A Database of Dispersion-Induction DI, Electrostatic ES, and

Article pubs.acs.org/JPCB

A Database of Dispersion-Induction DI, Electrostatic ES, and Hydrogen Bonding α1 and β1 Solvent Parameters and Some Applications to the Multiparameter Correlation Analysis of Solvent Effects Christian Laurence,*,† Julien Legros,‡ Agisilaos Chantzis,† Aurélien Planchat,† and Denis Jacquemin†,§ †

Laboratoire CEISAM, UMR 6230 CNRS, Université de Nantes, 2 rue de la Houssinière, 44322 Nantes, France Laboratoire COBRA, UMR 6014 CNRS, Normandie Université, 1 rue Lucien Tesnière, 76821 Mont-Saint-Aignan, France § Institut Universitaire de France (IUF), 103 Boulevard Saint-Michel, 75005 Paris, France ‡

S Supporting Information *

ABSTRACT: For about 300 solvents, we propose a database of new solvent parameters describing empirically solute/solvent interactions: DI for dispersion and induction, ES for electrostatic interactions between permanent multipoles, α1 for solute Lewis base/solvent Lewis acid interactions, and β1 for solute hydrogen-bond donor/solvent hydrogen-bond acceptor interactions. The main advantage over previous parametrizations is the easiness of extension of this database to newly designed solvents, since only three probes, the betaine dye 30, 4-fluorophenol, and 4-fluoroanisole are required. These parameters can be entered into the linear solvation energy relationship A = A0 + di(DI) + eES + aα1 + bβ1 to predict a large number of varied physicochemical properties A and to rationalize the multiple intermolecular forces at the origin of solvent effects through a simple examination of the sign and magnitude of regression coefficients di, e, a, and b. Such a rationalization is illustrated for conformational and tautomeric equilibria and is supported by quantum-mechanical calculations.

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δ a polarizability correction factor (1 for aromatic solvents, 0.5 for polychlorinated solvents, and 0 for other solvents), α a hydrogen-bonding acidity parameter, β a hydrogen-bonding basicity parameter, ξ a “coordinate covalency” parameter, and δH the Hildebrand solubility parameter. This parameter describes solvent/solvent interactions that will not be considered in the present paper devoted to solute/solvent interactions. The regression coefficients s, d, a, b, e, and h indicate the sensitivity of A to the different solvent parameters. However, after 30 years of use, convergent critical analyses have pointed out the limitations of this LSER. They concern (i) the peculiar blend of dipolarity and polarizability in π*,12−14 (ii) the discrete character and the oversimplification of δ,15,16 (iii) the improper values of β for such important solvents as water and alcohols,17 and (iv) the lack of a clear reference process for the definition of parameters.2,4,17−19 For these reasons, Catalán has reparameterized this LSER into eq 2

INTRODUCTION Solvents are used in a very large number of chemical, physical, and biological processes in science and technology.1−4 Their influence on such processes (the so-called “solvent effect”) comes from solute/solvent interactions and is generally so dramatic that it is mandatory to acquire a quantitative knowledge on these interactions to select, among hundreds, the proper solvent to achieve the success of the process under study. Thus, among equally efficient solvents, one can choose the less costly and the more sustainable one. This knowledge can be obtained by methods either empirical (e. g., the determination of solvent polarity scales5,6 such as ET(30)7 or π*8 and their use in linear solvation energy relationships,8 LSER), or statistical (e. g., the determination of the main factors characterizing solvents through a factor analysis of an m × n matrix built from m solvent-dependent properties and n solvents9,10), or theoretical (e.g., the polarizable continuum model11). Among empirical methods, the use of the solvatochromic parameters π*, α, and β through the Abboud−Abraham− Kamlet−Taft (AAKT) LSER8 A = Ao + s(π * + dδ) + aα + bβ + eξ + hδ H

A = Ao + sSP + dSdP + aSA + bSB

wherein SP, SdP, SA, and SB describe the polarizability, the dipolarity, the acidity, and the basicity of solvents, respectively.20 Now, the solvent polarizability and dipolarity are unraveled, and

(1)

is very popular. In this equation, A is a physicochemical solute property for a series of solvents, A0 the same property for a reference medium, π* a dipolarity-polarizability parameter, © XXXX American Chemical Society

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Received: December 12, 2014 Revised: January 13, 2015

A

DOI: 10.1021/jp512372c J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B

forward stepwise procedure, mostly at the 95% confidence level, i.e., p ≤ 0.05 for the p-value corresponding to the F-value associated with an increase in the determination coefficient r2 when increasing the number of solvent parameters from k to k + 1. This F-value is defined as

each solvent parameter is defined from well-understood reference processes. For example, SP is based on the first electronic transition energy of a polyene (ttbP9)21 and SdP on the difference between the first electronic transition energies of two nitrofluorenes.22 However, the determination of Catalán’s parameters for new solvents is not straightforward, since it requires no less than eight solvatochromic probes and since the synthesis of some of these probes is difficult or costly.23 This is rather unfortunate because of the growing interest in the design of new solvents for green chemistry and the corresponding necessity to characterize easily these neoteric solvents by empirical parameters.24 We therefore propose here a third way to the empirical quantification of solute/solvent interactions with the main objective to determine solvent parameters by simple, but nevertheless proper, methods. In the following, we use the language of intermolecular forces that are generally divided into long-range (dispersion, induction, and electrostatic) and shortrange (exchange−repulsion and charge transfer) ones.25,26 Lewis acid/base interactions are specific interactions with a particular combination of these forces.27 Among them, hydrogen bonding between a hydrogen-bond acceptor (HBA) and a hydrogen-bond donor (HBD) is the most prominent to determine solvent properties.4,17,18 We have recently published new methods to quantify (i) solute HBA/solvent HBD interactions, that is the hydrogen-bond acidity of solvents (α1),18 and (ii) solute HBD/solvent HBA interactions, that is the hydrogen-bond basicity of solvents (β1).17 We have also briefly introduced the parameter DI describing both dispersion and induction interactions and the parameter ES describing electrostatic interactions between permanent multipoles of the solute and solvent.28 However, these DI and ES scales have not been listed, nor formatted, nor compared to the corresponding AAKT and Catalán scales. In the first part of this paper, we recall the definitions of the parameters DI, ES, α1, and β1, give them a format, and compare them to the corresponding parameters of the literature. We also assemble in one reference a collection of DI, ES, α1, and β1 values for about 300 solvents in a convenient database representing, to the best of our knowledge, the most comprehensive set of empirical solvent parameters measured so far for organic liquids. In the second part, we show that our parameters can successfully predict many types of solvent-dependent physicochemical properties using the LSER A = Ao + di DI + e ES + aα1 + bβ1

F=

(rk + 12 − rk 2)(n − k − 2) 1 − rk + 12

(4)

where n is the number of solvents. The quality of prediction is judged by means of r2 (since 100 x r2 yields the percent of variance of the property A “explained” by the solvent parameters). In this work, the values of r2 will be appraised as follows: excellent (1.00 to 0.95), good (0.95 to 0.90), satisfactory (0.90 to 0.85), fair (0.85 to 0.80), and poor ( 0 in eq 6)37 and nearly cancel each other,20 thus making easier the separation of the electrostatic effect from the dispersion and induction effects. An electrostatic solvent parameter can be obtained as described below.

ΔET (30) = ET (30) − {30.06 + 4.446[(nD 2 − 1)/(2nD 2 + 1)]} (9)

To obtain a dimensionless ES electrostatic parameter, we take the ΔET(30) value of DMSO (14.01 kcal mol−1) as the scaling factor and define ES as ES = ΔET (30)/14.01

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In this way, ES is 0 for alkanes and also for the gas phase provided the value of ET(30) extrapolated to nD = 1 (30.06 kcal mol−1) is close to the experimental gas-phase value. Unfortunately, this hypothesis cannot be experimentally tested because of the low volatility of the betaine dye 30. The parameter ES is equal to 1 for DMSO, thus the ES scale has the same format as the SdP (solvent dipolarity) scale of Catalán.20 An advantage of ES over SdP is that ET(30) values are known for more than 300 non-HBD solvents, whereas SdP has presently been determined for about 100 non-HBD solvents. Moreover, it is easier to determine ES than SdP for newly designed solvents since the determination of ES requires the use of only one probe (the commercially available betaine dye 30), whereas the determination of SdP requires the use of three probes [the polyene ttbP9, 2-(dimethylamino)-7-nitrofluorene, and 2-fluoro-7-nitrofluorene]. Electrostatic Parameter ES (HBD Solvents). ET(30) values cannot be used directly for the determination of the ES values of HBD solvents because they contain a contribution of the hydrogen bonding of these solvents to the phenolate oxygen of the betaine dye 30. ET(30) values free from this hydrogenbonding contribution, i.e., measuring only nonspecific (nsp) solvent effects, hereafter denoted ET(30)nsp, can be calculated C


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The parameters β1 and SB are, by definition, hydrogen-bond basicity parameters since the probes used for their determination are hydrogen-bond donors (4-fluorophenol for β1 and 5-nitroindole for SB). The use of β1 as a solvent Lewis basicity scale will be discussed later. Charge-Transfer Indicator Variable ξ. Some correlations of physicochemical properties with β1 are linear only when bases having similar electron-donor sites are considered separately (the so-called “family-dependence”). To restore “familyindependent relationships”, Kamlet et al. have added to their parameter β a “coordinate-covalency” indicator variable ξ.44 Values of ξ equal to −0.2 for PO bases, 0.0 for carbonyl and SO bases, 0.2 for ethers, 0.6 for pyridines, and 1.0 for amines have been assigned empirically to the various families. For four protonated bases, Kamlet et al. have noticed a decrease in the Mulliken charge on the proton with an increase in ξ.44 Since this decrease is caused by a charge transfer from the base to the 1s orbital of the proton, “charge transfer” might be a better-understood term than “coordinate covalency” to denote ξ. To get a clearer look at ξ, we have calculated the proton charge for a series of protonated oxygen and nitrogen bases. The results are given in Table 1.

within the time-dependent density functional theory (TD-DFT) framework, using a polarizable continuum solvation model (PCM), provided that a calibration equation takes into account the typical overestimation of ET(30)nsp values by TD-DFT calculations. From CAM-B3LYP/6-31++G(d,p) calculations of the first excited state of the betaine dye 30,18 we have recently established the calibration equation ET (30)nsp = 0.693ET (PCM − TD − DFT) + 1.31

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2

with n = 31 and r = 0.953. Thus, the normalized ES value of HBD solvents can be calculated by eq 12: ES = {[0.693ET (PCM − TD − DFT) + 1.31] − [30.06 + 4.446f (nD 2)]}/14.01

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Lewis Acidity Parameter α1. The contribution to ET(30) values that is not modeled through PCM-TD-DFT calculations is taken as the contribution of specific interactions to the measured ET(30) values, allowing us to deduce a Lewis acidity parameter of solvents, α1.18 For most organic solvents, the specific interaction with the phenolate oxygen of the betaine dye 30 is a hydrogen bond, so α1 is mainly a hydrogen-bond acidity scale. However, our method can be applied to any solvent interacting with the phenolate oxygen of dye 30 through a Lewis acid/base interaction (e. g., BrCCl3 forming a halogen bond38,39 C−Br···O−). In this method, the contribution of specific (sp) interactions to ET(30), denoted ΔspET(30), can be calculated from eq 13

Table 1. Natural Bond Orbital Partial Atomic Charge on the Proton of Protonated Oxygen and Nitrogen Bases B, Calculated at the ωB97X-D/6-31+G(d) Level of Theory B

Oxygen Bases (CH3)2OH+ (CH3O)3POH+ (CH3)2SO2H+ CH3C(OH+)OCH3 HC(OH+)N(CH3)2 (CH3)2SOH+ (CH3)3POH+ CH3NO2H+ (CH3O)2SOH+ (CH3)2COH+ Nitrogen Bases methylamine CH3NH3+ N-methylimidazole C4H6N2H+ 3-bromopyridine 3-BrC5H4NH+ dimethylamine (CH3)2NH2+ pyridine C5H5NH+ piperidine C5H10NH2+ 4-methylpyridine 4-(CH3)C5H4NH+ trimethylamine (CH3)3NH+ N-methylcyclohexylamine c-C6H11NH2+CH3 N,N-dimethylcyclohexylamine c-C6H11NH+(CH3)2 tri-n-butylamine (n-C4H9)3NH+ triethylamine (C2H5)3NH+ tri-n-propylamine (n-C3H7)3NH+ dimethyl ether trimethyl phosphate dimethyl sulfone methyl acetate N,N-dimethylformamide dimethyl sulfoxide trimethylphosphane oxide nitromethane dimethyl sulfite acetone

ΔspET (30) = ET (30) − [0.693ET (PCM − TD − DFT) + 1.31] (13)

and transformed into a dimensionless Lewis acidity scale α1 by taking the ΔspET(30) value of methanol (12.87 kcal mol−1) as the scaling factor according to eq 14: α1 = ΔspET (30)/12.87

(14)

In this way, α1 = 0 for all solvents interacting with dye 30 nonspecifically, and α1 = 1 for methanol by definition. Thus, the α1 scale has the same format as the original α scale of Kamlet and Taft.40 The determination of the α1 value of newly designed solvents (elsewhere illustrated for biomass derived solvents)18 requires the use of only one probe, the betaine dye 30. On the contrary, three probes are necessary for SA, namely o-tertbutylstilbazolium betaine, o,o′-di-tert-butylstilbazolium betaine, and an aromatic tetrazine.41,42 Hydrogen-Bond Basicity Parameter β1. We have recently proposed a “solvatomagnetic comparison method” to determine the hydrogen-bond basicity of solvents.17 In this method, the basicity-dependent definition property is the 19F chemical shift of 4-fluorophenol, δ(19F, OH), and the 19F chemical shift of 4-fluoroanisole, δ(19F, OMe), is used to estimate non-hydrogenbonding effects on δ(19F, OH) so that the quantity 19

BH+

a

q(H+)a 0.587 0.577 0.575 0.570 0.565 0.563 0.562 0.561 0.560 0.559 0.494 0.495 0.492 0.489 0.489 0.486b 0.486 0.484 0.479c 0.475c 0.471 0.469 0.469

In au. bEquatorial isomer. cMean of equatorial and axial isomers.

19

Δ1 = [−δ( F, OH)] − {1.009[−δ( F, OMe)] − 1.257} (15)

They show that protonated oxygen bases have almost the same + au, whereas the charge on their proton, q(H ̅ ) = 0.568 ± 0.003 + proton bears a significantly lower charge, q(H ) = 0.483 ± 0.003 ̅ au, in protonated sp2 and sp3 hybridized nitrogen bases. Consequently, if q(H+) is a satisfactory charge-transfer parameter for Lewis acid/base interactions, only two values of ξ seem necessary, for example ξ = 0. 0 for oxygen bases and ξ = 0.8 for sp2 and sp3 nitrogen bases (to keep the format of the original ξ scale in which the averages for O and N bases are 0 and 0.8 respectively).

depends only on the strength of the hydrogen bond between 4-fluorophenol and HBA solvents. The format of the scale was chosen to be identical to the original β scale of Kamlet and Taft43 by setting β1 = 1 for hexamethylphosphoric triamide for which Δ1 = 3.041 ppm. The dimensionless β1 parameter is therefore obtained from eq 16: β1 = Δ1/3.041

(16) D


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Table 2. DI, ES, α1, and β1 Values for Selected Solvents (See Table SI-1 for a More Comprehensive Collection)

Description of the Database. A listing for the 323 solvents studied in this work is given in the Supporting Information. About 130 common solvents are selected in Table 2. Table SI-1 (Supporting Information) assembles 323 DI, 282 ES, 284 α1, and 264 β1 values, as well as 323 values of the refractive index nD and its f(nD2) function (for the calculation of DI), 291 values of the relative permittivity εr, and 296 values of the polarity scale ET(30) (for the calculation of ES and α1). Most values are from our previous works17−19,28 or from refractive index and relative permittivity compilations.45−47 A number of new α1 and β1 values (Tables SI-3 and SI-4 respectively) have been determined in this work from new PCM-TD-DFT calculations and 19F NMR measurements. The solvents are divided into chemical families and ranked in each of them into increasing values of the most pertinent parameter (e.g., DI for alkanes, ES for haloalkanes, β1 for pyridines, or α1 for alcohols). The ranking of α1 and β1 values has already been discussed.17,18 We underline that the α1 value of the halogenbond donor solvent BrCCl3 (0.17) is close to that of the corresponding HBD solvent HCCl3 (0.20). The DI ranking from the gas phase (0) to 1-iodonaphthalene (1.07) is characterized by (i) a large gap (0.52) between the gas phase and perfluorohexane, the less dispersive-inductive studied solvent, (ii) weak DI values for small molecules (e.g., water and methanol) and polyfluorinated ones, (iii) large DI values for polycyclic aromatics such as 1-methylnaphthalene (0.99) or quinoline (1.00), dibromobenzenes (0.98), and CS2 (1.00), and (iv) a large number of values (145) in the restricted interval of 0.75−0.86 (see Figure SI-1). This small variation of DI often makes statistically insignificant the DI term in LSERs. This may be an artifact caused by an insufficiently varied solvent sample. The histogram of the distribution of ES values from alkanes (ES = 0) to propylene carbonate (ES = 1.07) does not show the sharp histogram found for DI but almost equal frequencies for most intervals (see Figure SI-2). So, the statistical significance of the ES term in LSERs is less dependent on the solvent sample. Small ES values are for tertiary amines such as triethylamine (0.08) or 1-methylpiperidine (0.11) and quadrupolar solvents such as (E)-1,2-dichloroethene (0.05) or p-xylene (0.14), whereas large ES values are found for solvents with large relative permittivities such as water (0.89), or N-methylformamide (0.90), or large dipole moments such as sulfolane (0.93) or DMSO (1.00). ES values also depend on the dipole density (dipole moment divided by molar volume) as shown by the regular ES decrease with a chain length increase (and consequently with the molar volume) in a homologous series of methyl esters: acetate (0.56) > propanoate (0.49) > butanoate (0.45) > pentanoate (0.40) > hexanoate (0.38) > octanoate (0.33). We have studied the possible existence of a colinearity between the explanatory variables, since they must not be colinear to obtain meaningful regression coefficients. As shown in Table 3, this condition is fulfilled for the sample of solvents studied in this paper since the r2 of pairwise correlations is close to zero. For convenience, the spreadsheet data available in the Supporting Information can be easily transformed into a searchable database through various softwares (we selected ChemOffice in this work). The 1,1,1,3,3,3-hexafluoro-2propanol (HFIP) entry of such a database is displayed in Figure 2. The solvent is identified by means of four fields: 2D structure, solvent name, empirical formula, and molecular weight. Three fields are devoted to the refractive index nD, the f (nD2) function, and the relative permittivity εr. The other fields provide the empirical parameters DI, ES, α1, β1, and ET(30).

solvent gas perfluoro-n-hexane

DI

ES

α1

β1

0.00 0.52

(0.00) 0.00

0.00 0.00

0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.19 0.00 0.17

0.00 0.00 0.00 0.00

0.09 0.14 0.00 0.20 0.00 0.00 0.00 0.07 0.10 0.20 0.04 0.00

0.00 0.00 0.00 0.00 0.11 0.15 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.19 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.19 0.17 0.15 0.14 0.00 0.09 0.00 0.00 0.08 0.00 0.06 0.11 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.18 0.57 0.61 0.69 0.69 0.76 0.78

0.24 0.29 0.46 0.47

0.73 0.71 0.71 0.73

Alkanes 2-methylbutane n-pentane n-hexane n-heptane n-octane n-nonane n-decane n-dodecane cyclohexane cis-decalin

0.68 0.00 0.69 0.00 0.71 0.00 0.73 0.00 0.74 0.00 0.75 0.00 0.76 0.00 0.77 0.00 0.78 0.00 0.85 0.00 Haloalkanes and Haloalkenes tetrachloroethene 0.87 0.05 (E)-1,2-dichloroethene 0.80 0.05 tetrachloromethane 0.82 0.10 bromotrichloromethane 0.87 0.11 (halogen-bond donor) trichloroethene 0.84 0.26 tribromomethane 0.97 0.34 1,1,1-trichloroethane 0.79 0.37 trichloromethane 0.80 0.40 1-bromopropane 0.79 0.42 1-chlorobutane 0.75 0.43 2,2-dichloropropane 0.76 0.50 dibromomethane 0.91 0.53 dichloromethane 0.78 0.60 (Z)-1,2-dichloroethene 0.80 0.61 1,1,2,2-tetrachloroethane 0.86 0.62 1,2-dichloroethane 0.80 0.74 Arenes and Haloarenes 1,3,5-trimethylbenzene 0.87 0.13 p-xylene 0.86 0.14 toluene 0.86 0.20 benzene 0.87 0.23 hexafluorobenzene 0.71 0.24 iodobenzene 0.99 0.36 pentafluorobenzene 0.73 0.37 1,4-difluorobenzene 0.80 0.39 bromobenzene 0.93 0.39 1,3-dichlorobenzene 0.92 0.40 chlorobenzene 0.89 0.41 fluorobenzene 0.83 0.43 1,3-difluorobenzene 0.79 0.45 1,2-dichlorobenzene 0.92 0.49 1,2-difluorobenzene 0.80 0.59 Pyridines pentafluoropyridine 0.73 0.38 quinoline 1.00 0.58 3-bromopyridine 0.94 0.61 2-methylpyridine 0.87 0.52 pyridine 0.88 0.67 4-methylpyridine 0.87 0.61 2,6-dimethylpyridine 0.86 0.42 Water and Alcohols tert-butanol 0.72 0.69 tert-amyl alcohol 0.75 0.49 2-butanol, sec-butanol 0.74 0.73 cyclohexanol 0.82 0.72 E


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The Journal of Physical Chemistry B Table 2. continued solvent

Table 2. continued DI

Water and Alcohols 2-propanol 0.71 1-pentanol 0.76 1-hexanol 0.77 1-butanol 0.74 1-octanol 0.78 1-propanol 0.72 1-decanol 0.79 ethanol 0.69 benzyl alcohol 0.91 diethylene glycol 0.80 methanol 0.64 ethane-1,2-diol, glycol 0.78 2,2,2-trifluoroethanol 0.59 water 0.65 1,1,1,3,3,3-hexafluoro-2-propanol (HFIP) 0.56 Ethers furan 0.77 methoxybenzene, anisole 0.89 ethoxybenzene, phenetole 0.88 1,4-dioxane 0.77 dibenzyl ether 0.93 tetrahydropyran 0.77 diethyl ether 0.68 tetrahydrofuran (THF) 0.75 di-n-butyl ether 0.74 diisopropyl ether 0.70 Ketones acetophenone 0.91 acetone 0.69 cyclopentanone 0.79 2-butanone 0.72 cyclohexanone 0.81 Esters dimethyl carbonate 0.70 methyl formate 0.67 propylene carbonate 0.77 ethyl chloroacetate 0.77 diethyl carbonate 0.72 methyl propanoate 0.71 ethyl benzoate 0.87 methyl hexanoate, methyl caproate 0.75 methyl pentanoate, methyl valerate 0.74 methyl butanoate 0.73 methyl octanoate, methyl caprylate 0.77 methyl acetate 0.69 ethyl acetate 0.71 methyl decanoate, methyl caprate 0.78 Amides and Urea 1-methylpyrrolidin-2-one 0.83 N,N-dimethylacetamide 0.79 N,N-dimethylformamide 0.78 1,1,3,3-tetramethylurea 0.81 pyrrolidin-2-one 0.85 N-methylformamide 0.78 formamide 0.80 Nitriles benzonitrile 0.90 acetonitrile 0.67 n-propanenitrile 0.70 n-butanenitrile 0.72

ES

α1

β1

0.77 0.72 0.68 0.75 0.63 0.77 0.55 0.80 0.67 0.82 0.84 0.84 0.82 0.89 0.76

0.53 0.64 0.65 0.65 0.66 0.68 0.72 0.75 0.79 0.88 1.00 1.05 1.36 1.54 1.86

0.68 0.70 0.72 0.67 0.74 0.65 0.76 0.62 0.50 0.55 0.54 0.47 0.23 0.37 0.16

0.37 0.43 0.40 0.36 0.37 0.37 0.26 0.47 0.15 0.22

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.10 0.23 0.39 0.44 0.46 0.56 0.58 0.58 0.64 0.65

0.68 0.78 0.64 0.74 0.65

0.00 0.04 0.00 0.00 0.00

0.48 0.49 0.53 0.53 0.55

0.56 0.75 1.07 0.57 0.41 0.49 0.49 0.38 0.40 0.45 0.33 0.56 0.51 0.30

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.40 0.40 0.40 0.42 0.45 0.47 0.47 0.50 0.50 0.50 0.51 0.51 0.52 0.61

0.80 0.85 0.87 0.71 0.80 0.90 0.89

0.00 0.00 0.00 0.00 0.44 0.81 0.97

0.76 0.75 0.69 0.75 0.72 0.63 0.45

0.74 0.84 0.91 0.83

0.00 0.23 0.00 0.00

0.34 0.37 0.40 0.42

solvent

DI

Nitroalkanes and Nitroarene nitrobenzene 0.92 nitromethane 0.72 nitroethane 0.73 Amines N,N-dimethylaniline 0.93 aniline 0.96 morpholine 0.81 1,2-diaminoethane 0.82 triethylamine 0.75 tri-n-butylamine 0.78 1-methylpiperidine 0.79 n-butylamine 0.75 piperidine 0.81 Phosphorus Compounds tri-n-butyl phosphate 0.77 hexamethylphosphoric triamide (HMPT) 0.82 triethyl phosphate 0.75 trimethyl phosphate 0.74 Sulfur Compounds carbon disulfide 1.00 tetramethylene sulfoxide 0.89 sulfolane 0.85 dimethyl sulfoxide (DMSO) 0.84

ES

α1

β1

0.72 0.84 0.91

0.00 0.28 0.00

0.26 0.23 0.22

0.39 0.51 0.56 0.68 0.08 0.08 0.11 0.39 0.38

0.00 0.47 0.17 0.11 0.00 0.00 0.00 0.09 0.00

0.34 0.43 0.67 0.91 0.93 0.93 0.93 1.03 1.12

0.57 0.71 0.73 0.90

0.00 0.00 0.00 0.00

0.75 1.00 0.71 0.65

0.11 0.89 0.93 1.00

0.00 0.00 0.00 0.00

0.00 0.74 0.34 0.71

Table 3. Pairwise Determination Coefficients between DI, ES, α1, and β1 (Values from Table SI-1) DI ES α1 β1

DI

ES

α1

β1

1 0.019 0.029 0.016

1 0.132 0.169

1 0.014

1

Figure 2. Screenshot of the solvent database showing the 1,1,1,3,3,3hexafluoro-2-propanol entry.

The addition of a new column in the Excel spreadsheet generates a new field in the ChemOffice database. So any additional information can be easily added (e.g., physical and toxicological properties, sustainability, and other empirical solvent scales). Comparison of the DI, ES, α1, and β1 Scales to the AAKT and Catalán Scales. The degree of similarity (or not) between our parameters and previously published ones can be assessed from their correlations with the corresponding AAKT F


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The same holds for the β1 and β pair (r2 = 0.866 for all solvents but 0.625 for amphiprotic solvents). We believe that β1 quantifies more properly the hydrogen-bond basicity of amphiprotic solvents than SB and β because the solvatomagnetic comparison method used for β1 is free of the shortcomings of the solvatochromic comparison method used for SB and β.17 In particular, the astonishingly almost zero SB value of water (0.025) does not agree with the well-established significant hydrogen-bond basicity of this solvent.2−4,50 2. Prediction of Solvent-Dependent Physicochemical Properties. The usefulness of our parameters to predict solvent effects has been tested for selected examples. Table SI-2 reports 113 correlations involving rate and equilibrium constants as well as positions of absorption in NMR, ESR, IR, and UV/vis spectra. Solubility and partitioning processes are not considered because their prediction requires the introduction of the Hildebrand solubility parameter for solvent/solvent interactions that are not discussed here. The mean of the r2 values is 0.930 and the histogram of Figure 3 shows that most correlations

Table 4. Correlations between DI, ES, α1, and β1 and the AAKT and Catalán Solvent Parameters correlation Catalán

DI vs SP ES vs SdP α1 vs SA β1 vs SB

AAKT

ES vs π* ES vs π* and δ β1 vs β α1 vs α

solvent categories

n

r2

all HBD all all all amphiprotic all all all amphiprotic all

119 31 111 111 103 22 138 138 136 33 143

0.925 0.504 0.906 0.935 0.923 0.758 0.564 0.723 0.866 0.625 0.943

(from the Marcus review)48 and Catalán parameters.20 The results are given in Table 4. A good correlation is found between DI and SP. In spite of this good correlation, the reparameterization of dispersiveinductive effects is justified by the larger number of solvents in the DI scale (323) compared to the SP scale (164) and the easier extension of our scale to new solvents (vide supra). The correlation between ES and SdP is also good (r2 = 0.906) but falls dramatically to r2 = 0.504 for the HBD solvents. Other noteworthy differences are observed for CCl4 (ES = 0.10 but SdP = 0) and CS2 (ES = 0.11 but SdP = 0). The nonzero ES values of these solvents agree with the nonzero quadrupole moment of CS2 and octupole moment of CCl4. The better account of weak solute dipole/solvent quadrupole or octopole electrostatic interactions might be related to the larger solvatochromic shifts measured for the betaine dye 30 (ES probe) than for the nitrofluorenes (SdP probes). As expected, the correlation between ES and π* is very poor since π* describes a blend of dispersion, induction, and electrostatic forces. The addition of the correction term δ improves the correlation that nevertheless remains poor because of the oversimplification of the δ term. The variances of α1 explained by SA and α are 93.5 and 94.3%, respectively. However, noteworthy differences are found between SA and α1 for CH donors such as pyridine (SA = 0.033 but α1 = 0), benzonitrile (SA = 0.047 but α1 = 0), propylene carbonate (SA = 0.106 but α1 = 0), or acetone (SA = 0 but α1 = 0.04), and for NH donors such as morpholine (SA = 0 but α1 = 0.17) or n-butylamine (SA = 0 but α1 = 0.09). It is difficult to assert that α1 = 0 for pyridine, benzonitrile, and propylene carbonate since any compound containing CH groups can, in principle, be regarded as a potential donor of CH hydrogen bonds, but for a number of such compounds the tendency to give a hydrogen bond is so weak that they do not behave as HBD solvents toward ordinary solutes. It is easier to assert that acetone, morpholine, and n-butylamine have nonzero α1 values because there exists chemical evidence for their HBD character.18 Another important ranking difference is found for water and HFIP: HFIP is a slightly worse HBD than water on the SA scale (SA = 1.011 for HFIP and 1.062 for water), but a significantly better HBD on the α1 scale (α1 =1.86 for HFIP and 1.54 for water). The α1 ranking is supported by the much higher solute HBD acidity of HFIP49 and its lower self-association. The correlation between β1 and SB is good (r2 = 0.923) when all solvents are considered but falls severely to 0.758 for the amphiprotic solvents (e.g., water and alcohols).

Figure 3. Distribution of the r2 values (range 0.70−1.00 divided in 6 intervals) for the correlations of 113 physicochemical properties with the parameters DI, ES, α1, and β1 (data from Table SI-2).

Figure 4. Logarithm of solvolysis rate constants k (s−1) for 4-methoxyneophyltosylate at 75 °C against parameters DI, ES, and α1, r2 = 0.996; n = 12.

are excellent or good. Figure 4 illustrates an excellent correlation for the first-order rate constant of the solvolysis of 4-methoxyneophyltosylate. This reaction was formerly used to describe the “ionizing power” of solvents.51 Our analysis shows that this “ionizing power” is a blend of hydrogen-bond donation G


Article


Table 5. Results of Correlations with Eq 17 for Physicochemical Properties Dependent on the Lewis Basicity of Solvents Lewis acid

property A

ref

n

r2

solvents obeying eq 17

I2 Br2 IBr SbCl5 SbCl5 Cu(tmen)(acac)+a TCNEb

stretching frequency stretching frequency stretching frequency complexation enthalpy with THF complexation enthalpy with Oct3PO electronic transition energy log k of Ph2CN2 + TCNE

52 52 52 53 53 54 55

11 10 9 5 5 19 18

0.945 0.915 0.978 0.947 0.853 0.853 0.924

all the samplesc except π bases all the samplesc except π bases all the samplesc except π bases all the samplesd all the samplese all the samplesf mostg except π bases and acyclic ethers

a Cation of the acetylacetonato-N,N,N′,N′-tetramethylethylenediaminocopper(II)perchlorate coordination compound. bTetracyanoethene. cGas phase, nitro bases, nitriles, ethers, alcohols, and water. dBenzene, butyl acetate, nitrobenzene, CCl4, and 1,2-dichloroethane. eBenzene, nitrobenzene, butyl acetate, acetone, and 1,2-dichloroethane. fNitro bases, carbonyl bases, acetonitrile, THF, alcohols, HMPT, pyridine, and piperidine. gEsters, cyclic ethers, nitriles, nitro bases, trichloromethane, dichloromethane, 1,1-dichloroethane, and 1,2-dichloroethane.

n = 31) significantly increased compared to r2 = 0.790 for the correlation without the indicator variable.

(50%, p < 0.0001), electrostatic interactions (37%, p < 0.0001), and dispersion and induction (13%, p = 0.0003). We have also studied whether the hydrogen-bond basicity parameter β1 can predict solvent effects in which Lewis acid/base interactions other than hydrogen bonding occur. To check the validity (or not) of this assumption, we have collected literature data on the effect of solvents on a number of physicochemical properties of various Lewis acids (halogen-bond donors, covalent metal halide, metal cation, and π acceptor)27 and have correlated these properties with β1 through eq 17: A = A 0 + bβ1

ν(OH)/cm−1 = 3654 − 285β1 − 175ξ

(18)

3. Rationalization of Solvent-Dependent Physicochemical Properties. This section illustrates how our solvent parameters may be used to rationalize the multiple solute/ solvent interactions influencing physicochemical properties. The selected property is the equilibrium constant K, transformed into the Gibbs energy ΔG° using ΔG° = −RT ln K, and the equilibria studied are the conformational and tautomeric equilibria represented in Scheme 2. Indeed, a change of solvent or a change from the gas phase to solution can considerably affect these equilibria.2 In addition to the determination coefficient, the statistics discussed here are the regression coefficients (sign and magnitude of the standardized coefficients) of ΔG° = ΔG°o + di DI + eES + aα1 + bβ1. Whether the obtained regression coefficients are chemically meaningful will be studied by means of quantum-chemical calculations (summary of results in Table SI-5), for each conformer or tautomer, of the dipole moment, of the HB basicity (through the interaction energy with a water molecule as a reference HBD), or of the HB acidity (through the interaction energy with a DMSO molecule as a reference HBA). For example, negative e, a, and b regression coefficients (i.e., shift of the equilibrium to the right side by solvents with increasing ES, α1, and β1 values since ΔG° values become less positive or more negative) must correspond to a larger dipole moment, a stronger HB basicity, and a stronger HB acidity for the right-side species than for the left-side one, respectively. For these equilibria, it must be noticed that, because both conformers (tautomers) have almost the same polarizability, dispersion interactions will tend to cancel, so that the di coefficients mainly correspond to induction effects (solute permanent dipole/solvent-induced dipole). Axial−Equatorial Equilibrium (1) of 2-Chlorocyclohexanone.57,58 ΔG° values have been obtained in 13 solvents. Their correlation with ES

(17)

The results are given in Table 5. Excellent to satisfactory determination coefficients (0.853 ≤ r2 ≤ 0.978) are found for these correlations. This indicates that, at least for oxygen and nitrogen bases (the most common basic solvents), the β1 scale is a reasonably general Lewis basicity scale of solvents. Finally, we give an example of the usefulness of the ξ parameter in the prediction of solvent basicity-dependent properties. A family dependent relationship with β1 is provided by the OH stretching vibration of methanol.56 A plot of the wavenumber of this vibration in a series of 31 HBA solvents against β1 is linear, except for the families of pyridines and amines (Figure 5). These eight solvents can only fit the good

ΔG°/kJ mol−1 = 3.71 − 6.53ES Figure 5. Family dependent relationship between the OH stretching wavenumber of methanol and β1 in 31 HBA solvents. Pyridines and amines (triangles) fall below the line of other families (circles).

(19) 2

yields an excellent determination coefficient (r = 0.974) and a negative regression coefficient showing that the equilibrium is shifted toward the equatorial conformer in the most electrostatic solvents. Indeed, calculations show that this conformer has a larger dipole moment (4.72 D) than the axial conformer (3.36 D). There is no statistically significant improvement by adding either DI (p = 0.13) or α1 (p = 0.20) to eq 19. The absence of influence of hydrogen bonding is confirmed by the

correlation of other solvents (r2 = 0.932, n = 23) if an indicator variable is assigned to them. If pyridines and amines are assigned ξ = 0.80 and other solvents (mainly oxygen bases) ξ = 0, eq 18 results with a determination coefficient (r2 = 0.978, H


Article

The Journal of Physical Chemistry B Scheme 2. Conformational and Tautomeric Equilibriaa

electrostatic forces displace the equilibrium toward the ee conformer. Indeed, calculations yield a larger dipole moment for this conformer (4.75 D) than for the aa one (3.38 D). A significant contribution (27%, calculated from standardized regression coefficients) of the DI parameter can now be observed with a negative regression coefficient. It means that induction forces work in synergy with electrostatic forces. The adage that, in conformational equilibria, the conformer with greater dipole moment is favored in polar solvents, must therefore be completed: it is favored in polar and polarizable solvents. Axial−Equatorial Equilibrium (3) of 2-Isopropyl-5-methoxy1,3-dioxane.60 For 15 solvents, the correlation is satisfactory (r2 = 0.884) and the equation of the multiple regression is ΔG°/kJ mol−1 = − 8.14 + 5.09DI + 4.52ES + 1.41α1

(21)

The three positive regressions coefficients show that induction forces, electrostatic interactions, and solute HBA/ solvent HBD hydrogen bonding shift together the equilibrium toward the axial conformer, with contributions in the order: electrostatic (62%) > induction (21%) ≈ hydrogen bonding (17%). Indeed, calculations show that this axial conformer has the larger dipole moment (2.58 D compared to 1.42 D) and is the better HBA (interaction energy between a water molecule and the methoxy oxygen of −34.2 kJ mol−1 for the axial and −27.7 kJ mol−1 for the equatorial conformers; for a ring oxygen, −25.1 kJ mol−1 for the axial and −22.9 kJ mol−1 for the equatorial conformer). Gauche−Trans Equilibrium (4) of 1,1,2-Trichloroethane.61 For 22 solvents the regression equation is ΔG°/kJ mol−1 = 3.81 − 1.59DI − 2.53ES − 1.33β1

with r2 = 0.955. The three negative regression coefficients show that induction forces, electrostatic forces, and solute HBD/solvent HBA hydrogen bonding favor the trans conformer in the order of importance: electrostatic (63%) > hydrogen bonding (28%) > induction (9%). They also indicate that the trans conformer has a higher dipole moment and is a better C−H HBD. Indeed calculations yield μ (trans) = 2.75 D and μ (gauche) = 1.30 D and the interaction energy between the C1−H group of 1,1,2-trichloroethane and DMSO (as an example of HBA molecule) is more negative for the trans conformer than for the gauche conformer (see Table SI-5). Keto−Enol Tautomerism (5) of 9-Anthracenone.62 For 14 solvents, the regression equation is

a Equilibrium constants are defined as the ratio of concentrations K = [right-side species]/[left-side species]; i.e., K = [e]/[a] for the example of system 1. The temperature of measurements is 25 °C (30 °C for system 4)

calculation of the interaction energies of each conformer with a water molecule: these energies are found nearly equal (−27.5 and −28.8 kJ mol−1). However, the absence of influence of induction forces is surprising since they tend to accompany electrostatic forces. This absence is probably an artifact originating in the limited range of DI values in the sample of solvents (0.20, to be compared to 1.00 for ES values). Diaxial-Diequatorial Equilibrium (2) of trans-2-Chloro-5methylcyclohexanone.59 For 25 solvents, the correlation with DI and ES ΔG°/kJ mol−1 = 3.87 − 11.92DI − 8.00ES

(22)

ΔG°/kJ mol−1 = 18.82 − 6.60ES + 4.83α1 − 19.33β1

(23)

2

with r = 0.918. The signs of regression coefficients show that solute HBD/solvent HBA interactions and electrostatic interactions favor the enol form, whereas solute HBA/solvent HBD interactions favor the keto form. The main factor (49%) influencing the equilibrium is the hydrogen bonding of the enol with HBA solvents. Hydrogen-bond donation of HBD solvents is shown to favor the keto form; this is confirmed by a negative computed interaction energy with a water molecule larger for the keto form (−28.4 kJ mol−1) than for the enol form (−19.2 kJ mol−1). The negative sign of the ES coefficient agrees with dipole moment calculations if the dipole moment of the keto form (3.75 D) is compared to that of the hydrogen-bonded enol form (4.79 D for the complex with DMSO as an example). Diketo-Keto−Enol Tautomerism (6) of 5,5-Dimethylcyclohexane-1,3-dione.62−64 The correlation is excellent for

(20)

2

is fair (r = 0.846). In spite of the presence of water, methanol, ethanol, and 2-propanol in the sample of solvents, the addition of the α1 parameter to eq 20 does not improve significantly (p = 0.55) the correlation. This can again be explained by the close calculated interaction energies between a water molecule and each conformer (−27.8 and −29.4 kJ mol−1). The regression coefficient of the ES parameter is negative and shows that I


Article

The Journal of Physical Chemistry B this reaction studied in 15 solvents (r2 = 0.984). The regression coefficients of eq 24

stratégique, respectively. A.C. thanks the ERC (Marches278845) for his postdoctoral grant. This research used resources of the GENCI-CINES/IDRIS, of the CCIPL, and of a local Troy cluster.

ΔG°/kJ mol−1 = 21.25 − 12.85DI − 5.23ES − 5.23α1 − 25.30β1

■

(24)

show that solute HBD/solvent HBA hydrogen bonding (57%), solute HBA/solvent HBD hydrogen bonding (21%), electrostatic interactions (13%), and induction forces (9%) all stabilize the keto−enol form preferentially. These predictions are supported by calculations since (i) the negative interaction energy with a water molecule is larger for the keto−enol form (−32.5 kJ mol−1) than for the diketo form (−26.5 kJ mol−1) and (ii) the dipole moment of the keto−enol form (5.88 D) is larger than that of the diketo form (4.00 D).

(1) Wypych, G., Ed. Handbook of Solvents; 2nd ed.; ChemTec Publishing: Toronto, Canada, 2014; Vol. 1 (Properties). (2) Reichardt, C.; Welton, T. Solvents and Solvent Effects in Organic Chemistry; 4th ed., Wiley-VCH: Weinheim, Germany, 2011. (3) Buncel, E.; Stairs, R.; Wilson, H. The Role of the Solvent in Chemical Reactions; Oxford University Press: Oxford, U.K., 2003. (4) Marcus, Y. The Properties of Solvents; Wiley: Chichester, U.K., 1998. (5) Abboud, J.-L. M.; Notario, R. Critical Compilation of Scales of Solvent Parameters. Part I. Pure, Non-Hydrogen Bond Donor Solvents. Pure Appl. Chem. 1999, 71, 645−718. (6) Katritzky, A. R.; Fara, D. C.; Yang, H.; Tämm, K.; Tamm, T.; Karelson, M. Quantitative Measures of Solvent Polarity. Chem. Rev. 2004, 104, 175−198. (7) Machado, V. G.; Stock, R. I.; Reichardt, C. Pyridinium NPhenolate Betaine Dyes. Chem. Rev. 2014, 114, 10429−10475. (8) Kamlet, M. J.; Abboud, J.-L. M.; Abraham, M. H.; Taft, R. W. 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. J. Org. Chem. 1983, 48, 2877−2887. (9) Stairs, R. A.; Buncel, E. Principal Component Analysis of Solvent Effects on Equilibria and Kinetics − A Hemisphere Model. Can. J. Chem. 2006, 84, 1580−1591. (10) Chastrette, M.; Rajzmann, M.; Chanon, M.; Purcell, K. F. Approach to a General Classification of Solvents Using a Multivariate Statistical Treatment of Quantitative Solvent Parameters. J. Am. Chem. Soc. 1985, 107, 1−11. (11) Tomasi, J.; Mennucci, B.; Cammi, R. Quantum Mechanical Continuum Solvation Models. Chem. Rev. 2005, 105, 2999−3094. (12) Catalán, J. On the π* Solvent Scale. J. Org. Chem. 1995, 60, 8315−8317. (13) Abe, T. Improvements of the Empirical π* Solvent Polarity Scale. Bull. Chem. Soc. Jpn. 1990, 63, 2328−2338. (14) Sjöström, M.; Wold, S. Statistical Analysis of Solvatochromic Shift Data. J. Chem. Soc., Perkin Trans. 2 1981, 104−109. (15) Laurence, C.; Nicolet, P.; Luçon, M.; Reichardt, C. Polarité et Acidité des Solvants. II. Polarité des Solvants Aromatiques. Bull. Soc. Chim. Fr. 1987, 1001−1005. (16) Laurence, C.; Nicolet, P.; Luçon, M.; Dalati, T.; Reichardt, C. Polarity and Acidity of Solvents. Part 3. Polarity of Non-aromatic Polychloro-substituted Solvents. J. Chem. Soc., Perkin Trans. 2 1989, 873−876. (17) Laurence, C.; Legros, J.; Nicolet, P.; Vuluga, D.; Chantzis, A.; Jacquemin, D. Solvatomagnetic Comparison Method: A Proper Quantification of Solvent Hydrogen-Bond Basicity. J. Phys. Chem. B 2014, 118, 7594−7608. (18) Cerón-Carrasco, J. P.; Jacquemin, D.; Laurence, C.; Planchat, A.; Reichardt, C.; Sraïdi, K. Determination of a Solvent Hydrogen-Bond Acidity Scale by Means of the Solvatochromism of Pyridinium-NPhenolate Betaine Dye 30 and PCM-TD-DFT Calculations. J. Phys. Chem. B 2014, 118, 4605−4614. (19) Laurence, C.; Nicolet, P.; Dalati, M. T.; Abboud, J.-L. M.; Notario, R. The Empirical Treatment of Solvent-Solute Interactions: 15 Years of π*. J. Phys. Chem. 1994, 98, 5807−5816. (20) Catalán, J. Toward a Generalized Treatment of the Solvent Effect Based on Four Empirical Scales: Dipolarity (SdP, a New Scale), Polarizability (SP), Acidity (SA), and Basicity (SB) of the Medium. J. Phys. Chem. B 2009, 113, 5951−5960. (21) Catalán, J.; Hopf, H. Empirical Treatment of the Inductive and Dispersive Components of Solute-Solvent Interactions: the Solvent Polarizability (SP) Scale. Eur. J. Org. Chem. 2004, 4694−4702.

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CONCLUSIONS The new DI, ES, α1, and β1 parameters predict satisfactorily the solvent effect on many physicochemical properties through the LSER of eq 3. They also help to rationalize the multiple solute/solvent interactions influencing these properties. Our parameters present three main advantages over previous ones. First, they have been determined for the most comprehensive set of solvents reported to date. Second, they are based on single, well-understood, and solvent-sensitive definition processes (e. g., the outstanding solvatochromism of the betaine dye 30), an advantage over the π*, δ, α, and β parameters for which there is no clear knowledge of the processes used for their definition. Third, the extension of the DI, ES, α1, and β1 scales to newly designed solvents requires the use of only three probes, betaine dye 30 for ES and α1, and 4-fluorophenol and 4-fluoroanisole for β1; moreover, these probes are readily available. These are advantages over the SP, SdP, SA, and SB parameters, the determination of which requires the use of eight probes not all readily available.

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ASSOCIATED CONTENT

S Supporting Information *

Tables SI-1 (refractive index, relative permittivity, ET(30), DI, ES, α1, and β1 values for about 300 solvents), SI-2 (correlation of 113 physicochemical properties with solvent parameters DI, ES, α1, and β1), SI-3 (new PCM-TD-DFT calculations of α1 values), SI-4 (new 19F NMR measurements of β1 values), SI-5 (quantum-mechanical calculations of properties of conformers and tautomers of Scheme 2), and SI-6 (experimental and predicted ΔG° values for conformational and tautomeric equilibria of Scheme 2) and Figures SI-1 (histogram of DI values) and SI-2 (histogram of ES values). This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*(C.L) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS J.L. is grateful to Labex SynOrg (ANR-11-LABX-0029) and the Région Haute-Normandie for financial support. D.J. acknowledges the European Research Council (ERC) and the Région des Pays de Loire for financial support in the framework of starting grants (Marches-278845) and a recrutement sur poste J


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