J . Phys. Chem. 1991, 95, 5725-5736 of the free molecule might be split in a more ordered crystal lattice. The splitting of the 577-cm-l band suggests that as the molecular rotations are slowed, the symmetry is lowered. The high-pressure spectra are thus consistent with the NMR a~nclusions~ that a new phase may occur at low temperature, but the limited band splitting does not permit any conclusion regarding the factor group of the high-pressure phase. The pressure dependences of the frequencies, du/dP, are similar to those observed for C - C stretching and bending modes in aromatic molecules such as benzene" with the exception of the band a t 526 cm-I, which exhibited a negative pressure dependence. According to Weeks and Harter,I2 the lowest frequency mode involves a shift of opposite-sided pentagons in one direction with a compensating shift of all other carbons in the opposite direction while the highest frequency IR-active vibration involves the generation of a dipole moment by a contraction of a pentagon on one side of the molecule and an expansion on the other. Gas-phase emissionlo and argon matrix isolated" vibrational frequencies have been obtained for Cm If the frequency shifts between these two are taken as a measure of the ( 1 1 ) Ellenson, W. D.; Nicol, M. J. Chem. Phys. 1974,61, 1380. (12) Weeks, D. E.; Harter, W. G. J . Chem. Phys. 1989, 90,4744.
5725
sensitivity to environmental effects, then the higher frequency vibrations show the larger shifts and also have the higher dv/dP values. The pressure dependence of some of the additional bands in the spectrum, which are possibly due14JSto C, were also measured (Table 11). Three of the peaks showed a negative pressure dependence (Figure 3), and the peak at 535 cm-' showed splitting in the vicinity of 12 kbar.
Acknowledgment. This work was supported by grants from the NSERC (Canada) and FCAR (Quebec). Y.H.acknowledges the award of a Fellowship from McGill University. We thank L. P. F. Chibante for the sample of CW. (1 3) Haufler, R. E.; Conceicao, J.; Chibante, L. P. F.; Chai, Y .; Byrne, N. E.; Flanagan, S.;Haley, M. M.: OBrien, S. C.; Pan, C.; Xiao, Z.: Billup. W. E.: Ciufolini, M. A.; Hauge, R. H.: Margrave, J. L.; Wilson, L. J.; Curl, R. F.; Smalley, R. E. J . Phys. Chem. 1990, 94, 8634. (14) Bethune, D. S.; Meijer, G.; Tang, W. C.; Rosen, H. J.; Golden, W. G.; Seki, H.; Brown, C. A,; de Vriea, M. S. Chem. Phys. Lrrr. 1991,179,181. (15) Cox, D. M.; Behal, S.;Disko. M.;Gorun, S. M.; Greaney, M.; Hsu, C. S.;Kollin, E. B.; Millar, J.; Robbins, W.; Sherwood, R. D.; Tindall, P. J . Am. Chem. Soc. 1991, 113,2940.
FEATURE ARTICLE Solvated Electrons: What
Is Solvated?
Thomas R. Tuttle, Jr.,* and Sidney Goldent Department of Chemistry, Brandeis University, Waltham. Massachusetts 02254-91 10 (Received: January IS, 1991)
Optical absorption spectra of solvated electrons are compared with those of F centers in alkali-metal halides and those of solvated iodide ions. Marked spectral differences indicate little justification for regarding a solvated electron either as a cavity-type entity or as a prototype of conventional solvated anions. Its observed spectral behavior suggests that a solvated electron is best characterized as a solvated solventanion complex (SAC), consisting of a solvated combination of an excess electron and a small number of solvent molecules, possibly just one, about which the electron is localized. In this way, the observed characteristic spectral signatures of individual solvated electrons are maintained, both in pure solvents and in their mixtures.
I. Introduction The cavity model of solvated electrons was introduced nearly a half-century ago' to account for a number of observations pertaining to dilute solutions of alkali metals in liquid ammonia." The original proposal of Ogg was that ammoniated electrons and dielectrons occupy cavities within the solvent, analogous to F and F' centers in alkali-metal halides'" known to be single electrons and electron pairs, respectively, occupying anion vacancies in the crystal^.^^' However, much of the evidence that Ogg used to support his proposal has turned out to be either incorrect or un~ubstantiated.*-'~What remains-the similarity in color of the dilute metal solutions (they are blue) with that of some Fcenter systems and the observed volume expansion which accompanies dissolution of electrons in liquid ammoniaI4 (though much diminished from the original estimate3)-does suggest a possible relationship between ammoniated electrons and F centers, 'Emeritus Professor of Chemistry.
0022-3654/9 1/2095-5725$02.50/0
but falls far short of proving that solvated electrons are cavity-type entities. Nevertheless, the cavity model has been widely accepted ( I ) Ogg, Jr., R. A. Phys. Rev. 1946,69,668. ( 2 ) Ogg, Jr., R. A. Phys. Reo. 1946,69. 243; 544. (3) Ogg, Jr., R. A. J. Am. Chem. Soc. 1946,68, 155. (4) Ogg, Jr., R. A. J . Chem. Phys. 1946,14, 114. (5) Ogg, Jr., R. A. J . Chem. Phys. 1946, 14, 295. (6) Physics o/Color Cemers; Fowler, W. B a l l . Ed.;Academic Press: New York, 1968. (7) F' Cenrers in Alkali Hulides; Giorgiev, Mladen, Ed.;Springer-Verlag: Berlin, 1988. (8) Daunt, J. G.;Desirant, M.; Mendelssohn, K.; Birch, A. J. Phys. Rev. 1946, 70, 219. (9) Boorse, H. A.; Cook, D. B.; Pontius, R. B.; Zemansky, M. W. Phys. Rev. 1946, 70, 92. (IO) Ogg, Jr., R. A. Phys. Rev. 1946. 70.93. ( 1 1 ) Weissman, S. I. Phys. Rev. 1946. 70, 571. (12) Lipscomb, W. N. J . Chem. Phys. 1953, 21, 52. (13) Stairs, R. A. J . Chem. Phys. 1957, 27, 1431. (14) Gunn, S. R.; Green, L. G. J . Chem. Phys. 1962. 36. 363.
0 1991 American Chemical Society
5126 The Journal of Physical Chemistry, Vol. 95,No, IS, 1991
t
Tuttle and Golden
as I
* '
I
*.*
. ..
v
I
-LJ
(10Jchi-j
Figure 1. Solvated electron optical absorption spectra in ammonia at three temperatures. Absorbance relative to maximum is plotted versus frqu~ncy.~~
as providing a conceptual basis for the theoretical description15-22 of solvated electrons. More recently, solventanion-type models of solvated electrons have been proposed to account for a number of their properties not adequately accounted for by a cavity Thus, measured paramagnetic shifts of nuclear resonances in dilute alkali metal-ammonia solutions indicate the existence of a large unpaired electron-'*N contact interaction attributable to ammoniated electrons in close association with ammonia molecules2' in spite of (but not in contradiction to) the extremely narrow single line observed in the EPR spectrum of the electron, with a gvalue close to that of a free electron.2* The chemical kinetic behavior of solvated electrons observed in hydroxylic solvents also has prompted the proposal of solvent-anion-type species.25 Solvent-anion-like entities have been introduced in theory as examples of a small electron A hydrated, highly distorted H20species has been suggested most recently to account for the results of photokinetic experiments on ultrafast time scales.27 In what follows, the focus is on electrons dissolved in liquids (but not in glasses) essentially under conditions of thermodynamic equilibrium, with primary emphasis on their optical absorption spectra. These, we believe, provide the largest body of experimental and theoretical information which can help in deciding what is solvated. The general characteristics of experimentally determined solvated-electron optical absorption spectra are described in section 11. There they are compared with (1) F-center spectra, to assess the cavity-model analogy in the light of evidence which has been obtained since Ogg's original proposal, and (2) charge-transferto-solvent (ctts) spectra of solvated anions (principally iodide), to assess the correlations which have been obtained between the (15) (16) (17) 1189. (18) 2254. (19) (20)
,..
t
Jortner, J. J . Chem. Phys. 1959, 30, 839. Fueki, K.; Feng, D.-F.; Kevan, L. J. Phys. Chem. 1970, 74, 1976. Copeland, D. A.; Kwtner, N.R.; Jortner, J. J. Chem. Phys. 1970,53, Moskowitz, J. M.; Boring, M.; Wood,J. H. J. Chem. Phys. 1975,62,
Newton, M. J . fhys. Chem. 1975, 79, 2795. Kwtner, N. R. In Electrons in Nulds; Jortner, J., Kestner, N. R., Eds.; Springer-Verlag: Berlin, 1973; p 1 25. (21) Kcstner, N. R. In Electron-So8entkd Anion-Solooted Inteructions; Kevan, L., Webster, B. C., Us.; Elsevier: Amsterdam, 1976; pp 1-43. (22) Feng, D.-F.; Kevan, L. Chem. Reu. 1980, 80, 1. (23) Golden, S.;Guttman, C.; Tuttle, Jr., T. R. J. Chem. Phys. 1966,44,
[IO'CM-')
Figure 2. Solvated electron optical absorption spectra in methylamine at three temperatures. Absorbance relative to maximum is plotted versus frequency.29
two kinds of spectra. A summary of theoretically estimated spectra is given in section 111, to assist in evaluating the adequacy of past and current computational approaches in elucidating the nature of solvated electrons. In section IV, a fundamental many-particle theory of solvated-electron optical absorption spectra is described together with some of its results. This theory allows a number of properties of solvated electrons to be determined directly from their measured absorption spectra. Solvated-electron optical absorption spectra in binary-solvent mixtures are described and analyzed in section V. The results obtained give strong support to the solvated solvent-anion-complex (SAC) model of solvated electrons. In section VI, the results of the previous sections are summarized. Some suggestions are offered there for future experimental and theoretical investigations involving solvated electrons. 11. Spectral Properties: Comparison of Solvated Electrons
with Related Systems Typically, a solvated-electron optical absorption spectrum consists of a single broad, asymmetric, featureless, intense band which rises rather steeply to a maximum in the near-infrared or visible region and decreases gradually into the near-ultraviolet region. The spectra, F(v,T), of solvated electrons in ammonia and in methylamine, shown in Figures 1 and 2, respectively, illustrate these characteristics.29 These spectra are all normalized ~ 1, where to a maximum relative absorbance of unity, Le., F ( v , = v is the frequency of maximum absorbance and T is the temperature. Both Figures 1 and 2 illustrate the marked dependence of the spectra on temperature. almost always exceeds about 18 cm-'/K for solvated electrons.) %Ivated-electron optical absorption spectra almost invariably shift to the blue as either temperature is decreased or as pressure is increased.'O Although changing temperature and/or pressure can produce very large displacements of the spectra, they almost always retain their shape in the process. This remarkable near-invariance of shape, called shape stability of the spectral profile, occurs in many solvents at different temperatures and/or In such cases, the spectra obtained under different conditions can all be superimposed merely by shifting them relative to each other. This has been done for the ammonia spectra of Figure I , in Figure 3, and for the methylamine spectra of Figure 2, in Figure 4. The shifts needed to accomplish the superpositions are esstntially equal to the shifts of the absorption maxima, AV. The band shapes are different in Figures 3 and 4, as is usually the case for solvated-
(-(&/an
3791.
(24) Weissman, M.; Cohan, N. V. Chem. Phys. Lett. 1970, 7, 445; J . Chem. fhys. 1973,59, 1385. (25) Stradowski, Cz.; Hamill, W. H. J . fhys. Chem. 1976, 80, 1431. Razcm, R.; Hamill, W. H. J . Phys. Chem. 1977.81, 1625; 1978.82. 488,
73, 274. (27) Robinaon, G. W.; Hameka, H. F. SPIE, b s e r Appl. Chem. Dyn. 1987,742,82. Hameka, H. F.; Robinson, G. W.; Maden, J. J. Phys. Chem. 1987,91, 3150. (28) Kaplan. J.; Kittel. C. J . Chem. Phys. 1953. 21, 1429.
~
(29) Stupak. C.; Tuttle, Jr., T. R.; Golden, S.J . Phys. Chem. 1984,88, lRnA.. (30) Nagendrappa, R. R.; Olinger, R.; Schindewolf, U. Z . Phys. Chem., Munich 1974,88, 323. (31) Tuttle, Jr., T. R.; Golden, S.J. Chem. Soc., Faraday Truns. 2 1981,
---
,,.-.-. 77 A7l
(32) Tuttle, Jr., T. R.; Golden, S.;Hurley, I. J . fhys. Chem. 1982, 86, 1801. (33) Tuttle, Jr., T. R.; Golden, S.;Lwenje, S.;Stupak, C. J . Phys. Chem. 198488, 3811; 1985,89, 2436.
The Journal of Physical Chemisrry, Vol. 95, No. 15, 1991 5727
Feature Article
Figure 3. Demonstration of shape stability of solvated electron optical absorption spectra in ammonia at different temperatures: 0 , -70 O C ; 0, -30
OC.
OC;
B, -50
Absorbance relative to maximum is plotted versus reference frequency.29 I
I
I
I
I
I
1
I
I
I
I
I,0
0.8 F
0.6
0.4 0.2
0
1
4
I
6
I
I
I
I
I
I
I
I
I
8
IO
12
14
16
18
20
22
24
Figure 4. Demonstration of shape stability of solvated electron optical absorption spectra in methylamine at different temperatures: O C ; 0, -50 OC. Absorbance relative to maximum is plotted versus frequency.29
0 , -90 OC; X,
-70
electron bands in different solvents. In such cases, no shift of either band can bring it into coincidence with the other. Because the area under a solvated-electron band (integrated intensity) measures the number of electrons producing it,34 (34) Golden, S.;Tuttle, Jr., T. R.J . Chem. Soc., Faraday Trans. 2 1979,
75, 414.
unit-area-normalized absorption bands, G(u,T) = F(u,T)/.fdv F(u,T), offer a less arbitrary basis of comparison than those normalized to unit maximum height. In Fi ure 5, the G(u,T) for eight different solvents are e ~ h i b i t e d . ~ J * ~This mode of com-
!
(35) 321.
Stupak, C.; Tuttle, Jr., T. R.;Golden, S.J . Phys. Chem. 1982,86,
5128 The Journal of Physical Chemistry, Vol. 95, No. 15, 1991
Tuttle and Golden
3
2
G
.I
0.0
Figure 5. Solvated electron optical absor tion spectra in eight different solvents. Absorbance normalized to unit area is plotted versus frequency.
References: ammonia and methylamine;29ethylamine;331-propylamine;Mwater;37methanol and 1-propanol;3*etban01.)~ 1
1
I
I
I
I
I
1
I
I
I
1.0
0.8 0.6
F 0.4
0.2 0
Figure 6. Unit-height-normalized spectra of solvated electrons at -70 OC in mixtures of ammonia and methylamine containing 0,100%;A, 80%; X, 50%; 0,20%; 0 , 0 % NH3.29
parison emphasizes the differences between the solvated-electron spectra for different solvents, as inspection of Figure 5 clearly shows. For only two cases can a shift bring about near-coincidences of the spectra: for 1-propylamine and water, and for ethanol and 1-propanol. The spectra in binary-solvent mixtures generally do change in shape as solvent composition is changed. Values of W,the (36) Jou, F.-Y.; Freeman, G. R. Cun. J . Chem. 1982,60, 1809. (37) Jou, F.-Y.; Freeman, G. R. J . Phys. Chrm. 1979, 83, 2383. (38) Jou, F.-Y.; Freeman, G. R. J . Phys. Chrm. 1977,8/, 909. (39) Leu, A,-D.; Jha, K.N.;Freeman, 0. R.Can. J . Chem. 1982,60,2342.
half-height width, and of P for the mixtures are always intermediate to the pure-solvent ~ a l u e a . ' ~The . ~ unit-height-normalized spectra of Figure 6 illustrate this behavior for the spectra in ammoniamethylamine mixtures.29 Otherwise, thc mixed-solvent spectra exhibit much the same general characteristics as do their puresolvent counterparts. Optical absorption spectra of F centers generally consist of several bands designated by F, K,L,,L2,etc., ...$ as is shown by the unit-height normalized spectra in Figure 7.'' The F band (40) Golden, S.; Tuttle, Jr., T. R. J . Phys. Chrm. 1978. 82. 944. (41) Markham, J. J.; Konitzer, J. D.J . Chem. Phys. 1961, 31, 1936.
1.00
1.01-
-
o.8
0.6
- --
0.75
79.4~0.1"~ 170.5+0.2*~ 377.3tO.l.K
F 0.50
..
-
... ...
Y
:: 9
0.4
-
1.5
1.7
1.9 v/cm-l
2.1
2.3
x lo4
Figure 9. F-center spectra 78 K for (A)KCI, ( 0 )R E I , and ( 0 )47.5% I
.
/: \ ; I : I : \ ; I :
0.2
0.2 5
1 :
I 1
:
\ \
RbCl in KCI. The spectra of the RbCI-containing systems have been shifted so that their maxima coincide with that of the KCI system. Adapted from Figure 2 of ref 45. half-height widths which exceed those for the relevant pure-salt system^.^^^^ This behavior is illustrated in Figure 9 by the unit-height-normalized absorption curve for a KCl-RE1 mixture which encompasses both similarly normalized absorption curves for the pure salts." (The curves have been shifted for the purpose of comparison so that the maxima of all three curves coincide.) Clearly, solvated-electron spectra differ markedly from F-center spectra. The former are featureless; the latter exhibit structure. The former exhibit shape stability the latter do not. The former
Tuttle and Golden
5730 The Journal of Physical Chemistry, Vol. 95, No. 15, 1991
TABLE I: Comparison of Optical Spectral Properties of Solvated Electrons with "base of F Centers and of Solvated Iodide Ion shapeb system location' structure stability -(t3v/t37'))6 W d in binary mixtures Yes large intermediate to pure solvents single band solvated electrons infrared and visible intermediate to pure solvents multiple bands no usually small solvated iodide ultraviolet nonintermediate to pure crystals multiple bands no small F centers visible #Position of B of band of lowest frequency. dHalf-height width of band of lowest frequency.
pure system under different conditions. CTemperaturecoefficient of maximum absorption.
I
5
T = 203
1
1.5
K
2
Energy ( e V )
Figure 11. Comparison of calculated and experimental ammoniated electron optical absorption spectra.*'
t
I
/ I
40
I
I
I
1
I
4s
I
IJ
G iodide x 10J/cm-* Figure 10. Linear correlation of p of solvated electron optical absorption with that of a solvated iodide ctts absorption band.% The points are numbered to correspond with the entries in Table 1 of ref 50. The extreme points refer to (1) hexamethylphosphoramideand (41) glycerol.
while the latter exhibit negative temperature coefficients which are usually much smaller.& Solvated-electron bands exhibit a trend toward larger temperature coefficients for solvents with larger molecule^^^^^^^^^ while such a trend does not occur for solvated iodide ion bands.& Finally, the large changes that do occur in the shapes of solvated-electron bands in different solvents, illustrated in Figure 5 , do not appear to occur for ctts absorption bands in general nor for the ctts absorption bands of solvated iodide ions in p a r t i ~ u l a r . ~In~view ~ ~ *of~the ~ extraordinary variability exhibited by the optical absorption bands of solvated electrons in different solvents as compared to that shown by ctts bands of solvated iodide ions, there seems to be little justification in attributing all of the different solvated electron bands to any single species, let alone to a "zeroth halide". The comparisons that have been made between optical absorption spectra of solvated electron systems, of F centers, and of solvated iodide ions are summarized in Table I. These results, it should be noted, are independent of any model that may be suggested for solvated electrons. Nevertheless, it seems clear that the solvated-electron spectra resemble neither those of F centers nor those of solvated iodide ions but have features that are quite distinctive, viz., shape stability, absence of structure, and large negative temperature coefficient. It is not yet clear to what constitutional factors, if any, these characteristic features may be attributed.
apparently is to be viewed as a "zeroth halide"which can be formed by an electron occupying a cavity vacated by a halide ion with just an appropriate adjustment of cavity size. However, although an interchange of the type described between different halide ions is well-defined because the intrinsic sizes of the ions themselves fix the required adjustment in cavity size, extending the procedure to an electron is operationally undefined because it lacks the intrinsic size that a conventional ion has. Nevertheless, the absorption bands of chargetransfer-to-solvent (ctts) transitions attributable to solvated anions exhibit some behavior which resembles that observed for solvated-electron absorption b a n d ~ . ' ~ J ~This is illustrated by the empirical correlation between I values for the solvated-electron band and for the lowest energy ctts band of solvated iodide ions in a number of different solvent systems shown in Figure However, the similarity that this correlation may suggest is less 111. Theoretically Determined Optical Absorption Spectra of than the dissimilarity it reveals: the shift in 5 over the whole range Solvated Electrons is appreciably greater for solvated electrons (AD 14000 cm-I) Early theoretical estimates of the optical absorption spectra than it is for solvated iodide ions (AI = 9000 cm-'); the correof solvated electrons were derived on the basis of assumed cavity sponding fractional shift, AV/average I, for solvated electrons is model^.'^-^^ The spectra that were obtained consisted primarily -1.2 and for solvated iodide ions is -0.2. Furthermore, in pure of bound-bound transitions. Compared to experimentally desolvents solvated-electron absorption bands exhibit shape stability termined spectra, the calculated spectral profiles were too symwhile solvated iodide ion absorption bands do n0t.46951+s2The former also exhibit large negative temperature c o e f f ~ c i e n t s ~ ~ *metric, ~ ~ ~ ~were ~ too narrow, were located at too high frequencies, had too small temperature coefficients (in magnitude), and did not exhibit shape ~ t a b i l i t y . ~ l v Indeed, ~~ these spectra exhibited characteristics that resembled those observed for F-center spec(46) Blandamer, M. J.; Fox, M. F. Chem. Rev. 1970, 70, 59. (47) Fox, M . F.; Hunter, T. F. Nature 1969, 223, 177. (48) Luehrs, R.C.; Brown, R.;Godbole, K.A. J . Solution Chem. 1989, 18, 463. (53) Jha, K. N.; Bolton, G. L.; Freeman, G. R.J. Phys. Chem. 1972,76,
-
(49) (50) 1990. (51) (52)
Fox, M. F.: Hayon, E. Chem. Phys. Lett. 1974, 25, 51 I . Fox, M. F.; Hayon, E. J. Chem. SOC.,Faraday Trans. I 1976, 72,
Shapira, D.; Treinin, A. J . Phys. Chem. 1966, 70, 305. Stein, G.; Treinin, A. Trans. Faraday Soc. 1959, 55, 1091.
3876. (54) Jortner, J.; Treinin, A. Trans. Faraday Soc. 1967, 58, 1503. (55) FOX,M. F.; Hayon, E. J. Chem. SOC.,Faraday Trans. I 1977, 73, 1003. (56) Webster, B. C.; Carmichael, 1. C. J. Chem. Phys. 1978, 68, 4086.
Feature Article
The Journal of Physical Chemistry, Vol. 95, No. 15, 1991 5731 1.0
-
n
0
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I
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I
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,
,
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1.5v / ~ l l ~x -l
I.0EXPERIMENT
G 0.5 -
103
Figure 13. Comparisons of the optical absorption spectrum of ammoniated electrons at 198 K, @, with best fits of theoretical photoejection spectra of electrons from two different spherical-well potentials
+ and
0.64
That the expressions for the photoejection spectra of spherical-well models fit measured optical absorption spectra of solvated electrons so well is significant, because the photoejection spectra o.oo consist entirely of bound-continuum transitions of the absorbing I 2 3 4 5 particle. The unusual, distinctive shape stability exhibited by AE/eV solvated-electron spectra can be accommodated by the photoeFigure 12. Comparisons of simulated and hydrated electron optical jection spectra in a physically reasonable way (for example) by absorption spectra. Upper panel" comparison for spectra at 300 K. adjusting the depth of the well and its When shape Lower panels* gives comparisons at two temperatures. stability is extrapolatable to the absolute zero of temperature, fundamental many-particle theorf7 (to be considered later) yields tra6u4145 rather than those observed for the solvated-electron a formal expression for the spectra which resembles the corres p e ~ t r a ~ ~ *being ~ l - "calculated. ~~ An example of such spectra is sponding ones obtained from the spherical-well potentialsM and shown in Figure I I . Recently, quantum-statistical simulations of h ~ d r a t e d and ~ ~ - ~ ~ so gives additional support to the bound-continuum nature of the optical absorption spectra of solvated electrons. ammoniated@electrons have implied the existence of cavity-type An adaptation of the theory of photodetachment spectra of entities for these species. However, the calculated optical abmolecular anions provides a detailed analysis of solvated-electron sorption spectra obtained for these model systems only roughly optical absorption spectra in a number of different solvents." The approximate the observed spectra, as shown in Figure 12. As mathematical expressions produced, which are constructed to is also shown in this figure, the calculated spectra of different satisfy the high- and the low-frequency behavior prescribed by simulated hydrated electrons differ as much as do the spectra of theory, yield the best fits to the experimental spectra thus far simulated and real systems. In one case (as is illustrated in the obtained. lower panel of Figure 12) the simulated hydrated-electron spectra showed essentially no red shift with increasing t e m p e r a t ~ r e , ~ ~ IV. Many-Particle Theory for Solvated-ElectronOptical clearly in sharp disagreement with e~periment.'~Because of these Absorption Spectra discrepancies the support generated in favor of a cavity-type entity To deal with the optical absorption spectra of solvated electrons for real solvated electrons by these simulations is weak at best. so that the question of what is solvated remains open to experiAmong the most accurate mathematical representations of mental determination, an adaptation34 and extension^'^^^^ of exsolvated electron optical spectra are those that have been obtained isting theory70 have been used to obtain and to exploit a manyby fitting the theoretical expressions for the photoejection cross particle theory of thermalized spectral moments. This theory is section of electrons from spherical wells to the measured absorption essentially independent of any model that may be ascribed to the These results have been dismissed, nevertheless, as solvated-electron system. Accordingly, the results obtained by being arbitrarf5 and not to be taken too seriously." Two of the its application can be used in distinguishing between different results for ammoniated electrons at 198 K* are shown in Figure models of the same system. The central quantity in the theory 13. It is noteworthy that the experimental spectrum is extremely is the thermalized spectral density of oscillator strength of the well represented by several theoretical photoejection spectra that electron, Mu)).This quantity is obtained by identifying the are obtained from different spherical wells of both cavity-type and spectral transitions of a solvated electron with states of the entire non-cavity-type models.64 As a result, the optical absorption solution, taking into account both absorption and stimulated spectrum of the ammoniated electron proves insufficient to disemission and averaging the usual electricdipole-dependent spectral tinguish between these different models and, hence, to tell whether density of oscillator strength over the equilibrium distribution of or not a cavity-type model is correct. the system. In terms of the measured molecular absorption coefficient, t ( u ) (in atomic units) (57) Schnitker, J.; Motakabbir, K.; Rossky, P.J.; Friesner, R. Phys. Rev. kfr.1988, 60, 456. Rossky, P.J.; Schnitker, J. J . Phys. Chem. 1988, 92, 4277. where c is the speed of light and n(u) is the frequency-dependent ( 5 8 ) Wallquist, A.; Martyna, G.; Berne, B. J. J . fhys. Chem. 1988, 92, refractive index of the system. In what follows, the latter is taken 1721. (59) Romero, C.; Jonah, C. D.J. Chem. Phys. 1989, 90, 1811. (60) Sprik, M.;Impy, R, W.; Klein, M.L. J. Chem. Phys. 1985,83,5802. Marchi, M.; Sprik, M.;Klein, M.L. Furuduy Discuss. Chem. Soc. 1988,85, 373. (61) Kajiwara, T.; Funabashi, K.; Naleway, C. fhys. Rev. A 1972,6, 808. (62) Brodskii, A. M.;Tsarevskii, A. V. Elekrrokhimiya 1973, 9, 1671. (63) Mazzacurati, V.; Signorelli, G. Nuovo Cim. Left. 1975, 12, 347. (64) Tuttle, Jr., T. R.; Golden, S.J . Chem. Soc., Furuduy Truns. 2 1979, 75, 1 146. (65) Kestner, N. R.;Logan, J. J . fhys. Chem. 1975, 79, 2615. (66) Thompson, J. C. EIecfronsin Liquid Ammonia; Clarendon: Oxford, U.K.,1976; p 139.
as its absorption-averaged value,
no = x m d un(u) r ( u ) / x m d u t ( u ) (67) Golden, S.;Tuttle, Jr., T. R. J . Chem. Soc., Furaday Truns. 2 1981, 77, 889. (68) Tuttle, Jr., T. R.; Golden, S. Rudiar. Phys. Chem. 1988, 32, 525. (69) Golden, S.; Tuttle, Jr., T. R. J . Chem. Soc., Faraday Truns. 2 1988, 84, 1913. (70) Fano, U.;Cooper, J. W . Rev. Mod. fhys. 1968,40, 441.
5732 The Journal of Physical Chemistry, Vol. 95, No. 15, 1991
Tuttle and Golden
TABLE II: Equilibrium Crod-State Properties of SOlVited Electrons solvent NH, CHjNH2 CHjCH2NHZ CHACHzhNHz HZO CHjOH CHjCH20H CHdCHzhOH
(9)XI@"
(9)"
T/K 203 203 208
41.7 35.8 34.0 32.8 21.0 18.6 18.9 18.2
190
274 300 298 300
5.93 7.27 8.02 8.14 11.84 13.86 14.36 14.56
P
(P)"
(t)'l2b
2.47 2.60 2.73 2.67 2.48 2.59 2.72 2.65
0.147 0.218 0.316 0.279 0.154 0.224 0.312 0.267
3.42 3.17 3.08 3.03 2.42 2.28 2.30 2.27
Rb 3.24c d d d 51.13* 1.20'
rmb
rllP
2.79 2.59 2.51 2.47 1.96 1.86 1.88 1.85
3.03 2.82 2.74 2.69 2.15 2.02 2.04 2.02
1.36 1.36 Oln atomic units; (9)= dispersion in position, (p2) = dispersion in momentum, P = Heisenberg product, ( P ) = orbital angular momentum angstrom units, squared, ( ) = thermal average. = average root-mean-square radius, R = cavity radius, r,,, = maximum of radial spatial density, rlI2= radius of half-accumulation. CCalculated from volumetric data of ref 14. "No estimates available. CCalculatedfrom volumetric data of ref-72..'fTheoretical estimates from ref 73.
without introducing serious error. The thermalized spectral moments are given by
( M K ) ) Jmdu 0
+Mu)>
(3)
Of particular interest are the expressions for K = -1, 0, + I (M(-l)) = (21-1/3)(9)
(4)
(WO)) = 1 ( M ( + 1 ) ) = (21+1/3) ( P 2 )
(5)
c(v)
(3/2)(F1) (7)
and from eqs 1-3, 5, and 6 (p') = ( 3 / 2 ) S m d u u c ( u ) / l d v c(u) 0
(3/2)(b)
(8)
From these expressions it is clear that relative absorbances alone suffice to determine the dispersion in position and dispersion in momentum without any knowledge of the molecular absorption coefficients. When the molecular absorption coefficients are known, combining eqs 1-3 and 5 yields no[( c / 2 n 2 ) i m d ue ( u ) ]
P
(6)
in which the l's are factors that take the effect of stimulated emission into account, (9) is the dispersion in position of the electron about its mean position, and ( p 2 ) is the dispersion in momentum. For virtually all solvated-electron spectra the s'l differ negligibly from unity and so can be disregarded. When the temperature approaches absolute zero, eqs 4-6 reduce to the usual sum rules.70 These thermalized moments yield values of the indicated intrinsic properties of a solvated electron directly from its measured spectrum. From eqs 1-534 (assuming that Z, = 1)
(9) = (3/2)Jmdu v-le(v)/Xmdu
they must, but clearly fall short of the minimum P value of 3.0 that obtains for hydrogen-like atoms. For solvated electrons in a given solvent, P values hardly change at all when temperature is changed. For example, in ammonia in the range 198-243 K, P = 2.49 f 0.04 and, in water in the range 274-380 K, P = 2.50 f 0.03. Because of these observations, a constant value of P has been used as a constraint in determining a solvated electron's single-particle density matrix of maximum entropy associated with its motion relative to its mean location
n$ = 1
(9)
in which f is an empirical oscillator strength often referred to simply as the "oscillator ~ t r e n g t h " . ~With ~ no taken to be the refractive index of the solvent for the sodium D line, a number of systems for which f had been determined gave34 naf= 0.99 0.07 (10) a good test of the TRK sum rule,O ' and, accordingly, the adequacy of the many-particle theory. Values of (r2)34*69 and ( p 2 )determined for a number of solvated-electron systems are given in Table 11. While both of these quantities can vary appreciably from one system to another, their Heisenberg Product, P, does not. From (7) and (8) (in au)
*
P E ( Z ) ( p Z ) = (9/4)(5-')(5) 2 9 / 4 (11) the last relationship arising from the inequality of Schwarz. The lower bound gives an expression of the Uncertainty Principle in three dimensions, which is attained only for the ground state of a spherically symmetric, three-dimensional harmonic oscillator. All of the values of P in Table 11 exceed the minimum 2.25, a s
= exp[-28(r2)H1/Tr exp[-2LW)H1
(12)
Here H
p2/2
+ (P/2(9)*)9
(13)
is a pseudo-single-particle H a m i l t ~ n i a nfor ~ ~the motion of the solvated electron relative to its mean location and j3 is determinable from P1I2tan j3 P1I2= 3/2 (14) Since (9), ( p 2 ) ,and, hence, P are determined directly frcm the measured optical absorption spectrum of the solvated electron, so is p. As a result, all single-particle properties that depend upon just the position and conjugate momentum of the electron are likewise determinable. As an example, mean values of the squared orbital angular momentum, ( P ) , have been determined for several solvents, as given in Table 11. For ammonia and water, (P)= 0.15; so it would appear that their equilibrium ground states involve a nonspherical p-state contribution of no more than about 11%. A partial test of (12) has been afforded by its coordinate-diagonal form, the spatial probability density69 p ( r ) = (3 /2n( 9 ) ) 3 exp(-39/2 /2 (r Z ) )
(15)
Just such which is clearly a Gaussian with rms radius a distribution has been obtained from the quantum-statistical simulation of a hydrated electron, with a resulting ($)I/' closely approximating the observed experimental v a l ~ e . ~ ~ , ~ ' Useful quantities derivable from the spatial probability density are the radius of maximum radial density, rm,where d -[4nr2p(r)] = 0 at r = r m (16) dr and the radius of half-accumulation, r I l 2 , where 4aLr1"dr r2p(r) = 1/2 Values of these radii are independent of any model for the solvated-electron system. Representative values of these radii, ( $ ) ] I 2 , rm,and rl/z,together with radii, R,which have been estimated from e ~ p e r i m e n t a l land ~ . ~t~h e ~ r e t i c a data l ~ ~ for primitive cavity (71) Tuttle. Jr., T. R.; Golden, S.Chem. Phys. Lett. 1990, 170, 69. (72)Hentz, R.R.;Farhataziz; Hansen, E. M. J . Chem. Phys. 1972,57, 2959.
(73) Dorfman, L. M.; Jou, F.-Y. In Electrons in Fluids, The Nature of Meld-Ammonia Soluriom; Jortner, J., Kestner, N. R., Eds.;Springer-Verlag: New York, 1973; p 456.
The Journal of Physical Chemistry, Vol. 95, No. 15, 1991 5733
Feature Article I
I
I
17
‘8
.
-&
”‘ 16
-3
-4
I5
b k u l mol-‘
Figure 14. Plot of average absorption frequency of solvated-electron optical absorption spectra in liquid ammonia, versus average molar energy of sol~ent.’~
models of these systems are listed in Table 11. The values for ammonia indicate that the r, falls within the presumed cavity and its r l l 2 is just about the computed cavity radius. The values of r, and of r l I 2for water and alcohols fall far outside the presumed cavities; between about 12% and 21% of an electron is contained within them. In addition, the differences in cavity sizes for water and alcohols are just opposite to corresponding differences in the values of r,,, and r1/2.The foregoing extreme variability and lack of meaningful correlation between presumed cavity sizes and maxentropic spatial distributions of solvated electrons raise serious doubts as to the physical significance of a cavity model for solvated electrons. Indeed, as in the cases of water and the alcohols, the idea that the solvated electron itself can sustain a cavity while existing mostly outside of it seems physically unreasonable. Since current quantum-statistical simulations of solvated electrons provide more reliable estimates of their spatial distributions7’than is provided by primitive cavity models, the simulations may help in establishing when a cavity is inconsistent with a solvated electron’s spatial distribution requirements. As a consequence of the fundamental many-particle nature of solvated-electron spectral transition^^^ and the inherent shape stability that their spectra e ~ h i b i t , ~ *an ~ limportant ”~ relationship has emerged7‘ between the spectral energies of a solvated electron and the molecular energies of the solvent in which it is dissolved. Within a justifiable degree of appr~ximation,~‘ it is (in atomic units) 3 ( T ) 4NeffEs(T)= constant (18)
+
where T stands for temperature, Es( T ) is the mean energy of a typical molecule of the solvent, referred to some appropriate reference value, and Nd is an effective number of localizing solvent molecules which provide the energy transfer (measured in units of the molecular energy excess above that at the absolute zero of temperature) required of them during the optical absorption process.73 Tests of eq 18 for ammonia and water are shown in Figures 14 and 15, respectively. From the figures, it is clear that solvent-dependent constant values of Ncffare obtained, which provide an important test of the linear relation. The Neffvalues, 0.76 for ammonia and 0.94 for water, are notably less than unity. When shape stability prevails, other characteristic frequencies, e&, the frequency of maximum absorbance, 3, can be used. With constant Ncr values, we may then differentiate (1 8) to obtain
where
cs,.is the molecular heat capacity of solvent under the
(74) Golden, S.;Tuttle, Jr., T. R. J. Chem. S a . , Faraday Trans. 2 1981. 77, 1421. (75) Golden, S.;Tuttle, Jr., T. R. J . Phys. Chem., in press,
0
I
2
&kCd mol-‘
Figure 15. Plot of average absorption frquency of solvated-electron optical absorption spectra in water versus average molar energy of solvent.”
constraint represented by *. ne^ values so determined for several solvents7‘ are all less than unity. If such were to be found true for all solvated electrons it would suggest that no more than a single localizing solvent molecule need be involved in providing the energy transfer required of it in the optical absorption process. An important application of (1 8) has been made recently75to the SAC model of solvated electrons. That model was used to derive (18) and then to derive an expression for the mean energy of the SAC, E,, in terms of the mean energy of a typical solvent molecule, Es. When measured relative to their energy values at the absolute zero, we obtained MSAC (5/2)NeffAES (20) As a result, the molecular entropy of a SAC and that of a typical solvent molecule were linearly related, viz., (21) $SAC = (5/2)NeJ’gs + k In 2 the k In 2 arising from the spin degeneracy of the SAC. With this, it was possible to calculate a standard entropy of solvation for electrons in water of +118 J/(mol-K), while the most recently reported experimental value76 is +118 f 20 J/(mol-K). For ammonia, the calculated standard entropy of solvation was +120 J/(mol*K),while the most recently reported experimental value7’ is +154 f 30 J/(mol-K). A further consequence of the SAC model application of (18) is that standard entropies of solvation of electrons in all pure solvents should be positive, as observed for ammonia and water. Conventional anions exhibit standard entropies of hydration which are negative. This provides additional support for nor regarding solvated electrons as a prototype of conventional anions, as discussed earlier.
V. Solvated-Electron Optical Absorption Spectra in Solvent Mixtures The most impressive and the most direct spectral evidence supporting the solvent-anion-complex (SAC) model of solvated electrons, mentioned earlier, comes from their solutions in binary mixtures of mutually nonreacting solvents. This evidence and its analysis are independent of any detailed structural model of the SAC’s.
In these solutions, the solvated-electron optical absorption spectra are accounted for by just two independent absorber^^^,'^ characteristic of the two solvents. Just this number is expected from two kinds of SAC’s presumably formed from individual solvent molecules which serve as localization sites for excess electrons in the mixture. The solvated SAC’S are assumed to be (76) Han, P.; Bartels, D. M. J . Phys. Chem. 1990, 91, 7294. (77) Schindewolf, U.Ber. Bunsen-Ges. Phys. Chem. 19%2,86, 887.
5734 The Journal of Physical Chemistry, Vol. 95, No. 15, 1991
Tuttle and Golden SymW J 0 EOA
as-
EDA
U p r o l Hfl EtoH n.$
A
0
0.1
10.0
1.0
K HMPA THF
100.0
Yr'Y,
Figure 16. Tests of the two absorber model of solvated-electronoptical absorption spectra in the binary mixtures ethylenediamine (EDA)hexamethylphosphoric triamide (HMPA),and EDA-tetrahydrofuran (THF).Note that the s l o p of these log-log plots are 1.0 in both cases, as expected by q 25."
in chemical equilibrium with each other and with the solvents (J and K) via sJ-(solv)
+ SK 9 SJ + SK-(SOlv)
(22)
0.a
0.6
0.4
1.0
XJ
Figure 17. Summary of the tests of the two-absorber model of solvated-electron optical absorption spectra in seven different binary solvent systems using half-height-width data" to test q 26.
with an equilibrium constant, KjK, defined by KJK€JK E CJK= X K Y J / X J Y K
0.2
0
I '
'
'
'
'
.
'
.
"
' I
(23)
where
XJ + XK = YJ+ YK = 1
(24) the Xs and Ys are SAC and solvent mole fractions, respectively, and t j K is a factor containing the appropriate composition-dependent activity coefficients of the salient species. In the applications to be described, [jK is taken to be essentially independent of composition. The earliest investigation testing (22)-(24) assumed that binary-solvent spectra of solvated electrons consisted of a pair of unresolvable, broadly overlapping bands, each of which was a shifted version of a solvated-electron band in the appropriate pure solvent. Under these conditions, to an acceptable degree of approximation," it was deduced that 1/W
X J / W J+ X K / W K
(25)
where WJand WKare the half-height widths of the pure solvent spectra and W is the half-height width of the spectrum in the solvent mixture. The SAC mole fractions are determined from (24) and (25) using measured half-height widths. In addition, (23)-(25) combined to give ( l / w - I / W J ) / ( I / W K 1/w) -
=
C J K Y K / Y=XJ/XK J (26)
This provided a means of determining the CJK'Sfrom the measured values of the half-height widths and the mole fractions of the solvents. Figure 16 illustrates a test of (26) for a pair of solvent mixtures. The CJK'Sare the ordinates corresponding to YK/Yj = 1. Equations 24 and 26 allowed the SAC mole fractions to be determined from the determined CJK'Sand the measured solvent compositions. All of the reliable half-height-width data then available could be summarized in terms of the relation (l/wK- l / w ) / ( l / W K -
l / w J )= X J
(27) as is illustrated in Figure 17. Clearly, the data are well accounted for by the two-absorber model. More demanding tests of the two-absorber SAC model of solvated-electron optical spectra have been carried out for the ammonia-methylamine systemm at two temperatures and for several wateralcohol systems at ambient temperature." In every case, a least-squares procedure yielded linear combinations of shifted pure-solvent spectra which reproduced the measured mixed-solvent spectra well within experimental uncertainties. Examples of the results obtained in the ammonia-methylamine system a t 203 K are shown in Figure 18. Because the spectra
1
. V (10' C d l )
Figure 18. Detailed tests of two-absorber model of solvated-electron optical absorption spectra in binary mixtures of ammonia and methylamine at 203 K: 0 , experimental; X, best fits. (a) 50% NH,,(b) 80%
NH,,
(c) 20% NH3.29
of the individual absorbers in the mixtures were taken to be just shifted versions of the respective pure-solvent spectra, it seems most reasonable to infer that the absorbers are essentially the same as those that occur in the pure solvents. The spectral shifts are merely the inevitable consequence of the changes in the solvating medium which must accompany the changes in solvent composition. The above identification of the absorbing species actually present in binary-solvent mixtures of solvated electrons is rein-
The Journal of Physical Chemistry, Vol. 95, No. 15, 1991 5735
Feature Article
a 0.2 1
.Inn-’
8
x 1Y
Figure 19. Area-normalized optical absorption spectra of solvated electrons in mixtures of ammonia and methylamine at 203 K: (a) pure methylamine; (b) 20% ammonia; (c) 50% ammonia; (d) 80% ammonia; (e) pure ammonia.’8
D/Pn-‘
X
1c
Figure 21. Partial molal absorption spectra (open symbols) of solvated SACS for ammonia in panel (a) and for methylamine in panel (b) at 203 K in 50/50 mixtures of ammonia and methylamine, compared with the respective pure-solvent spectra (filled symbols) (0,A, A), 50/50 mixture with K = 2.0, 1.0, and 0.5, re~pectively.’~
0.024 0
0.2
0.4 0.6 ammonia mole fnaion
0.1
-I
1.0
Figure 20. Dependence of area-normalized absorbances at several frequencies versus solvent composition in mixtures of ammonia and methylamine. The symbols designate data points and the lines quartic fits tothedatapoints: @I,-) 10000cm-l(1000nm);(0,--)8333cm-l (1200nm); (A,---) 7143 cm-l (1400nm); (A,---) 6250 cm-l (I600 nm); (0, - - -) 5556 cm-’ ( 1 800 nm).78
forced by an exhibition of their individual spectra. Despite the experimental unresolvability of their combined spectra, an adaptation of the theory of partial molal quantities permits a determination to be made of the partial molal absorption spectra of the two absorbers presumed to coexist in binary-solvent mixtures of solvated electrons.’* By means of that theory under the constraint of the equilibrium in (22), expressed in (23) and (24), the partial molal absorbances AJ(u)and AK(Y)of the two SAC’s are given by
pendence of the a(u)’s (at selected frequencies) from which the area-normalized partial molal absorptions of (28) and (29) can be determined. The curves are quartic polynomials. Because of the sparsity of experimental points available, the determinations were carried out only for equimolar ammonia-methylamine mixtures. Because of uncertainty in CJKvalues (from the twoabsorber-model analysis, CjK = 1.1 at YJ = 0.5 and 203 K29) the determinations were carried out for CjK values of 0.5, 1.O and 2.0. The slopes at YJ= 0.5 were determined from the curves and the resulting area-normalized partial molal absorptions, AJ(u)and AK(u), are shown in Figure 21. The pure-solvent spectra are included for comparison. Despite some slight dependence on the values of CjK, each partial molal absorption spectrum is essentially a shifted version of the appropriate pure-solvent spectrum. In view of the fact that no assumption whatever was made regarding the shapes of the two partial molal absorption bands which emerged, the close resemblance of their shapes to those of the respective pure-solvent spectra represents a compelling demonstration of the correctness of the assumed shape stabilitya of the individual absorption bands in the two-absorber-model a n a l y s i ~ , * described ~ - ~ ~ * ~earlier. The spectra exhibited in Figure 21 are the most direct evidence obtained to date supporting the SAC model of solvated-electron constitution. Although additional evidence is clearly needed, it does seem that some solvated electrons are indeed solvated SAC’s. In no other way, and particularly not in terms of cavity-type entities, does it seem reasonable to have the partial molal absorption spectra of solvated electrons in solvent mixtures retain the spectral signatures that they exhibit in pure solvents. VI. Summary and Suggestions
where &), the molar absorbance of the solvated-electron mixture, is assumed to be given by area-normalized absorptions. The A(u)’s are shown in Figure 19 for several ammoniamethylamine mixtures. Figure 20 shows the composition de(78) Golden, s.; Tuttle, Jr., T. R.;Obremski, Trans. 2 1989,85, 651,
s.J . Chem. Soc., Faraday
There seems to be no compelling reason to accord solvated electrons a cavity-type or a prototypal-conventional anion constitution on the basis of the detailed comparisons we have given of the salient experimental and theoretical facts pertaining to the spectral behavior of the entities involved. Indeed a solvated-anion-complex (SAC) constitution for solvated electrons seems to be the simplest way to account for spectral features which characterize them. Thus, as we have seen, solvated electrons exhibit evidence of a specific influence of solvent molecules through
5136 The Journal of Physical Chemistry, Vol. 95, No. 15, 1991 the virtually invariant, characteristic shapes of their optical absorption spectra. Solvation effects in both pure solvents and binary-solvent mixtures are manifested primarily through a shifting of the individual, characteristic absorption bands. Shifting is a behavior to be expected from spectra of a cavity-type entity and is a behavior actually exhibited by the distinct electronic absorption spectra of conventional solvated anions. However, the specific influence of solvent molecules on spectra neither is to be expected from a cavity-type entity nor is it exhibited in conventional anion spectra. The spectral behavior of an F center exemplifies that of a physical model of the absorbing entity whose properties are almost entirely determined by the physical parameters of the system that embodies it. The spectral behavior of a solvated conventional anion exemplifies that of a chemical model of the absorbing entity whose properties are very largely determined by the chemical species to which the absorbing electron is bound. The spectral behavior of a SAC exemplifies a quasi-chemical model, making SAC's a distinctive new class of anion radicals, whose properties are determined by both their localizing chemical core and by the physical parameters of the surrounding medium. Perhaps the simplest of such species is the one in which the solvated electron of the cavity model is accompanied by one or more solvent molecules (possibly distorted from their equilibrium structure) in the putative cavity. With an annular space of appropriate volume surrounding the localizable solvent molecules, any volume increase that has been observed upon electron solvation could be readily accounted for. However, insufficient evidence is currently available for us to decide on the molecular framework of even this simplest SAC. As a result, much more evidence than that which has been cited will surely be needed before this characterization can be accepted without qualificat.ion. To provide some of this evidence, it would be helpful to have experiments that determine the solvent-composition dependence of solvated-electron spectra in many different mixtures with much more precision than has been done so far. If such data consistently
Tuttle and Golden yield partial molal absorbances that exhibit shapes characteristic of the pure solvents, the actual existence of SAC's could hardly be doubted. Although Newvalues less than unity have been obtained for SAC's in systems investigated to date," there is no innate reason either to infer from this that only one solvent molecule alone is involved as a localization site for a solvated electron or to conclude that clusters of solvent molecules may not serve in that role. Evidence that an electron can bind to an aggregate of certain solvent molecule^"^^ would certainly reinforce such a SAC constitution. Relevant evidence might be obtained in studies of the effect of a solvated electron on the infrared spectral properties of the solvent in both pure solvents and in mixtures. From the theoretical aspect, some of the additional evidence needed is to be found in properties of the SAC model that can be calculated and can be tested against their experimentally determined counterparts. Worthwhile additions would be standard solvation enthalpies and solvation free energies of electr0ns,8~both in pure solvents and their mixtures. Finally, it would be extremely useful to improve current methods of quantum-statistical simulation of solvated electrons to effect better agreement between the spectra calculated for the simulated system and those that are observed for the real system. Application of such methods to mixed-solvent systems merits particular attention since it is these systems that provide the strongest spectral arguments that solvated electrons are neither cavity-type nor conventional-anion-type entities but that they are, in fact, the radical anions that we have termed solvent anion complexes. (79) Kenney-Wallace, G. A.; Jonah, C. D. J . Phys. Chem. 1982,86,2572. (80) Baxendale, J. H. Can. J . Chem. 1977,55, 1996. (81) Brandon, J. R.; Firestone, R. F. J . Phys. Chem. 1974, 78, 792. (82) Brown,B. J.; Barker, N. T.; Sangster, D. F. J. Phys. Chem. 1971, 75, 3639. (83) An inequality involving the solvated-electronchemical potential has been given: see ref 34; also: T. R. Tuttle, Jr.; Golden, S. Rudiut. Phys. Chem. 1984, 23, 629.
