6794
J. Phys. Chem. 1995,99, 6794-6800
Temperature Dependence of Optical Absorption Spectra of Solvated Electrons in CD30D for T IT, V. Herrmann and P. Krebs* Institut fllr Physikalische Chemie und Elektrochemie der Universitat Karlsruhe, Kaiserstrasse 12, 0-76128 Karlsruhe, Federal Republic of Germany Received: September 21, 1994; In Final Form: February 13, 1995@
Brodsky and Tsarevsky (J. Phys. Chem. 1984, 88, 3790) developed a theory on solvated electrons (esolv-) which is based on the concept that the excess electron is localized in a medium predominantly by shortrange interactions. Including many-body collective effects of the solvent, they tried also to explain the temperature dependence of the optical absorption spectra of esolv-. To substantiate their point of view, they presented experimental spectra of esolv- in CH30H measured over a wide range of temperatures which were in “satisfactory quantitative agreement” with theory. We have carefully repeated optical absorption measurements on esolv- in CD30D in the temperature range 298 5 T 5 510 K. We report on these experimental results and on the static dipole polarizability (a(0)) of solvated electrons in different media determined by means of optical sum rules. Both results are inconsistent with the above-mentioned theory. The comparison of other ground-state properties of solvated electrons in methanol such as the mean dispersion in position (A$) and the mean quantum mechanical kinetic energy (Q following from the spectra with those obtained by a quantum molecular dynamics simulation shows poor agreement.
I. Introduction It is obviously a very difficult task to get a physically meaningful model to describe an excess electron localized in a disordered polar medium, the so-called solvated electron. The properties of the solvated electron have been studied by a variety of theoretical methods such as ab initio MO calculation^,'-^ semiempirical model^,^-^^ and quantum path-integral molecular dynamics (QUPID)computer calculation^.^^-^^ One of the most frequently investigated property of esolv- in polar liquids is its optical absorption ~ p e c t r u m which ~ ~ . ~ ~is extremely broad, asymmetric, and structureless. It is the common feeling that up to now most of the existing theories are unsuccessful in treating the optical absorption, although occasionally some characteristic features find an explanation. However, the most extensive theoretical calculations like QUPID calculations leading to bound statehound state (s p) transitions do not reproduce the line shape of the optical absorption spectrum (see, e.g., ref 32). On the other hand, a detailed analysis of the experimental results based upon sum rules provides convincing arguments that the high-energy tail of the observed optical spectrum is due to a transition between a bound state and the continuous s p e ~ t r u m . ~ But ~ - ~it cannot be excluded that bound statehound state transitions may contribute to the low-energy side of the absorption spectrum.42.u Besides theoretical arguments photodetachment and photofragmentation experiments on “solvated” electrons in large water clusters (H20)30- support both po~sibilities.~~ Recently, Brodsky and Tsarevsky (BT)37,3s,40,42,u draw a very important conclusion from a model-independent analysis of the optical absorption spectra of esolv- in different media: the interaction responsible for electron localization is predominantly of short range. On this basis they developed a theory on the temperature dependence of the spectra, which is determined by many-body collective effects of the s ~ l v e n t . ~As. ~a ~support of their idea they presented experimental spectra of electrons in methanol as a function of The temperature
-
@Abstractpublished in Advance ACS Absrracts, April 1, 1995.
0022-3654/95/2099-6794$09.00/0
dependence of the peak position and of the line shape of the spectra show a peculiar behavior. However, BT found a “satisfactory, quantitative agreement” between theory and e~periment.~.~~ Since Tuttle et began to interpret the spectral line-shape characteristics at the low energy side of the spectra of esolv- in CH30H within a modified theory of photoejection spectra of molecular anions, we feel that these experimental results have too far reaching theoretical consequences. Therefore, it seems to be necessary to repeat these measurements very carefully. In section 11, we will summarize fiist the theoretical and experimental results of BT and those of Tuttle et al.. A short description of our experiments is given in section III. In section IV we present our experimental results which are compared with those of BT. Conclusions are drawn in section V. 11. Zero-Range Potential Model for the Solvated Electron
In a number of publications BT37x38*40*42944 deduced from experimental optical absorption spectra of esolv- by means of sum rules and threshold formulas that the so-called zero-range potential-used in nuclear physics-should be a possibility to describe the localized electron theoretically. This zero-range potential characterized by a single parameter has the following meaning: a square-well potential where the well width goes to zero while the depth is increasing infinitely so that a single stationary state is fixed. For this zero-radius potential one has a simple formula for the dependence of the phototransition cross section 0 between the bound 1s state (Ei < 0) and the continuum spectrum on the phase angular speed Q of light and the initial state Ei:37
+
where h 2 ~ = 2 -2mEi and = 2m(Ei hS2) (in this publication we use the nomenclature of B F ) . It was pointed out by BT that one can increase the number of (fitting) parameters by introducing finite-range potentials.u 0 1995 American Chemical Society
Spectra of Solvated Electrons in CD30D
J. Phys. Chem., Vol. 99, No. 18, 1995 6795
One of the most recent works along this line is that of Golden and T ~ t t l e . ~However, ' according to BT eq 1 reproduces quite well the properties of the solvated electron spectra in different solvents. The most important results obtained by BT are as follows: (i) There must exist a linear relationship between the extinction coefficients at the absorption maximum-which are x proportional to (T(Qm,,Ei)-and C2mm-l (the energetic position of the absorption maxima is hQm,). Apart from deviations in h the order of f 2 0 % such a linear relationship is observed (see, e.g., Figure 1 in ref 44).37,38,42,44 However, it was found out by Tuttle et al. that not the Bethe-Peierls cross section (eq 1) but the Breit-Condon cross section (see ref 41) with three fitting parameters describes the absorption line-shape satisfactorily but not in all details. Electrons in NH3 do not obey the abovementioned linear relationship. Therefore, it was suggested by BT that just in this case one has to assume a relatively large interaction range for electron localization (cavity f ~ r m a t i o n ) . ~ ~ - ~ (ii) From eq 1 follows a relation between Qmax and the threshold energy IEi(:42,44
1.0
-
3'
which according to BT does hold quite well. In our opinion there are no low-frequency data of sufficient accuracy at relative absorbances below about 0.1 in order to determine lEil satisfactorily from threshold formulas (see below). (iii) A stringent test of the idea of BT is provided by the mean static dipole polarizability (a(Q=O))of esolv-in a static electric field (zero-frequency property). It was emphasized by BP2,44that (a(0))obtained from experimental optical absorption spectra by means of optical sum rules is well reproduced by the theoretical formula for an electron bound to a level with energy Ei:
(a(0))= Ke2h2/mE;
(3)
where K is a numerical factor. For an electron in a ground 1s state and a long-range Coulomb-type potential one has K = 9/2. In the case of a zero-radius potential (long-range Coulombtype interactions should be of no significance) K is much smaller, Le., K = '116, and it is just this value in eq 3 which describes according to BT the experimental polarizability data for esolv-in various media almost quantitatively (see, e.g., Figure 2 of ref 44). We will come back to this important point in section IV. Brodsky and Tsarevsky are also concemed with the temperature dependence of the shape and position of the absorption peak of esolv- in the optical frequency r e g i ~ n Again . ~ ~ ~esolv~ will be considered within the zero-radius potential model, but now long-range interactions with long-wave collective excitations of the disordered medium are taken into account. It cannot be our aim to present the essentials of this work in mathematical formulas. We rather discuss the experimental results of optical absorption measurements on electrons in methanol published by these authors as a support of their theoretical results. In Figure l a are given the normalized optical absorption spectra of esolv- in subcritical methanol (under its own vapor pressure) at several temperatures. As can be seen, the lineshapes are asymmetric as usual, but more important, the asymmetry is increasing with increasing temperature. With rising temperature the absorption maximum is redshifted. However, above T x 481 K a change in the direction of the temperature shift is observed (see Figures l b and 2). In addition, a structure on the low-energy side of the absorption spectrum
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ha (eV) Figure 1. Spectra of esolv-in CH30H as a function of temperature: (a) 0 , T = 293 K; 0, T = 421 K; x, T = 481 K. CH3OH was under its own vapor pressure (from refs 44 and 46). The lines are only a guide to the eye. (b) 0 , in supercritical CH30H at T = 517 K (p = 91.2 bar), from refs 44 and 46. The dashed line has no theoretical meaning.
2'o
9
%
d
rt:
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t1 t
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T (K) Figure 2. Temperature dependence of the position hR,, of the absorption maximum of esolv- in CH3OH. 0 , experiments (from refs 44 and 46); -, numerical calculation of BT according to eq 23 of ref 44.
of esolv- in supercritical methanol appears (Figure lb: T > Tc (T' = 512.6 K), p = 91.2 bar). BT assert now that with their theory they can describe quantitatively both the increasing asymmetry with increasing temperature and the observed temperature shift of the absorption
Henmann and Krebs
6796 J. Phys. Chem., Vol. 99,No. 18, 1995 maximum. Let us have look on the first point following their argumentation. Since the effective interaction of the excess electron with the medium is a function of the density Q of the medium the total temperature shift of the absorption maximum in constant pressure experiments is given by
where the second term on the right-hand side has been calculated theoretically by BT. The first term has been estimated from independent experiments at 298 K. The threshold QOis equal to IEJh. It depends only on medium density Q at all temperatures. Therefore, the temperature dependence of the threshold energy hQ0 is in contrast to h Q m a x given by only one term which takes into account the density dependence of the interaction between the electron and the solvent: Figure 3. Optical autoclave (T 5 550 K, p 5 200 bar) used for the absorption measurements of esolv-in CD30D at high temperatures: QC, quartz sample cell; WL, sapphire window for excimer laser light pulse (transmission at A = 248 nm is about 0.70 at 296 K and 0.65 at 473 K; WA, sapphire windows for the analysing light; H, electrical heating
Using eq 2, one has
system; C, high-pressure capillary for the external argon gas pressure (see the text). Thermocouples are not shown in the figure.
within the zero-range potential model. Since the estimated shift (8iQmax/8Q)daQ/aT') % - 1.3 x eV K-I is much weaker than the shift ( d h Q m a x l d T ) % -3 x eV K-I given by the expermental results in Figure 2 (see refs 44 and 46), it follows that (7) which would explain the increasing asymmetry of the spectra. We do not go into further details. We want to mention only that the authors have determined 8iQmax/ae)daelaT) quantitatively applying their theory to the low-energy parts (ha < hQmax) of the spectra of esolv-in subcritical CH3OH at T = 293 and 481 K, respectively. According to BT the result was quite consistent with eq 6. They have also calculated with their theory ( 8 i Q m a x l a T ) e and thus the temperature dependence of hQmax given in Figure 2 with the linear segment, the break, and the small m a ~ i m u m . ~ ~ . ~ ~ Recently, Tuttle et al.47 adapted the theory of photoejection spectra of molecular anions for application to the analysis of optical absorption data of esolv-in a number of different solvents. They analyzed also the low-energy side of the spectrum given in Figure l b (T = 517 K) to get some information on the symmetry of states involved in the transitions comprising the optical absorption spectrum. According to Tuttle et al. the curvature on the low-energy side of the spectrum (0.5 < hQ -= 0.8 eV) is characteristic of p s bound-to-continuum transitions. This result clearly implies a substantial if not dominant p-character in the electron ground state. Consequently, the ground state of esolv-cannot be spherically symmetric, as is very often assumed in theory. We have listed so far a series of very far reaching theoretical consequences based on experimental results which have never been reproduced by another research group. Therefore, we have done such optical absorption measurements on electrons solvated in methanol as a function of t e m ~ e r a t u r e . ~ ~
-
111. Experimental Section To avoid an overlap of the esolv-absorption spectrum with the absorption of CH30H in the wavelength region 1000 -= d
< 1750 nm, we have used fully deuterated methanol (CD30D, MSD, minimum isotopic purity 99.8 atom % D). CD30D was purified by NaBD4 (MSD, minimum isotopic purity 98.73 atom % D). In a special glass apparatus which was flushed with argon (5.0, Messer-Griesheim) 1 g of NaBD4 was added to 100 mL of CD30D. The solution was gently bubbled with argon and refluxed for 3 h. Then it was fractionally distilled through a 50 cm Vigreux column. The middle fraction (about 40%) was collected and kept in a reservoir attached to a vacuum line. Solvated electrons were produced by irradiation of light in the CTTS-spectrum of iodide ion I- according to49,50
I-
+ hcc,-I' + esolv-
M, Merck, Suprapur 99.5%) was Therefore, KI (about dissolved in CD30D. Samples were prepared in a cylindrical quartz cell (Hellma, heralux with Suprasil windows; for p < 20 bar) with an optical path length of 1 cm. The solutions in this cell are made free of 0 2 and C02 by at least 10 freezembar). pump-thaw cycles at a vacuum line (better than After this the cell was hermetically sealed and placed in an optical autoclave (p i 200 bar, T i 550 K) which can be heated electrically (Figure 3). The autoclave is equipped with three sapphire windows: one for the laser light producing esoIv-,two for the absorption measurements. The solution was always under its own vapor pressure. To prevent the destruction of the quartz cell at high temperatures-for instance, at T = 510 K the vapor pressure is about 75 bar-the pressure inside the quartz cell was compensated by the external pressure of argon supplied to the optical autoclave. The temperature was controlled by thermocouples to within < f l K. The laser used to produce esolv-was a Kr/F excimer laser (Questek 2000: d = 248 nm; pulse duration 30 ns; pulse energy The lifetime of esolventering the optical autoclave 1 2 5 d). in CD30D at T = 298 K was about 2 ,us; at 5 10 K it was reduced to about 150 ns. In CH3OH which was purified by the same procedure, but where we have taken a smaller middle fraction of about 15% a longer lifetime of about 4 ,us was observed at 298 K. The pulse energy of the laser was always controlled by a calibrated energy monitor (Lumonics) in order to get a relative
Spectra of Solvated Electrons in CD30D I
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An (eV) 298 K immediately after the laser pulse: A, total spectrum; x , spectrum of 12-; 0 ,spectrum of solvated electrons. Each data point is the average of 20-50 measurements.
measure for the produced electron concentration. As detectors we used for hQ > 1.1 eV a W silicon photodiode (EG&G FND lOOQ) and for 0.71 hQ 1.1 eV an InGaAs photodiode (RCA C30642). The time constant for the detecting system (with some additional electronics) is in the order of 20 ns. The high-energy limit of the experimental spectral range, i.e., hQ 4 eV is presently given by the available gratings for the monochromator (Jobin-Yvon M25) used in our setup. As analyzing light source we used a high-pressure xenon arc lamp (Osram XBO 450). To obtain a higher signal-to-noise ratio the intensity of the lamp was pulsed up for about 2 ms by a factor of 10 during the absorption measurement. Of course we have placed suitable filters (Schott) in front of the optical cell to stop higher order diffraction of the gratings.
IV. Experimental Results and Discussion
(94
and the disproportionation5' 21,-
-
1,-
+ 1-
Figure 5. Absorption spectra of
I
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12- with its absorption bands at 1.65 and about 3.2 eV49,50 has a much longer lifetime than esolv-. Therefore, the overlapping spectra of esolv- and 12- are easily separated (see Figure 4). In addition, using CO;? as an effective scavinger only the 12- absorption is observed after a laser pulse. Thus it is in principle possible to register a pure spectrum of 12-.52 In our present experimental setup a reasonable separation of both spectra with sufficient accuracy is possible only for hS1 < 3.5 eV. Subtracting the absorption bands of 12- we obtain a pure esolv-spectrum (Figure 4). To demonstrate the quality of these measurements, we show in Figure 5 esolv- in CD30D and in CH3OH, both at T = 298 K in comparison with the result of BT44,46in CH30H at 293 K. The esolv- absorption measured by us in CH30H fully agrees with the best available spectrum of esolv- in CH30H published by Jou and Freeman.53 The steeper fall of the esolv-absorption
esolv- in
CD3OD (0)and in CH30H
(O), both at T = 298 K in comparison with the spectrum of esolv- in
CH3OH at T = 293 K given by BT (0).Some vertical error bars representing the maximum error are drawn. The horizontal error bar at the high energy side shows the maximum bandwidth of the grating monochromator.
0.0 0.0
On irradiation of light in the CTTS band of I- the solvated electrons are not the only species absorbing light in the spectral range 0.7 hQ 4 eV. The production step (eq 8) is followed by49SO
+ I- - 1,-
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Figure 4. Optical absorption of a solution of lo-' M KI in CH3OH at
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ha (eV) Figure 6. Optical absorption spectra of
eS& in CD30D at different temperatures: 0, T = 298 K; 0 , T = 393 K; 0, T = 481 K; +, T = 500 K.
in CH30H at the low-energy side in comparison with that of esolv-in CD3OD is due to the absorption of the solvent CH30H itself?* In Figure 6 we present esolv- spectra in CD30D at different temperatures which show no increasing asymmetry with rising temperature. To demonstrate the significant difference between the experimental results of Brodsky et al. and our measurements, we compare the corresponding results for T = 48 1 K in Figure 7. The deviations are tremendous at least at the low-energy side of the spectrum -although it was pointed out by B F 6 that the error in determining the optical density did not exceed 10%. And it was just the low-energy side of this spectrum which was used to support their theory (see especially ref 46) and to determine (ahQdap)l(ap/aT) quantitatively. We wanted to probe also the new band at the low-energy side of the absorption spectrum at high temperatures (T = 517 K, see Figure lb). However, with our method of production of esolv-it is not possible to reach supercritical temperatures because KI precipitates. Therefore, we present in Figure 8 the absorption spectrum of esolv- in subcritical CD30D at T = 500 K and 5 10 K in comparison with the result of BT in supercritical CH30H at T = 517 K. We did not observe any structure at the low-energy side of the absorption spectrum for hS1 2 0.73 eV.
6798 J. Phys. Chem., Vol. 99, No. 18, 1995
H e m a n n and Krebs I
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fin (eV) Figure 7. Optical absorption spectra of eS& in CD30D at T = 481 K (0)in comparison with the results of BT in CH30H at the same temperature4 (0).The vertical error bars representing the maximum errors in different parts of our spectrum demonstrate the quality of the optical absorption measurements. The horizontal bar at the high-energy side shows the maximum bandwidth of the grating monochromator. I
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fin (eV) Figure 8. Optical absorption spectra of esolv-in subcritical CDsOD at T = 500 K (0)and T = 510 K (0)in comparison with the spectrum of eS& in supercritical CHsOH at T = 517 K given by BT (0).
Moreover, it follows from our measurements in the temperature range 298 < T < 510 K that there is only a redshift of hQ,, with increasing temperature and not a blue-shift beginning at T > 480 K (see Figure 9). Just the change in the sign of the temperature shift dhQ,,/dT should support the theory of BT. The redshift dhQm,/dT = -(2.98 f 0.04) x eV K-' observed by us is in accord with the results from other sources .54,5 We suggest that all these effects observed by BT are due to the absorption of the solvent CH30H itself and that the more because the optical path length they used in the absorption measurements was 2.0 and 3.7 cm. Therefore, our optical absorption measurements as a function of temperature eliminate the experimental basis for the theoretical description of solvated electrons within the model of zero-radius potential. Indeed it was not possible in our present set-up to measure the optical absorption of esolv-in CD3OD at 500 and 510 K in the threshold region hQ < 0.7 eV. Nevertheless, these spectra show that the result of the analysis of the spectrum of esolv-in CH30H at 517 K given by Tuttle et al. can be revised. We find no indication of an appreciable deviation from spherical symmetry of the ground-state of esolv-in CD30D.
550
600
T (K) Figure 9. Temperature dependence of the position of the absorption maximum hQ, of the esolv-absorption spectrum in methanol. CH3OH: 0 ,BT,44,46 276 5 T 5 538 K; V, Jha et al.,54183 5 T I 358 K; 0 Arai et T = 195 K; A, this work, 298 I T I393 K. CD30D: 0, this work, 298 IT I510 K.
One of the most stringent arguments for the zero-radius potential model given by BT were the mean static dipole polarizabilities (a(0))of esolv-in different media which almost quantitatively agree with eq 3 using K = I / I ~ . Evaluating ground-state properties of solvated electrons, we have found out that the results of BT are not corrects6 Assuming that the ground-state of esolv-is spherically symmetric (see above) one obtains with help of sum rule
(a(Q=O))= nocA-'Jmy(Q)S2-2 dSZ
h
0.0 I
150
(10)
where y(Q) is the measurable molar decadic extinction coefficient of esolv- in units of M-' cm-I. no is the refractive index of the solvent (the solvent refractive index m(S2) undergoes only little dispersion in the range of the esolv-absorption; therefore, we have no@) = constant = no); c is the light velocity and A = 2 n 2 N ~x 10-3/ln 10. To evaluate the integral on the righthand side of eq 10 the complete absorption spectrum of esolvhas to be determined experimentally. To get (a(O)), we need in addition no for the different solvents. The sum rule
which corresponds to the Thomas-Reiche-Kuhnsum rule was verified for esolv-in different solvents by Golden and T ~ t t l e . ~ ~ Therefore, we can combine eqs 10 and 11 obtaining the following expression:
which does not depend on no. In this formulation we have neglected small corrections in the sum rules due to the finite temperature in the system esolv-lsolvent(see ref 41). If we are sure that the Thomas-Reiche-Kuhn sum rule is fulfilled for the solvated electron spectrum, then we can use eq 12 instead of eq 10. Due to the normalization with eq 11 we can calculate (a(0)) from eq 12 not only with y(Q) but also with the optical density or the relative absorbance AIA,, as a function of 52. We have evaluated esolv-absorption spectra of this work and spectra from literature. In addition we have used data of C a r m i ~ h a e l .The ~ ~ results are listed in Table 1. To determine (a(0))with high accuracy, the whole spectrum should be
Spectra of Solvated Electrons in CD30D
J. Phys. Chem., Vol. 99, No. 18, 1995 6799
TABLE 1: Static Dipole Polarizability (a(0))of esolv- in Polar Media solvent CH3OH
CD30D
CzHsOH l-C3H70H 1-C4H90H 1-CgH170H Hz0 2-NH2CzbOH CH3NH2 1-C3H,NH2 NH3
THF
refa
TIK
53,59
299 298 353 393 298 393 48 1 500 510 299 299 299 299 274 298 380 299 183 190 198 155 298
this work this work this work this work this work this work this work this work 59 59 59 59 60 60 60 59 61 62 63,57 64 65
N11022~m-3
hS2,,leVc 1.95 (1.94) 1.93 f 0.03 1.74 f 0.03 1.62 f 0.03 1.96 f 0.03 1.65 f 0.03 1.42 f 0.03 1.36 f 0.02 1.31 f 0.04 1.74 (1.82) 1.98 (1.93) 1.94 (1.94) 1.98 (1.96) 1.793 1.72 (1.71) 1.53 1.39 1.08 1.09 0.9 0.85 0.58
1.4787 1.3764 1.2917 1.4787 1.2917 x0.98 %0.75 x0.55
(a(0))e.plA3
(a(0))YA3
designation
21.3 25.9 31.0 35.0 28.5 38.6 50.5 52.8 55.4 23.5 22.7 21.9 22.0
23.7 24.0 30.0 34.6 26.1 39.0 57.8 61.0 65.0 26.4 24.3 24.6 24.6 30.5 34.1 46 5 60 82 75.7 122 125 x285d
0 0 0 0
32.8 54.3 81 74.4 122
115
0 0 0 0 0 A Ae
Ae Ae V V V
0
0
+ X
a Reference for the experimental spectrum. N is the number density of liquid methanol under its own vapor pressure. The values have been calculated from the experimental data for CH3OH (298.15 5 T 5 473.15 K) published in ref 58. Neglecting small isotopic effects we have used them likewise for CD30D. The number densities for 481 5 T 5 510 K have been roughly estimated from the experimental data of ref 58 and the ~ . first number gives the experimental position of the absorption maximum; the number in the critical density N, = 5.1688 x loz1~ m - 'The brackets gives the position of the maximum obtained by a skewed Gaussian fit.43 Obtained by extrapolation of the correct linear relationship presented in Figure 10. e These points are hidden by the point for CH30H (T = 2981299 K).
100
h h
E?
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0 0.0
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(~n,,,)-2((ev)-2) Figure 10. Mean static dipole polarizability (a(0)) of solvated electrons in different solvents vs (hQ,,J2. For the symbols see Table 1. The numbers at the points are the temperatures of CH30H and CD3OD, respectively. determined experimentally with adequate precision to evaluate the needed integrals by direct numerical means. For instance, this is the case for solvated electrons in NH3. However, very often the precision, but more important the spectral range is restricted due to the lack of suitable detectors or due to other experimental difficulties. This becomes obvious in the case of esolv- in methanol. Jou and Freemad9 have determined the solvated electron spectrum in CH30H at 299 K in the spectral range 0.9 IhQ 5 4.75 eV with high precision; however, the high-energy part of the spectrum is not complete. Because the low-energy side of the spectrum contributes-due to the dependence of the first integral of eq 12-an important part to (a(O)), the lacking high-energy part of the spectrum has only a small effect on the accuracy of (a(0)) (see Table 1, first line: Carmichael has used a skewed Gaussian to complete the spectrum43). Due to the absorption of 12- our spectrum of solvated electrons in CH30H at T = 298 K is well resolved on
the low-energy side but drastically restricted to 3.7 eV at the high-energy side. A Gaussian (for hQ I hQ,,) and a Lorentzian fit (for hQ 1 hQm,) yields (a(0))= 24 A3 which is in satisfactory agreement with the result of C a r m i ~ h a e l , ~ ~ although the Lorentzian underestimates slightly the experimental absorption for hQ > 2.5 eV (for details see ref 56). All analytical fits have disadvantages (see, for instance, Figures 1 and 2 in ref 43) but despite this they have also the advantage to determine hQ,, with higher precision because one obtains hQ,, as an extrapolation from many measured points around the absorption maximum (see Table 1). In the case of esolv- in CD30D the spectra determined by us were all restricted at the high-energy side due to 12- absorption and at higher temperatures also at the low-energy side (hQ > 0.73 eV) due to the limits of the InGaAs photodiode. Despite the completion technique of both sides of the spectra we suggest that the maximum error of (a(0)) does not exceed &lo%. In Figure 10 we have plotted (a(0)) from Table 1 vs (hQmm)-*.The observed linear relationship expresses the shape stability of the esolv- absorption spectra: according to eq 12 one has
where the average is formed with the distribution function y(S2). Obviously, there is a simple linear relationship between (hQmax)-2 and ((ha)-*). For comparison we have plotted in Figure 10 the result of Brodsky and Tsarevsky,42,44where we have used for simplicity the approximation lEil = hS2,,,/2 in eq 3 with K = '/16, i.e.
There is no agreement between experiment and theory. This means that the main argument for the zero-radius potential model breaks down. We suggest that BT obtained a quantitative agreement between theory (eq 14, dashed line in Figure 10) and the experimental results because evaluating the experimental
6800 J. Phys. Chem., Vol. 99, No. 18, 1995 TABLE 2: Equilibrium Ground-State Properties of Solvated Electrons in Methanol. Comparison between Theory and Experiment
Herrmann and Krebs
(13) Gaathon, A.; Jortner, J. In Electrons in Fluids; Springer-Verlag: New York, 1973; p. 429. (14) Tachiya, M.; Tabata, Y.; Oshima, K. J. Phys. Chem. 1973, 77,263. (15) Carmichael, I.; Webster, B. C. J. Chem. SOC., Faraday Trans. 2 theory" 1974, 70, 1570. (16) Fueki, K.; Feng, D. F.; Kevan, L. J. Phys. Chem. 1974, 78, 393 model 1 model 2 experiment and references therein. (r2)lA2: 9.61 6.92 (A$)/A2: 5.08b 5.2' 5.1d (17) Tachiya, M.; Mozumder, A. J. Chem. Phys. 1974, 61, 3890, and (T)/eV: 1.3 1.6 (T)leV: 1.866 1.89' 1.86d references therein. (18) Baird, J. K. J. Phys. Chem. 1975, 79, 2862. a Reference 66. Reference 43, T = 299 K. Reference 35, T = (19) Kestner, N. R. In Electron-Solvent and Anion-Solvent Interactions; 300 K. References 48 and 56, T = 298 K. Kevan, L., Webster, B., Eds.; Elsevier: Amsterdam, 1976; Chapter 1. (20) Kestner, N. R. Can. J. Chem. 1977, 55, 1937. (21) Bush, R. L.; Funabashi, K. J. Chem. Soc., Faraday Trans. 2 1977, spectra with the aid of moment theory they have probably used 73, 274. the wrong constant A = 2 n 2 N ~x In 10: Therefore, their (22) Banerjee, A,; Simons, J. J. Chem. Phys. 1978, 68, 415. (a(0))'sare by a factor of (In smaller than the correctly (23) Webster, B. C.; Carmichael, I. J. Chem. Phys. 1978, 63, 4086. determined experimental (a(0))'s.This fact was not recognized (24) Bartczak, W. M.; Kroh, J. J. Chem. Phys. 1979,44, 251. in the work of Ca1michael.4~ (25) Bartczak, W. M.; Hilczer, M.; Kroh, J. J. Phys. Chem. 1979, 44, 251. (26) Abramczyk, H. J. Phys. Chem. 1991, 95, 6149. V. Conclusions (27) Abramczyk, H.; Kroh, J. J. Phys. Chem. 1991, 95, 6155. (28) Chandler, D. J. Phys. Chem. 1984, 88, 3400. We have performed new experiments on optical absorption (29) Sprik, M; Klein, M. L.; Chandler, D J. Chem. Phys. 1985,83,3042. of esolv- in CD30D as a function of temperature up to 510 K. (30) Sprik, M.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1985, 83, These results together with the static dipole polarizability (a(0)) 5802. of esolv- in different solvents eliminate the experimental basis (31) Rossky, P. J.; Schnitker, J. J. Phys. Chem. 1988, 92, 4277. (32) Wallquist, A,; Matyna, G.; Beme, B. J. J. Phys. Chem. 1988, 92, for the theoretical ansatz given by Brodsky and Tsarevsky which 1721. is based on the assumption that short-range interactions (de(33) Jonah, C. D.; Romero, C.; Rahman, A. Chem. Phys. Lett. 1986, scribed by a zero-radius potential) are responsible for electron 123, 209. localization. (34) Proceedings of the Fifth and Sixth International Conference on Excess Electrons and Metal-Ammonia Solutions. J. Phys. Chem. 1980,84, Recently, a quantum molecular dynamics simulation of an 1065; 1984, 88, 3702 and references therein. excess electron in methanol at T = 298 K was published. Zhu (35) Tuttle Jr., T. R.; Golden, S. J. Phys. Chem. 1991, 95, 5725 and and Cukier66 used two different pseudopotentials for the references therein. interaction of the excess electron with a methanol molecule. (36) Fano, U.; Cooper, J. W. Rev. Mod. Phys. 1968, 40, 441. (37) Brodsky, A. M.; Tsarevsky, A. V. Int. J. Radiat. Phys. Chem. 1976, Their calculations show that the electron ground-state is 8, 455. spherically symmetric and approximately Gaussian. Among (38) Brodsky, A. M.; Tsarevsky, A. V. Sov. Phys.-JETP 1976,43, 111. other things they have determined the mean squared radius of (39) Carmichael, I. Chem. Phys. Lett. 1978, 56, 339. gyration (r:) and the mean quantum mechanical kinetic energy (40) Brodsky, A. M.; Tsarevsky, A. V. High Energy Chem. 1978, 12, (T) of the ground-state excess electron in methanol for both 267. (41) Golden, S; Tuttle Jr, T. R. J. Chem Soc., Faraday Trans. 2 1979, models. From the application of the model-free spectral moment 75, 474. theory on experimental optical absorption spectra, one obtains (42) Brodsky, A. M.; Tsarevsky, A. V. Adv. Chem. Phys. 1980,44,483. the equilibrium-averaged dispersion in position (AS) and (T) (43) Carmichael, I. J. Phys. Chem. 1980, 84, 1076. of esolv-in the ground state.56 The theoretical and experimental (44) Brodsky, A. M.; Tsarevsky, A. V. J. Phys. Chem. 1984,88, 3790. (45) Campagnola, P. J.; Lavrich, D. J.; Deluca, M. J.; Johnson, M. A. results are compared in Table 2. It shows that esolv-is more J. Chem. Phys. 1991, 94, 5240. compact than predicted by theory irrespective of the used (46) Brodsky, A. M.; Vannikov, A. V.; Chubakova, T. A,; Tsarevsky, pseudopotential. Zhu and Cukier concluded in addition that A. V. J. Chem. Soc., Faraday Trans. 2 1981, 77, 709. the electron in water is more strongly bound than in methanol (47) Tuttle Jr., T. R.; Golden, S.; Rosenfeld, G. Radiat. Phys. Chem. by comparing their results with those of Schnitker and R o s ~ k y . ~ ~ 1988, 32, 525; Int. J. Radiat. Appl. Instrum. Part C. (48) Henmann, V. Doctoral Thesis, University of Karlsruhe, FRG, 1992. We will show in a further publication that this conclusion is (49) Grossweiner, L. I.; Zwicker, E. F.; Swenson, G. W. Science 1963, also in contradiction to e ~ p e r i m e n t . ~ ~ 141, 1180. (50) Dobson, G.; Grossweiner, L. I. Radiat. Res. 1964, 23, 290. Acknowledgment. Financial support by the Deutsche For(51) Grossweiner, L. I.; Matheson, M. S. J. Phys. Chem. 1957,61, 1089. (52) Bertran, C. A.; Krebs, P., unpublished results. schungsgemeinschaft and by the Fonds der Chemischen Ind. is (53) Jou, F.-Y.; Freeman, G. R. J. Phys. Chem. 1977, 81, 909. gratefully acknowleged. (54) Jha, K. N.; Bolton, G. L.; Freeman, G. R. J. Phys. Chem. 1972, 76, 3876. References and Notes (55) Arai, S.; Sauer, M. C. J. Chem. Phys. 1966, 44, 2297. (56) Bertran, C. A.; Krebs, P.; Marbach, W., manuscript in preparation. (1) Newton, M. D. J. Phys. Chem. 1975, 79, 2795. (57) Tuttle Jr., T. R.; Golden, S.J. Chem Soc., Faraday Trans. 2 1981, (2) Rao, B. K.; Kestner, N. R. J. Chem. Phys. 1984, 80, 1587. 77, 873. (3) Clark, T.; Illing, G. J. Am. Chem. Soc. 1987, 109, 1013. (58) Machado, J. R. S.; Streett, W. B. J. Chem. Eng. Data 1983, 28, (4) Mumhv. S. V.: Hibbert. D. B. Radiat. Phvs. Chem. 1986. 28. 319. 218. (5) Tichtkawa, H.; Ogasawara, M.; Lingre; M.; Lund, A.'J. khys. (59) Jou, F.-Y.; Freeman, G. R. Can. J. Chem. 1979, 57, 591. Chem. 1988, 92, 1712. (60) Jou, F.-Y.; Freeman, G. R. J. Phys. Chem. 1979, 83, 2383. (6) Jortner, J. J. Mol. Phys. 1962, 5 , 257. (61) Stupak, C.; Tuttle, Jr., T. R.; Golden S. J. Phys. Chem. 1984, 88, (7) Copeland, D.; Kestner, N. R.; Jortner, J. J. Chem. Phys. 1970, 53, 3804. 1189. (62) Jou, F.-Y.; Freeman, G. R. Can. J. Chem. 1982, 60, 1809. (8) Fueki, K.; Feng, D. L.; Kevan, L.; Christofferson, R. J. Phys. Chem. 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