J. Phys. Chem. 1984, 88, 381 1-3818
3811
The Shape as a Characteristic Property of Solvated Electron Optlcal Absorption Bands T. R. Tuttle, Jr.,* Sidney Golden,+Salia Lwenje, and Catherine M. Stupak Department of Chemistry, Brandeis University, Waltham, Massachuetts 02254 (Received: August 24, 1983; In Final Form: January 15, 1984)
Shapes of solvated electron optical absorption bands change radically from one solvent to another. However, for many polar solvents the shape of the spectrum is virtually independent of thermodynamic conditions over a range of such conditions. As a consequence, the spectral shape appears to be a characteristic property of the solvent and of the corresponding solvated electron. Different polar solvents support different solvated electrons which may coexist in chemical equilibrium with one another in solvent mixtures. Recently obtained data not previously analyzed support a two-absorber model of solvated electron optical absorption spectra in a variety of solvent mixtures. These results lend support to the solvated solvent anionic complex model of solvated electrons and suggest that solvated electrons are not the cavity-type entities they have been unquestioningly presumed to be until just recently. Changes in spectral shape correlate with changes in the chemical constitution of the solvent.
Introduction The idea that the shape of the optical absorption band of a solvated electron is an invariant, characteristic spectral property was originally postulated in a correlative theory applied to analyze the then available optical absorption data in binary mixtures of polar solvents in terms of a two-absorber model.' The success of the model in providing a quantitative accounting of the dependence of the spectral widths on solvent composition, of course, lends support to the postulated shape stability of the absorption bands attributable to individually absorbing species. However, the changes in widths alone are insufficient to define fully the concomitant changes in shape. More recently, direct, detailed evidence of the near constancy of shape (shape stability) of solvated electron absorption bands has been obtained in several different pure polar solvents over ranges of thermodynamic condition^.^-^ In chemically different polar solvents the average spectral profiles were shown to be considerably different,* although all of the different profiles are similar in being (more or less) broad, featureless asymmetric bands with long tails extending to high frequencies. The implications of shape stability have been investigated in terms of a rigorous, fundamental, many-body, quantum-statistical mechanical theory of solvated electron system^.^ It has been shown for excess electron systems in which shape stability is extrapolatable to the absolute zero of temperature that the solvated electron absorption band is equivalent to one in which the radiative transitions have an essential discrete-to-continuum nature. Furthermore, shape stability has been shown to arise necessarily from such discrete-to-continuum transitions according to a new adiabatic model of solvated electron systems.6 As a result, the theory provides a fundamental justification for a dual role which has been attributed to the solvent' in solvated electron formation and thereby to the solvated solvent anion' model of solvated electrons. In contrast, the currently popular and widely accepted cavity model of solvated electronss has yet to provide an accounting for shape stability. In fact, by attributing the absorption band to bound-to-bound transitions, the cavity model appears to require a broadening of the absorption band as temperature increases. This is in contradiction with virtually all available relevant spectral data. Furthermore, the cavity model seems to be intrinsically incapable of accounting for the dual role which the solvent appears to assume in determining the optical absorption spectra of solvated electrons. In what follows the occurrence of shape stability of solvated electron optical absorption bands is demonstrated in eight chemically distinct pure solvents. In addition, the Occurrence of a new frequency scaling of the average spectral profiles of solvated electrons is illustrated. This Occurs in four pairs of isoelectronic solvents but not for the profiles in nonisoelectronic pairs. This Professor Emeritus.
0022-3654/84/2088-3811$01.50/0
behavior can be anticipated for solvated electron absorption bands in isoelectronic solvents according to the new adiabatic model of solvated electron systemse6 Finally, the two-absorber model of solvated electron absorption bands is shown to account quantitatively for the compositional variations of the shapes of solvated electron absorption bands in several different binary mixed-solvent systems. Accordingly, solvated electron spectra in these mixedsolvent systems exhibit an extended shape ~ t a b i l i t ywhich ~ . ~ may occur even in pure solvent systems.8 Experimental Section The experimental procedures used here have been for the most part described in detail e l ~ e w h e r e . ~ Spectra of lithium solutions in ethylamine were measured at -40 and -65 OC. Three or four successive spectra were measured for each solution at each temperature. Decomposition half-lives of these solutions were from 15 min to 1 h at -40 O C and from 1 to 4 h at -65 OC. Spectra corrected for the variation in absorbance caused by solution decomposition were determined by an interpolation procedure. Linear least-squares fits of the logarithms of absorbance for the decomposing spectra vs. time were determined for each solution at each temperature. These fits were then used to determine a spectrum at a fixed time. The spectra corrected with this procedure were employed in the extrapolations to infinite dilution. The results of these extrapolations are plotted in Figure 1 along with a solvated electron spectrum in ethylamine at -80 O C obtained by pulse radiolysis.10 The spectra at -40 and -80 O C have been shifted to minimize absorbance differences between them and the -65 OC spectrum. The details of the shifting procedure are given in the following section of this paper. Root-mean-squared deviations in absorbance are also plotted in Figure 1. Shape Stability and Average Spectral Profiles References to the data used in testing for shape stability and parameters determined through application of the required analysis to the data are collected in Tables I-IV. The procedure used (1) Golden, S.; Tuttle, T. R. Jr. J . Phys. Chem. 1978, 82, 944. (2) Tuttle, T. R., Jr.; Golden, S. J. Chem. SOC.,Faraday Trans. 2 1981, 77, 873. (3) Stupak, C. M.; Tuttle, T. R., Jr.; Golden, S. J . Phys. Chem 1982,86, 327. (4) Tuttle, T. R., Jr.; Golden, S.;Hurley, I. J . Phys. Chem. 1982,86, 1801. (5) Golden, S.; Tuttle, T. R. Jr. J . Chem. SOC.,Faraday Trans. 2 1981, 77, 889. ( 6 ) Golden, S.; Tuttle, T. R., Jr. J. Chem. Soc., Faraday Trans. 2 1982, 78, 1581. (7) Golden, S.; Guttman, C.; Tuttle, T. R., Jr., J . Chem. Phys. 1966, 44, 3791. (8) Tuttle, T. R., Jr.; Golden, S. J . Phys. Chem. 1980, 84, 2457. (9) Stupak, C.; Tuttle, T. R., Jr.; Golden, S. J . Phys. Chem., this issue. (10) Seddon, W. A,; Fletcher, J. W.; Sopchyshyn, F. C. Can. J . Chem. 1978, 56, 839.
0 1984 American Chemical Society
3812 The Journal of Physical Chemistry, Vol, 88, No. 17, 1984 0041
‘
I
I
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I
I
1
I
I
1
TABLE 111: Data and Spectral Parameters for Solvated Electron Spectra in Water
t
$
0 6 fF
04
-
a
i c
0 2 -
01 4
6
-
I
1
,
1
8
IO
12
14
Y*
I
I
16 18 (crn-lxi~~)
0
1
20
24
22
26
Figure 1. Plot of height-adjusted relative absorption, fF,vs. reference frequency, u* = v Au, for solvated electron spectra in ethylamine. Values offand Av and references to data are given in Table 11. The rms deviations of all the data at regular frequency intervals are given on a fivefold expanded absorbance scale in the histogram above the plot of the data themselves: 0, 208 K; A, 233 K; v, 193 K.
+
TABLE I: Data and Parameters for Solvated Electron Spectra in Liquid Ammonia P Aub P 6d refe 198 0 0.0076 12 1.000 12 0.0018 1.ooo 208 199 218 417 0.0059 12 0.998 0.0043 9 203 27 0.998 0.0057 9 223 479 1.001 0.0078 9 243 876 0.993 0.0106 13 296 1791 1.048 0.0102 282 1362 13 1.001 13 0.0134 248 96 1 1.019 0.0199 13 226 58 1 1.001 0.0215 13 198 32 0.995 11 200 -27 0.0042 0.992 0.0129 11 220 412 0.969 0.0046 11 240 787 0.994 0.0047 11 255 1047 0.994 OTemperature in Kelvin. bShift in wavenumbers (cm-’) required to minimize rms difference in absorbance with reference spectrum. Multiplicative factor which minimizes rms difference between shifted spectrum and reference spectrum. Rms difference of shifted, heightadjusted spectrum with reference spectrum. e Literature reference. fRms difference of all shifted, height-adjusted spectra used in computing the average profile from the average spectral profile.
TABLE 11: Data and Spectral Parameters for Solvated Electron Spectra in Methylamine, Ethylamine, and 1-Propylamine T Aub P 6d ref‘ CHSNHz 183 0 1.000 0.0083f 3 203 539 1.003 0.0063 3 223 1040 0.996 0.0104 3 24 1 1376 1.022 0.0143 14 208 632 1.016 0.0140 14 184 -37 1.002 0.0103 14 208 233 193 190 200 225 265 295
0 490 -4 3 0
228 1166 2568 367 1
CH,CH,NH, 1.ooo 1.007 1.036
0.0136 0.0116 0.0327
CH~CHZCH~NH~ 1.000 0.0076 0.983 0.0148 1.008 0.0123 1.009 0.0134 1.002 0.0136
Tuttle et al.
g
269 298 363 298 298 298 298 300 300 300 300 283 295 316 339 369 274 298 340 380 302 302 302 302 302 302
h h h h h h h h 0.68 1.35 2.04 h h h h h h h h h h 1.1 2.13 3.53 4.88 6.26
-802 -32 1462 -329 -396 70 -37 19 -321 -744 -929 -628 103 342 1093 1521 -620 0 886 1809 -33 -392 -1015 -1493 -2148 -2725
0.987 0.975 0.961 0.956 0.969 1.004 0.968 0.985 0.968 0.952 0.956 1.006 0.991 1.004 0.990 0.994 1.005 1.000 0.992 0.965 1.017 1.006 0.969 0.918 0.885 0.903
0.0171 0.01 15 0.0374 0.0338 0.0279 0.0090 0.0157 0.0107 0.0157 0.0210 0.0229 0.0145 0.0082 0.0123 0.0191 0.0159 0.0068 0.0159f 0.0127 0.0185 0.0144 0.0293 0.0358 0.0533 0.0512 0.0820
u-fSee footnotes to Table I. gPressure in kilobars. condition.
20 20 20 16 17 18 19 21 21 21 21 22 22 22 22 22 23 23 23 23 24 24 24 24 24 24 Orthobaric
TABLE IV: Data and Spectral Parameters for Solvated Electron Spectra in Methanol, Ethanol, and 1-Propanol P P 6d refe Pg AVb h 298 0 1.000 0.0164‘ 25 303 h 21 0.994 0.0167 26 195 -1876 1.011 h 0.0222 29 300 h 0.0184 150 1.015 21 298 h 0.0467 328 1.012 28 300 h 74 1.019 0.0187 21 0.65 300 0.0161 -671 1.019 21 300 0.0218 21 1.38 -1324 1.013 300 2.10 0.0161 21 -1799 1.010 183 h -1147 0.996 0.0531 27 243 h -1016 1.003 0.0255 27 294 h 0.0205 27 -49 1.013 336 h 0.0151 27 602 1.007 h 356 0.0427 27 839 1.051
h h h h h h h h 0.69 1.38 2.03
CH3CH20H 0 1.000 1176 1.208 -2404 1.036 368 1.043 -2903 1.025 -1233 1.026 317 1.005 804 1.017 1318 0.994 261 1.042 349 1.038 -671 1.037 -1397 1.032 -1906 1.004
0.0203f 0.1463 0.0317 0.0320 0.0363 0.0250 0.0223 0.0128 0.0098 0.0308 0.0355 0.0264 0.0258 0.0373
25 26 29 30 27 27 27 27 27 28 21 21 21 21
h h h h 0.79 1.55 2.41
CH3CHZCH20H 1200 1.102 1452 1.096 3186 1.233 0 1.000 -1150 1.001 -2061 1.010 -2851 1.010
0.0745 0.0853 0.2027 0.0063f 0.01 12 0.0139 0.0128
25 30 28 21 21 21 21
298 303 195 299 173 234 296 323 343 RT 300 300 300 300
h h
298 299 RT 300 300 300 300
n
g
14 15 15 15 15 15
‘TfSee footnotes to Table I. gThis work.
here to test for shape stability differs from the one previously employedZin that the shifts, Av, of the different sets of data to
”-/See footnotes to Table I.
gqh
See footnotes to Table 111.
the reference frequency scale, v * , are determined by minimizing differences in absorption between shifted spectra and reference
The Journal of Physical Chemistry, Vol, 88, No. 17, 1984 3813
Shape of Solvated Electron Adsorption Bands
0.04
8 01 0
a L
1
I
I
I
I
I
I
I
I
0.02
0
I .o
e
1.2
e.
0.8 I .o
0.6 fF
04
0.8
02 0 1 ' 6
9 abn
'
'
8
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"
12
14
I
16
*
'
'
'
'
'
1
18
20
22
24
26
28
1
ut ( c r n - ' x 1 0 ~ ) Figure 2. Plot of height-adjusted relative absorption, fF,vs. reference frequency, u* = u Au, for solvated electron spectra in 1-propylamine. Values offand Au and references to data are given in Table 11. The rms deviations of all the data at regular frequency intervals are given on a tenfold expanded absorbance scale in the histogram above the plot of the data themselves: 0, 190 K, A, 200 K; V; 225 K; 0,265 K; 0 , 295 K.
+
spectrum rather than frequency differences. Specifically, the quantity which is minimized is the root mean square (rms) difference in absorbance given by
f F 0.6
0.4 0.2
0 0
C I
I
0 IO
I
I
I
1
I
I
22 26 30 34 38 (cm-1 x 103) Figure 3. Plot of height-adjusted relative absorption, fF,vs. reference frequency, u* = u + Au, for solvated electron spectra in ethanol. Values o f f and Au and references to data are given in Table IV. The rms deviations of all the data used in constructing the average spectral profile are given on a fivefold expanded absorbance scale in the histogram above the plot of the data themselves: 0, 298 K; 0, 303 K; 0, 195 K; A, 299 K; A, 173 K V, 234 K; V, 296 K; 0,323 K W, 343 K 0 , RT; e, 300 K; 0,300 K, 0.69 kbar; +, 300 K, 1.38 kbar; X, 300 K, 2.03 kbar. Reference to the different data sets here is made in the same order as in Table IV. Note that the data set represented by the symbol 0 has been excluded from the calculation of the average spectral profile and therefore also from calculation of the values of 6 plotted in the histogram. (See text for details.) 14
18
u*
in which F'(v) and F(v) are the unit height normalized spectra. The values of Av determined in this way do not differ greatly from values determined by the earlier method. However, the minimization of absorbance differences is preferred because it provides a more realistic weighting of the experimental data in determining the shifts. An additional minimization of absorbance differences between shifted and reference spectra is effected by varying the amplitude of the shifted spectra, simply by multiplying it by the factor, f. This second minimization removes the special role originally accorded the maximum absorbances by normalizing each spectrum independently to unit maximum absorbance. Values of 6, Av,andfdetermined by the described procedure for the eight different solvent systems are given in Tables I-IV. Only solvated electron spectra corresponding to infinite dilution I .o in metal or from pulse radiolysis experiments were included in the present analyses. 0.8 Ammonia and Amines. Shape stability has been tested previously for solvated electron optical absorption spectra in ammonia2 f F 0.6 and in The present tests have included newly acquired data for spectra in ethylamine, and propylamine.I5 The results of these tests are summarized in Tables 0.4 I and 11, and graphical representation of shape stability for the newly tested systems are given in Figures 1 and 2. The values 0.2 of 6 given in the tables indicate that shape stability is maintained "'0" within experimental uncertainty by the solvated electron spectra I I I 1 I I I I 0 in each of the four systems over a range of conditions. IO 1 4 18 22 2 6 3 0 34 38 42 Water ana' Alcohols. Shape stability of solvated electron optical v* ( c r n - ' x ~ ~ - ~ ) absorption spectra has been tested previously2 for water and for Figure 4. Plot of height-adjusted relative absorption, fF,vs. reference methanol. As a measure of the experimental error of the available frequency, u* = u + Au, for solvated electron spectra in 1-propanol. data average 6 values for a number of spectra determined under Values off and Au and references to data are given in Table IV. The nearly the same conditions were obtained. Their values are 0.0175, 0.0242, and 0.0302 for water,16-19 m e t h a n ~ l , ~ l ,and ~ ~ - ~ ~ rms deviations of all the data used in constructing the average spectral profile are given on a tenfold expanded absorbance scale in the histogram above the plot of the data themselves: 0, 300 K; A, 300 K, 0.79 kbar;
(11) Jou, F.-Y.; Freeman, G. R. J . Phys. Chem. 1981,85,629. (12) Rubinstein, G. Thesis, Brandeis University, 1973. (13) Farhataziz; Perkey, L. M. J. Phys. Chem. 1975, 79, 1651. (14) Seddon, W. A.; Fletcher, J. W.; Sopchyshyn, F. C. Can. J . Chem. 1978,56, 839. (15) Jou, F.-Y.; Freeman, G. R. Can. J. Chem. 1982,60, 1809. (16)Gordon, S.; Hart, E. J. J. Am. Chem. SOC.1964,86,5343. (17) Keene, J. P. Discuss. Faraday SOC.1963,36, 307. (18) Fielden, E. M.; Hart, E. J. Trans. Faraday SOC.1967, 63, 2975. (19) Boyle, J. W.; Ghormley, J. A.; Hochanadel, C. J.; Riley, J. F. J. Phys. Chem. 1969, 73,2886. (20) Michael, B. D.; Hart, E. J.; Schmidt, K. H. J . Phys. Chem. 1971,75, 2798.
V, 200 K, 1.55 kbar; 0,300 K, 2.41 kbar; 0 , 298 K; 0,299 K; + RT. Note that the data sets represented by the symbols 0, 0, and + have been excluded from the calculation of the average spectral profile and therefore also from calculation of the value of 6 plotted in the histogram. (See text for details).
e t h a n ~ l , Z ~respectively. ~ * , ~ ~ Accordingly, we have excluded spectra with 6 > 0.05 from determinations of average spectral profiles (21) Jou, F.-Y.; Freeman, G. R. J. Phys. Chem. 1977,81,909. (22) Gottschall, W. C.; Hart, E. J. J . Phys. Chem. 1967,71,2102.
The Journal of Physical Chemistry, Vol. 88, No. 17, 1984
3814
Tuttle et al.
TABLE V Parameters Obtained in Relative Frequency Scaling of Some Average Spectral Profiles
P
R" 3"
CH3NH2 CHjCH2NH2 CH3(CH2)2NH2
d
H2O CH30H CHSCH20H CH3(CH2)20H
0.4493 0.4484 0.4467 0.4155
CH3NH2 CHBCHZNHZ CH,(CH2)2"
0.6486 0.5544 0.4542 0.6385 0.5633 0.4749
CH3OH CH3CH20H CH,(CH2)20H
f"
p' 1.020 1.202
be
a$
ad
0.007
0.016 0.016 0.020 0.006
1.015 1.005 0.995 0.994
0.015 0.025 0.017 0.015
1.619 2.710 3.081
1.000
0.007 0.007 0.007
0.013
1.005
0.047 0.066 0.060
3.214 4.843 5.710
1.000 0.995 0.983
0.050 0.065 0.050
0.016 0.016 0.016
0.016 0.020 0.006
1.118 1.369
1.010
0.008 0.013
0.008
0.008
0.008
Reference substance. Substance whose spectral profile is transformed. CParameters determining transformed spectra, FT(w + 0). dMultiplicativefactor used to minimize 6. e Rms deviation between reference and transformed spectra. fRms deviations of average spectral profiles for substances R and T, respectively. I .o
0.8
- 0.6 F
0.4 0.2 0
4
6
8
IO
12 v*
14
16
18
20
22
24
(crn-lxt~~)
Figure 5. Average spectral profiles for solvated electron optical absorption spectra in ammonia and some aliphatic amines. Average relative absorbances,F, are plotted against frequency on a reference frequency scale. Values of v* have no particular absolute significance: 0,ammonia; 0, methylamine; A, ethylamine; V, I-propylamine.
either as being too inaccurately determined or a showing significant departures from shape stability. The results of the tests for shape stability are given in Tables I11 and IV, and graphical representation of shape stability for the newly tested systems are given in Figures 3 and 4. For ethanol all but one of the spectra seem to fall on a single spectral profile. The reason for the single exceptional spectrum is not known at present. For propanol three distinct profiles are evident. The broadest of these, which contains the preponderance of data, has been selected here as the spectral profile of the solvated electrons. However, neither of the other two profiles can be eliminated from consideration on the basis of available evidence. The values of 6 given in Tables I11 and IV indicate that shape stability is maintained within experimental uncertainty by the solvated electron spectra in each of the four systems over a range of conditions. Average Spectral Profiles and Frequency Scaling of Spectral Shape The average profiles of solvated electrons in ammonia and the three amines are plotted in Figure 5 . Each one of these profiles differs from the others and so serves to characterize the solvent and its solvated electron. Likewise, the average spectral profiles of solvated electrons in water and the three alcohols, plotted in Figure 6, differ from one another sufficiently so that each spectrum can serve as an identity tag. Comparison of the spectral profiles of corresponding -NH2 and -OH compounds plotted in Figures (23) (24) 4974. (25) (26) (27) 3876. (28) (29) (30)
Jou, F.-Y.; Freeman, G. R. J . Phys. Chem. 1979, 83, 2383. Hentz, R. R.; Farhataziz; Hansen, E. M. J . Chem. Phys. 1971, 55, Leu, A.-D.; Jha, K. N.; Freeman, G. R. Can. J . Chem. 1982,60,2342. Hentz, R. R.; Kenney-Wallace, G. A. J . Phys. Chem. 1974,78,514. Jha, K. N.; Bolton, G. L.; Freeman, G. R. J . Phys. Chem. 1972,76,
Sauer, M. C.; Arai, S.; Dorfman, L. M. J . Chem. Phys. 1965,42,708. Arai, S.; Sauer, M. C. J . Chem. Phys. 1966, 44, 2297. Jou, F.-Y.; Freeman, G. Can. J . Chem. 1979, 51, 1591.
6
IO
14
18 Y*
22
26
30
34
38
(crn-lx 1 0 3 )
Figure 6. Average spectral profiles of solvated electron optical absorption spectra in water and some aliphatic alcohols. Average relative absorbances, E, are plotted against frequency on a reference frequency scale. Values of v* have no particular absolute significance: 0,water; 0, methanol; A, ethanol; v, 1-propanol.
5 and 6 reveal striking similarities. However, because the frequency scales differ by a factor of two, we can readily recognize that, though apparently similar, the spectral profiles of the corresponding compounds actually differ appreciably in breadth. Accordingly, for each of the solvents dealt with here the solvated electron spectral profile is a distinctive, characteristic property of the solvent and its solvated electron. Nevertheless, the perceived similarity of spectra plotted in Figures 5 and 6 suggests that the profiles characteristic of similarly substituted -NH2 and -OH compounds may be related through a simple frequency scaling such that FT(av
+ 6 ) = FR(y)
(2)
in which the Fs are the unit maximum normalized spectra for solvents R and T, respectively, and a and are constants. To test this idea we choose values of a and 0 so as to minimize
for a number of pairs of solvents. An inspection of the last three ~ 6, + ST or 6 , = ~ 6, + columns in Table V indicates that 6 , < 6 , for similarly substituted -NH2 and -OH compounds and SRT >> 6 , 6T for other pairs. Apparently the linear transformation of the frequency scale brings about the equality expressed in eq 2 in some cases but not in others. According to the new adiabatic model of solvated electron systems,6 only isoelectronic pairs of systems can be expected to have spectral profiles related by a linear frequency scaling. This is just the result we have obtained for the four similarly substituted -NH2, -OH pairs. This theory also leads us to expect that a will depend on the change in the Hamiltonian of the anionic complex which occurs in converting one member of an isoelectronic pair
+
The Journal of Physical Chemistry, Vol, 88, No. 17, 1984 3815
Shape of Solvated Electron Adsorption Bands 1.0
-
I
l
e
P
0.8
-
I
I
I
I
I
I
e
-
I .o
O
0
?
-
P
0.8
06
1
f?
0.4
0.2
4
6
8
IO
12
14
18
16
20
,
(cm-'x103)
u*
Figure 7. Demonstration of frequency scaled shape stability for solvated electron spectral profiles in the isoelectronic pair of solvents NH3-H20. Height-adjusted relative absorbances are plotted vs. u * . For NH3,f = 1.000, u* = u; for H,O,f; 1.015, u* = 0.4493 + 1.020u, cf. Table V: 0, ammonia; water.
+,
6
1
I
12
IO
8
u*
I
14
1
18
I
(crn-lx10~)
Figure 9. Demonstration of frequency scaled shape stability for solvated electron spectral profiles in the isoelectronic pair of solvents CH3CH2NH2-CH3CHzOH. Height-adjusted relative absorbances are plotted vs. v*. For CH,CH,NH,, f = 1.000, u* = u; for C H 3 C H 2 0 H , f = 0.995, u* = 0 . 4 1 5 5 ~ 1.369, cf. Table V: 0, ethylamine; ethanol.
+
1.0
I
16
+,
I .o
0.8
0.8
0.6
fF
0.6
fC
0.4
0.4
0.2 0.2
6
I
I
8
IO Y*
I
1
12 14 (cm-'x103)
I
I
16
18
0
IO
8
6
12 V*
Figure 8. Demonstration of frequency scaled shape stability for solvated electron spectral profiles in the isoelectronic pair of solvents CH3NH2C H 3 0 H . Height-adjusted relative absorbances are plotted vs. u * . For CH3NH,, f = 1.000, u* = u; for CH30H, f = 1.005, u* = 0.4484~ 1.202, cf. Table V: 0,methylamine; +, methanol.
+
to the other. Inspection of the values of a given in Table V shows that this expectation of the theory is fulfilled rather well for the four pairs of isoelectronic systems included there for which a = 0.440 h 0.012. Comparisons of the transformed and reference spectra for the isoelectronic pairs are presented in Figures 7-10. For the nonisoelectronic pairs the linear scaling is not adequate to superimpose their spectra. The comparison of the transformed methylamine spectral profile to that for ammonia given in Figure 11 serves to illustrate the inadequacy of the linear frequency scaling for the nonisoelectronic pairs. Nevertheless, the fact that a particular chemical substitution is associated with a nearly constant value of a suggests that a common though more complicated transformation, which depends only on the change in the solvent system, may be appropriate for nonisoelectronic pairs. We shall defer this point for future investigation.
14
16
20
18
(crn-'x103)
Figure 10. Demonstration of frequency scaled shape stability for solvated electron spectral profiles in the isoelectronic pair of solvents CH3(CHz)2NH2-CH3(CH2)20H. Height-adjusted relative absorbances are plotted vs. u * . For CH3(CHz),NHz,f = 1.000, u* = u; for CH3(CH J 2 0 H , f = 0.994, u* = 0 . 4 1 5 5 ~ 1.369, cf. Table V: 0,l-propylamine; +, 1-propanol.
+
I
d
'0
0.6
fF 0.4 0.2
Two-Absorber Model The two-absorber model of solvated electron absorption spectra which we employ here in analyzing recently obtained absorption spectra in binary mixtures of water and four different alcohols has been presented earlier in conjunction with an analysis of the compositional dependence of half-weight widths of solvated electron spectra in a variety of binary mixed polar solvents.' The procedure used here in fitting the spectra is described in the previous paper.g Briefly, by first shifting the pure solvent spectra so that their maximum absorbances coincided, and then shifting
0 6
IO
8 u*
12
14
16
(crn-lx10~)
Figure 11. Demonstration of lack of frequency scaled shape stability for solvated electron spectral profiles in the nonisoelectronic pair of solvents NH, - CH3NH2. Height-adjusted relative absorbances are plotted vs. u * . For N H , , f = 1.000, u* = u; for C H 3 N H , , f = 1.000, u* = 0 . 6 4 8 6 ~ + 1.619, cf. Table V: 0, ammonia; methylamine.
+,
3816 The Journal of Physical Chemistry, Vol. 88, No. 17, 1984 the mixed-solvent spectrum, we minimized the root-mean-squared differences in absorbances between each experimentally determined mixed-solvent spectrum and a suitably constructed linear combination of (shifted) pure solvent spectra. The relative amounts of the two pure solvent spectra in the linear combinations are automatically determined in the fitting procedure usedg so that the only adjustable parameters in obtaining the fits are the spectral shifts. In practice, we have found that the quality of the fits turned out to be insensitive to the relative shifts of the two pure solvent spectra over a rather broad range of values centered about the value which brings the maxima of the two bands into coincidence. Because of this insensitivity, this relative shift was fixed in the fitting procedure so as to require coincidence of the two maxima. The results of applying this two-absorber model to solvated electron absorption spectraz5 in four different water-aliphatic alcohol systems are displayed in Table VI. Results previously obtained for the ammonia-methylamine system9 are included in the table for comparison. The rms differences between the experimental spectra and their best fits for the wateralcohol systems in no case exceed about 2% of the maximum absorption. More detailed comparisons of the fits for water-1-propanol mixtures are given in Figure 12. These comparisons are representative of those obtained for all four systems. The difference spectra included in the figures illustrate the quality of the fits in detail. Note that these difference spectra are plotted on an absorption scale which is expanded by a factor of five compared to the absorbance scales for the spectra themselves. It appears that the two-absorber model accounts for the observed variations in spectral shape of solvated electron bands with changing solvent composition within experimental uncertainty in all four water-alcohol systems. The rms deviations given in Table VI for the ammoniamethylamine system appear to exceed the estimated experimental uncertainties ~ l i g h t l y .These ~ discrepancies could arise from a lack of strict adherence of the individual absorption bands to shape stability in this mixed-solvent system, or from the presence of small amounts of additional absorbing species. Additional experimental results will be required to determine the source of the apparent discrepancies in the ammonia-methylamine system.
Discussion Shape stability of solvated electron optical absorption bands has now been demonstrated to occur in a total of eleven different pure solvent systems over a range of thermodynamic conditions. In addition, the use of shape stability with a two-absorber model accounts quantitatively for the observed variations in five different binary mixed-solvent systems. (Some slight departures from the expectations derived from the two absorber model were found for one of the systems, ammonia-methylamine.) Table VI1 summarites the cases both where shape stability occurs and where it does not. In view of the evidence presented it seems proper to regard the shape of its optical absorption band as a characteristic property of the solvated electron which gives rise to the absorption. Furthermore, because the band shapes in different solvents are different, the band shape is a distinctive, characteristic property capable of being used to identijy a particular solvated electron and to distinguish it from other solvated electrons. Evidently, the so-called solvated electron is not at all a unique chemical species. It is, rather, a number of chemical species. The number at least equals, and most probably exceeds, the number of different pure solvent systems in which such species may be produced. By contrast, the position of the solvated electron optical absorption band (as measured, say, by its position of maximum absorption), the focus of many theoretical calculations, is not entirely a characteristic property of individual solvated electrons. It depends on thermodynamic conditions as well as the identity of the particular solvent. As a result, two different kinds of properties are required in describing solvated electron absorption bands: a characteristic property independent of conditions such as the band shape and an environmentally dependent property such as the band position. Herein lies an observational basis for invoking a dual role for the solvent in solvated electron formation. N o theoretical model of
Tuttle et al.
I
0 02 0 14
IO
22
18
0.002 -0.002
+*+++
26
30
34
38
(crn-lx10~)
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**
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-I
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I 0.002 0 t A ( f G '- 0.002 . -0.004 f I*
14
+++*I t +
+
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0.02
i
0
10
14
22
18 Y'
26
30
34
38
(crn-l X I 0 3 1
Figure 12. Tests of two-absorber model in 1-propanol-water mixtures. In each case the experimental spectrum, 0,normalized to unit area is compared to a calculated "best fit", X. See the text for a description of the fitting procedure. Values of the parameters,fand Au, which define the "best fits" are given in Table VI. Values offG are plotted vs. vt on a relative frequency scale conveniently chosen for the comparisons shown. Difference spectra are plotted above each comparison on a fivefold expanded scale: (a) 98% H20; (b) 50% H20; (c) 10% HzO.
solvated electrons which fails to incorporate this dual role of the solvent can hope to provide a full description of these species. In particular, the currently popular cavity model attributes only a solvating role to the solvent. As a consequence, all variation of properties obtained from this model as environmental conditions change must reflect the variation of solvation produced by the change in these conditions. To account for the specific characteristic features observed in the shape stability of solvated electron
The Journal of Physical Chemistry, Vol. 88, No. 17, 1984 3817
Shape of Solvated Electron Adsorption Bands
TABLE VI: Parameters for the Fits of Mixed-Solvent Spectra Using the Two-Absorber Model P J* YIC Xld CW' if Avg 298 CH3OH 1 .oo 15.912 0 0.90 0.817 2.01 15.373 0.562 0.50 0.319 2.14 14.771 1.078 0.02 0.088 0.21 13.927 1.852 0.00 13.886 2.025 298
298
298
203
223
CHACH2)zOH
(CH3)ZCHOH
(CH3)BCOH
CH3NH2
CH3NH2
P
6'
1.005 1.010 1.010
0.00084 0.00107 0.00070
17.576 13.153 9.892 9.040 8.705
1.033 1.020 1.013
0.00153 0.00096 0.00069
Ah 15.254 13.577 10.123 9.069 8.705
1.00 0.90 0.50 0.02 0.00
0.669 0.237 0.07 1
4.44 3.22 0.27
15.628 13.925 14.366 14.148 13.886
0 1.688 1.266 1.531 1.742
1.oo 0.90 0.50 0.02 0.00
0.520 0.131 0.108
8.31 6.61 0.17
12.457 12.729 13.975 14.100 13.886
0 -0.250 -1.527 -1.664 -1.430
16.425 11.527 9.279 9.173 8.705
1.030 1.020 1.010
0.00110 0.00093 0.00039
1.oo 0.90 0.50 0.02 0.00
0.781 0.272 0.194
2.53 2.68 0.09
9.696 11.537 14.011 14.062 13.886
0 -1.641 -4.125 -4.3 13 -4.190
10.791 10.272 9.207 9.048 8.705
1.000 1.020 1.015
0.00094 0.00140 0.00089
1.oo 0.80 0.50 0.20 0.00
0.666 0.473 0.217
1.95 1.11 0.90
8.022 7.974 7.877 7.643 7.238
0 0.088 0.251 0.421 0.784
6.698 5.519 5.024 4.469 4.086
1.016 1.025 1.034
0.00415 0.00428 0.00274
1 .oo 0.80 0.50 0.20 0.00
0.640 0.514 0.264
2.25 0.95 0.70
7.500 7.557 1.395 7.201 6.775
0 -0.013 0.188 0.338 0.726
6.924 5.492 5.060 4.517 4.018
1.020 1.025 1.035
0.00327 0.00394 0.00268
OTemperature in Kelvin. bSolvent J of J-K mixtures. Solvent K is water when J is an alcohol, and ammonia when J is methylamine. CMole fraction of solvent J. dMole fraction of solvated electron J. eConcentration product for reaction Sc + SK+ SJ + SK-,Le., CJK= X,Y,/XjYK. /Frequency of maximum absorption in thousands of wavenumbers. ZFrequency shift of experimentally determined solvated electron absorption bands in thousands of wavenumbers in two-absorber model analysis. Area of experimentally determined solvated electron absorption band in thousands of wavenumbers. 'Multiplicative factor used to minimize difference between the linear combination of pure solvent spectra and the spectrum in the mixed solvent. 'Rms difference between best-fit and experimental spectrum. 1006A gives the rms difference as a percentage of the maximum absorption.
TABLE VI1 Summary of Evidence Pertaining to Spectral Shape Stability and the Two-Absorber Model solvent svstem SSS" non-SSSb Figures" 3" 198-302 K 302 K, 1.06-6.7 kbar 202-246 K ND3 CH3NH2 183-241 K CH3CH2NH2 193-233 K (193 K)e 1 CH3(CH2)2NH2 190-295 K 2 H2O 269-380 K 302 K, 3.53-6.26 kbar 300 K, 0-2.04 kbar 302 K, 0-2.13 kbar D20 274-634 K CH3OH 195-356 K 183 K 300 K, 0-2.1 kbar CHjCHZOH f 3 173-343 K 300 K, 0-2.03 kbar g 4 CH3(CH2)20H 300 K, 0-2.41 kbar
TablesC I I1 I1 I1
refd 2, 4, 12 2, 4 2, 3
111
2
IV
2 2
IV IV
-0-
CHZCH2CHZCH2 H2O-CHjOH HZO-CH, (CH2)ZOH H,O-(CH,),CHOH H,O-(CH3),COH NHj-CH,NH, NHS-CH,NHz
155-273 K 298 K 298 K 298 K 298 K 203 K 233 K
2 12
h h
VI VI VI VI
9 9
" Conditions under which spectral shape stability occurs or, for mixed solvents, condition under which two-absorber model applies. Conditions under which spectral shape stability does not persist or, for mixed solvents, condition under which two-absorber model does not apply. 'Numbers of figures or tables in this paper which present evidence of spectral shape stability or tests of the two-absorber model. dLiterature references in which evidence of spectral shape stability or tests of the two-absorber model are presented. 'Possible deviation at lowest temperature. /One spectrum deviates in shape strongly from all the others even though obtained under essentially the same conditions as several other spectra. See text for discussion. gAvailable data define three distinct spectral profiles. See text for discussion. hThe deviations of the two absorber model fits appear to exceed experimental error suggesting that the shapes of the individual solvated electron absorption bands may change in shape slightly as solvent composition is changed.
J . Phys. Chem. 1984,88, 3818-3820
3818
optical absorption bands in just this way seems rather unlikely, if not entirely impossible. In contrast, the solvent anion (solvated solvent anionic complex) model of solvated electrons incorporates the dual role of the solvent in a physically relevant and appropriate manner. The anionic complex, in which the electron is intimately associated with a small cluster of solvent molecules, presumably gives rise to the distinctive, characteristic shape of the optical absorption spectrum while the bulk of the solvent in its solvating role stabilizes the complex and gives rise to the environmentally dependent position of the optical absorption spectrum. This description of solvated electrons does not require for its validity that the small cluster of solvent molecules which localizes the electron has a positive electron affinity in the gas phase as, for example, the stability of solvated S2(sulfide ion) does not require a positive gas-phase electron affinity of the singly charged sulfur anion. In conclusion, the observed prevalence of shape stability of solvated electron absorption bands and its successful applications in the two-absorber model analyses provide a measure of exper-
imental support for the solvent anion model of solvated electrons. It still remains for the cavity model to provide a reasonable quantitative account of the observed spectral shape stability. Until it can do so, any claim that it represents solvated electrons correctly should be viewed with skepticism.
Acknowledgment. We are grateful to F.-Y. Jou and G. R. Freeman for providing us with tabulated versions of their solvated electron spectra in water23and in l-pr~pylamine’~ and to A,-D. Leu, K. N. Jha, and G. R. Freeman for tabulated versions of their solvated electron spectra in the several alcohols and their mixtures with watersz5 This project was supported in part by BRSG SO7 RR07044 awarded by the Biomedical Research Support Grant Program, Division of Research Resources, National Insitutes of Health. Registry No. NH3, 7664-41-7; CH3NH2, 74-89-5; CH3CH2NH2, 75-04-7; CH,(CH2)2NH2, 107-10-8; H20,7732-18-5; CH,OH, 67-56-1; CH&!H20H, 64-17-5; CH3(CH2)20H, 71-23-8; ND3, 13550-49-7; D20, 7789-20-0.
Studies of the Stability of Negatively Charged Water Clusters Neil R. Kestner* Chemistry Department, Louisiana State University, Baton Rouge, Louisiana 70810
and Joshua Jortner Chemistry Department, Tel Aviv University, Ramat Aviv, 69978 Tel Aviv, Israel (Received: August 24, 1983; In Final Form: January 15, 1984)
The polarization model of water interactions developed by Stillinger and co-workershas been used for calculations on various types of small water clusters which have been proposed for both the neutral (H20), species and for the (H,O); ( n = 4-8) negative ions. These results are combined with the recent quantum mechanical results of Rao and Kestner to estimate the energetics of small negative clusters. The formation of a (H,O); cluster by electron attachment to an equilibrium cluster is accompanied by large configurationalchanges, resulting in considerable cluster reorganization energies. The electron affinities of equilibrium (H20), clusters are negative, while electron attachment can occur to metastable neutral clusters with n 2 6.
Introduction Over the past ten years a great many studies have been made of the trapped electron in the fluid These studies have included many model calculations as well as the detailed ab initio calculations of Newton4 in which accurate first coordination calculations were combined with a self-consistent interaction with a continuum polar fluid. These calculations have been quite successful in describing the electronic properties of the trapped species (except for the absorption line shape’), but they have had rather large uncertainties in the predictions of the stabilities of these species because of the uncertainties in calculating the energy to distort the medium, especially where hydrogen bonding is important. Central information on the energetics and dynamics of electron localization will be provided from the exploration of electron attachment to clusters of polar molecules. Studies of the absorption spectra of excess electrons in supercritical ammonia5V6 and have provided conclusive evidence for electron (1) D. A. Copeland, N. R. Kestner, and J. Jortner, J . Chem. Phys., 53, 1189 (1970). (2) K. Fueki, D-F. Feng. L. Kevan, and R. Christofferson,J. Phys. Chem., 75, 2291 (1971). (3) K. Fueki, D-F. Feng, and L. Kevan, J . Am. Chem. SOC.,95, 1398 (1973). (4) M. Newton, J . Chem. Phys., 58, 5833 (1973). ( 5 ) R. Olinger, S. Hahne, and U. Schindewolf, Ber. Bunsenges. Phys. Chem., 76, 349 (1972). (6) (a) A. Gaathon, G. Czapski, and J. Jortner, J . Chem. Phys., 58,2648 (1973): (b) J. Jortner and A. Gaathon, Can. J . Chem., 55, 1801 (1977).
0022-3654/84/2088-3818$01.50/0
localization at moderately low densities6b ( p 1 8 X g for D,O, while p 2 5 X for ND3 near the thermog dynamic coexistence curve and p 1 0.15 g cm-3 at 200 “C).These observations were interpreted6bin terms of electron trapping in preexisting clusters, which originate from density ,fluctuations. However, the information emerging from these bulb experiments is intrinsically limited because of two reasons. Firstly, the size of both the preexisting clusters and the final cluster, which attach the excess electron, cannot be determined directly and can only be inferred indirectly. Secondly, this information pertains to the fluid regime and is not really characteristic of isolated clusters. The remarkable recent progress in the applications of supersonic jets and nozzle beams’ led to experimental studies of electron attachment to “isolated” clusters. Of primary interest, of course, has been negative clusters of water molecules. Several groups8 have searched for the (H,O),- cluster. Recently, Haberland et aL9 have reported the observation of (HzO); and (DzO); ( n 1 11) clusters. In this short paper we will try to present a theory of the electronic and nuclear structure of the (H20); ( n = 4-8) clusters. (7) (a) 0. F. Hagena, Surf. Sci., 106, 101 (1981). (b) J. Farges, M. F. de Feraudy, B. Rauolt, and G. Torchet, ibid., 106, 95 (1981). (8) (a) D. Herschbach, Harvard University, private communication. (b) R. Compton, Oak Ridge, privatee communication. (c) H. Haberland, Freiburg University, private communication. (9) (a) M. Arbuster, H. Haberland, and H. G. Schneider, Phys. Reu. Lett., 47, 323 (1981). (b) H. Haberland, H. Langosch, H. G . Schnieder, and D. R. Worsnop, to be submitted for publication.
0 1984 American Chemical Society
