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Nonlinear Polarization of Solvatochromic Betaine 30 Indrek Renge* Institute of Physics, UniVersity of Tartu, 142 Riia Street, EE51014 Tartu, Estonia ReceiVed: March 4, 2010; ReVised Manuscript ReceiVed: April 26, 2010
Evidence is presented that solvatochromism of 2,6-diphenyl-4-(2,4,6-triphenylpyridinio)-phenolate (Reichardt’s dye or Betaine 30) results not only from a large reduction of dipole moment and hydrogen bonding, but also from the modulation of mesomeric effect. The polarizability change between the ground and the excited state, estimated from the refractive index (n) dependence of absorption energy ET(30), increases from 20 to ∼150 Å3 on going from apolar to highly polar media. The dependence of ET(30) on dielectric permittivity () could be linearized using an empirical function of susceptibility difference ( - n2), but not in terms of conventional expressions written as φ() - φ(n2). As a result of solvent-induced change in ionicity and bond alternation, the dipole moments and polarizabilities of the chromophore cannot be treated as invariables. Hypsochromic shifts caused by solvent quadrupoles and bond dipoles were quantified. 1. Introduction The resonance theory states that in many cases, for example, carbonate anion or benzene, the chemical structure must be depicted as a superposition of several canonical formulas. Donor-acceptor substituted polyenic chromophores can be rationalized as a hybrid of neutral and zwitterionic forms
D-(CHdCH-)nCHdA T D+d(CH-CHd)nCH-A(1) It was proposed a long time ago that change in the relative weights of limiting structures can be the cause of solvatochromism1 (see also discussions in refs 2-7). This conjecture was soon abandoned in favor of Onsager theory that enabled calculations in terms macroscopic dielectric properties of solvents and dipole moments and polarizabilities of solutes.2,3,8-14 Consideration of solvent shift as a difference in the stabilization energies of states, involved in the optical transition, simplified the problem, constituting a paradigmatic change. Occasional agreement between the dipole moment values, obtained on the basis of Onsager model, and those derived from electrochromism in external fields12 has led to an opinion that solvatochromism is, in principle, well understood. Regrettably, a large scatter of data often rendered the continuous dielectric approach impractical. Hydrogen bonding between the solute and solvent molecules has been recognized as the main cause of deviations.15,16 Both specific and nonspecific interactions were formally incorporated into multiparameter regressions15 that were subject to further elaborations, bringing, however, little advancement.17-19 More recently, the solvent tuning of mesomerism has attracted new interest in the studies of nonlinear properties of push-pull chromophores.7,20 Bond length alternation under the influence of substitution patterns and externally applied electric field was assessed for several donor-acceptor polyenes.21 Dramatic change in the electrochromic behavior as a function of solvent polarity has been observed.7,22,23 A useful diagnostic feature pointing to a quinoid-benzenoid structural change is the distor* To whom correspondence should be addressed. Phone: +3727-374716. Fax: +3727-383033. E-mail:
[email protected].
tion of Franck-Condon envelopes of spectra, extending beyond the overall shift and (symmetrical) broadening.5-7,20,24 The empirical polarity scale basing on the absorption maxima of Dimroth-Reichardt’s zwitterionic betaines is notoriously poorly correlated to dielectric functions.25 Nevertheless, the ET(30) scale (peak energy of Betaine 30 at 25 °C in kcal/mol units) often describes the chemical properties of solvents better than the expressions containing bulk dielectric constant and refractive index n.26 Notwithstanding, such relationships, and, as a matter of fact, the polarity concept itself,26,27 remain obscure, until the mechanisms of nonspecific and specific solvation are disclosed. The hydrogen bonding interactions are quite succinctly restricted to molecules carrying >N-H and -O-H fragments. Further, if aprotic solute and solvent particles are represented as polarizable dipoles, four types of nonspecific solvation may be discerned. The dispersion, dipole-induced-dipole (two cases) and dipole-dipole interactions possess characteristic n and dependencies.8-14,28-30 In the condensed phase the approximation of molecules as point dipoles is rather crude, and ought to be adjusted by considering quadrupole and bond dipole moments, giving rise to additional reaction fields. Peak maxima of Betaine 30, reported by C. Reichardt for more than 350 liquids,26 provide an excellent testing ground for solvent shift theories. Quite extensive theoretical work has not yet lead to a coherent understanding of the ET(30) polarity scale.31-44 Major blue shifts, caused by electrostatic interactions and hydrogen bonding are reproduced well, in general,31,32,34-36,39,41-44 but the role of dispersive-repulsive potential32,33,36,39 and solvent driven geometry change in this flexible molecule35-37,39-44 remain controversial. The extinction coefficient of Betaine 30 decreases by a factor of 6, on going from dioxane to polar glycol (12 300 and 2040 M-1cm-1, Table 5 in ref 25), indicating a possible structure change. Remarkably, mesomeric effect was mentioned in connection with solvatochromism in this paper (p 7 in ref 25). The present quest to the dependence of ET(30) on optical and static susceptibilities was undertaken, since serious inconsistencies have been exposed in the applications of both dielectric theory29 and computer chemistry.33,36 First, apolar solvents obeying the Maxwell relation ( ) n2) are considered, and
10.1021/jp101953r 2010 American Chemical Society Published on Web 05/07/2010
Nonlinear Polarization of Solvatochromic Betaine 30
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Figure 1. Refractive index dependence of absorption maxima of Betaine 30 in apolar solvents ( e 1.15n2); filled circles - alkanes (2: iso-pentane, 3: n-pentane, 11: n-dodecane, 12: cyclohexane, 14: cisdecaline); asterisks - arenes (55: benzene, 63: 1-methylnaphthalene, 67: 1,4-difluorobenzene, 68: 1,3,5-trifluorobenzene, 70: hexafluorobenzene); open circles - other apolar solvents (1: tetramethylsilane, 23: CCl4, 225: dioxane, 329: CS2); and in highly polar aprotic solvents ( > 25) - filled squares (269: propylene carbonate, 299: acetonitrile, 303: acrylonitrile, 306: benzonitrile, 307: nitromethane, 310: nitrobenzene, 330: DMSO). Numbers correspond to Table 2 in ref 26.
microscopic polarity of molecules, other than alkanes, is specified. Strong refractive index dependence was ascertained for highly polar solvents, in contrast to apolar media.30 For proper characterization of internal Stark effect in a dipolar reaction field, explicit correction for polarizability was introduced. Data fitting was considerably improved by using difference susceptibility - n2, as compared to usual expressions, written as φ() - φ(n2), that are also of doubtful theoretical validity.29,45-47 2. Results and Discussion 2.1. Refractive Index Dependence. Solvents with negligible contribution of permanent dipoles to dielectric permittivity are selected according to a criterion e 1.15n2. The solvent polarizability effect is a superposition of dispersive ∆νdisp and induction ∆νind shifts, approximately expressed as28-30
∆νdisp[cm-1] ) -5.5 × 104∆RMw-1φ(n2)
(2)
∆νind[cm-1] ) 6.3 × 103(µ2g - µ2e )Mw-1φ(n2)
(3)
where polarizability difference ∆R is in Å3 units, dipole moments of the ground and the excited state µg and µe are in Debye (1 D ) 3.336 × 10-30 Cm), the molecular weight Mw was used for cavity volume,48 and φ(n2) is the Lorenz-Lorentz function φ(n2)(φ(n2) ) (n2 - 1)/(n2 + 2)). Figure 1 shows the band maxima of Betaine 30, ET(30), plotted versus φ(n2). Usually excellent linear dependencies are obtained, especially for n-alkanes, extrapolating to transition energy of the free chromophore in vacuum ν048,49
ν ) ν0 + pφ(n2)
(4)
The 2,6-diphenyl-4-(2,4,6-triphenylpyridinio)-phenolate is poorly soluble in less polar media, so the ET(30) values have been obtained from a correlation to maxima of a lipophilic pentakis-tert-butyl derivative.26,50,51 Solvents are designated by numbers according to Table 2 in Reichardt’s review.26 No
Figure 2. Corrected (eq 6) absorption maxima of Betaine 30 in aprotic polar solvents plotted vs the dipolarity function (eq 7) (circles - aliphatic and some olefinic solvents (233: 1,1,1-trichloroacetone); asterisks aromatic solvents; filled circles - aliphatic monofunctional solvents).
systematic influence of solvent polarizability (p ∼ 0 cm-1) can be detected within sets of aliphatic hydrocarbons (including cyclohexane (No. 12) and cis-decaline (No. 14)), aromatic hydrocarbons (including fluoroarenes (Nos. 67, 68, and 70), and other solvents (halogenated compounds, as well as Si(CH3)4 (No. 1), dioxane (No. 225), and CS2 (No. 329)). The insensitivity of solvatochromic probe to solvent polarizability is a result of mutual cancellation of dispersive and inductive shifts, similar to the n-π* transition in acetone.29 Dipole moments, measured in dioxane (µg ) 14.8 D, µe ) 6 D)12 yield the slope component due to induction, equal to 2100 cm-1 (eq 3, Mw ) 551.7). One can estimate the polarizability change of ∆R ) 20 Å3 from the opposite slope of eq 2, -2100 cm-1. By contrast, a large red shift with increasing φ(n2) is evident in solvents with > 25 (p ) -14000 ( 4000 cm-1, correlation coefficient R ) 0.61, 20 solvents), despite of considerable scatter of data (Figure 1). From this slope a huge polarizability change (∆R ) 150 ( 40 Å3) can be deduced.30 This controversy reveals that in the reaction field the electronic structure change must extend beyond linear polarization. The evolution of bond alternation as a function of electric field strength has been calculated for donor-acceptor substituted polyenes (see Figure 12 in ref 21). The bonds in different merocyanines are rendered equal at externally applied fields of 6 × 109 Vm-1 to 9 × 109 Vm-1.21 In even higher fields, a charge-separated, zwitterionic structure is formed (Scheme 1). On the other hand, the Onsager formula for reaction field (eq 4.31 in ref 52) yields the value of ∼4 × 109 Vm-1 in neat polar solvents, such as acetone and nitrobenzene, that is of the same order of magnitude. The reaction field created by Betaine 30 molecule in these liquids should not be very different, because the larger volume of solute is compensated by its bigger dipole moment. The correlation of polarizability difference ∆R with bond order was investigated by Bublitz et al.,22,23 basing on results of ref 21. In already zwitterionic structure, a small increase in the degree of ionicity can produce a remarkable change of ∆R from zero to large positive values. At the same time, the dipole moment difference ∆µ remains constant (see Figure 2 in ref 22 or Figure 8 in ref 23). Consequently, the reaction field can indeed account for the observed variation of refractive index dependencies in polar and apolar media. Reasons of hypsochromism in apolar media other than alkanes (Figure 1) become apparent, if we consider quadrupole moments, Q, or in more general terms, charge distributions in solvent molecules.53 The predominant role of Q (equal to an
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effective axial quadrupole moment , as calculated in ref 53) in causing an average blue shift in aromatic media of ∼1000 cm-1 can be confirmed by comparing Q with ET(30) for benzene (No. 55) (Q ) 8.4 DÅ, ET(30) ) 34.3 kcal/mol) or hexafluorobenzene (No. 70) (9.4 DÅ, 34.2 kcal/mol) to 1,3,5-trifluorobenzene (No. 68) (0.5 DÅ, 33.2 kcal/mol). Negligible quadrupole of the latter is responsible for a decrease of ET(30) by 1 kcal/mol (350 cm-1). As expected, two opposing bond dipoles in 1,4-difluorobenzene (No. 67) give rise to a large quadrupole and a corresponding blue shift (Q ) 13.3 DÅ, 36.4 kcal/mol), similar to that in 1,4-dioxane (No. 225) (Q ) 11.7 DÅ, 36.0 kcal/mol). Bond dipoles and higher multipole moments can produce small additional hypsochromism relative to nalkanes (ET(30) ) 31.0 kcal/mol), for example, in CCl4 (No. 23) with ET(30) ) 32.4 kcal/mol. It is obvious from the previous discussion that ET(30) provides a sensitive probe to microscopic polarity, since hypsochromic shifts with respect to alkanes up to 2000 cm-1 occur even in solvents obeying the Maxwell’s relation ) n2. 2.2. The (Di)polarity Dependence. The upshift of ET(30) by more than 10 kcal/mol in polar aprotic solvents (Figure 1) is a result of Stark effect in the reaction field. As expected, the influence of molecular dipole density, or equivalent static dielectric constant ,15,54-56 is much more pronounced than that of bond dipoles. At first, the dispersion and polarization shifts (eqs 2 and 3), depending on the high-frequency susceptibility (n2 - 1) must be separated from the measured frequency, ν, by using the slope of eq 429,30
ν′ ) ν + pφ(n2)
(5)
The procedure is less straightforward in the case of Betaine 30, as the slope p is a function of . In polar liquids with > 25 the effect of φ(n2) is very strong, whereas in alkanes there is no influence at all (see above). For ranging between 5 and 7 (15 solvents), and 7 and 10 (27 solvents), smaller absolute p values were obtained (-3600 ( 2000 and -3000 ( 3000 cm-1, respectively). In spite of large scatter of data, the following expression with an average p ) -7000 cm-1 is appropriate for a rough correction
ν′ ) ν + pφ(n2)( - 1)/( + 2)
(6)
The corrected frequency ν′ is plotted versus the function φ() - φ(n2) (φ() ) ( - 1)/( + 2)) (Figure 2)29
ν′ ) ν0 + y[φ() - φ(n )] 2
(7)
The dependence shows a clear upward curvature for 92 nonaromatic polar solvents. The deviation is even more conspicuous for a set of 42 monofunctional liquids. These include molecules with a single bond dipole, such as (mono)halogenides and nitriles (C-H dipoles are ignored), or bond dipoles centered at a single atom (ethers, ketones, esters, amides, nitroalkanes, and DMSO), but omit oligohalogenides (e.g., CH2Cl2), as C-H acidic and electron accepting. Such solvents, containing either a short linear alkyl chain up to C4 or an aliphatic cycle form a homogeneous set, well-performing in terms of point dipole/dielectric continuum models. Long alkyl chains are prone to enrichment/exclusion phenomena, whereas branched ones create empty space, so these are not included.
Figure 3. Linear dependence of corrected Betaine 30 absorption maxima in aprotic polar solvents on empirical static susceptibility function (eq 8, c ) 7) (circles - aliphatic and some olefinic solvents; asterisks - aromatic solvents; filled circles - aliphatic monofunctional solvents). Linear regressions: dashed line - for all aprotic polar solvents (aliphatic and aromatic); solid line - for monofunctional solvents.
“Good” solvents display smaller blue shifts for a given permittivity value (filled circles in Figure 2). In general, solvents carrying several bond dipoles appear more polar locally to optical probe molecule than expected on the basis of bulk that depends on the vector sum of (noncollinear) group moments. The plots of band maxima versus φ() - φ(n2) are usually linear for most electronic transitions,29,30,54,57 and the curvature is an anomaly pointing to a nonlinear polarization of Betaine 30 chromophore. It must be noted that the nonlinearity of plots (Figure 2) is by no means affected by the two corrections for φ(n2), introduced in eqs 6 and 7. A straightforward (unphysical) correlation between ET(30) and ( - 1)/( + c) is also curved for c ) 2, and a linear fit is possible with c ) 4.4 (91 nonaromatic polar liquids) or c ) 6.6 (subset of 42 wellbehaving solvents) (not shown). Expressions in the form of eq 7 do actually not follow from Onsager theory29,45-47 (see discussion in ref 29), although claimed otherwise by McRae,8 and Bakhshiev,9,11 who cites his obsolete Ph.D. thesis.9 The partition of optical and static permittivity appears first in Ooshika’s paper2 and is later accepted without criticism by most workers.3,8-11,13,14,36,53,57 Perhaps, it would be more appropriate to build an empirical relationship between corrected band maxima ν′ and the difference between the static and optical susceptibilities (( - 1) (n2 - 1)), equal to - n2.29 The dependence of ν′ on - n2 approaches a plateau (not shown), so it can be linearized with the aid of a function
ν′ ) ν0′ + y′[( - n2)/( - n2 + c)]
(8)
Linear fitting is obtained for all polar liquids (except for 1,1,1trichloroacetone, No. 233, a C-H acid) with c ) 7 (y′ ) 5190 ( 200 cm-1, R ) 0.914, N ) 133) (dashed line in Figure 3). The correlation is even better for monofunctional solvents (y′ ) 6330 ( 270 cm-1, R ) 0.965, N ) 42) (solid line in Figure 3). Further, if we remove slightly H-bonding formates (Nos. 253 and 254), excellent linear fit with R ) 0.977 can be obtained at c ) 10.6 (40 solvents). As compared to eq 7, eq 8 affords an improved fitting for spectral shift data, apart from the theoretical invalidity of the former. The adjustable parameter c in eq 8 has no direct physical meaning. In Onsager’s theory of reaction field, c depends on the ratio of polarizability to radius a cubed R/a3.52 The function with c equal to 1/2 in eq 7 (usually written as ( - 1)/(2 + 1))
Nonlinear Polarization of Solvatochromic Betaine 30 is a poor choice, because it corresponds to a nonpolarizable point dipole model (R/a3 ) 0), whereas other widely applied values of c ) 1 and c ) 2 follow from more realistic R/a3 equal to 1/4 and 1/2, respectively. In general reaction field expression for neat solvents (eq 4.31 in ref 52), where the contributions of and n2 cannot be separated, the Lorenz-Lorentz equality R/a3 ) (n2 - 1)/(n2 + 2) is applied. 2.3. Calculations of ET(30). At the present stage of development, the computer-based modeling work should maintain close contact with semiquantitative, empirical treatment of experimental data, such as that exemplified previously. Dipolar solvation32,33,36,42,43 and hydrogen bonding,31,32,36,42,43 each contributing ultimately 10-15 kcal/mol, are generally well reproduced in most calculations. The phenomena exposed by Figure 1, such as the shifts in aromatic and other quadrupolar media, and a strong solvent polarizability dependence in highly polar environments can be more challenging. Remarkably, a shift of 3 kcal/mol in benzene and toluene was correctly obtained by Perng et al.32 In the work by Mente and Maroncelli,36 basing on ref 32 and using Monte Carlo simulations in addition, only several aprotic solvents were treated, and unfortunately, the dioxane effect (5 kcal/mol) was not included. Thus, the extra blue shifts in solvents carrying several group dipoles, compared to a monofunctional set, as shown in Figure 3, should be within the reach of computations. The largest set of ∼60 solvents (excluding dioxane) was analyzed by Matyushov et al.33 from the point of view of induction, dispersion, and dipole-dipole forces. The induction component (e.g., 1.05, 1.3, and 1.39 kcal/mol for C5, CCl4, and benzene, respectively) is refractive index dependent, as expected, and of the same magnitude as predicted by eq 3 (1.45 kcal/mol for n ) 1.4). On the other hand, the dispersive term shows no correlation to φ(n2), in particular, for alkanes, CCl4, and benzene. This is surprising, since eq 2 works very well empirically.48,49 In a set of normal alkanes, the Lorenz-Lorentz function grows by a factor of 1.16 on going from C5 to C12, whereas the dispersive component increases from -4.4 to -7.6 kcal/mol, or 1.73 times (Table 2 in ref 33). The reason of such discrepancy is that eq 2 ignores the contraction of solute-solvent interaction radius with increasing cohesion energy, which is roughly correlated with internal pressure, molecular weight, or boiling point. Indeed, a slight curvature is sometimes detected in n-alkanes,58 but the extrapolation to the solvent-free state is nearly perfect nevertheless.49 On the other hand, the model used by Matyushov et al.33 seems to overestimate gravely the influence of “internal pressure” on dispersive stabilization. We believe that explicit incorporation of φ(n2) dependence, and as a next approximation, the polarizability densities of solvent atoms,29,49 into computer models would produce a tremendous improvement in dispersive shift calculations. 2.4. Some Other Mysteries of ET(30). The absorption of Betaine 30 in the solvent-free state, its luminescent properties, and the temperature (T) dependence of spectra still remain poorly known. The extrapolation of band maxima in liquid n-alkanes to unity refractive index (eq 4) yields the ET(30) of 31.0 kcal/mol, as a result of zero slope (Figure 1). The C-H bond dipoles may cause some blue shift, but this is probably less than, for example, the effect of benzene quadrupole. Thus, we arrive at an estimate of 30 ( 0.5 kcal/mol (or 10 500 cm-1), slightly higher than the value given by Reichardt (27.1 kcal/mol).26 The extrapolated ET(30) is comparable to quantum mechanical transition energies (11 220 and 11 480 cm-1 for two conformers,31 11 344 cm-1,34 10 700 cm-1,39 and 14 200 and 12 250 cm-1 for two conform-
J. Phys. Chem. A, Vol. 114, No. 21, 2010 6253 ers44). However, the exact meaning of calculated transition frequencies often remains unclear (a vertical transition at the frozen core?),59 since the excited-state vibrations and the respective Franck-Condon factors can hardly be taken into account with sufficient precision. Much higher ET(30) (37.45 kcal/mol in refs 33 and 40.3 kcal/mol in ref 30) resulted from the overestimation of dispersive shifts, because, in contrast to this work, the constancy of ET(30) in alkanes26,50 was without grounds considered as unreliable.30,33 The homogeneous spectrum of Betaine 30 has not been explored, due to low fluorescence yield,44,60 nonvolatility, and insolubility in Shpol’skii host matrices. There is little doubt that the smooth, broad band hides multiphonon transitions, including the high-frequency stretching modes of the core combining with torsional degrees of freedom, and the soft modes of solvent cage.40 For a pentakis-tert-butyl substituted derivative some vibronic structure could be resolved in weakly polar 2-methyltetrahydrofuran (MTHF) glass at 77 K.60,61 It would be tempting to assign the low-intensity shoulder at 15 000 cm-161 to an adiabatic transition, but unfortunately, the maxima in refs 61 (Figure 3, 17 200 ( 100 cm-1) and 60 (Figure 5, 14 800 ( 100 cm-1) do not coincide. The difference of about 7 kcal/mol points to possible hydrogen bonding with residual moisture in ref 61. By comparing to a similarly broad n-π* transition in acetone,29 one may assume that the purely electronic origin ν00 could lie at least by 10 kcal/mol (3000-5000 cm-1) below the peak of vibronic envelope, that is, in the near-IR around 20 kcal/mol (7000 cm-1). Strong thermochromism of betaines has been noticed a long time ago.25,50,62 With increasing T there is a shift of -4600 cm-1 (between 100 and 275 K) or -3500 cm-1 (77-298 K, for the tert-butyl derivative) in MTHF (Figure 4 in ref 60 and Figure 3 in ref 61, respectively). Kharlanov and Rettig44 report shifts of -5000 cm-1 (180-300 K) in 1-chlorobutane and -2600 cm-1 (128-294 K) in ethanol, whereas Morley and Padfield43 show shifts of -4150 cm-1 in THF and -3500 cm-1 in acetone (both 195-295 K, for a simpler 4-(2,4,6-triphenyl-1-pyridinio)phenolate). Bathochromism with rising T is associated with the liquid state and the liquid-to-glass transition, since in solid poly(vinyl butyral) the shift is much smaller, -570 cm-1 (10-293 K).63 Although the permittivity change with T can be dramatic, from 17.3 to 5.2 (100-300 K for MTHF),60 or from 12 to 7.51 for THF, and from 36.1 to 20.8 for acetone (195-295 K),43 it is not enough for causing such shifts. One may suspect the formation of a quasi-solid domain of spontaneous macroscopic polarization, surrounding the large betaine dipole, that is, materialization of the so-called Clausius-Mossotti catastrophe (ref 52, p 171). A less exotic explanation based on a T-dependent conformational change via the torsional angle between the phenolate and pyridinium moieties43 seems not to be fully supported by other calculations.35,38,39 However, more trivial reasons, such as hydrogen bonding to traces of water and dimerization of the dye at low T cannot be excluded. Obviously, additional very carefully performed measurements are needed. The emergence of visible luminescence has been noticed in MTHF below 205 K,60 and several fluorescence and excitation spectra were recorded in 1-chlorobutane and ethanol glasses.44 Commercial Betaine 30 is known to contain highly fluorescent impurities (pyrylium precursors?) that had to be removed before resonance Raman spectra could be run,64 so a further study is necessary.
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3. Conclusions Absorption energy of Betaine 30 is poorly correlated to conventional dielectric functions of solvents, even after the exclusion of specifically interacting protic media. Three main reasons responsible for this failure were specified. First, the chromophore is sensitive to quadrupole and bond dipole moments that can create reaction fields, but do not contribute to bulk . Second, the change of electronic structure of the dye in the reaction field is not restricted to linear polarization, but consists of a more profound structural rearrangement, so that polarizabilities and dipole moments cannot be regarded as constants. Finally, the expressions for the dipole-dipole interaction (eq 7), used until recently for correlating band shifts, are not only inconsistent with theory,29,45-47 but also yield inferior regressions. An empirical formula is proposed in terms of susceptibility difference - n2 (eq 8), enabling linear fitting with correlation coefficient R ) 0.914 for all polar aprotic solvents (133 values), and as high as 0.965 for polar monofunctional solvents (42 values). The ET(30) scale has been successful, due to its preferential sensitivity to local charges and H-bonding that affect the rates and equilibria of many chemical processes in solutions. The transition states of ground-state chemical reactions involve mostly changes in charge and spin densities, rather than polarizabilities. Therefore, solvatochromic probes basing on push-pull chromphores, such as nitroanilines, whose spectra depend strongly on refractive index,15-17,48,54,57 are less useful in chemistry than the ET(30). Acknowledgment. Professors Ivo Leito and Ilmar Koppel are thanked for very inspiring discussions. This work was supported by the Estonian Science Foundation grant No. 8369. Supporting Information Available: Refractive indices, dielectric constants15,54-56 and ET(30) values26 are tabulated for groups of solvents depicted in Figures: 1 and 2 alkanes, aromatic, and other apolar solvents, highly polar solvents ( > 25), nonaromatic, aromatic, and monofunctional polar solvents. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Brooker, L. G. S.; Keyes, G. H. J. Am. Chem. Soc. 1951, 73, 5356. (2) Ooshika, Y. J. Phys. Soc. Jpn. 1954, 9, 594. (3) Lippert, E. Z. Elektrochem. 1957, 61, 962. (4) Jacques, P. J. Phys. Chem. 1986, 90, 5535. (5) Ca´talan, J.; Mena, E.; Meutermans, W.; Elguero, J. J. Phys. Chem. 1992, 96, 3615. (6) da Silva, L.; Machado, C.; Rezende, M. C. J. Chem. Soc. Perkin Trans. 2 1995, 483. (7) Wu¨rthner, F.; Archetti, G.; Schmidt, R.; Kuball, H.-G. Angew. Chem., Int. Ed. 2008, 47, 4529. (8) McRae, E. G. J. Phys. Chem. 1957, 61, 562. (9) (a) Bakshiev, N. G. Opt. Spektrosk. 1961, 10, 717. (b) Opt. Spectrosc. 1961, 10, 379. (10) Basu, S. AdV. Quantum Chem. 1964, 1, 145. (11) (a) Bakshiev, N. G.; Girin, O. P.; Piterskaya, I. V. Opt. Spektrosk. 1968, 24, 901. (b) Opt. Spectrosc. 1968, 24, 483. (12) Liptay, W. Angew. Chem. Internat. Ed. 1969, 8, 177. (13) Mataga, N.; Kubota, T. Molecular Interactions and Electronic Spectra; Marcel Dekker: New York, 1970. (14) Amos, A. T.; Burrows, B. L. AdV. Quantum Chem. 1973, 7, 289. (15) Koppel, I. A.; Palm, V. A. In AdVances in Linear Free Energy Relationships; Chapman, N. B.; Shorter, J., Eds.; Plenum: London, 1972, pp 203-280. (16) Taft, R. W.; Kamlet, M. J. J. Am. Chem. Soc. 1976, 98, 2886.
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