6004
J. Phys. Chem. B 2001, 105, 6004-6009
Study of Aqueous Acetone Solution at Various Concentrations: Low-Frequency Raman and Molecular Dynamics Simulations A. Idrissi,* S. Longelin, and F. Sokolic´ Laboratoire de Spectrochimie Infrarouge et Raman (UMR CNRS 8516), Centre d’Etudes et de Recherches Lasers et Applications, UniVersite´ des Sciences et Technologies de Lille, 59655 VilleneuVe d’Ascq Cedex, France ReceiVed: NoVember 15, 2000; In Final Form: March 15, 2001
The low-frequency Raman spectra of pure water, pure acetone, and their mixtures at different proportions have been analyzed. New experimental (low-frequency Raman spectra) and calculations (molecular dynamics simulations) show that the band observed at 60 cm-1 in the low-frequency Raman spectra of water is associated with the oscillation of a water molecule within the cage formed by its neighbors. On the basis of this model, an analysis has been made of the variation of the position and width of the band assigned to intermolecular oscillations. The influence of the acetone concentration on this feature has been analyzed, and its interpretation has been proposed. The position of the peak at 60 cm-1 has a nonlinear dependence on the mole fraction of acetone. On the hypothesis that the translational dynamics of water contributes mainly to the low-frequency Raman spectra, the shift to higher frequencies of the peak at 60 cm-1 is interpreted as an indication of the stiffening of the cage formed by the neighboring molecules. The shift of the peak at about 190 cm-1 to lower frequencies and the nonlinear concentration dependence of its width is an indication that acetone acts as a water structure breaker.
Introduction Low-frequency Raman spectroscopy is a powerful tool for analyzing the influence of solutes on the structure and dynamics of water. The changes in the position and the width of the two intermolecular vibration bands at 190 and 60 cm-1 constitute a basis for the quantitative analysis of the influence of the solute. Several dynamical processes contribute to the broadening and the shift of spectral bands in liquids. The most important arises from the environmental fluctuation around the active oscillator. As pointed out in previous work,1,2 the role of the local environment in determining the intermolecular structure and dynamics of liquids can be revealed in a controlled fashion through dilution studies. Hence, it is possible that quite different molecular interaction mechanisms can be involved at low and high mole fractions of the solute. A damped oscillator model3-8 was used to interpret the changes in the spectral profiles of these two bands. In all of these studies, the high-frequency mode at about 190 cm-1 is interpreted as arising from the vibration of an oxygen atom with respect to its nearest neighbor oxygen when a linear or a weakly bent hydrogen bond, O-H...O, is present. This stretching of the hydrogen bond is often described alternatively as a restricted translation of the H2O molecules. The mode observed at 60 cm-1 is assigned to a restricted translational motion perpendicular to the O-H...O direction, i.e., bending of the hydrogen bond. A recent molecular dynamics simulations calculation of the dynamical properties of a ureawater system allows the attribution of the two peaks at 190 and 60 cm-1, observed in the low-frequency Raman spectra of pure water, to the two distinct translational motions of water molecules. The one at 60 cm-1 is associated to the cage effect, and the one at 190 cm-1 is attributed to the relative motion of the two molecules along the hydrogen bond axis. In this work, * To whom correspondence should be addressed.
we propose an interpretation of the low-frequency Raman band features of acetone aqueous solution in the light of the former attribution. A curve fitting procedure was used to quantify the changes in positions and widths of the low-frequency Raman bands in the liquid mixtures. Experimental Methods The Raman experiments were performed at room temperature by the use of 514.5 nm radiation from an argon laser operating at power levels in the range of 250-350 mW. The Raman signal was analyzed with the use of a Coderg T800 triple monochromator coupled to a photomultiplier and photon counting electronics. Because the instrumental spectral width was usually 0.5 cm-1, much smaller than that of the band profiles observed in these experiments, its influence was assumed to be negligible. The 90° geometry was employed in all of these experiments. Ultrapure water and spectroscopic grade acetone were used in the preparation of the solutions. It is common to present the spectra in the so-called reduced form R(νj). The use of this procedure removes the Rayleigh peak at νj ) 0 cm-1. The reduced form is obtained from the Raman spectra I(νj) by application of the expression
R(νj) )
νjI(νj) , 1 + n(νj)
(1)
where (1 + n(νj)) is Bose-Einstein factor. Results and Analysis The spectra of water, acetone, and aqueous acetone solutions are presented in the reduced form in Figure 1. They are shown as a function of the mole fraction of acetone (χacetone) in the region from 10 to 350 cm-1. The raw spectra were first reduced by application of eq 1 to yield R(νj). Then, each spectrum was
10.1021/jp004217r CCC: $20.00 © 2001 American Chemical Society Published on Web 06/02/2001
Aqueous Acetone Solution at Various Concentrations
J. Phys. Chem. B, Vol. 105, No. 25, 2001 6005
Figure 1. Reduced Raman spectra of aqueous acetone solutions as functions of the mole fraction of acetone (χacetone).
divided by its surface evaluated between 10 and 300 cm-1. The existence of an isosbestic point indicates that the procedure of normalization was made correctly. It is known that the different motions of water molecules (reorientation, rotation, and translation) have different characteristic times. It is thus of interest to evaluate their respective contribution to the frequency domain. Accordingly, a molecular dynamics simulation of SPC/E water was performed. The time auto-correlation functions of reorientation, C2(t), rotation, Ω(t), and translation, Ψ(t), were calculated. The corresponding power spectra obtained by the Fourier transform of these functions were calculated to provide a comparison with the low-frequency Raman spectrum of water. The reorientational time auto-correlation function is given by
C2(t) ) 〈P2(u(t)‚u(0))〉
(2)
Figure 2. (a) Correlation functions C2(t), Ψ(t), and Ω(t), which are associated with the reorientational, translational, and rotational dynamics, respectively. (b) Power spectra C ˜ 2(νj), Ω ˜ (νj), and Ψ ˜ (νj) and the experimental low-frequency Raman spectrum, R(νj), in reduced form.
where u is the unit vector along the principal axis of the water molecule and P2 is the second Legendre polynomial P2(u1‚u2) ) 3/2 cos2(u1‚u2) - 1/2. Its Fourier transform (FT) is represented by C ˜ 2(νj) ) FT[C2(t)]. The angular velocity auto-correlation function (VACF) Ω(t) is given by the expression
the polarizability by intermolecular interactions (rotation and interaction-induced dipoles). The polarizability is given by
Ω(t) ) 〈ω(t)‚ω(0)〉
where R 5(0) j is the polarizability tensor of a single molecule i in the laboratory frame and 6 Tij is the dipole-dipole interaction tensor between molecules i and j. 6 Tij depends on the distance and orientation between the molecules i and j. On the basis of the interaction-induced dipole, it has been established 7,8 that the features, which appear in the Raman spectra of water between 10 and 300 cm-1, are related to the translational dynamics of water molecules. To have information on the contribution in the frequency domain of the reorientational dynamics of water, the long time decay of C2(t) was fitted by an exponential function. After its subtraction from C2(t), the remaining contribution is the shorttime of C2(t). The power spectrum C ˜ 2(νj) is then calculated and is presented in reduced form in Figure 2b. The short-time reorientational dynamics contribution is in the same frequency domain as that due the rotational dynamics, Ω ˜ (νj), and agrees quite well with the experimental low-frequency Raman spectrum of water in the spectral range between 300 and 1200 cm-1. These results indicate that only the translational dynamics of the water/acetone system should be considered to interpret the variation of the position and the width of the spectral bands with the acetone mole fraction observed in the low-frequency Raman spectra.
(3)
and its FT by Ω(νj) ) FT[Ω(t)]. Finally, the velocity autocorrelation function (VACF) of the center of mass of a water molecule is given by the expression
Ψ(t) ) 〈v(t)‚v(0)〉
(4)
and its FT by Ψ ˜ (νj) ) FT[Ψ(t)]. These functions are plotted in Figure 2a. For comparison, the calculated power spectra and the lowfrequency Raman spectrum of pure water are given in Figure 2b, where the power spectra are also presented in the reduced form. The positions of the peaks of Ψ ˜ (νj) are the same as those in the Raman spectrum of water R(νj), namely near 60 and 190 cm-1. The broad band centered at approximately 650 cm-1 is also observed in Ω(νj). It appears that the low-frequency Raman spectrum of water, in the range of 300-1400 cm-1, is associated with the rotational dynamics. Translational dynamics contributes to the spectrum in the range between 20 and 300 cm-1. These results give an obvious way of interpreting the low-frequency Raman spectra. In fact, the low-frequency Raman is due to the modulation of
5i(t) ) R R 5(0) i +
5(0) R TijR 5(0) ∑ i 6 j j*i
(5)
6006 J. Phys. Chem. B, Vol. 105, No. 25, 2001
Figure 3. liquids.
Low-frequency reduced Raman spectra of different
The bands which appear in the low-frequency Raman spectra of water contain the information concerning the intermolecular interactions. In the literature,9 the high-frequency mode at about 190 cm-1 is interpreted as arising from the vibration of an oxygen atom with respect to its nearest neighbor oxygen when a linear or a weakly bent hydrogen bond, O-H‚‚‚O, is present. This stretching of the hydrogen bond is often described as a restricted translation of the H2O molecules along the hydrogen bond. The mode observed at 60 cm-1 is assigned to a restricted translational motion perpendicular to the O-H‚‚‚O direction, i.e., the bending of the hydrogen bond. The results of recent molecular dynamics calculations with the use of the SPC/E model of water10 are in complete agreement with the interpretation of the high-frequency peak at 190 cm-1. Indeed, these calculations show that this frequency corresponds to restricted translational motion associated with the hydrogen bond. On the other hand, these calculations suggest that the peak at 60 cm-1 is due to a translational cage effect. In fact, the water molecules oscillate in the “cage” formed by their neighbors. This latter interpretation is further supported by the analysis of the temperature dependence of the VACF and the corresponding power spectra. In fact, at higher temperatures, it was found that the band associated with the translational cage (at 60 cm-1) increases in intensity and shifts to lower frequencies, whereas that associated with the hydrogen bond (at 190 cm-1) decreases in intensity and shifts to lower frequencies. This behavior supports the assignment in which the mode at 60 cm-1 is not due to the hydrogen bonds, because their number decreases with increasing temperature. The shift toward lower frequencies with increasing temperature of the mode at 60 cm-1 is related to the softening of the translational cage. This effect disappears at higher temperatures in the pure-diffusion regime, where the VACF has an exponential form. Such a band is not specific to water and was found both experimentally and by MD simulations11 carried out on liquid argon. Therefore, a study was made of the low-frequency Raman spectra of several liquids to determine if this feature occurs generally. The low-frequency Raman spectra of several liquids were then recorded at room temperature. The chosen liquids have different chemical and physical properties, and for some of them, there is no hydrogen bonding to be expected. The spectra are shown in Figure 3. This figure shows that each liquid studied exhibits a relatively broad band. The position of the maximum of the band is in the frequency range between 40 and 70 cm-1. It can then be argued that the occurrence of this band in the spectra of all of these liquids could be associated with the translational dynamics. The position of the frequency of this peak provides information
Idrissi et al. concerning the oscillations of the molecule and the degree of hardening/softening of the surrounding cage formed by its neighbors. On the basis of the above interpretation concerning the peaks observed in the low-frequency Raman spectra of water, an analysis was undertaken of the low-frequency Raman spectra of the acetone/water system. To quantify the changes observed in the spectra with the addition of acetone, the positions and bandwidths of the two bands attributed to intermolecular vibrations in the low-frequency Raman spectra were measured. A nonlinear curve fitting procedure was employed to characterize the changes in the low-frequency Raman spectra with the addition of acetone. In the case of solutions, it is more difficult to rationalize the nature and origin of the low-frequency Raman spectra than in pure liquids. The low-frequency Raman spectrum of pure water is in the same frequency domain as that of pure acetone. This makes the interpretation of the low-frequency Raman spectra of the acetone aqueous solutions more difficult. In fact, all studies dealing with the interpretation of such spectra have to cope with the fundamental problems of a large number of different interaction mechanisms and their coupling, which contribute to this spectral region. Thus, in the present analysis of the experimental data, the hypothesis was made that intermolecular interactions which involve water molecules contribute mainly to the profile of the low-frequency Raman spectra in the low mole fraction range. For samples at higher mole fractions, it is the interactions which involve acetone molecules that contribute mainly to the lowfrequency Raman spectra. Thus, two Gaussian functions were used in the entire mole-fraction range to follow the changes exhibited by the bands at around 60 and 190 cm-1. The results of the fit are the averages over many fitting procedures where the initial values of the different parameters were varied. Examples of the result of a fit are depicted in Figure 4 parts a and b for χacetone) 1.0 and 0.11. In the following sections, νji (i ) 1 and 2) is the position of the band, and ∆νji (i ) 1 and 2) is the corresponding width at half-maximum. The subscripts 1 and 2 refer to the band at around 60 and 190 cm-1, respectively. Low Acetone Mole Fractions. In this range of mole fractions, the quantity νj1 is the position and the quantity ∆νj1 is the width of a band which is due to the oscillation of the water molecule in a cage formed by its neighbors. Similarly, νj2 and ∆νj2 are attributed to the intermolecular interactions associated with the hydrogen bond which involves water molecules. As is shown in Figure 5a, the width ∆νj1 increases with χacetone, reaching its maximum at χacetone ) 0.06. It subsequently narrows in the low mole-fraction range of acetone between 0.06 and 0.14. By further increasing χacetone, ∆νj1 increases again. The position of νj1 shifts to higher frequencies as χacetone increases, reaching a maximum value at χacetone ) 0.14 and then shifts to the lower frequencies for the higher mole fraction of acetone. Figure 5b shows that the width ∆νj2 increases with increasing χacetone, reaching its maximum at χacetone ) 0.14. A small decrease of ∆νj2 is observed, followed by an increase for increasing values of χacetone. The position of the peak of νj2 shifts monotonically to lower frequencies with increasing χacetone. High Acetone Mole Fractions. In this mole fraction range, the band positions νj1 and widths ∆νj1 are parameters that are associated with an oscillation of an acetone molecule within a cage formed by its neighbors. The quantity νj1 decreases
Aqueous Acetone Solution at Various Concentrations
J. Phys. Chem. B, Vol. 105, No. 25, 2001 6007
Figure 4. (a and b) Examples of the result of a fit. (1) R(νj), lowfrequency reduced Raman spectrum of water and its fit and (2) R(νj) R(νj1)calculated for χacetone ) 1.0 and 0.11.
monotonically with increasing χacetone (Figure 5a). The value of ∆νj1 is found to increase in the mole fraction range between 0.4 and 0.6 and appears to decrease with further increase of χacetone. The results of the curve-fitting show that a second band νj2 (the corresponding width is ∆νj2) is present for pure acetone and an acetone/water mixture at higher mole fractions of acetone (Figure 5b). Although there is no obvious interpretation of the origin of this feature, νj2 is probably associated with the interaction of acetone molecules which self-associate through dipole-dipole alignment.12,13 The position of νj2 is almost constant. The corresponding width of this band ∆νj2 apparently increases with acetone χacetone, reaching a maximum at χacetone ) 0.8. The values of νj1 for χacetone ) 0.0 and 1 are almost the same. As pointed out, these frequencies are associated with the oscillation of a water or an acetone molecule in a cage formed by their neighbors. these frequencies are related to the Einstein frequencies given by the following expression 14
〈Fcage2(0)〉 Ω ) mkBT 2
(6)
where m is the mass of a single molecule, kB is the Boltzmann constant, and T is the absolute temperature. One can deduces the average force 〈Fcage2(0)〉 exerted on the center of mass of the molecule. 〈Fcage2(0)〉 is a part of the total forces 〈Fcage2(0)〉 associated to the different intermolecular interactions (van der
Figure 5. (a) Position of the translational peak νj1 and its width ∆νj1 and its dependence on the mole fractions of acetone. (b) Mole fraction of acetone dependence of the band νj2 and its width ∆νj2 associated to intermolecular interactions (hydrogen bond...).
Waals, hydrogen bond, ...). Because 〈Fcage2(0)〉 is calculated from the given values of νj1, these forces are responsible for the occurrence of the caging effect. Using eq 5 and the values of νj1 for χacetone ) 0.0 and 1, it can be deduced, therefore, that 〈Fcage2(0)〉 is three times greater for acetone than for water. Before proposing an interpretation of this result, it is appropriate to summarize some of the properties of water and acetone that are relevant to this problem. An important result concerning the structure of water was obtained by X-ray analysis.15 This investigation indicates that a water molecule has, on the average, 4.4 first-neighbors water molecules. The result is a pseudotetrahedral structure where one water molecule is connected through hydrogen bonds to four water molecules. Acetone molecules self-associate through dipole-dipole alignment.12,13 It could be expected from these results that the values of the average total force in water are higher than those in acetone. This fact, together with the values of 〈Fcage2(0)〉 for water and for acetone, indicate that hydrogen bonding interactions are not responsible for the occurrence of the caging effect. At low mole fractions, the increase of the peak position νj1 with the addition of acetone suggests that the average force 〈Fcage2(0)〉 increases. The shift of the peak position νj1 is related to the changes in the environment of water molecules which includes higher number of acetone molecules when the mole fraction of acetone increases. The coordination number gives information on the environment of a probe molecule. Molecular dynamics simulations are in progress to calculate the coordination number of water molecules around a water molecule at different mole fractions of acetone. Moreover, molecular
6008 J. Phys. Chem. B, Vol. 105, No. 25, 2001
Figure 6. Intramolecular OH stretching mode of water as a function of acetone mole fractions.
dynamics results16 on the urea/water system (urea has the same geometrical structure as acetone) show that the coordination number of water around water molecules has the values 4.8, 4.6, and 4.3 for mole fractions of urea 0.0, 0.04, and 0.10, respectively. This result suggests that, because the number of water molecules around a probe water molecule is almost constant, the increase of the average force 〈Fcage2(0)〉 (related to νj1) is due to the interaction of water molecules with acetone molecules. The increase of ∆νj1 in this range of acetone mole fractions indicates that the distribution of the environment of a water molecule is inhomogeneous. At high acetone mole fractions, the peak position νj1 describes the caging effect “seen” by acetone molecules. The increase of the peak position νj1, indicates that the cage becomes increasingly rigid. This result suggests that the interaction between acetone and water is stronger than the interaction between acetone molecules. At the low mole fractions, the hypothesis is made that νj2 expresses the stretching of the two oxygen atoms in the unit O-H‚‚‚O belonging to two water molecules. The decrease of the peak position νj2 with increasing the mole fraction of acetone suggests that the associated force constant decreases. Thus, the distance between the two oxygen atoms increases. Consequently, the distance O-H in the unit O-H‚‚‚O decreases. Thus, the intramolecular vibration of water, which involves a stretching of the O-H, should shift to higher frequencies with increasing mole fraction of acetone. This result is confirmed experimentally. As is shown in Figure 6, the intramolecular stretching vibration of the O-H shifts to higher frequencies with increasing acetone mole fraction. The shift of the peak position νj2 with χacetone indicates that acetone molecules tend to alter progressively the hydrogen bond between water molecules. The nonlinear behavior of the mole fraction dependence of the width of the band associated with intramolecular vibration has been observed for several liquid mixtures17,18,19. It was suggested that the physical origin of the nonlinear mole fraction dependence of the width of the peak, and therefore the occurrence of the bandwidth maximum for a certain values of the mole fraction of the solute, can be traced back to a structurebreaking effect in this mole fraction range. The variation of the excess enthalpy of acetone-water solutions with the mole fractions of acetone is an indication of the structure-breaking role of acetone. The evolution of the excess enthalpy of acetone aqueous solutions is presented in Figure 7 for different mole fractions of acetone and for two different temperatures, at T ) 29820 and 363 K.21 Raman spectroscopic22 data for liquid water between 276.5 and 362.3 K show that the intensity of the band
Idrissi et al.
Figure 7. Excess enthalpy of the acetone-water system as a function of acetone mole fractions from refs 20 and 21.
at 190 cm-1 (νj2) decreases with increasing temperature. This result has been attributed to the increase in the number of nonhydrogen-bonded water molecules. Accordingly, it would be expected that the change in excess enthalpy with temperature is associated with the formation/breaking of intermolecular hydrogen bonds. Thus, the decrease in the excess enthalpy at T ) 298 K (which corresponds to the temperature at which our low-frequency Raman spectra were recorded) in the mole fraction of acetone between 0.0 and 0.2 is associated with the hydrogen-bond formation that takes place in the solution. The increase in excess enthalpy in the region 0.2 < χacetone < 0.4 is an indication of hydrogen bond breaking. It is suggested that the decrease in the excess enthalpy of the acetone aqueous solutions at low mole fractions is associated with a complex formation between water and acetone. It has been shown that such a complex exists. In fact, the observed spectral features of the Fourier transform infrared absorption spectrum of acetonewater systems are consistent with hydrogen-bonded acetonewater complexes.23 A similitude between the dependence of ∆νj2 on the mole fractions of acetone and that of the excess enthalpy in the mole fraction range between 0.0 and 0.4 for T ) 298 K suggests the formation of the acetone/water complex (Figure 5b). The increase in the excess enthalpy in the range 0.2 < χacetone < 0.4 can be related to the breaking of hydrogen bonds between water molecules. Evidently, the formation of hydrogen bonds between acetone and water at acetone low mole fractions is counter-balanced by the breakdown of the water structure, with a subsequent net decrease in hydrogen bonding between water molecules. This result is correlated with the decrease in the intensity ratio of the bands at 190 cm-1 to that at 60 cm-1 with increasing acetone concentration. Acknowledgment. Institut du De´veloppement et des Ressources en Informatique Scientifique is thankfully acknowledged for the CPU time allocated on the NEC-SX5 computer. The Centre d′Etudes et de Recherches Lasers et Applications is supported by the following organizations: Ministe`re Charge´ de La Recherche, Re´gion Nord/Pas de Calais, and Les Fonds Europe´en de De´veloppement Economique des Re´gions. We would like to thank Professor G. Turrell and Dr. W. G. Rothschild for their valuable discussions of this work. References and Notes (1) McMorrow, D.; Thantu, N.; Melinger, J. S.; Kim, S. K.; Lothshaw, W. T. J. Phys. Chem. 1996, 100, 10389-10399. (2) Idrissi, A.; Ricci, M.; Bartolini, P.; Righini, R. J. Chem. Phys. 1999, 111, 4148.
Aqueous Acetone Solution at Various Concentrations (3) Wang, Y.; Tominga, Y. J. Chem. Phys. 1994, 101, 3453; 1990, 100, 2407; 1996, 104, 1; Phys. ReV. E 1998, 58, 7553; Phys. ReV. E 1999, 60, 1708. (4) Tominga, Y.; Takeuchi, S. M. J. Chem. Phys. 1996, 104, 7377. (5) Suziki, Y.; Suziki, N.; Takasu, Y.; Nishio, I. J. Chem. Phys. 1997, 107, 5890. (6) Mizoguchi, K.; Hori, Y.; Tominga, Y. J. Chem. Phys. 1992, 97, 1961. (7) Impey, R. W.; Madden, P.; Mcdonald, I. R. Mol. Phys. 1982, 46, 513-539. (8) Madden, P. A.; Impey, R. W. Chem. Phys. Lett. 1986, 123, 502. (9) Walrafen, G. E. J. Chem. Phys. 1964, 40, 3249. (10) Idrissi, A.; Sokolic´, F.; Perera, A. J. Chem. Phys. 2000, 112, 94799488. (11) Egelstaff, P. A. An Introduction to the Liquid State; Clarendon Press: Oxford, U.K., 1992. (12) Bradley, M. S.; Krech, J. H. J. Phys. Chem. 1993, 97, 575580.
J. Phys. Chem. B, Vol. 105, No. 25, 2001 6009 (13) Shindler, W.; Sharko, P. T.; Jonas, J. J. Chem. Phys. 1982, 76, 3493. (14) Hansen, J. P.; McDonald, I. R. Theory of Simple Liquids; Academic Press: London, U.K., 1986. (15) Narten, A. H.; Danford, M. D.; Lavy, H. A. Discuss. Farady. Soc. 1967, 43, 97. (16) Idrissi, A.; Sokolic´, F.; Perera, A. To be published. (17) Shindler, W.; Posch, H. A. Chem. Phys. 1970, 43, 9. (18) Fujiyama; Kakimoto, T. M.; Suzuki, T. Bull. Chem. Soc. Jpn. 1976, 49, 606. (19) Musso, M.; Torii, H.; Giorgini, M. G.; Do¨ge, G. J. Chem. Phys. 1999, 110, 10076. (20) Kister, A. K.; Walman, D. C. J. Chem. Phys. 1958, 62, 245. (21) Nicholson, D. E. J. Chem. Eng. Data 1960, 5, 35. (22) Walrafen, G. E.; Fisher, M. R.; Hokmabadi, M. S.; Yang, W. H. J. Chem. Phys. 1986, 85, 6970. (23) Zhang, X. K.; Lewars, E. G.; March, R. E.; Parnis, J. M. J. Phys. Chem. 1993, 97, 4320.
