967	0.972	3.635	0.966	0.971	4.161
	70%-30%	0.961	0.968	3.876	0.952	0.962	4.964
	50%-50%	0.947	0.964	4.276	0.944	0.958	6.226
	3.3. Cross database performance
	Cross-database experiments have been conducted in order to
	verify the generalization ability of the proposed approach.
	The implemented tests are shown in

Table 3 .

 3 Metrics shown are all NR methods. They have been trained in the former database and tested on the latter. Comparing with the NR metrics, our method has outstanding quality prediction performance in terms of PLCC. Saliency-SIQA, DECOSINE and Wang algorithms deliver decent performance, but the proposed one is the only metric which gives performance over

Table 3 .

 3 PLCC Performance of cross-database tests using the two databases (Expressed as: Train database/Test database).

Table 4 .

 4 Performance obtained of ablation tests on Waterloo-P1 and Waterloo-P2.

			Waterloo-P1			Waterloo-P2
	Model	SROCC	PLCC	RMSE SROCC	PLCC	RMSE
	Without global score	0.924	0.946	5.480	0.936	0.942	5.703
	Without left, Right MOS	0.949	0.962	4.965	0.955	0.966	4.562
	Proposed: With left, Right MOS	0.967	0.972	3.635	0.966	0.971	4.161