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).
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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
Stability of Negatively Charged Water Clusters TABLE I: Energies (kcal/mol) of Clusters (H20), Using the Polarization Model n eouil cluster cluster with cavitv“ 4 6
-29.1b -36.5
+9.5 (4 coord) +27.1 (6 coord) +6.3 (4 2 coord) +5.4 (4 2 1 coord) (+23)‘ (6 1 coord) +5.4 (4 2 2 coord) +4.3 (4 1 1 1 1 coord) (+19)c (6 2 coord)
+ 7 -56.7 + + + 8 -72.gd + + + + + + + ‘Notation is the first coordination and + is the added second layer
molecules. When there are several numbers, these were added separately and are not in groups. It is important to note that these molecules were added not to maximize the total hydrogen bonding energy, but rather to minimize the energy of the negative ion energy. From ref 13. CUsingthe approximate value of 4 kcal/mol bond energy obtained from the 4 + 1 calculation for second layer molecules. The values in parentheses have errors of 3-4 kcal/mol. dFrom ref 16. We shall combine the recent quantum mechanical calculations of Rao and Kestner’O on small water clusters with some estimates of the energy required to form various clusters, as obtained from the polarization model of Stillinger et al.,” in order to evaluate the energetic stability of the localized electron state in these clusters.
Calculations Stillinger et al.” in a series of papers have developed a polarization model of water interactions which includes most of the important features of water-wter interactions in a reasonable quantitative manner. We will use in this work their 1980 parameters” and will assume fixed molecular geometry of the individual water molecules. The polrization model of water interactions is a self-consistent procedure in which there are both normal electrostatic interactions as well as induced moments in the molecular near the oxygen. The magnitude of the polarization is fixed by a parameter, and the charges are screened in order to yield good hydrogen bond energies. In order to compare these energies with the quantum mechanical results we must use the coordinates of the species from the Rao and Kestner’O study. They did calculations of small clusters of water with an extra electron, allowing the water structure to distort to accommodate the electron, Le., allow the dipole moments to orient to minimize the energy. These calculations are simply extensions of the Newton calculations4 and his coordinates were used as starting points. They also used the 4-31G basis set in a Gaussian S C F program. Rao and Kestner’O considered both four- and sixfold coordinated electrons, e.g., the dipole oriented as well as the bond-oriented geometry of the water molecules. As a simple statement of geometry the center to oxygen distance is 2.65 8,in the fourfold coordination and 3.05 8,in the sixfold coordination. This latter distance corresponds to the geometry observed by Kevan and co-workers in their electron spin-echo modulation magnetic resonance studies.12 The neutral clusters used in the analysis were the lowest energy subclusters with maximum hydrogen bonding possible from the most stable octamer generated by David and Sti1linger.l’ The energy of small clusters from other studies are almost identical at the level of accuracy in this work. the negatively charged clusters were those found by N e ~ t o n namely, ,~ four first coordination water molecules with hydrogens pointing inward around a void or “cavity” area plus extra waters added on the outside as second and third coordination layers usin the normal hydrogen bond lengths found in liquid water (2.03 ) and linear hydrogen bonds. The distance from the center of the cavity to the oxygens
1
(10) B. K. Rao and N. R. Kestner, J . Chem. Phys., in press. (1 1) A primary reference for this work is F. H. Stillinger and C. W. David, J . Chem. Phys., 73, 3384 (1980), with earlier work in such references as J . Chem. Phys., 69, 1473 (1978). (12) S.Schlick, P. A. Narayana, and L. Kevan, J . Chem. Phys., 64, 3 153 (1976).
The Journal of Physical Chemistry, Vol. 88, No. 17, 1984 3819 TABLE I1 Energy (kcal/mol) To Form Negatively Charged Clusters
n
4 6 6 7 8
(4 coord) (4 2 coord) (6 coord) (6 + 1 coord) (4 1 + 1 + 1
+ +
+ 1)
quantum binding energya
net stabilityb
stability with respect to equil neutral clustersC
-2.1 -15.1 -7.0 -1 3.8 -28.8
+7.4 -8.8 +20.1 +8.3 -24.5
+37.0 +27.7 +56.6 +65.0 +49.0
“From ref 10. bSee Table I for notation. Stability is relative to separate molecules and a free electron. ‘Stability is with respect to the neutral cluster in its equilibrium configuration. was 2.65 A and the hydrogen-oxygen-hydrogen angle is bisected by the radius vector from the center of the cavity to the oxygen. In Table I we present the calculations of selected water clusters calculated by the polarization model. Based on other parameterizations these should be good to about 1.5 kcal/mol per water rnole~ule.’~We have also used the results of Vernon et al.14 on n = 4 water clusters. Other have also determined the energies of stable water clusters. Brink and Glasserl5 using Jorgensen’s potential obtain 26.44 kcal/mol for the tetramer and 13.44 kcal/mol for the trimer; Kistenmacher et a1.I6 get about 20 kcal/mol for the tetramer, 33 kcal/mol for the hexamer, 38-41 kcal/mol for the heptamer, and 42-47 kcal/mol for the octamer, using a multiparameter potential, while Campbell and Belford17 obtain a the same energy for the tetramer as Kistenmacher, using a cooperative potential model. In Table I1 the calculations of the energy of the water clusters are combined with the quantum mechanical results of Rao and Kestner’O to estimate the energetic stability of (H,O),- clusters. The energy change accompanying the process
-
nHzO + e (H20); (1) which corresponds to the stability of the negative cluster relative to a free electron and a separated molecule is presented as the net stability in Table 11. We have also included in Table I1 the energy change for the process (H20)n(qui’) e (H20);
+
-
which corresponds to the stability of the negative cluster with respect to the neutral cluster in its equilibrium nuclear configuration. These calculations are for various groupings of water molecules around the electron with four or six molecules in the first coordination layer. Then, more molecules are added in such a way as to minimize the energy but not necessarily the hydrogen bonding. Thus, the orientational effects due to the electronmolecule interactions are very strong in the second coordination layer, at least stronger than the hydrogen-bonding effects in the clusters. The situation could be quite different in the liquid. It should be recalled that the quantum calculations probably constitute upper limits to the energy as the basis set used tends to exaggerate the charge-dipole interaction. From these results two conclusions emerge. First, as established by Rao and Kestner,lo (H20),- clusters with n 1 6, which contain at least one molecule in the second coordination layer, are stable with respect to the separate molecules and a free electron. Second, within these negatively charged water clusters, the excess electron has forced a sizable distortion of the normal neutral cluster structure. Accordingly, the (H20); clusters, which are energetically stable with respect to reacton 1, are considerably unstable with respect to (13) Based on octamer calculations using the 1982 parameters, see T. A. Weber and F. H. Stillinger, J . Chem. Phys., 86, 1314 (1982). (14) M. F. Vernon, J. M. Lisy, D. J. Krajnovich, A. Tramer, H-S. Kwok, Y . Ron Shen, and Y . T. Lee, Faraday Discuss. Chem. SOC.,73, 387 (1982); J. Chem. Phys., 77, 47 (1982). (15) G. Brink and L. Glasser, J . Compt. Chem., 3, 219 (1982). (16) H. Kistenmacher, G. C. Lie, H. Popke, and E. Clementi, J . Chem. Phys., 61, 546 (1974). (17) E. S.Campbell and D. Belford, Theor. Chim. Acta, 61, 295 (1982).
J . Phys. Chem. 1984, 88, 3820-3826
3820
reaction 2. We thus assert that neutral equilibrium water clusters have a negative electron affinity. Conclusions
We have been concerned with the energetic stability of small water clusters containing an excess localized electron, considering both the electronic binding energy and the cluster nuclear reorganization energy. The approximation inherent in our approach should be elaborated on. Firstly, we did not consider entropy effects. Water clusters in supersonic beams may be quite hot7b and entropy contributions should be incorporated in a more complete treatment. Secondly, we have considered only one type of excess electron state, namely, the one in which the electron is sufficiently localized, so that the molecules of water are oriented by its presence, resulting in a negative cluster, whose structure is quite different from that of a neutral cluster. It is possible that electrons could be bound to surface states on the outside of large clusters of polar (and even nonpolar) species, as shown by Antoniewicz, Bennett, and Thomspon,Is but such species would be weakly bound, e.g., of the same energy as negative ions of LiCl, LiF, etc.,19s20and would have ultralow energy excitation spectra. For reference, the total binding energy of an electron on LiCl, which has a dipole moment of 7.2 D, is 0.6 eV, but the dipole moment only accounts for about 0.08 eV of this energy. The water octamer studied by Stillinger and David" has a dipole moment of only 4.61 D, and this should have a significantly lower stability and excitation energy. For these reasons that type of surface states is not treated in more detail in this paper. The general conclusions emerging from these model calculations on the energetic stability of (H20); clusters lead to the following conclusions (18) P. R. Antoniewicz, G. T. Bennett, and J. C. Thompson, J . Chem. Phys., 77,4573 (1982). (19) K. D. Jordan and W. Luken, J . Chem. Phys., 64, 2760 (1976). (20) K. D. Jordan, K. M. Griffing, J. Kenney, E. L. Anderson, and J. Simons, J . Chem. Phys., 64,4730 (1976).
(1) Interactions beyond the first coordination layer are essential for the localization of an excess electron. This is apparent from the minimal size n = 6 (4 2) of a cluster, which is energetically stable with respect to nHzO e. The crucial interactions beyond the first coordination layer in the cluster are analogous to the "long-range" electron-medium interactions in the dense fluid, which are crucial for the energetic stability, spectra and localization, and dynamics of excess electrons in These interactions in a fluid are in a sense cooperative, depending on the fluid density. The calculations on (H,O),- clusters provide insight into the nature of these cooperative effects in fluids, as explored from the microscopic point of view. (2) The localization of an excess electron in a preexisting equilibrium cluster is accompanied by large configurational changes within the cluster, resulting in a considerable cluster rearrangement energy. (3) An excess electron will not bind to a preexisting neutral, stable, equilibrium, water cluster. This conclusion, which rests on the negative electron affinity estimated for stable clusters (Table II), is in accord with the recent experimental works,9 which demonstrated that electrons do not attach to preformed water clusters in the low-pressure domain of supersonic jets. (4) Metastable (H,O), (n 1 6) neutral clusters are required for the initial localization of an excess electron. These negative small clusters once formed can subsequently attach additional water molecules. (H,O); ( n 2 11) clusters were experimentally observedsb when a water vapor in an expanding supersonic jet is mixed with electrons. These experimental conditions favor electron attachment to small metastable water clusters.
+
+
Acknowledgment. This work is partially supported by the Department of Energy (Contract DE-AS05-77ER05399) in the Office of Basic Energy Sciences, Solar Photochemistry Division awarded to N.R.K. Registry No. H,O, 7732-18-5; (H,O)-, 12259-30-2.
Thermodynamics, Electrochemistry, and Kinetics of Sodium-Ammonia Solutions U. Schindewolf Institut fur Physikalische Chemie und Elektrochemie der Universitat Karlsruhe, Karlsruhe, West Germany (Received: August 24, 1983)
EMF measurements are reviewed which in combination with some extrathermodynamic assumptionsyield the thermodynamics of solvated electrons in liquid ammonia. We think the best experimental data for the solvation enthalpy and entropy at -40 OC are AHo = -95 & 10 kJ/mol and ASo= 154 i 20 J/(mol K). The individual data for the electron are used to outline the energetics of the solution process of a metal, its solubility, and the absolute potential difference between a metal and its saturated solution. The concept of absolute electrode potential helps us to understand the electrochemical response of a metal electrode to solvated electrons or to any redox system. Kinetic data are reported for the reaction e- + H20in ammonia, casting some doubts on the estimated thermodynamics of the hydrated electron which are based on its kinetics in water. Thermodynamicsof the solid sodium cryptand compound Na'CNa- is given which is easily prepared from a sodium-ammonia solution. Finally, the experimental findings of another phase instability above the normal miscibility gap of sodium-ammonia solutions will be reported.
will return to the original aim and restrict ourself entirely to some physicochemical properties of the sodium-ammonia system. Colloque Weyl 1organized by Lepoutre and Sienko and held First a short review of the thermodynamics of sodium-ammonia 1963 in Lille' was devoted to physicochemical properties of solutions and solvated electrons will be given. On the basis of this Ever since, the topics of c~~~~~~~~ metal-ammonia solutions, the energetics of a metal electrode in contact with a solvent will Weyl have expanded in general to electrons in fluid phases be discussed. This leads to the concept of the absolute equilibrium In this paper we including other solvents, metallic systems, potential difference between the metal electrode and the solvent; it shows that the metal ions as well as solvated electrons are determining the electrode potential. Then some experimental (1) G. Leputre and M. J. Sienko, Ed., "Metal-Ammonia Solutions-,w, material will be presented on the kinetics of the solvated elecA. Benjamin, New York, 1964. Introduction
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0 1984 American Chemical Society
