The ability of a solvent to solvate a particular species is often referred to in terms of the rather ill-defined idea of ‘‘solvent polarity.’’2,9,10This is not simply related to the overall dipole moment of the solvent, but may depend on the presence of polar groups and local dipoles, and the ability
to solvate will also depend on the polarizability of the solvent. Reichardt suggests that ‘‘solvent polarity’’ should be regarded as a measure of overall solvation capability, including all possible specific and nonspecific interactions.10
Since the solvating ability of a solvent is not easily described using well-defined parameters10such as dielectric constant, dipole moment, or refractive index, the solvatochromism of transition-metal complexes has most frequently been correlated with various empirical parameters. These may be derived from the behavior of one species or from an average of many different ones.10,25 An advantage of such parameters is that, in many cases, one can be found that provides a good fit to the data and allows easy comparison of solvatochromic behavior in systems where the causes are similar, with or without specific interactions. Their empirical nature means that they are composite measures of specific and nonspecific interactions between the solvent and solute from which the parameter was derived. Thus a given parameter may be biased towards contributions from dipole–dipole forces or dipole–induced dipole forces, which have a large polarizability component;
and hydrogen-bonding tendencies (as either a donor or acceptor) may or may not be reflected by the parameter. However, it is not the aim of this chapter to analyze the parameters themselves.
Potentially, the modeling of solvatochromic behavior using theoretical methods such as reac- tion field theory, in which the solvent is treated as a dielectric continuum and the solute as a point dipole in a spherical cavity, may provide more fundamental information than can be obtained using empirical parameters.8,11 In principle this may allow calculation of ground- and excited- state dipole moments, gas-phase transition energies, and the relative magnitudes of some of the contributions to the solvatochromic shift. Deviations from the theory can also be useful in indicating the presence of specific interactions, and if either the solvent or solute has the potential to form hydrogen bonds with itself (alcohols, for example) or with another species, the dielectric continuum model is invalid8,11and empirical parameters are usually used.
2.27.2.2 Dielectric Continuum Theory
The various contributions to the solvatochromic shift (Equation (1), i.e., solþo) can be described using the reaction field method, such as is used in generating McRae’s equation.26 The solvent is treated as a dielectric continuum, and the solute as a point dipole in a spherical cavity embedded in the continuum. This assumes no short-range ordering of the solvent around the solute due to local bond dipoles or to hydrogen bonding. This approach has been used by a number of authors and various equations have been developed which differ slightly in the assumptions made, such as those of Kirkwood,27Ooshika,28Lippert,29and McRae.26The general theoretical background and some of these approaches are discussed by Marcus.18There have been many more recent discussions and attempts to improve upon these treatments.21,30–37
McRae’s equation, which uses the Onsager38dielectric functions, has been used to interpret the solvatochromism of a number of coordination compounds. Meyer19,23 and one of us20 have also used Kirkwood’s approach,27which is simpler since it neglects dispersion forces. Lippert’s method is used for species in which absorption and emission data are available for the same excited state—when the difference between absorption and emission energies is known a number of terms in the equations will cancel, and it is then relatively simple to obtain the ground- and excited-state dipole moments.8,29 This method is not usually applicable for coordination complexes as, if emission is observed, the emitting state is usually different from the main absorption band, e.g., in many cases absorption is to a singlet state and emission is from the corresponding triplet.
Applying McRae’s equation,26and neglecting the Stark-effect (quadratic) term the shift,, in the transition energy from the gas phase to that in a given solvent is expressed as:
ẳADop1
2Dopþ1þB Dop1
2Dopþ1þC Ds1
Dsþ2Dop1 Dopþ2
ð2ị whereA,B, andCare constants characteristic of the solute,Dopis the optical dielectric constant (equal to the square of the refractive index) of the solvent andDsis the static dielectric constant of the solvent. The three terms includingA,B, andCin the equation represent the three main types of contribution to the solvent-induced shift: dispersion forces, dipole–induced dipole forces, and dipole–dipole forces, respectively. A involves a sum over all the electronic transitions of the molecule, including those of the excited state. A simpler equation for this contribution is given by Bayliss,39 but it is generally estimated to be rather small.15,19,40 B and C depend upon the
354 Solvatochromism
ground- and excited-state dipole moments of the solute,gande, and upon the cavity (assumed to be spherical) radius,a:
Bẳ2g2e
a3 ð3ị
Cẳ2gðgeị
a3 ð4ị
There are a number of assumptions implicit in this equation, such as that the refractive index of the solvent in the visible-region wavelengths is the same as at zero frequency. This is reasonable for solvents other than water, but for water there is quite a large difference between the values at zero and visible- region frequencies.26The ground-state isotropic polarizability of the solute is assumed to bea3/2.
McRae’s approach and other similar approaches have been criticized by Brady and Carr,34and more recently by Klamt,41 on the grounds that the orientational and electronic parts of the polarizability are not independent. Details are not given here but the reader is referred to their work, and to that of Tomasi et al.,42 Brady and Carr, however, point out that in spite of the erroneous assumptions, statistically superior correlations are generally obtained with McRae’s equation, compared to the corrected formulae.34
This model also breaks down theoretically in large solute molecules that have polar parts but are nonpolar overall, although good correlations may still be obtained in such cases. A further weakness, in practice, is that the A and B terms involving Dop are often small and ill defined, because of the errors inherent in poor statistical fits. Some of the scatter normally observed may result from solvent molecules whose dielectric constants are an average of the properties of a functional group and, for example, an aliphatic chain. Where there is some degree of preferential interaction between the solute and one part of the solvent molecule, the solute will ‘‘see’’ the part of the solvent that has dielectric properties differently from the average of the solvent as a whole.
2.27.2.3 Empirical Parameters
Many different empirical solvent parameters have been developed and these have been reviewed by Reichardt.10 Here we discuss only those which are commonly used to correlate with solvato- chromism of coordination complexes. Kosower’s ‘‘Z values,’’43 derived from the absorption maximum of 1-ethyl-4-methoxycarbonylpyridinium iodide, were one of the earliest comprehensive solvent-polarity scales. These provide an empirical measure of the solvation behavior of a solvent, mainly reflecting dipole–dipole solute–solvent interactions, and they do not correlate well for nonpolar solvents. Reichardt and Dimroth’sET(30) values, developed a decade later, are sensitive to polar and hydrogen-bonding interactions, and also to some extent to other interactions such as dispersion forces.2,44These are based upon the spectrum of a pyridiniumN-phenolbetaine, and have been applied to the solvatochromism of a number of coordination complexes. TheET(30) parameter is the original parameter, in kcal mol1, and there is also a normalized version of the scale,ET(N).10 Kamlet, Abboud, and Taft have developed in detail a set of parameters based on*, which is derived by averaging the behavior of a set of closely related solvatochromic probe molecules:
substituted nitrobenzenes.45–48 The * scale is normalized, with cyclohexane as the zero and DMSO having a value of 1.00. It reflects contributions from polarizability and polarity, but for solvents where polarizability is particularly important a second parameter is needed. The coefficient of , d, is 0.5 for polyhalogenated solvents and 1.0 for aromatics).48 These authors define a ‘‘select solvent set’’ of nonchlorinated, nonprotonic, aliphatic solvents with a single, dominant bond dipole. This set is sometimes useful for correlations with other parameters, or with equations such as McRae’s.26Two additional parameters,and, were developed for systems in which hydrogen-bond formation is a factor; the scale reflects hydrogen-bond donating ability (acidity) and thescale is for hydrogen-bond acceptor ability (basicity).47,48Equations of the form:
XYZẳXYZ0ỵsð ỵdị ỵaỵb ð5ị
are used with the* scale. The relationships of these parameters to other empirical parameters and to various dielectric functions have been discussed by Abboudet al.49 An updated version
of the * scale has been published, based on a single probe molecule, which is considered to be a superior approach compared to that of averaging data from several species.25
Gutmann’s donor and acceptor number (DN and AN)50,51are designed to correlate with solvent effects where the interactions with the solute are dominated by those of the donor–acceptor type, including hydrogen bonding. These parameters have proved to be very useful for understanding the solvatochromism of a number of coordination complexes in which these types of interactions are important. Donor number is defined as the negativeHvalue for the interaction of the electron- pair donor/nucleophilic solvent (Lewis base) with 103MSbCl5in 1,2-dichloroethane solution; it correlates with theparameter of Kamletet al. The acceptor number is based on the chemical shift of the31P NMR of triethylphosphineoxide in the acceptor solvent of interest. However, donor and acceptor properties cannot be completely explained by independent parameters, due to their mutual interactions. Donor and acceptor numbers of some solvents have been estimated from electronic absorption spectra of indicators such as [FeII (phen)2(CN)2] and other metal complexes.50,52,53 Although AN andET(30) are considered to be linearly related, a detailed analysis54yields different groups of solvents characterized by their functional groups.
There are three parameters in the literature based on the solvatochromism of carbonyl com- plexes. Both Lees’E*MLCTparameter55and Walther’s56earlierEKare based on the solvatochro- mism of [M(CO)4(diimine)] complexes. Lees’ parameter, which has been used in many subsequent studies, is based on the solvatochromism of bipyridinetetracarbonyl- tungsten(0).55 The third scale is ECT(), developed by Kaim’s group.57 This group have investigated the solvatochromism of a number of complexes, plotting much of their data against E*MLCT. However, in the case of [M(CO)5(2-TCNE)] complexes (where MẳCr, W, and TCNE, tetracyanoethylene, is bound as an olefin) the solvatochromism differed qualitatively from that of other transition-metal carbonyls, and did not correlate with parameters such asET, Z,*, DN, orE*MLCT. The failure of these scales was attributed by Kaim to a specific type of interaction between the complex and the solvent, in which a solvent molecule lies on the opposite side of the TCNE to the metal carbonyl fragment, and in the case of aromatic solvents lies coplanar with the TCNE. The solvent competes with the metal fragment for the -accepting ability of the TCNE. The ECT() parameter scale is derived from the average of the results for the Cr and W complexes.
2.27.2.4 Theoretical Simulations
Relatively recently there have been attempts to model solvent effects on electronic spectra by incorpor- ating them into theoretical calculations using methods such as INDO (discussed in Chapter 2.33 and in various reviews12,58,59). Most work has involved organic species, but a number of groups have calculated the spectra of ruthenium ammines surrounded by solvent molecules or in solution (see below).60–67Calculations without inclusion of solvent give charge-transfer band energies significantly higher than those observed. Dielectric continuum theory also breaks down for these species, because of their capacity for hydrogen-bond formation with acceptor solvents. The various methods of performing spectroscopic calculations involving solvent are reviewed by Hush and Reimers12specif- ically for transition-metal complexes, and also more generally by Zerner and co-workers.68