Sergui Mansour

Valmir B Silva

Elisa S Orth

Julien Legros
email: julien.legros@univ-rouen.fr

Soft detoxification of chemical warfare agent simulants and pesticides under pressure

The neutralisation of structurally varied chemical warfare agent simulants (blister and nerve agents) and pesticides (Paraoxon) with the assistance of high pressure is reported. Chloroethyl amine and sulfide (nitrogen and sulfur mustards), phosphonothioate (V-series nerve agents) and phosphate (pesticide) readily react with simple nucleophilic scavengers (alcohols, amines) at P>14000 bar.

Introduction

In the last decades, an increased global attention has been conducted towards the chemical security and the prohibition of chemical warfare agents (CWAs). [1][2][3][START_REF] Hafemeister | Nuclear Proliferation and Terrorism in the Post-9/11 World[END_REF] Among them, the most common ones are blister agents (sulfur-and nitrogen mustards, HD and HN3) and organophosphorus nerve agents (OPNA), such as the persistent VX. Moreover, some organophosphorus compounds (OPs) are still among the most used agrochemicals in the world, such as Paraoxon (Scheme 1). [START_REF] Silva | [END_REF] The harmful impact caused by such substances on human health and the environment necessitates the development of efficient degradation processes into safe products. [START_REF] Silva | [END_REF] Therefore, there is a growing request to develop new flexible methods for a sustainable neutralisation of chemical warfare agents and pesticides under mild conditions and to ensure effective minimization of toxic products generation. [START_REF] Silva | [END_REF][6][7][8] Since the toxicity of these substances is directly connected to their high electrophilicity, the use of water as nucleophilic scavenger of such compounds (ie hydrolysis) could look as an ideal detoxification path. Unfortunately, this is a deceptively simple method for several reasons. 6,9,10 Scheme 1. Chemical warfare agents (red), pesticides (red), their respective harmless simulants (green), and the corresponding detoxification paths through nucleophilic substitution. (a) blister agents: sulfur mustard HD, nitrogen mustard HN3 and relevant Indeed, yperite HD, which is insoluble in water, reacts very slowly and undergoes partial oligomerization/hydrolysis, rearranging into micelles that still contain important quantities of unaltered yperite in their core; 11,12 this direct route is therefore little used for mustard agents. Expectedly, this path is also poorly effective for lipophilic OP V-series CWA and phosphate pesticides, which have been precisely designed to resist hydrolysis. For example, Paraoxon exhibits a half-life >20 years in aqueous medium. [START_REF] Silva | [END_REF] Moreover, this reaction must proceed with high selectivity to avoid the formation of still toxic products (Scheme 1). If the insolubility of these harmful molecules can be circumvented by using alcohols as nucleophiles, CWAs are still reluctant to the direct solvolysis and either metal-catalysts or -alcoholates are required for efficient abatement. [START_REF] Silva | [END_REF]6,8,[13][14][15] Beside the choice of the chemical path, the technology used to perform this detoxification can play a prominent role. Recently, continuous flow reactors have attracted attention as an alternative to classical batch chemistry to ensure rapid and selective neutralization of such harmful chemicals with oxidizing agents. [16][17][18][19] Moreover, successful neutralisation by direct introduction of an aqueous solution of sodium hydroxide in the flow system has also been reported, 20 whereas a 3Dprinted chemical generator of lithium ethanolate has been later reported as a reliable method. 21 Importantly, all these methods are not general and each focuses on a specific class of compounds: yperite, 16,17,19 V-series OPNA, 21 sulfur-containing CWA, 18 or Paraoxon. 20 Regarding alternative technological tools for chemistry, hyperbaric reactors (ie affording a pressure of several thousand bars) exhibit several features of high interest in the frame of the decomposition of these toxic chemicals. Indeed, high pressure is particularly well suited to cases where fragile and/or nonreactive reagents/products are needed. [22][23][24] High pressures are even used for sterilization in food industry. 25 Pressure, like temperature, is a parameter that influences the equilibrium of a chemical reaction and it can be considered as a 'physical catalysis' with numerous advantages for the neutralization of toxic chemicals: 1) inert molecules (eg for steric reasons), usually become reactive: CWA are highly persistent (ie stable) and could thus become more sensitive towards nucleophiles; 2) the involvement of heat-sensitive reagents/products is not a concern: this is of particular interest for CWA since they are often weaponized under gaseous form; 3) the selectivity can be modified since the pressure may allow to obtain compounds thermodynamically less favoured at Patm: in the degradation of CWA, selectivity is essential, since competitive reaction may afford toxic compounds. It is also worth to note that hyperbaric reactors consume energy only during the initial compression step, in contrast to thermal activation with continuous heating. Along these lines, we now report that high pressures promote the detoxification of several categories of OPs compounds (phosphonothioate, phosphate) and blister agents (nitrogenand sulfur mustards) in the presence of simple nucleophiles.

Results and discussion

Our investigations began with the most relevant analogue of Vseries OP: the compound PhX, which keeps all the functionalities of the original phosphonothioate but with reduced toxicity due to the steric hindrance of the phenyl group instead of a methyl (Scheme 2 and Table 1 On a formal standpoint, ethanolysis of VX (and its surrogate PhX) allows a specific substitution at the P-S bond that avoids the formation of toxic by-products (Schemes 1 and 2). Unfortunately, as already observed in previous reports, PhX is fully stable in alcoholic solutions under ambient conditions, 21 and no conversion of PhX into diethyl phenylphosphonate 1 was therefore observed at P = 1 bar (entry 1). Even by heating at 50 °C, only 10% of PhX were transformed after 24 h. Since CWAs are often weaponized by spraying (some of them even have high vapour pressure values), the treatment of these toxic chemicals assisted by thermal activation, with the risk of vapour formation, is highly undesirable. Thus, for the reasons cited above, the decomposition of PhX at ambient temperature (20 °C) was assessed in anhydrous ethanol under 14 000 bars (1.4 GPa) in a hyperbaric reactor (entries 2 and 3): at this pressure 25% conversion were obtained after 4 h that increased to 50% of conversion within 24 h. Delightfully, increasing the pressure to 16 kbar allowed full conversion of PhX into the desired product 1b entry 4). These results clearly demonstrate the benefits of the physical activation by high pressure to perform solvolytic detoxification by nucleophilic substitution with simple ethanol.

Then our studies moved to a more resistant family of OPs: phosphates. Among them, the Paraoxon analogue DEDNPP (diethyl-2,4-dinitrophenylphosphate) is known to exhibit the highest reactivity toward hydrolysis (entries 5-7). In the presence of commercial aqueous ethanol 96%, three products are expected: the detoxified compounds 2 and 3, corresponding to the substitution of the dinitroaryl group by ethanol and water, respectively. The substitution of one ethoxy group by a hydroxyl group, with the remaining dinitroaryl group would maintain the toxicity (product 4a). Also, solvolysis with ethanol at ambient conditions proved to be ineffective (entry 5), whereas under 14 kbar a full degradation of DEDNPP into more innocuous ethanolyzed product 2 (43%) and, above all, hydrolyzed compound 3 (57%) occurred in 24 h. Provided that only 4% v/v of water in ethanol was enough to significantly detoxify DEDNPP into diethyl phosphate 3, the reaction medium was switched to MeCN/H2O (99:1, v/v). In this new solvent system, we were very pleased to observe a fully selective transformation into 3 at 14 kbar (entry 7). It is worth to note that toxic product 4a was never observed, and that DEDNPP is known to have a half-life of 56 days in water under ambient conditions. 27 Unfortunately, these conditions were not successful with the live pesticide Paraoxon (0% conversion, entry 8). Increasing the pressure to 16 kbar also appeared disappointing since only 21% of the desired product 3 was afforded along with 14% of the toxic aryl alkyl phosphate 4b (entry 9).

Previous studies proposed imidazole as a nucleophilic catalyst that allows total Paraoxon detoxification in 77 h, in aqueous medium at room temperature. 28 Thus, with 6 equiv. of imidazole MeCN/H2O under 14 kbar, results showed a 95 % conversion after only 24 h into the desired diethyl phosphate 3 accompanied with 5 % of the toxic compound 4b (Table 2, entry 2). However, we succeeded to improve selectivity of the neutralisation process by increasing the pressure at 16 Kbar and we obtained a 100 % conversion into the innocuous 3 in only 24 h (entry 3). Despite apparent very similar structures, Paraoxon and methyl Paraoxon (diethyl vs dimethyl, respectively) exhibit distinct behaviours. Methyl Paraoxon has a greater tendency to transfer the alkyl group to a nucleophile when compared to (ethyl) Paraoxon. This behaviour was observed in reactions with imidazole, where imidazole selectively attacks the phosphorus atom of (ethyl) Paraoxon and mainly attacks the CH3 group of methyl Paraoxon. 28,29 Thus, for methyl Paraoxon, the same afforded as major product the undesired dealkylated product 4c (44 %), with a mixture of desired diethyl phosphate 3 (30%) along with the over-hydrolyzed and harmless ethyl phosphate 5 (26%). Even after increasing the reaction time at 72 h, the results reminded similar which demonstrate that the reaction had attend its equilibrium at this given pressure. Delightfully, when the pressure was raised at 16 kbar we succeeded to eliminate the toxic product and obtained a mixture of non-toxic products 3 and 5 at 70 % and 30 % respectively. Mustards agents constitute a structurally different family of compounds. The toxicity of these chloroethyl sulfides and amines (respectively sulfur and nitrogen mustards) also stems from their electrophilicity, albeit with the anchimeric assistance of the S and N atom (Scheme 1). 30 These hydrophobic blister agents and their corresponding surrogates (CEES and CTEA, Scheme 1) are poorly reactive in polar solvents as water and methanol. For example, CEES in methanol-d4 undergoes a nucleophilic substitution of the chlorine atom to form 2-methoxyethyl ethyl sulfide with a 50% conversion in 48 h at ambient conditions (still uncomplete after 5 days), 31 whereas a complex mixture of hydrolyzed product and oligomers are afforded in water. 11 Based on our success with OP neutralization under high pressure, the direct solvolysis of CEES and CTEA with the environmentally desirable ethanol solvent was attempted under 14 to 16 kbar. Whereas CEES is fully stable in anhydrous ethanol and exhibit no significant reaction for 24 hours, applying a high pressure only afforded less than 30% conversion into to 2-ethoxyethyl ethyl sulfide 6a within 24 h, and poor conversion was also obtained with the nitrogenmustard surrogate CTEA into 7a (Scheme 4).

A common strategy to enhance the nucleophilicity of an alcohol is to use its conjugate base. Whereas this method was reported to be successful with OP compounds, 21 century-old reports claim that HD undergoes competitive dehydrochlorination in the presence of an alcoholate, but few details are provided. [32][33][34] In our hands, CEES reacted very slowly with EtOLi (3 equiv.) in EtOH at ambient conditions (20 °C, 1 bar) to afford nucleophilic substitution product 6a (21%) along with <1.5% of ethyl vinyl sulfide (EVS) after 24 h. In contrast, the ethanolysis of CEES under 14 kbar showed full neutralization of the CWA simulant into the desired harmless product 6a within only 24 h (Scheme 4). Pleasingly, the nitrogen-mustard surrogate CTEA behaved exactly the same way to yield 7a (Scheme 4). Scheme 4. Detoxification of blister agents by pressure-assisted nucleophilic substitution However, in the frame of environmentally friendly process, metal salts could be seen as an issue and neutral nucleophiles could be preferred. In this frame, the aminolysis of mustard agents is an interesting alternative that has been poorly studied.

Here also, old reports describe the qualitative formation of the aminoethyl sulfide from HD and amines, 32,35,36 and more recent works by Bowman-James showed that reacting CEES with Me2NH (1.25 equiv.) in CDCl3 by 1 H NMR afforded <10% conversion after 7 days. Whereas these conditions were obviously not optimised to reach the highest conversion (<2 equiv. of amine, apolar solvent), it clearly suggest that the nucleophilic substitution is rather slow under ambient conditions, and hyperbaric conditions could be worthy. 31 Thus, with 3 equiv. of the nucleophilic pyrrolidine in ethanol at 14 kbar, the expected nucleophilic substitution occurred with CEES, as well as with CTEA (100% conversion in each case), the target 6b and 7b as single products.

Conclusions

We have described a straightforward method for the detoxification of structurally varied chemical warfare agent simulants and pesticides in a hyperbaric reactor. Conversely to most neutralization methods that employ corrosive (and possibly explosive) oxidants, this one only involves accessible nucleophilic reagents with no undesirable side effects, nor byproducts with unknown toxicity. Thanks to the high pressure applied (14-16 kbar) chloroethyl amines and -sulfides (nitrogen and sulfur mustards), phosphonothioate (V-series nerve agents) and phosphate (pesticide) readily react with ethanol, water and amine at P>14000 bar to afford the target harmless compounds with full selectivity. This reaction proceeds smoothly without the need of thermal activation (poorly compatible with chemical weapons because of hazardous vapour emission) and involves inexpensive chemicals (amines in excess being possibly recoverable by acid-base extraction).

Whereas hyperbaric reactors are not yet widely developed in laboratories, these preliminary results highlight the role of pressure as a green and sustainable tool for the treatment of toxic compounds.

  simulants (CEES and CTEA respectively); (b) OP nerve agent VX and its simulant PhX; (c) OP pesticides Paraoxon and methyl Paraoxon.

aScheme 3 .

 3 Scheme 3. Decomposition of Paraoxon and methyl Paraoxon in the presence of imidazole.

Table 1 .

 1 ). 26 Scheme 2. Reactivity of OP compounds with ethanol and/or water under high pressure: PhX, DEDNPP and Paraoxon Detoxification of organophosphorus compounds: PhX, DEDNPP and Paraoxon a

	Entry Substrate Solvent	P	Time	Conv. (%)
				(kbar)	(h)	(1 or 2/3/4) b
	1	PhX	EtOH c	1•10 -3	24	1 0 d
	2		EtOH	14	4	1 25
	3		EtOH	14	24	1 53
	4		EtOH	16	24	1 100
	5	DEDNPP	EtOH e	1•10 -3	24	0
	6		EtOH	14	24	100
						(43:57:0)
	7		MeCN/H2O f 14	24	100
						(0:100:0)
	8	Paraoxon	MeCN/H2O	14	24	0
	9		MeCN/H2O	16	24	35
						(0:21:14)

a According to Scheme 2. b 2/3/4 stands for the detoxification of DEDNPP and Paraoxon. c Anhydrous ethanol. d At 50 °C, 10% conversion into 1 were observed after 24 h. e Commercial ethanol 96%. f MeCN/H2O, 99:1, v/v.

Table 2 .

 2 Paraoxon detoxification under high-pressure with imidazole. a

	Entry	Substrate	Pressure (kbar)	Conversion (%)
				3/4/5
	1	Paraoxon	1•10 -3	0
	2		14	100
				(95:5:0)
	3		16	100
				(100:0:0)
	4	Methyl Paraoxon	1•10 -3	50
				(0:100:0)
	5		14	100
				(30:44:26)
	6		16	100
				(70:0:30)

Acknowledgements

The authors from Normandie Université gratefully acknowledge the European France-(Manche)-England cross-border cooperation program INTERREG V A "SMARTT", co-financed by ERDF, for financial support. This work has also been partially supported by University of Rouen Normandy, INSA Rouen Normandy, the Centre National de la Recherche Scientifique (CNRS), Labex SynOrg (ANR-11-LABX-0029), Carnot Institute I2C, the graduate school for research XL-Chem (ANR-18-EURE-0020 XL CHEM), and by Région Normandie. The authors from the Federal University of Parana are grateful to CNPq, CAPES, L'Oréal-UNESCO-ABC, PhosAgro/UNESCO/IUPAC, CAPES/PRINT/ UFPR/ Materiais Avançados, National Institute of Science and Technology of Carbon Nanomaterials (INCT Nanocarbon) and the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brasil, finance code 001.

Conflicts of interest

There are no conflicts to declare.


Christian Laurence
email: christian.laurence@univ-nantes.fr

Sergui Mansour

Daniela Vuluga

Khadija Sraïdi

Julien Legros
email: julien.legros@univ-rouen.fr

Theoretical, semi-empirical, and experimental solvatochromic comparison methods for the construction of the α 1 scale of hydrogen-bond donation of solvents

Keywords: Acidity, Empirical solvent parameters, Hydrogen bond, Solvatochromism, Solvent Effects

The misused Kamlet-Taft solvatochromic comparison method (SCM) must be replaced by theoretical (PCM-TD-DFT calculations) or semi-empirical (Mc Rae equation) or experimental (comparison of two betaine dyes) SCMs.

Abstract: Today, the hydrogen bonding donation (HBD) ability parameter of new solvents, α, is generally determined either by the Kamlet-Taft solvatochromic comparison of two probes, Reichardt betaine dye B(30) and 4-nitroanisole, or by the measurement of a single probe (e.g. solvatochromism of an iron coordination complex). This work highlights the shortcomings of these probes, and recommends three replacement methods: (a) the theoretical comparison of the experimental and PCM-TD-DFT calculated transition energies E T (30) of B (30), (b) the semi-empirical comparison of the experimental and McRae calculated E T (30), and (c) for ionic liquids, the experimental comparison of E T (30) and E T (33) lying on the lower basicity of the betaine dye B(33) compared to B (30). These methods yield a new HBD parameter, α 1 , for 101 molecular solvents and 30 ionic liquids. The novelty is emblematic for water, with α 1 = 1.54 instead of α (Kamlet-Taft) = 1.17. The solvent parameter α 1 is not equivalent to the solute hydrogen-bond acidity parameter , partly because of the self-association of HBD solvents.

Introduction

One of the most important chemical properties of solvents, their effectiveness as hydrogen-bond donors (HBDs), is also one of the most difficult to determine. This difficulty arises from the many solute-solvent intermolecular forces at the origin of solvent effects. [START_REF] Rigby | The Forces between Molecules[END_REF] For example, even a simple HBD like 1-octanol can interact with solutes not only in donating hydrogen bonds but also in interacting by three kinds of non-specific (van der Waals) forces: dispersion and induction because of its molecular polarizability and electrostatic forces because of its permanent dipole moment.

To isolate the specific hydrogen bond from non-specific solvent effects, Kamlet and Taft devised forty-six years ago a so-called "solvatochromic comparison method" (SCM) [START_REF] Kamlet | The Solvatochromic Comparison Method. I. The β-Scale of Solvent Hydrogen-Bond Acceptor (HBA) Basicities[END_REF][START_REF] Taft | Solvatochromic Comparison Method .2. α-Scale of Solvent Hydrogen-Bond Donor (HBD) Acidities[END_REF] that yielded the Kamlet-Taft scales of hydrogen-bond acceptance (β) [START_REF] Kamlet | The Solvatochromic Comparison Method. I. The β-Scale of Solvent Hydrogen-Bond Acceptor (HBA) Basicities[END_REF] and donation (α) [START_REF] Taft | Solvatochromic Comparison Method .2. α-Scale of Solvent Hydrogen-Bond Donor (HBD) Acidities[END_REF] ability of solvents. Shortly, the method consists in the comparison of the solvatochromism of two probes having similar non-specific effects, one capable, one incapable or less capable of hydrogen bonding. This comparison generates a pure hydrogen bonding scale if three important conditions are satisfied: (a) a good linear correlation must be observed between the solvatochromic shifts in a series of solvents of varying non-specific effects; (b) points in this correlation representing solvents in which hydrogen bonding occurs should show significant deviations from the comparison line (all in the same direction); and (c) the direction of deviations should be consistent with the solvatochromism involved and their magnitudes should reflect a reasonable order of solvent HBD strengths (for the α scale) or solvent hydrogen-bond acceptor (HBA) strength (for the β scale).

The method cannot suffer much criticism since it is based on the similarity principle, a fundamental principle in science successfully used in many fields of chemistry. [START_REF]Similarity Models in Organic Chemistry, Biochemistry, and Related Fields[END_REF] But this important and original method has been misused by generations of chemists since 1975. Today, most chemists determine new α values from the solvatochromic comparison of the Reichardt pyridinium N-phenolate betaine dye B(30) [START_REF] Machado | Pyridinium N-Phenolate Betaine Dyes[END_REF] (the probe capable to accept hydrogen bonds) and of 4-nitroanisole (the probe less capable to receive hydrogen bonds)(Scheme 1). In this work we show that the solvatochromic comparison of B(30) and 4-nitroanisole does not satisfy the above conditions (a)-(c) and yields unreliable α values not only for important molecular liquids such as glycol ethers, [START_REF] Lagalante | Kamlet-Taft Solvatochromic Parameters for 25 Glycol Ether Solvents and Glycol Ether Aqueous Solutions[END_REF] hydrofluoroethers, [START_REF] Lagalante | Taft Thermosolvatochromic Parameters of Hydrofluoroethers and Hydrofluoroether Azeotropic Mixtures[END_REF] and alkanolamines [START_REF] Lagalante | Taft Solvatochromic Parameters of Eight Alkanolamines[END_REF] but also for ILs. In order to avoid the difficulty to find two solvatochromic probes with similar non-specific effects but dissimilar HBA effects, we have proposed in 2014 to determine an α 1 scale by means of the solvatochromism of B (30) and PCM-TD-DFT (polarizable continuum model-time dependent-density functional theory) calculations (hence the name "theoretical SCM" used in this paper). [START_REF] Cerón-Carrasco | Determination of a Solvent Hydrogen-Bond Acidity Scale by Means of the Solvatochromism of Pyridinium-N-Phenolate Betaine Dye 30 and PCM-TD-DFT Calculations[END_REF] The validity of these α 1 values will be confirmed in this work. However, PCM-TD-DFT calculations on such a large molecule as B (30) are not easily performed by noncomputational chemists. So, we propose here to analyze the solvatochromism of B (30) by means of a simplified McRae equation [START_REF] Mcrae | Theory of Solvent Effects on Molecular Electronic Spectra. Frequency Shifts[END_REF] of which the theoretical coefficients are adjusted to the experimental solvatochromic shifts (hence the name "semi-empirical SCM"). The α 1 values determined by the semiempirical SCM agree so well with the theoretical ones that we have used the semi-empirical method as a secondary one to extend the α 1 database to many molecular liquids. Nevertheless, the PCM used in the theoretical and semi-empirical SCMs does not apply to ILs. We have therefore imagined to compare the solvatochromism of B (30) with that of the betaine dye B(33) [START_REF] Machado | Pyridinium N-Phenolate Betaine Dyes[END_REF] (Scheme 1), having two chloro instead of two phenyl substituents in ortho of the phenolate oxygen. Because of the structural similarity of their chromophores the two betaines should interact with solvents similarly through nonspecific effects but B( 33) is much less capable to receive hydrogen bonds on its phenolate oxygen than B(30) by virtue of the electron-withdrawing effects of the chloro substituents. This method is called "experimental SCM" since two experimental solvatochromic shifts are now compared, those of B (30) and B (33). The agreement of the experimental SCM results with those of the theoretical SCM for molecular solvents leads to the application of the experimental SCM to ILs. The objective of this work is to put an end to the misuse of the solvatochromic comparison method and to provide chemists with reliable methods to determine the α parameter of molecular solvents and ionic liquids using commercially available probes and spectroscopic techniques available in any chemistry laboratory. 131 α 1 values of HBD solvents are thus obtained and their validity is tested on physicochemical properties mainly α-dependent. The validity of this comprehensive new α 1 scale makes it possible to statistically analyze many α-type scales proposed in the literature. This analysis aims to determine the purity of these scales, i. e. the presence or absence of non-specific contaminating effects. There are also scales in the literature measuring the HB acidity of molecules as solutes (e.g. the scale [START_REF] Abraham | Hydrogen Bonding. Part 7. A Scale of Solute Hydrogen-Bond Acidity Based on Log K Values for Complexation in Tetrachloromethane[END_REF] ); they will be compared with the solvent scale α 1 to study the possible equivalence of solute and solvent scales of hydrogen-bond donation.

Results and Discussion

The hundred of a 1 values determined by the theoretical SCM [START_REF] Cerón-Carrasco | Determination of a Solvent Hydrogen-Bond Acidity Scale by Means of the Solvatochromism of Pyridinium-N-Phenolate Betaine Dye 30 and PCM-TD-DFT Calculations[END_REF] and the semi-empirical SCM (this work) are collected in Table 1(in bold for the semi-empirical values and in normal characters for the theoretical ones).

Preliminary considerations

As most chemists, we have chosen as the source of our α 1 parameter the solvatochromism of B (30) measured by the parameter E T (30) defined [START_REF] Machado | Pyridinium N-Phenolate Betaine Dyes[END_REF] as the molar electronic transition energy (historically in kcal mol -1 ; 1 cal = 4.184 J) of the dye:

(1) E T (30) = hcN A = 28591/λ where h, c, and N A are Planck's constant, speed of light, and Avogadro's constant, respectively, is the wavenumber (cm -1 ), and λ the wavelength (nm) of the solvatochromic band attributed to an intramolecular charge-transfer transition from the phenolate moiety to the pyridinium ring. Indeed, (a)

this dye shows an exceptional solvatochromism with ΔE T (30) = 32.9 kcal mol -1 from CCl 4 to 1,1,1,3,3,3-hexafluoro-2-propanol (HFIP), (b) we have now at hand 270 E T (30) values carefully measured in the same laboratory with the same experimental conditions on purified solvents , (c) the charge-transfer transition of B( 30) is accompanied by a loss of electron density at the phenolate oxygen, therefore by a decrease of its HBA character, hence E T (30) contains an important α 1 contribution. However, there is also a significant contribution of non-specific solvent effects that must be subtracted to isolate α 1 .

This task will be accomplished by different kinds of SCMs (theoretical, semi-empirical, and experimental). One could also calculate the contribution of the non-specific interactions by applying the Kamlet-Abboud-Taft linear solvation energy relationship (LSER) [START_REF] Kamlet | Linear Solvation Energy Relationships. 23. A Comprehensive Collection of the Solvatochromic Parameters, π*, α, and β, and Some Methods for Simplifying the Generalized Solvatochromic Equation[END_REF] of eq 2 to E T (30):

(2)

E T (30) = + s π* + d δ + a α + b β
wherein is the intercept and π*, α, and β, respectively, describe the solvent's dipolarity/polarizability, HBD ability, and HBA ability, while δ corresponds to a polarizability correction. The regression coefficients s, d, a, and b measure the sensitivity of E T (30) toward a change of the corresponding four parameters. This method is not to be encouraged since the α values obtained by eq 3 depend upon the quality of too many solvent parameters, and on the robustness of the regression coefficients.

(

) α = [E T (30) -( + s π* + d δ + b β)]/a 3
The LSER methodology will however be used for the statistical analysis of the many physicochemical properties claimed to be only α-sensitive, but we will prefer to use the LSER of eq 4:

(4)

P = P 0 + di DI + e ES + a α 1 + b β 1
wherein P is the property, P 0 is the intercept, and DI, ES, α 1 , and β 1 , respectively, describe the dispersion-induction, electrostatic, solute HBA/solvent HBD, and solute HBD/solvent HBA interactions. [START_REF] Laurence | A Database of Dispersion-Induction DI, Electrostatic ES, and Hydrogen Bonding α 1 and β 1 Solvent Parameters and Some Applications to the Multiparameter Correlation Analysis of Solvent Effects[END_REF] The advantages of eq 4 over eq 2 have been explained elsewhere. [START_REF] Laurence | A Database of Dispersion-Induction DI, Electrostatic ES, and Hydrogen Bonding α 1 and β 1 Solvent Parameters and Some Applications to the Multiparameter Correlation Analysis of Solvent Effects[END_REF] The analysis will focus on the percent of contribution of the α 1 parameter to the variance of P in order to know if the determination of the HBD ability of solvents can be accomplished from a single probe.

To perform any SCM, it is necessary to classify solvents according to their capabilities to donate or not donate hydrogen bonds to the solute. The criterion on which this classification is accomplished lies on the IUPAC definition of the hydrogen bond [START_REF] Arunan | Definition of the Hydrogen Bond (IUPAC Recommendations[END_REF] as discussed in a previous paper. [START_REF] Cerón-Carrasco | Determination of a Solvent Hydrogen-Bond Acidity Scale by Means of the Solvatochromism of Pyridinium-N-Phenolate Betaine Dye 30 and PCM-TD-DFT Calculations[END_REF] With this criterion, all solvents with O-H, N-H, and Csp-H groups are classified as HBDs. Solvents with Csp 2 -H and Csp 3 -H groups are classified as HBDs only when there is experimental (e.g. spectral, thermodynamic, and/or crystallographic) and/or theoretical evidence of hydrogen bond formation in ordinary conditions (liquid state, room temperature, and atmospheric pressure). This is the case of (non-exhaustively): pentafluorobenzene, trichloroethene, (Z)-and (E)-1,2-dichloroethene, trichloromethane, dichloromethane, pentachloroethane, tribromomethane, dibromomethane, acetonitrile, nitromethane, and acetone. The case of acetone is interesting since this solvent was found non-HBD (SA =0) in the Catalán SA scale of HBD strength of solvents. [START_REF] Catalán | A Generalized Solvent Acidity Scale: The Solvatochromism of o-tert-Butylstilbazolium Betaine Dye and Its Homomorph o,o′-di-tert-Butylstilbazolium Betaine Dye[END_REF] However, there is spectroscopic and thermodynamic evidence of hydrogen bonding between acetone and pyridine Noxide in cyclohexane. [START_REF] Kolling | Hydrogen Bond Donor Acidity Parameters for Kinetics Studies in Nonaqueous Solvents[END_REF] Therefore acetone must be classified as HBD solvent. However, a simple look at the structures of the two indicators in Scheme 1 casts doubt on their similar solvatochromism in non-HBD solvents, especially since the latter is negative for B(30) but positive for 4-nitroanisole (hence the negative slope of the comparison line). We have therefore reexamined the comparison of B( 30) and 4-nitroanisole on a very large diversified sample of 150 non-HBD and 67 HBD solvents. These data originate from our laboratory and were published in 1991 and 1994 for 4-nitroanisole [START_REF] Dalati | Etude des Paramètres de Van Der Waals et de Liaison Hydrogène de 276 Solvants Organiques[END_REF][START_REF] Laurence | The Empirical Treatment of Solvent-Solute Interactions: 15 Years of π*[END_REF] and 2014 for B (30). [START_REF] Cerón-Carrasco | Solvent Polarity Scales: Determination of New E T (30) Values for 84 Organic Solvents[END_REF] inferior to those of most alcohols (between 4 and 6 k cm -1 ) despite the well-known higher HBD ability of phenols compared to alcohols. [START_REF] Abraham | Hydrogen Bonding. Part 7. A Scale of Solute Hydrogen-Bond Acidity Based on Log K Values for Complexation in Tetrachloromethane[END_REF] As a consequence, α values calculated by means of eq 6 must be considered cautiously. Thus, the α values of glycol ethers [START_REF] Lagalante | Kamlet-Taft Solvatochromic Parameters for 25 Glycol Ether Solvents and Glycol Ether Aqueous Solutions[END_REF] Therefore, the determination of α values by comparing the solvatochromism of B( 30) and 4nitroanisole must be abandoned in favor of the theoretical SCM that we will recall and whose validity we will now confirm. 16 HBDs displaced abnormally below the line.

The solvatochromic comparison of the

Validity of the theoretical solvatochromic comparison method

In this method 9 E T (30) values were calculated by a PCM-TD-DFT method with the CAM-B3LYP exchange-correlation functional and the 6-31++G(d,p) atomic basis set. For the electronic excited state, the linear-response PCM model in its non-equilibrium limit was used. The PCM model accounts only for non-specific effect. The method takes advantage of this limitation as follows.

Firstly, experimental E T (30) values are plotted against calculated E T (30)(PCM-TD-DFT) ones for a series of 31 non-HBD solvents from alkanes to DMSO. As shown on Figure 1 in ref 9, these solvents draw a comparison line of eq 7 ( 7)

E T (30)(experimental) = 0.693 E T (30) (PCM-TD-DFT) + 1.31
with n = 31, a determination coefficient r 2 = 0.953, and a standard deviation of the estimate s = 1.0 kcal mol -1 (to be compared with a maximum experimental error of 0.5 kcal mol -1 ). Because B(30) has a merocyanine-like electronic structure and that TD-DFT calculations overshoot the electronic transition energies of this family of cyanine dyes, the calculated E T (30) values are overestimated and the slope of the comparison line (0.693) is far from unity. However, we need only a relative agreement between experimental and calculated values. This agreement is excellent since r 2 is greater than 0.95.

Secondly, data points representing HBD solvents are added to this graphic. It is found that they are all displaced above this comparison line by an amount ΔE T (30) ranging from 0.30 kcal mol -1 for cyclohexylamine to 23.95 kcal mol -1 for HFIP. These displacements are explained by the hypsochromic band shifts induced by hydrogen bonding to the phenolate oxygen atom of B(30) that are not accounted for in the PCM model. They are calculated by eq 8

(8) ΔE T (30) = E T (30)(experimental) -[0.693 E T (30) (PCM-TD-DFT) + 1.31]
Lastly, to obtain a dimensionless scale of HBD ability, we take the ΔE T (30) value of 12.87 kcal mol -1 for methanol as the scaling factor and define an α 1 scale according to eq 9 ( 9) α 1 = ΔE T (30)/12.87

In this way α 1 = 0 for non-HBD solvents and α 1 = 1 for methanol and the α 1 scale has the same origin and format as the α scale of Kamlet and Taft.

PCM-TD-DFT calculations of the E T (30) values of 63 HBD solvents and 1 halogen-bond donor solvent [START_REF] Cerón-Carrasco | Determination of a Solvent Hydrogen-Bond Acidity Scale by Means of the Solvatochromism of Pyridinium-N-Phenolate Betaine Dye 30 and PCM-TD-DFT Calculations[END_REF] yield the 64 theoretical α 1 values collected in Table 1. To test the validity of these values, we have applied eq 10 to varied physicochemical properties P known to depend almost only on the solvent's HBD ability.

(10)

P = P 0 + a α 1
The results are given in Table 2 and illustrated by Figures 2 and3. The satisfactory to excellent determination coefficients constitute a first validation of the α 1 scale. and HBD (red circles) solvents. Data from ref [START_REF] Gutmann | Solvent Effects on the Redox Potential of Hexacyanoferrate(III)-Hexacyanoferrate(II)[END_REF] . For water, the α 1 value (1.54) correlates the solvent effect much better than the Kamlet-Taft α (1.17).

A second validation is found in the agreement between the α 1 scale and the results of a solvatochromic comparison of the two 2,6-di(carbamoyl)-substituted pyridinium N-phenolate betaine dyes 4 and 5 [START_REF] Reichardt | Syntheses and UV-Visible Spectroscopic Properties of Two New Hydrophilic 2,6-di(Carbamoyl)-Substituted Solvatochromic Pyridinium N-Phenolate Betaine Dyes[END_REF] of Scheme 1. In 5 two intramolecular hydrogen bonds N-H…O -are formed so that the formation of intermolecular hydrogen bonds with added HBD solvents must be reduced. [START_REF] Reichardt | Syntheses and UV-Visible Spectroscopic Properties of Two New Hydrophilic 2,6-di(Carbamoyl)-Substituted Solvatochromic Pyridinium N-Phenolate Betaine Dyes[END_REF] Consequently, the solvatochromic comparison of 4 and 5 shows the following:

E 1/2 / V a 1 (12) ΔE T (4-5) = E T (4) -[0.864 E T (5) -3.27]
ranging from 1.14 kcal mol -1 for acetonitrile to 9.73 kcal mol -1 for 2,2,2-trifluoroethanol (Table SI-1).

Since these displacements are explained by the reduced ability of 5 to receive intermolecular hydrogen bonds from HBD solvents on its phenolate oxygen, they reflect the HBD ability of solvents. They are related to the α 1 scale by eq 13 ( 13) ΔE T (4-5) = 7.56 α 1 + 0.13(±0. 45) with n = 14, r 2 = 0.915, s = 0.81 kcal mol -1 , and an intercept not statistically different from zero (Figure 4). The fact that α 1 is able to explain 91.5% of the variance of an experimental measure of the HBD ability of solvents and is proportional to this quantity confirms the validity of the theoretical SCM and of the resulting α 1 scale.

A semi-empirical solvatochromic comparison method

Thanks to commercial user-friendly packages and to computational details given in ref 9, the calculation of E T (30)(PCM-TD-DFT) values is straightforward for computational chemists.

However, the task is harder for experimental chemists. So, we have devised an easier method based on the McRae formulation of solvatochromic shifts [START_REF] Mcrae | Theory of Solvent Effects on Molecular Electronic Spectra. Frequency Shifts[END_REF] to partition E T (30) into a nonspecific and an HBD part.

McRae has analysed the effects of electric dipole interactions on the electronic states of a solute and derived an expression for the corresponding solvatochromic shifts by means of the perturbation theory considering solvent effect as the perturbation. The introduction of a number of approximations regarding both the application of the second-order perturbation theory and the solute model (reduced to a point dipole in the centre of a spherical cavity) permits the relation of solvatochromic shifts to the refractive index n and static relative permittivity ε of the solvent. A simplified McRae's expression [START_REF] Tomasi | Molecular Interactions in Solution: An Overview of Methods Based on Continuous Distributions of the Solvent[END_REF] for the S 0 S 1 transition energy of the dye B(30) can be written as eq 14:

(14) E T (30) = + (A+B) + C ( - ) + D ( - ) 2
represents the transition energy in the gas phase and the parameters A-D are functions of the properties of the dye: oscillator strength, dipole moments and polarizabilities in the ground and excited states, and cavity radius. In this work, parameters A-D will be viewed as empirical constants evaluated from the multiple linear regression of experimental E T (30) values into the explanatory variables f(n 2 ), g(n 2 ,ε), and h(n 2 ,ε) of eq 14. Each term of this equation represents a dye-solvent interaction as follows:

-A term: interaction between mutually induced dipoles of dye and solvent (London dispersion force)

-B term: interaction between permanent dye dipole and induced solvent dipole (induction force)

-C term: interaction between permanent dipoles of dye and solvent (electrostatic force) -D term: interaction between induced dye dipole and permanent solvent dipole (Stark solvent effect).

This list does not contain the hydrogen bonding to the phenolate oxygen of B (30). Indeed, like the PCM, the McRae calculations only take into account non-specific interactions. This limitation is exploited to estimate the hydrogen-bonding contribution to E T (30) by the semiempirical solvatochromic comparison method in a way similar to that of the theoretical one.

We start from our database [START_REF] Cerón-Carrasco | Solvent Polarity Scales: Determination of New E T (30) Values for 84 Organic Solvents[END_REF] with r 2 = 0.904 and s = 1.17 kcal mol -1 for 172 non-HBD solvents. Each regression coefficient is significant at a confidence level greater than 99.99%. The C term (interaction between permanent dipoles of dye and solvent) is the greatest contributor (53%) to the variance of E T (30) , as expected from the large dipole moment change (-7 D) [START_REF] Budzák | Exploring the Solvatochromism of Betaine 30 with Ab Initio Tools: From Accurate Gas-Phase Calculations to Implicit and Explicit Solvation Models[END_REF] during the transition.

Satisfactorily, the intercept of 27.0 kcal mol -1 is found close to the value of 26 kcal mol -1 range calculated [START_REF] Budzák | Exploring the Solvatochromism of Betaine 30 with Ab Initio Tools: From Accurate Gas-Phase Calculations to Implicit and Explicit Solvation Models[END_REF] for the gas-phase vertical excitation energy at a high ab initio level (the experimental gas-phase value of E T (30) is not experimentally measurable [START_REF] Machado | Pyridinium N-Phenolate Betaine Dyes[END_REF] ).

The second category of solvents consists of 72 HBD solvents. This set includes all molecules containing O-H, N-H, and Csp-H groups, as well as a number of molecules with Csp 2 -H and Csp 3 -H groups (vide supra). In the plot of experimental against calculated (by eq 15) E T (30) values shown in Figure 5, all (except the very weak HBD piperidine) data points representing HBD solvents are displaced above the line of slope unity corresponding to non-HBD solvents. These displacements are evidently the consequence of the hypsochromic shift caused by hydrogen bonding to the phenolate oxygen not taken into account by eq 15. They are calculated from eq 16:

(16) ΔE T (30) = E T (30)(experimental) -E T (30)(calculated by eq 15)

They are given in Table SI-2. They range from 12s of eq 15 for HFIP to 0.4s for acetone. A number of aliphatic amines, Csp 2 -H, and Csp 3 -H donors show displacements less than 2s, but this is inherent to their very weak HBD strength.

To assess the validity of the semi-empirical SCM, we have related the ΔE T (30) values of Table SI-2 to the α 1 scale (Figure 6). The linear correlation is The high statistical significance of this correlation enables to consider the semi-empirical SCM as a secondary method to determine new α 1 values (the primary method being the theoretical SCM). The linear regression of α 1 into ΔE T (30) yields eq 18 that is used for 37 solvents: 1alkynes, amides, amines, alcohols (mainly diols), ethyl lactate, alkanolamines, and hydrofluoroethers. These values are gathered in bold in Table 1.

(18) α 1 = 0.0797 ΔE T (30) -0.033

The α 1 values of five classes of solvents are worthy of comments, the monosubstituted acetylenes HC CX, the solvolytic solvents, the green solvents, the alkanolamines, and the hydrofluoroethers.

When the theoretical α 1 value of phenylacetylene is added to the semi-empirical ones of 1-nonyne, propargyl chloride, and ethyl propiolate, it is found than the α 1 values of this set are closely related (r 2 = 0.969) to the hydrogen-bond acidity scale lg K of monosubstituted acetylenes, [START_REF] Laurence | A Thermodynamic Hydrogen-Bond Acidity Scale for Monosubstituted Acetylenes[END_REF] where K is the hydrogen-bond formation constant of the hydrogen-bonded complex XC CH…OPPh 3 in CCl 4 . This excellent correlation lends confidence to the α 1 values of this class of organic liquids.

The α 1 values of hydroxylic solvolytic solvents are important to know since hydrogenbond donating solvents stabilize developing anion in the transition state of the S N 1 solvolysis reaction. [START_REF] Laurence | Correlation Analysis of Solvent Effects on Solvolysis Rates: What Can the Empirical Parameters of Solvents Actually Say?[END_REF] It is satisfactory that the mixed semi-empirical and theoretical α 1 values of hydroxylic solvents correlate well a consistent set 30 of 23 solvolysis rates of tert-butyl bromide (r 2 = 0.920) and tert-butyl iodide (r 2 = 0.929) as illustrated by Figure 7. Concerning the green solvent ethyl lactate, it is found here an α 1 (0.78) significantly higher than the one determined [START_REF] Schleicher | Kinetics and Solvent Effects in the Synthesis of Ionic Liquids: Imidazolium[END_REF] by the Kamlet-Taft solvatochromic method (0.64). This situation is also encountered for other green HBD solvents [START_REF] Jessop | Solvatochromic Parameters for Solvents of Interest in Green Chemistry[END_REF] as shown in Table 3. It is particularly dramatic that the α values of such important green solvents as water and glycerol have been so heavily underestimated for so many years. We insist that the α 1 value of water is 1.54 and not in the range 1.17-1.23 obtained 32 by the misused Kamlet-Taft method. In the same vein, the Kamlet-Taft α values of alkanolamines 8 are underestimated. For example, the Kamlet-Taft α = 0.59 for diethanolamine is clearly too low compared to the α 1 = 0.87 of the structurally similar diethylene glycol HOCH 2 CH 2 OCH 2 CH 2 OH. Lastly, although seemingly high for Csp 3 -H donors, the α 1 values of hydrofluoroethers (0.38 and 0.40) are nevertheless more chemically significant than the Kamlet-Taft excessive values of 0.60. [START_REF] Lagalante | Taft Thermosolvatochromic Parameters of Hydrofluoroethers and Hydrofluoroether Azeotropic Mixtures[END_REF] The addition of the theoretical and of the semi-empirical α 1 values gives a comprehensive list of 101 values for molecular solvents gathered in Table 1. There remains to characterize the HBD ability of ionic liquids. This will be accomplished in the next part by a method comparing the solvatochromism of two pyridinium N-phenolate betaine dyes, B(30) and B(33).

An experimental solvatochromic comparison method for ILs

Looking at the structures of Scheme 1, it is evident that B(33) is a much better model of nonspecific effects for B(30) than 4-nitroanisole. Moreover B( 33) is a worse proton acceptor (pK a = 4.78) [START_REF] Machado | Pyridinium N-Phenolate Betaine Dyes[END_REF] than B(30) (pK a = 8.64) [START_REF] Machado | Pyridinium N-Phenolate Betaine Dyes[END_REF] by virtue of the electron-withdrawing effect of the chloro substituents in B (33). Lastly, both B(30) and B(33) are commercially available. We have so been able to obtain E T ( 30) and E T (33) for 22 non-HBD and 24 HBD molecular solvents (Table SI-3) as well as for 30 ILs (from the literature, [START_REF] Spange | Complementary Interpretation of E T (30) Polarity Parameters of Ionic Liquids[END_REF][START_REF] Zhang | Distinct Influence of the Anion and Ether Group on the Polarity of Ammonium and Imidazolium Ionic Liquids[END_REF][START_REF] Zhang | Hydroxyl Ionic Liquids: The Differentiating Effect of Hydroxyl on Polarity Due to Ionic Hydrogen Bonds between Hydroxyl and Anions[END_REF][START_REF] Yalcin | Solvation Properties of Protic Ionic Liquids and Molecular Solvents[END_REF] Table 4) with diversified cations and anions (Scheme 2). Table 4. Literature E T ( 33) and E T (30) values (kcal mol -1 ) of ionic liquids, enhancement of the hydrogen-bonding contribution in E T (30) compared to E T (33), ΔE T (30-33) In a plot of E T ( 30) vs E T (33) (Figure 8 with n = 24 molecular HBDs, r 2 = 0.904, and s = 0.14. The results are reported in Table 4.

Their reliability is strongly dependent on the purity and dryness of the ILs, so that the E T values reported by various authors for the same IL are sometimes different from each other. In this case, Machado et al [START_REF] Machado | Pyridinium N-Phenolate Betaine Dyes[END_REF] recommend choosing the lower value since acidic impurities and water increase E T .

Thus, the E T (33) value of 60.18 kcal mol -1 from Spange et al [START_REF] Spange | Complementary Interpretation of E T (30) Polarity Parameters of Ionic Liquids[END_REF] was preferred to that of 61.40 from

Zhang et al [START_REF] Zhang | Hydroxyl Ionic Liquids: The Differentiating Effect of Hydroxyl on Polarity Due to Ionic Hydrogen Bonds between Hydroxyl and Anions[END_REF] for [C4mim] + [N(CN) 2 ] -and consequently an α 1 value of 0.62 was deduced instead of 0.32 from the Zhang datum.

The variation of the α 1 values of studied ILs is quite important (from 0.34 to 1.47). It depends on the strength of the dye-IL interactions. These are hydrogen bonding to the phenolate oxygen and charge-charge interaction between the IL cation and the anionic oxygen. For the cations of the studied ILs, the positive charge is either delocalized in an imidazolium aromatic ring or sterically hindered in tetraalkylammonium cations, so that the charge-charge interaction must be less important than hydrogen bonding. It is seen in Table 4 that α 1 values depend not only on the structure of the IL cation but also on the basicity of the anion.

Concerning the cation, the α 1 order is: The range of α 1 variation of alkylimidazolium ILs (0.40-0.68) is generally explained by the basicity order of the anions X -. Indeed, imidazolium ILs are structured through C(2)-H… X - hydrogen bonds. Such hydrogen bonds disadvantage the hydrogen bond C(2)-H… O -all the more the more basic the anion. [START_REF] Crowhurst | Solvent-Solute Interactions in Ionic Liquids[END_REF] So, for the [C4mim] and [C8mim] ILs, the α 1 values increase from 0.54 for the very basic anion Cl -to 0.68 for the poorly basic anion BF 4 -in the regular order of β 1 values of HBA basicity of anions:

Cl -< Br -< (CN) 2 N -< BF 4 -
The influence of the anion basicity is less regular in the [C2mim] ILs, although it is also found that the more acidic IL corresponds to the less basic anion PF 6 -. Surprisingly, the anion influence is dramatic in tetraalkylammonium ILs, since α 1 increases from 0.

N] + [NTf 2 ] -.
Whatever the chemical significance of these results, the standard deviation of the estimate of α 1 values from eq (21) is rather high (0.14 unit). Thus, we have looked for a more accurate method.

Many groups have proposed methodologies to determine α values using a single solvent-dependent process, such as the solvatochromism of the dicyano-bis(1,10-phenanthroline)iron(II) complex [START_REF] Lungwitz | New Aspects on the Hydrogen Bond Donor (HBD) Strength of 1-Butyl-3-Methylimidazolium Room Temperature Ionic Liquids[END_REF] or the solvent effect on the difference d 24 between the 13 C chemical shifts of the C(2) and C(4) carbons of pyridine N-oxide. [START_REF] Madeira | Alternative Probe for the Determination of the Hydrogen-Bond Acidity of Ionic Liquids and Their Aqueous Solutions[END_REF] These methods are attractive since, for a given solvent, they require a single measurement on a single probe. Nevertheless, their validity lies on the assumption that the chosen property depends only on the HBD strength of solvents and is not contaminated by non-specific effects. The validity of this assumption is studied in the following part.

Critical analysis of single probe methods for the determination of α-like scales

A (non-exhaustive) list of physicochemical properties P claimed to be only α-dependent is given in Table 5, with the structures of the corresponding probes in Scheme 3. This assertion will be checked by correlating P through the LSER P = P 0 + di DI + e ES + a α 1 + b β 1 and calculating the % variance of P explained by α 1 . The higher this percentage, the better the property will be to determine an α scale. However, this percentage is highly dependent on the number and variety of solvents available for the correlation. In particular the number of non-HBD and HBD solvents must be well-balanced in the sample. Since this is not always the case, and since a solely α-dependent property should remain constant for non-HBD solvents (α 1 = 0), we chose a second criterion. It consists in calculating the ratio of the P variation for non-HBDs to the P variation for HBDs:

(22) % R = 100[∆P(non-HBDs)/ ∆P(HBDs)]
The lower this percentage, the more we can consider that the property depends only on α. The results given in Table 5 show that there is no property exclusively α-dependent (with 100% α 1 and 0% R).

This conclusion is justified in the following. 5.

Property 1. HBD solvents form hydrogen bonds with the cyano groups of Fe(LL) 2 (CN) 2 complexes and shift their t 2g π* transition to higher wavenumbers. Spange et al [START_REF] Lungwitz | New Aspects on the Hydrogen Bond Donor (HBD) Strength of 1-Butyl-3-Methylimidazolium Room Temperature Ionic Liquids[END_REF] chose the Fe complex with 1,10-phenanthroline as the ligand L to determine the α values of ILs.

However, eq 23 indicates that, for molecular solvents, this transition is not only sensitive to HB donation (80%) but also to HB acceptance (13%) and to electrostatic interactions (7%): with n = 47(29 HBDs), r 2 = 0.969, and s = 0.18 k cm -1 . Migron and Marcus [START_REF] Migron | Two Reintroduced Solvatochromic Indicators for Hydrogen Bond Donation and Acceptance[END_REF] find similar results with the Kamlet-Taft parameters π*, α, and β, and conclude that this Fe complex "is not an exclusively α indicator". The data of Burgess [START_REF] Burgess | Solvent Effects on Visible Absorption Spectra of Bis-(2,2'-Bipyridyl) Biscyanoiron(II), Bis-(1,10-Phenanthroline)Biscyanoiron(II), and Related Compounds[END_REF] on this Fe complex confirm this conclusion with α 1 contributions to the solvatochromism of 76% (n = 20) and of 78% (n = 18) when L is a Schiff base. [START_REF] Burgess | Solvent Effects on Charge-Transfer Spectra of Compounds of the Type Fe(LL)2(CN)2[END_REF] Property 2. Walter and Bauer 41 claim that the transition energies of the long-wavelength band of N, N-(dimethyl)thiobenzamide S-oxide (E T SO ) "are thought to be useful empirical solvent parameters for characterizing the protic character of solvent". However, eq (24) indicates that this transition is not only sensitive to HB donation (74%) but also to electrostatic interactions (26%):

(24) E T SO /kcal mol -1 = 80.06 + 2.17 Property 4. The oxygen of triethylphosphane oxide is a strong HBA and forms hydrogenbonded complexes in HBD solvents, with a consequent downfield shift in the NMR chemical shift δ of the 31 P atom. [START_REF] Mayer | The Acceptor Number -A Quantitative Empirical Parameter for the Electrophilic Properties of Solvents[END_REF] The acceptor number scale, AN, was defined by Mayer et al [START_REF] Mayer | The Acceptor Number -A Quantitative Empirical Parameter for the Electrophilic Properties of Solvents[END_REF] with n = 17(11 HBDs), r 2 = 0.942, and s = 0.18 ppm.

In conclusion, there is, until now, no unambiguous single physicochemical property for α 1 .

Solvent and solute α scales

There are two types of α scale. The solvent α 1 scale 9 (subscript 1 for solvent) corresponds to compounds in bulk, acting as solvents. The solute scale [START_REF] Abraham | Hydrogen Bonding. Part 7. A Scale of Solute Hydrogen-Bond Acidity Based on Log K Values for Complexation in Tetrachloromethane[END_REF] (subscript 2 for solute and superscript H for hydrogen bonding) corresponds to compounds in dilute solutions, acting as solutes. It is useful to study the relationship of α 1 with α 2 H since it can throw some light on the bulk behavior.

The solute HB acidity scale is constructed from equilibrium constants for the 1:1 hydrogen bond complexation, eqs 33 and 34, in CCl 4 at 25°C The scaling factor of 4.636 serves to yield a suitable spread of .

Another solute HB acidity scale, lg K α , has been constructed 53 against a single reference HBA, N-methylpyrrolidin-2-one, in CCl 3 CH 3 . Cyclohexane was used as the measurement solvent for the construction of a third solute HB acidity scale, [START_REF] Kolling | Hydrogen Bond Donor Acidity Parameters for Kinetics Studies in Nonaqueous Solvents[END_REF][START_REF] Abboud | Studies on Amphiprotic Compounds. 4. Application of the Hydrogen-Bonding Acidity Scale to Complexation between Pyridine N-Oxide and Monomeric Hydrogen-Bond Donors in Cyclohexane[END_REF][START_REF] Sraïdi | Chimiométrie de la Basicité et de l'Acidité de l'Eau et des Alcools Monomères et Polymères[END_REF] lg K PyO , against pyridine Noxide as the reference HBA in equilibrium (33). This very inert solvent permits to determine the complexation constants K PyO even of very weak HBDs such as acetone [START_REF] Kolling | Hydrogen Bond Donor Acidity Parameters for Kinetics Studies in Nonaqueous Solvents[END_REF] and, consequently, from this experimental evidence for the formation of hydrogen bonding, to classify acetone as a HBD solvent according to the IUPAC definition of the hydrogen bond.

Table 6 summarizes the results of the correlations of the solvent α 1 scale with these three solute scales of HB acidity. From 78% to 86% of the variance of the solvent α 1 scale are explained by the solute scales. Thus, the solute and solvent scales of HBD strength are not entirely equivalent. A probable origin of this difference comes from the self-association of HBDs in the liquid state into cyclic dimers or linear and cyclic aggregates. [START_REF] Marcus | The Properties of Solvents[END_REF][START_REF] Frange | A Quantitative Study of Structural Effects on the Self-Association of Alcohols[END_REF][START_REF] Henkel | Polarisation Effects on the Solvation Properties of Alcohols[END_REF] The self-association of alcohols into aggregates (ROH) n is particularly important compared to the self-association of C-H donors or amines. [START_REF] Singh | Spectroscopic Studies of Self-Association due to Hydrogen Bonding[END_REF] Indeed, for all 24 HBDs having both α 1 and known, the determination coefficient is 0.775 but it falls to 0.597 when only the O-H donors are considered. On the contrary, r 2 rises to 0.898 when only the amines and the C-H donors are taken into account. The weak self-association of 1-alkynes 61 permits a high determination coefficient (0.969) between their solvent α 1 scale and their solute scale of HB acidity (vide supra). In the same vein, the important self-association of ROH molecules prevents a high correlation of their α 1 values with the Taft constant 60 * of the R substituent (r 2 = 0.747, n = 18 from R = tert-Bu to R = (CF 3 ) 2 CH), a molecular descriptor of the free molecule. The last one, intended for ILs, called "experimental comparison method", exploits the difference of basicity of the commercially available betaine dyes B(30) and B (33). The α 1 values are calculated by eq 21 from the solvatochromic displacements ΔE T (30-33) attributable to enhanced hydrogen bonding by the HBD solvents to the strong HBA solute B(30) relative to the weaker HBA solute B (33).

At the end, a comprehensive list of 131 α 1 values is obtained. These values must be preferred to the Kamlet-Taft α ones.

A critical analysis of methods based on a single process shows that the physicochemical properties chosen are not exclusively α-dependent. Such is particularly the case of the solvatochromism of an iron complex Fe(LL)(CN) 2 and of the [START_REF] Laurence | A Database of Dispersion-Induction DI, Electrostatic ES, and Hydrogen Bonding α 1 and β 1 Solvent Parameters and Some Applications to the Multiparameter Correlation Analysis of Solvent Effects[END_REF] C NMR chemical shifts of pyridine N-oxide. On the contrary, solvatochromic comparison methods are able to deliver physicochemical quantities such as ΔE T (30)(exp.-calc.), ΔE T (4-5), or ΔE T (30-33) that are free from non-specific solvent effects and only dependent on the HBD strength of solvents.

The comparison of the solvent α 1 scale to solute HB acidity scales shows that they are not entirely equivalent. The ROH HBDs are the most dissimilar because of their self-association in the liquid state.

Experimental section 4.1 Chemicals

The betaine dyes B(30), B (33), and the two 2,6-di(carbamoyl)-substituted pyridinium Nphenolate betaine dyes were generously given by Pr Reichardt (Marburg). Solvents were purified as already described. [START_REF] Cerón-Carrasco | Solvent Polarity Scales: Determination of New E T (30) Values for 84 Organic Solvents[END_REF]

Visible/near IR spectra

Because of the thermosolvatochromism of betaine dyes, the cell temperature was regulated at 25°C. The cell length was 1 cm or 10 cm for the betaine dyes soluble with difficulty.

13 C NMR spectra

Carbon 13 NMR spectra were recorded at 300 K on a Bruker spectrometer operating at 75 MHz for [START_REF] Laurence | A Database of Dispersion-Induction DI, Electrostatic ES, and Hydrogen Bonding α 1 and β 1 Solvent Parameters and Some Applications to the Multiparameter Correlation Analysis of Solvent Effects[END_REF] C. Chemical shifts were referenced internally to acetone d-6 at δ = 206.26 ppm.

Statistical calculations

They were performed by a least-squares linear method when there is one explanatory variable, or a multiple linear method when there are several explanatory variables (LSER eq 4 and

McRae eq 14). For the LSER the statistically significant solvent parameters are found by a downward stepwise procedure. Solvent parameters are accepted or rejected one by one by means of a Student two-sided t test on each regression coefficient at the 95% confidence level.

Reichardt's dye and of 4 -

 4 nitroanisole does not fulfill the Kamlet-Taft conditions for a safe SCM The initial construction (1976) of the Kamlet-Taft α scale 3 involved the systematic application of the SCM to many processes strongly dependent on the HBD ability of solvents such as: (a) the solvatochromism of the Reichardt's dye, Brooker's merocyanine dye, and Burgess' dye (an iron coordination compound), (b) the Gibbs energy of transfer of the Et 4 N + I -ion pair from methanol to solvents, and (c) the solvolysis of tert-butyl chloride. They were compared to the solvatochromism of 4-nitroanisole, and the results were averaged and given an origin (α = 0 for non-HBD solvents) and a format (α = 1 for methanol). New solvents are difficult to incorporate in this statistical framework, so chemists were obliged to determine new α values from a single reference solvatochromic comparison, and they often selected the comparison of B(30) with 4-nitroanisole. The equation of the line comparing the non-HBD solvents being 3(5) [B(30)] = -1.873 (4-nitroanisole) + 74.58 k cm -1 and the displacement of methanol from this line being 6.24 k cm -1 , most new α values are calculated by means of the Kamlet-Taft eq 6: (6) α = [ (B30) -(-1.873 (4-nitroanisole) + 74.58)]/ 6.24

  At the time of Kamlet and Taft much less experimental data were available since they could study only 17 non-HBDs and 13 HBDs. Our results are dramatically different of those of Kamlet and Taft since the requirement that the solvatochromic shifts of B(30) and 4-nitroanisole in non-HBD solvents should be similar is not observed, the determination coefficient r 2 being only 0.670 as illustrated in Figure1. The second requirement for a reliable SCM that all data points representing HBD solvents should be displaced from the comparison line of non-HBD solvents in the same direction is also not fulfilled in Figure1since 16 HBD solvents out of 67 ones corresponding to Csp-H, Csp 2 -H, Csp 3 -H, and N-H donors (e.g. phenylacetylene, trichloroethene, trichloromethane, and diallylamine) deviate downwards from the comparison line whereas the other HBD solvents deviate upwards. Finally, the relative magnitudes of displacements are not always consistent with the chemistry involved. For example (a) the displacement of chloroacetonitrile (1.47 k cm -1 ) is less than acetonitrile (2.30 k cm -1 ) despite the electron-withdrawing effect of the chloro substituent that increases the HBD ability; (b) similarly the displacement of 2,2,2trichloroethanol (3.00 k cm -1 ) lower than that of ethanol (5.15 k cm -1 ) does not take into account the electron-withdrawing effect of CCl 3 , and (c) 3-methylphenol shows a displacement of 3.15 k cm-1

  with α = 0.40 for CH 3 CH(OMe)CH 2 OMe, and those of hydrofluoroethers[START_REF] Lagalante | Taft Thermosolvatochromic Parameters of Hydrofluoroethers and Hydrofluoroether Azeotropic Mixtures[END_REF] with α = 0.602 for CH 3 O(CF 2 ) 3 CF 3 and α = 0.598 for C 2 H 5 O (CF 2 ) 3 CF 3 are clearly too high compared to those of the best Csp 3 -H donors (α 1 = 0.31 for chloroacetonitrile). On the contrary, those of alkanolamines 8 (from 0.40 to 0.64) appear too weak compared to that of ethanol (0.75).

Figure 1 .

 1 Figure 1. Kamlet-Taft solvatochromic comparison of the Reichardt betaine dye B(30) with 4-nitroanisole. Black circles: 150 non-HBDs fixing the reference line. Red circles: 51 HBDs displaced above the line. Yellow circles:

  cis-trans isomerization of Pt(PEt 3 ) 2 (3-MeC 6 H 4 )Cl 8number of data points (number of HBD solvents in parentheses), r 2 = determination coefficient. b This coefficient rises to 0.986 when the outlier 2-methoxyethanol is excluded.

Figure 2 . 1 Figure 3 .

 213 Figure 2. Plot of the proton-transfer time of 7-azaindole in 12 alcohols from tert-butanol to 2,2,2trifluoroethanol against the theoretical α 1 scale. Data from ref 23 .

  (a) in a plot of E T (4) vs E T (5) data points representing non-HBD solvents draw a comparison line of equation 11 (11) E T (4) = 0.864 E T (5) -3.27 with n = 8, r 2 = 0.980, and s = 0.55 kcal mol -1 (b) all HBD solvents are significantly displaced above this comparison line by an amount ΔE T (4-5) calculated by eq 12

Figure 4 .

 4 Figure 4. Enhanced hypsochromic band shifts induced by hydrogen bonding to the phenolate oxygen of the betaine dye 4 compared to betaine dye 5 against the theoretical α 1 scale for 14 HBD solvents from acetonitrile to 2,2,2-trifluoroethanol. Data from Table SI-1.

( 17 )

 17 ΔE T (30) = 12.47 α 1 + 0.47 (±0.10) with n = 58 HBDs, r 2 = 0.994, and s = 0.40 kcal mol -1 .

Figure 5 .

 5 Figure 5. Semi-empirical solvatochromic comparison method. Plot of experimental E T (30) values against E T (30) calculated by the McRae equation. Black circles: non-HBD solvents. Red circles: HBD solvents.

Figure 6 .

 6 Figure 6. Correlation between the α 1 scale calculated from the theoretical SCM and the hydrogen bonding contribution to E T (30) calculated by the semi-empirical SCM for 58 HBD solvents from acetone to HFIP.

1 Figure 7 .

 17 Figure 7. Correlation between the logarithm of the solvolysis rate (s -1 ) of tert-butyl iodide and the theoretical and semi-empirical α 1 values of 23 solvolytic solvents from pentan-3-ol to water. Data from ref 30.

  ) 22 non-HBD molecular solvents spanning a large range of E T (30) values from benzene (34.3 kcal mol -1 ) to propylene carbonate (46.0 kcal mol -1 ) draw a comparison line of eq 19 (19) E T (30) = 0.752 E T (33) + 4.08 with r 2 = 0.995, and s = 0.25 kcal mol -1 . The very high determination coefficient testifies to the similarity of non-specific effects on the solvatochromism of the two betaines. On the contrary, because B(30) is more capable of hydrogen bonding acceptance than B(33), HBD molecular solvents stand systematically above this comparison line as shown in Figure 8. Their deviations ΔE T (30-33) are calculated by eq 20 (20) ΔE T (30-33) = E T (30) -[0.752 E T (33) + 4.08] They range from 0.14 kcal mol -1 for the very weak HBD acetone to 7.41 kcal mol -1 for the strong HBD HFIP. Their relative magnitudes are chemically significant since well related to the reliable theoretical α 1 scale (r 2 = 0.904, n = 24).

Figure 8 .

 8 Figure 8. Solvatochromic comparison of betaine dyes B(30) and B(33). The line fits the non-HBD solvents (black circles). The molecular HBDs (red circles) and the ILs (yellow circles) stand above this line. Data from Table SI-3 for molecular solvents and Table4for ILs.

monoalkylammonium ( 1 .

 1 08-1.37) ≈ hydroxyethylmim (1.05-1.37, excluding the acetate) » alkylmim (0.40-0.68) Unsurprisingly, the OH group of hydroxyl ILs and the NH 3 + group of ammonium ILs are much better HB donating than the C(2)-H group of imidazolium ILs. The importance of O-H…O -hydrogen bonds can be confirmed if one compares the α 1 value of [hydroxyethylmethylimidazolium][NTf 2 ] with that of [methoxyethylmethylimidazolium][NTf 2 ]: the methylation of the OH group decreases α 1 by 0.71 unit.

Scheme 3 .

 3 Scheme 3. Structures of HBA probes claimed for the determinations of α scales. The numbers under structures correspond to the property number of Table5.

  /k cm -1 ) =16.10 + 0.62(±0.21) ES + 2.03(±0.06) α 1 -0.61(±0.10) β 1

Property 3 .

 3 (±0.60) ES + 3.64(±0.36) α 1 with n = 27(17 HBDs), r 2 = 0.898, and s = 0.71 kcal mol -1 . Moreover, the transition energy is clearly not constant for non-HBDs (R = 20% from CCl 4 to DMSO). The negative solvatochromism of the n π* absorption band of the 2,2,6,6tetramethylpiperidine N-oxyl radical was used by Janowski et al 42 "to introduce a new scale of Lewis acidity of solvents E B ", because HBD solvents (Lewis acids) stabilize the nonbonding orbital more than the antibonding π*orbital. The parameter E B is defined as the transition energy of the n π* band. From the standardized regression coefficients of eq 25 it is found that only 73% of the variance of E B is explained by α 1 : (25) E B /kcal mol -1 = 60.25 + 1.48(±0.17) ES + 3.29(±0.14) α 1 with n = 45(18 HBDs), r 2 = 0.959, and s = 0.30 kcal mol -1 . The significant contribution (27%) of ES to the variance of E B is confirmed by the significant variation of E B for non-HBD solvents from pentane to propylene carbonate (R = 26%).

( 26 ) 52 Properties 5 and 6 .

 26526 from δ ( 31 P) by setting up AN = 0 for hexane and AN = 100 for the adduct Et 3 PO-SbCl 5 . The standardized regression coefficients of eq 26 indicate that 83% of the variance of AN is explained by α 1 : AN = 5.8 + 11.5(±2.6) ES + 26.5(±1.2) α 1with n = 37(17 HBDs), r 2 = 0.945, and s = 3.7. With the significant contribution (17%) of the electrostatic parameter ES to the variance of AN, and a R value of 32%, it is clear that AN does not exclusively measure the HBD strength of solvents. This was already demonstrated by Riddle and Fowkes.[START_REF] Riddle | Spectral Shifts in Acid-Base Chemistry. 1. van Der Waals Contributions to Acceptor Numbers[END_REF] According to Marcus,[START_REF] Marcus | The Properties of Solvents[END_REF] "it is clear that AN includes a non-specific polarity effect" since non-HBD solvents have "non-vanishing acceptor numbers" and that this acceptor number can reach values as high as 19 for DMSO. Shortcomings of the Kamlet-Taft α parameters and contamination of the AN parameter by non-specific effects might explain the absence of correlation between AN and α for ILs. The 13 C NMR chemical shifts of the ipso carbon atom of N, N-diethyl-(or dimethyl)-benzamide relative to the carbonyl carbon atom, i.e. the quantity d 1 = δ (C1)δ(C=O), are very sensitive to the HBD strength of solvents, 45 as indicated by eqs 27 and 28: (27) d 1 (PhCONEt 2 ) = 32.1 + 3.76 (±0.26) α 1 with n = 21(17 HBDs), r 2 = 0.918, and s = 0.62 ppm. (28) d 1 (PhCONMe 2 ) = 33.4 + 3.51 (±0.28) α 1 with n = 25(13 HBDs), r 2 = 0.873, and s = 0.64 ppm.The parameters ES and DI are not statistically significant at the 95% confidence level in these equations, but (a) in eq(27) the sample of solvents is not well-balanced since only 4 non-HBD solvents out of 21 are present, (b) only 87.3% of the variance of d 1 is explained by α 1 in eq 28, and (c) the ratio R is far from zero for both set of data. Properties 7 and 8. According to Schneider et al, 47 the 13 C NMR chemical shifts of the C2 and C3 atoms of pyridine N-oxide relative to the C4 atom, i.e. the quantities d 24 = δ (C4)-δ(C2) and d 34 = δ (C4)-δ(C3), are independent of non-specific solvent effects and are sensitive only to the HBD ability of solvents.

( 33 )

 33 AH + B AH…B (34) K c = [AH…B]/[AH][B] where AH is the HBD and B the HBA. A special statistical treatment of the equilibrium constants (as lg K c ) for the complexation of a series of HBDs with 45 reference HBAs yields a lg scale of HB acidity for some 190 HBDs. The observation that lg = -1.1 corresponds to a quasi-absence of complexation enables a HB acidity parameter, α 2 H , to be defined with an origin of zero, via eq 35 (35) = (lg +1.1)/4.636

  can be easily determined by recording the visible-near IR spectrum of a commercially available probe, the Reichardt's dye B(30), in the solvent of interest, this dye is generally chosen as the reference HBA probe for the determination of α-like scales. But there is no evident structurally similar probe non or less capable of accepting hydrogen bonds. Kamlet and Taft used many such probes to establish an averaged α scale, and among them 4-nitroanisole.Today, the majority of chemists who want to know the α parameter of a new solvent, such as a green solvent or an ionic liquid, choose the pair of B(30)/4-nitroanisole indicators to perform a solvatochromic comparison. In this work we have shown that this choice is unfortunate and most often yields incorrect α values. Instead, we propose here three reliable comparison methods.The first one, called "theoretical solvatochromic comparison method" is mainly intended for computational chemists. It compares experimental E T(30) values to PCM-TD-DFT calculated ones. With the CAM-B3LYP functional, the 6-31++G(d,p) basis set, and, for the excited state, the linear-response PCM model in its non-equilibrium limit, the α 1 values are obtained by eq 36: (36) α 1 = {E T (30)(experimental) -[0.693 E T (30) (PCM-TD-DFT) + 1.3]}/12.87 They correlate well a number of thermodynamic, kinetic, and electrochemical properties depending mainly on the HBD strength of solvents. They also correlate with the solvatochromic displacements ΔE T (4-5) attributable to enhanced hydrogen bonding by the HBD solvents to the strong HBA solute 2,6-bis(dimethylaminocarbonyl)-4-(2,4,6triphenylpyridinium-1-yl)phenolate 4, relative to the weaker HBA solute 2,6-bis(Nmethylaminocarbonyl)-4-(2,4,6-triphenylpyridinium-1-yl)phenolate 5. Here, the two intramolecular hydrogen bonds N-H…O -in this latter betaine dye disadvantage the intermolecular hydrogen bonds of HBD solvents. Since betaine dyes 4 and 5 are not commercially available we cannot recommend the calculation of new α 1 values from ΔE T (4-5). The second one, called "semi-empirical comparison method", compares experimental E T (30) values to calculated ones by the McRae simplified equation 14 in which the coefficients A,B,C, and D are adjusted to experimental data by a multiple linear regression. The α 1 values are calculated from the experimental E T (30) value, the refractive index n, and the relative permittivity ε of the solvent by eq 37 (37) α 1 = 0.0797 {(E T (30)(experimental) -[27.0 + 24.7 f(n 2 )+ 10.0 g(ε , n 2 )+ 9.4 h(ε , n 2 )]}-0.033.

Table 1 .

 1 a 1 scale of hydrogen-bond strength of HBD solvents (in bold 37 new values determined by the semi-empirical SCM).

	HBD Solvent		a 1	HBD Solvent	a 1
	C-H donors			2-Propanol	0.53
	1-Nonyne		0.03	2-Methyl-1-butanol	0.54
	1,1,2,2-Tetrachloroethane	0.04	2-Methyl-1-propanol, iso-butanol	0.57
	Acetone			0.04	1-Phenylethanol	0.57
	Dibromomethane		0.07	3-Methyl-1-butanol	0.62
	Trichloroethene		0.09	1-Pentanol	0.64
	Pentachloroethane		0.09	1-Heptanol	0.64
	Dichloromethane		0.10	1-Hexanol	0.65
	Tribromomethane		0.14	1-Butanol	0.65
	Bromo-trichloromethane
	(HalBD)			0.17	1-Octanol	0.66
	(E)-1,2-Dichloroethene		0.19	1-Nonanol	0.66
	Pentafluorobenzene		0.19	2-Ethoxyethanol	0.67
	Trichloromethane		0.20	1-Propanol	0.68
	(Z)-1,2-Dichloroethene		0.20	Monoethanolamine	0.70
	Acetonitrile		0.23	1-Decanol	0.72
	Phenylacetylene		0.26	2-Phenylethanol	0.72
	3-Chloro-1-propyne, propargyl chloride		0.26	Pentane-1,5-diol	0.74
	Nitromethane		0.28	Ethanol	0.75
	Chloroacetonitrile		0.31	Butane-2,3-diol	0.77
	Ethoxy-nonafluorobutane (HFE7200)	0.38	1,3-Dimethoxy-2-propanol	0.78
	Methoxy-nonafluorobutane (HFE7100)	0.40	Ethyl lactate	0.78
	Ethyl	propynoate,	ethyl
	propiolate		0.58	2-(n-Butoxy)ethanol	0.79
	N-H donors			Benzyl alcohol	0.79
	Piperidine		0.00	Allyl alcohol	0.79
	Cyclohexylamine		0.02	Butane-1,3-diol	0.80
	N-(tert-Butyl)-benzylamine	0.03	2-Methoxyethanol	0.83
	Diethylamine		0.04	Butane-1,2-diol	0.83
	tert-Butylamine		0.06	Butane-1,4-diol	0.85
	Diallylamine		0.07	Diethanolamine	0.86
	n-Butylamine		0.09	Diethylene glycol	0.87
	N-Benzyl-methylamine		0.10	Triethanolamine	0.88
	1,2-Diaminoethane		0.11	Diethylene glycol	0.88
	Allylamine		0.12	2-Phenoxyethanol	0.89
	Morpholine		0.17	Propane-1,2-diol	0.90
	3-Amino-1-propyne, propargylamine		0.25	Triethyleneglycol	0.90
	N-Methylaniline		0.38	3-Methoxy-1,2-propanediol	0.92
	Pyrrolidin-2-one		0.44	2,2,2-Trichloroethanol	0.92
	Aniline			0.47	Propane-1,3-diol	0.94
	N-Methylpropionamide		0.55	1,1,1,3,3,3-Hexafluoro-2-phenylpropan-2-ol	0.95

Table 2 .

 2 Correlations of thermodynamic, kinetic, and electrochemical properties P according to eq 10 a .

	no.	property P	n	r 2	ref
	1	Gibbs energy of transfer of Cl -from water to solvents	11(11)	0.943

  of 248 solvents for which both E T(30), n, and ε have been carefully determined in our laboratory and divide these solvents in HBDs and non-HBDs. With the criterion used above, 176 solvents are considered non-HBDs. Their E

	exclusion yields eq 15:
	(15) E T (30) =	+ 24.7	+ 10.0 (	-	) + 9.4 (	-	) 2

T

(30)

values span from 30.8 (2-methylbutane) to 46.0 (propylene carbonate) kcal mol -1 , while their n values from 1.291 (methyl trifluoroacetate) to 1.702 (1-iodonaphtalene) and ε values from 1.84 (n-pentane) to 62.93 (propylene carbonate) vary in a very large range. This permits a satisfactory fit of E T

(30)

with f(n 2 ), g(n 2 ,ε), and h(n 2 ,ε), with a determination coefficient r 2 = 0.879 and a standard deviation of the estimate s = 1.30 kcal mol -1 . The four more deviating solvents (by more than 2s) are: 1,4-difluorobenzene, 1,4-dioxane, dimethyl carbonate, and diethyl carbonate. These molecules carrying several opposed bond dipoles appear more polar locally to the dye molecule than expected on the basis of their weak bulk relative permittivity. Their

Table 3

 3 Comparaison of the α 1 values of green solvents, alkanolamines, and hydrofluoroethers determined by the semi-empirical solvatochromic comparison method to the α values determined by the misused Kamlet-Taft method.

	Solvent

  Structures and abbreviations of the cations and anions of the studied ILs.

	[PeNH 3 ]MeCO 2	63.68	55.73	36	3.72	1.08
	[EtNH 3 ]NO 3	70.08	61.75	36	4.93	1.37
	[HOCH 2 CH 2 NH 3 ]NO 3	71.30	62.02	36	4.28	1.21
	[PrNH 3 ]NO 3	69.57	61.36	36	4.92	1.36
	[BuNH 3 ]NO 3	68.40	60.32	36	4.76	1.33
					(kcal mol -1 ), and
	HBD parameter α 1 .
	IL	E T (33)	E T (30)	Ref	ΔE T (30-33)	α 1
	[C8mim]Br [C4mim]Cl Scheme 2.	60.07 59.93	50.86 50.61	33 33	1.57 1.42	0.57 0.54
	[C4mim]BF 4	61.36	52.26	33	2.01	0.68
	[C4mim]N(CN) 2	60.18	51.15	33	1.77	0.62
	[C4mim]NTf 2	60.70	51.60	34	1.84	0.64
	MeO-[C2mim]N(CN) 2	60.60	52.40	34	2.71	0.84
	MeO-[C2mim]NTf 2	66.20	54.50	34	0.60	0.34
	[(Me 2 EtBu)N]N(CN) 2	58.00	49.00	34	1.27	0.50
	[(Me 2 EtBu)N]NTf 2	66.20	59.00	34	5.10	1.49
	[(MeOCH 2 CH 2 )(Me 2 Bu)N]N(CN) 2	58.70	49.00	34	0.74	0.22
	[(MeOCH 2 CH 2 )(Me 2 Bu)N]NTf 2	66.50	58.80	34	4.67	1.31
	HO-[C2mim]NTf 2	70.60	60.80	34	3.59	1.05
	HO-[C2mim]MeCO 2	60.80	51.20	35	1.36	0.52
	HO-[C2mim]PF 6	69.40	61.70	35	5.39	1.47
	HO-[C2mim]ClO 4	68.10	60.30	35	4.97	1.37
	[C2mim]PF 6	61.80	52.60	35	2.01	0.68
	[C2mim]NTf 2	61.80	52.00	35	1.41	0.54
	[C2mim]ClO 4	61.80	52.40	35	1.81	0.63
	[C2mim]N(CN) 2	61.10	51.70	35	1.63	0.59
	[C2mim]NO 3	61.90	51.50	35	0.83	0.40
	[C2mim]MeCO 2	58.70	49.80	35	1.54	0.57
	[EtNH 3 ]HCO 2	67.75	59.81	36	4.74	1.32
	[BuNH 3 ]HCO 2	65.28	57.99	36	4.78	1.33
	[PeNH 3 ]HCO 2	64.98	56.96	36	3.97	1.14
	[PrNH 3 ]MeCO 2	64.98	56.96	36	3.97	1.14

  Table SI-3 for molecular solvents and Table 4 for ILs.The validity of the solvatochromic comparison of E T (30) with E T(33) for molecular solvents leads us to extend it to ILs. On the graph of Figure8, we now report the E T values of 30 ILs. They are

	all displaced upwards from the comparison line by statistically significant amounts ranging from
	ΔE T (30-33) = 0.60 kcal mol -1 (2.4s of eq 19) for 1-(2-methoxyethyl)-3-methylimidazolium
	bis(trifluoromethanesulfonyl)amide to ΔE T (30-33) = 5.39 kcal mol -1 (21.6s of eq 19) for 1-
	hydroxyethyl-3-methylimidazolium hexafluorophosphate. These ΔE T (30-33) values of ILs can be

translated into α 1 values of ILs by means of eq 21 established from molecular solvents: (21) α 1 = 0.236 ΔE T (30-33) + 0.20 (±0.05)

  50 for [Me 2 EtBuN] + [N(CN) 2 ] -to as much as 1.49 for [Me 2 EtBuN] + [NTf 2 ] -and from 0.22 for [Me 2 Bu (CH 2 CH 2 OMe)N] + [N(CN) 2 ] -to 1.31 for [Me 2 Bu(CH 2 CH 2 OMe)

Table 5

 5 Properties P used for the definition of α-type scales, contribution of α 1 to the variance of P (%α 1 ), and ratio of the P variation for non-HBDs to the P variation for HBDs % R = 100[∆P(non-

	HBDs)/ ∆P(HBDs)].
	no. P 1 ν(t 2g π*)(cis-dicyano)bis(1,10-phenanthroline)iron II 2 E T (n π*) N,N-(dimethyl)thiobenzamide S-oxide (E T SO ) 3 E T (n π*) 2,2,6,6-tetramethylpiperidine N-oxyl radical	% α 1 80 74 73	%R 20 20 26	ref 40 41 42
	4	(E B ) 31 P chemical shift triethylphosphane oxide (AN)	83	32	43,44

  Madeira et al[START_REF] Madeira | Alternative Probe for the Determination of the Hydrogen-Bond Acidity of Ionic Liquids and Their Aqueous Solutions[END_REF] have exploited this finding to determine the Kamlet-Taft α parameter of 15 ILs with various cations and anions. However, only 78% and 73% of the variance of, respectively, d 24 and d 34 are explained by α 1 in eqs 29 and 30:Properties 9 and 10. Schneider et al 47 also reported that the[START_REF] Laurence | A Database of Dispersion-Induction DI, Electrostatic ES, and Hydrogen Bonding α 1 and β 1 Solvent Parameters and Some Applications to the Multiparameter Correlation Analysis of Solvent Effects[END_REF] C NMR chemical shifts of the C2 and C3 atoms of pyridine relative to the C4 atom, i.e. d 24 = δ (C4)-δ(C2) and d 34 = δ (C4)δ(C3), depend only on the HBD ability of solvents. This finding was based on literature data from different laboratories on 11 solvents. To make more significant the multiple linear regression analysis with DI, ES, α 1 , and β 1 and more consistent the NMR data, we have recorded the[START_REF] Laurence | A Database of Dispersion-Induction DI, Electrostatic ES, and Hydrogen Bonding α 1 and β 1 Solvent Parameters and Some Applications to the Multiparameter Correlation Analysis of Solvent Effects[END_REF] C NMR spectra of pyridine in 17 solvents (results in Table SI-4). It turns out that neither d 24 nor d 34 depend only on α 1 , since the variable ES is significant in eqs 31 and 32

	at a confidence level greater than 99%.
	(31) d 24 = -15.26 + 1.47 (±0.40) ES + 2.82 (±0.22) α 1
	with n = 17(11 HBDs), r 2 = 0.950, and s = 0.50 ppm.
	(32) d 34 = 11.66 + 0.44 (±0.15) ES + 0.96 (±0.08) α 1
	(29) d 24 = 16.85 -3.04 (±1.21) ES -4.77 (±0.53) α 1
	with n = 24(19 HBDs), r 2 = 0.850, and s = 1.30 ppm.
	(30) d 34 = 7.12-4.47 (±2.22) DI -2.15 (± 0.89) ES -4.80 (±0.41) α 1
	with n = 24(19 HBDs), r 2 = 0.904, and s = 0.94 ppm.
	Moreover, there is a large variation of d 24 and d 34 for non-HBD solvents from cyclohexane to

DMSO. Therefore, it does not appear that d 24 and d 34 of pyridine N-oxide are totally independent of non-specific effects.

Table 6 .

 6 Determination coefficients r 2 for the correlation of the solvent α 1 scale with the solute scales , lg K α , and lg K PyO . The solvatochromic comparison method devised by Kamlet and Taft in 1976 is probably the most appropriate method to yield pure (i.e. not contaminated by non-specific solvent effects) hydrogen-bond parameters. Because the parameter E T (30) (a) is very sensitive to the HB donation of solvents, (b) is available for a very large number of diversified solvents, and (c)

	Solute scale	n	r 2
		24(all HBDs)	0.775
		15(OH HBDs)	0.597
		9(NH and CH HBDs)	0.898
	lg K α	12	0.858
	lg K PyO	27	0.836
	3 Conclusion

Acknowledgements

Prof. H. Oulyadi is thanked for his kind assistance. This work has been partially supported by the European Regional Development Fund (ERDF), Labex SynOrg (ANR-11-LABX-0029), Carnot Institute I2C, the graduate school for research XL-Chem (ANR-18-EUR-0020 XL CHEM), and by Région Normandie.

The quality of prediction is judged by means of the determination coefficient r 2 , since 100r 2 yields the percent of variance of the dependent variable P explained by the explanatory variables. The relative contribution of each solvent parameter to the explained variation of the dependent variable P is obtained by calculating the standardized regression coefficients by the following equation:

(38) a' = |a| ( α1 / P )

for the example of the regression coefficient a of the α 1 parameter in the LSER of eq 3, where the apostrophe means "standardized", the bars denote absolute magnitude,  α1 represents the standard deviation of α 1 , and  P the standard deviation of P. The magnitudes of standardized regression coefficients can now be compared since they are on the same scale. For convenience di', e', a', and b' are normalized [START_REF] Krygowski | Complementary Lewis Acid-Base Description of Solvent Effects. I. Ion-Ion and Ion-Dipole Interactions[END_REF] in the way shown in eq 39 for the example of the coefficient a': (39) % α 1 = 100 a'/(di' + e' + a' + b') Thus % DI, % ES, % α 1 , and % β 1 may be regarded [START_REF] Krygowski | Complementary Lewis Acid-Base Description of Solvent Effects. I. Ion-Ion and Ion-Dipole Interactions[END_REF] as estimates of the percentage contribution from dispersion-induction, electrostatic, HBD, and HBA interactions.

Supporting Information

Detailed physico-chemical data for all solvents.