Electron attachment to water clusters under collision-free conditions

J. Phys. Chem. 1987, 91, 2601-2607 Si,-Silm all have IPSbetween 4.99 and 6.42 eV. Si+ll+are found to be dominant photofragments from the larger silicon clusters. The overall silicon cluster distribution produced from this source is nearly independent of cluster size, showing only minor intensity alterations and the expected decrease to larger sizes. From this

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we conclude that the previous interpretation5 of the high-intensity PMS at 6.42 eV is likely incorrect because ion photochemistry was not taken into consideration. Registry No. Si, 7440-21-3.

Electron Attachment to Water Clusters under Collision-Free Conditions Martin Knapp, Olof Echt,* Dietmar Kreisle, and Ekkehard Recknagel Fakultat f u r Physik, Universitat Konstanz, 0-7750 Konstanz, West Germany (Received: July 15, 1986)

Long-lived water cluster anions (H20),-, n 2 11, can be formed by electron attachment to preformed, cold water clusters. Attachment occurs resonantly at energies very close to 0 eV. Obviously, the adiabatic electron affinity of these clusters is nonnegative, and electron trapping is not impeded by a potential barrier. Under comparable expansion conditions, attachment to cold, preexisting clusters yields the same minimum cluster anion size as injection of low-energy electrons into the condensation zone of neat water vapor, as reported previously by Haberland and co-workers. The smallest cluster anions being observed show a high probability for electron detachment in the field free drift tube of the time-of-flight mass spectrometer.

Introduction The electron affinity of the free water molecule is exceedingly small, if a bound state exists a t all.l-3 Excess electrons in condensed water, however, are known to be strongly bound (with respect to a free electron in vacuo). In its ground state, the electron will be self-trapped; i.e. the geometrical arrangement of the solvent molecules around the localized electron will be completely different from that of neutral water."1° The molecules have to reorient with respect to the electron; and the local density will be reduced because of dipole-dipole repulsion and weakening of hydrogen bonds. The interaction of the excess charge with molecules beyond the first coordination shell will be crucial to obtain the net stability of the solvated electron. A sufficiently large water cluster will certainly feature a sizeable adiabatic electron affinity, but a large rearrangement of the molecules will be required to solvate the electron. Thus, it has been argued that excess electrons will not bind to preexisting neutral, stable, equilibrium water This picture has been apparently confirmed by the failure to produce (H,O); by electron attachment" or charge transferI2 to free neutral water clusters. A different approach has been recently pursued by Haberland and c o - w o r k e r ~ . ~These ~ ~ ' ~ authors (1) Chipman, D. M. J . Phys. Chem. 1978,82, 1080. ( 2 ) Jordan, K. D.; Wendoloski, J. J. Chem. Phys. 1977, 21, 145. (3) Crawford, 0. H.; Garrett, W. R. J . Chem. Phys. 1977, 66, 4968. (4) Jortner, J. Eer. Bunsen-Ges. Phys. Chem. 1984, 88, 188. (5) Kestner, N. R.; Jortner, J. J. Phys. Chem. 1984, 88, 3818. (6) Rao, B. K.; Kestner, N. R. J . Chem. Phys. 1984, 80, 1587. (7) Krebs, P. J. Phys. Chem. 1984, 88, 3702. Eer. Bunsen-Ges. Phys. Chem. 1984,88, 275. (8) Thompson, J. C. In Physics and Chemistry ofElecrrons and Ions in Condensed Mutter, Acrivos, J. V., et al., Eds.; Reidel: Dordrecht, 1984; p 385. (9) Kenney-Wallace, G.A. Adv. Chem. Phys. 1981,47, 535. (10) Copeland, D. A,; Kestner, N. R.; Jortner, J. J. Chem. Phys. 1970, 53, 1189. (11) Klots, C. E. Radiur. Phys. Chem. 1982, 20, 51. Compton, R. N. In Electronic and Aromic Collisions, Oda, N . , Takayanagi, K., Eds.; North Holland: Amsterdam, 1980; p 251. (12) Herschbach, D. R., private communication to J. Jortner (ref 69 in ref 4). Quitevis, E.L. Ph.D. Thesis, Harvard University, 1980. (13) Haberland, H.; Ludewigt, C.; Schindler, H A . ; Worsnop, D. R. Surf. Sci. 1985, 156, 157. (14) Haberland, H.; Schindler, H.-G.; Worsnop, D. R. Ber. Bunsen-Ges. Phys. Chem. 1984,88, 270. Habedand, H.; Langosch, H.; Schindler, H.-G.; Worsnop, D. R. J . Phys. Chem. 1984, 88, 3903.

0022-3654/87/2091-2601$01.50/0

injected electrons (kinetic energy below 2 eV) into the condensation zone of a supersonic jet of water vapor. For an expansion without carrier gas, they observed anions (H20),- for cluster sizes n I 11 (n 1 12 in case of deuteriated water). In these experiments transient cluster anions are presumably formed by electron attachment to warm clusters; they are stabilized and grown further by subsequent collisions with cold water molecules. In this paper we show that, contrary to common belief, electron attachment to free, cold, preexisting water clusters does result in long-lived cluster anions; subsequent stabilization by collisions is not required. The cross section for attachment is surprisingly large, but the electron energy has to be close to 0 eV. The size distributions of the cluster anions are strikingly similar to those obtained by Haberland et al. under comparable expansion conditions. In the time range of microseconds after their formation, the probability for electron detachment from the smallest cluster anions being observed is large, it decreases rapidly with increasing cluster size. This behavior probably reflects the rapid increase of the adiabatic electron affinity of (H,O), for n 1 1 1. A partial account of these results has been published previo~sly.'~ Experimental Section The cluster source and the time-of-flight mass spectrometer Neutral water have already been used in previous e~periments.'~.'~ clusters are formed by adiabatic expansion of neat water vapor through a nozzle (diameter 80 pm) into vacuum. The stagnation pressure is estimated from the temperature of the reservoir containing the liquid water. The temperature of the nozzle is kept slightly higher than that of the reservoir. For most experiments, deuteriated water (obtained from Riedel-de Haen, isotopic purity 99.7%) is used without further purification. The use of deuteriated water allows us to distinguish more easily between "pure" water cluster ions (stoichiometry (H,O); or (D,O);) and oxygenated or hydroxygenated cluster ions. Some experiments were also run with undeuteriated water; this was bidistilled and purified by ion exchange. (15) Knapp, M.; Echt, 0.;Kreisle, D.; Recknagel, E. J . Chem. Phys. 1986, 85, 636. (16) Echt, 0.;Knapp, M.; Sattler, K.; Recknagel, E. Z. Phys. 1983, B53, 71. (17) Echt, 0.; Reyes-Flotte, A,; Knapp, M.; Sattler, K.; Recknagel, E. Eer. Bunsen-Ges. Phys. Chem. 1982, 86, 860.

0 1987 American Chemical Society

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The supersonic jet, containing neutral clusters of various sizes including the monomer, passes through a collimator (diameter 0.5 mm) at a distance of 10 mm from the nozzle exit. Thirty millimeter further downstream, the beam passes through another collimator (diameter 1.0 mm) before it enters the mass spectrometer. The walls of the expansion chamber and of the differentially pumped second chamber are cooled to 77 K; they act very efficiently as cryopumps. The collimators are heated slightly in order to prevent clogging. Noncondensable impurities in the expanding gas are removed by a 10 L/s rotary pump and a 100 L/s turbomolecular pump. Even for a strong expansion (stagnation pressure up to several atmospheres, cluster size n > 1000 molecules), the background pressure in the expansion chamber and in the differential pumping chamber does not exceed and Torr, respectively. The main chamber of the mass spectrometer is evacuated by another cryopump, operating at 77 K, and a 500 L/s turbomolecular pump. The background pressure in this region is a few times lo-’ Torr with the cluster source in opera tion. At a distance of 10 cm from the nozzle, the collimated cluster beam is intersected by a pulsed electron beam. The electron gun follows a design as described recently by Erdman and Zipf.I8 It features a directly heated filament, a pulsed control aperture, and a focusing element. The design has been modified in order to achieve optimum performance for electron energies down to 0 eV. The ion extraction field is switched off while the electron beam is on. Additionally, a magnetic field, produced by a solenoid, helps to align the electron beam. This double pulse technique avoids the deterioration of the electron energy distribution which would result from electron deflection in a static extraction field. Furthermore, it allows for higher beam intensities, because the duration of the electron beam can be made rather long (typically 1 ps) without loss in mass resolution. The electron beam is collected in a Faraday cup. Its current (typically 1 pA for low electron energies during “beam on”) is fed to a gated amplifier and electronically stabilized by adjusting the filament power supply. At very low energies, below -0.5 eV, the filament is heated with a constant power. The electric potential of the central part of the filament is read from a voltage divider connected in parallel to the filament. A corrected electron energy scaleI9 is obtained from the position of well-known resonances in the yield of SF6- (at 0 ev), 0- from N 2 0 (at 2.25 eV), and 0from C 0 2 (at 4.4 and 8.2 eV).20 The width of the electron energy distribution can be estimated from these resonances, too. It is less than 1.O eV (full-width a t half-maximum) for energies above 1 eV,21*22 and slightly larger than 1.0 eV for very low energies. The ion extraction field is switched on as soon as the electron beam is off. The direction of the extraction field is parallel to the direction of the neutral cluster beam. This arrangement avoids detection discrimination against large clusters, which already have an appreciable kinetic energy in the neutral jet.I6 The strength of the extraction field (typically 100 V/cm) in the first acceleration gap is chosen such that the mass resolution of the time-of-flight mass spectrometer is optimized.23 The kinetic energy of the ions in the grounded drift tube (length 110 cm) is about 2 keV per elementary charge. At the end of the drift tube, the ions pass three grids, stacked closely together. Application of a repelling potential to the central grid allows a study of the decomposition (18) Erdman, P. W.; Zipf, E. C. Rev. Sci. Instrum. 1982, 53, 225. (19) The zero of the energy scale can be determined from a linear extrapolation of the electron emission current to zero, cf. Rapp, D.; Briglia, D. D. J. Chem. Phys. 1965, 43, 1480. With this method, the ion yield from a true-zero resonance will peak at a slightly positive value on the corrected energy scale. A “near-0-eV resonance”, however, is established more reliably by direct comparison with the position and shape of the SF,- resonance. (20) Christophorou, L. G.; McCorkle, D. L.; Christodoulides, A. A. In Electron-Molecule Interactions and their Applications, Vol. 1, Christophorou, L. G., Ed.; Academic: New York, 1984; chapter 6 and references therein. (21) Knapp, M.; Echt, 0.;Kreisle, D.; Mark, T. D.; Recknagel, E. Chem. Phys. Lett. 1986, 126, 225. (22) Knapp, M.; Echt, 0.; Kreisle, D.; Mark, T. D.; Recknagel, E. In The Physics and Chemistry of Small Clusters, Jena, P., Rao, B. K., Khanna, S. N . , Eds.; NATO AS1 Series, in press. (23) Wiley, W. C.; McLaren, L. H. Rev. Sci. Instrum. 1955, 26, 1150.

Knapp et al.

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time o f f l i g h t ( p s e c ) Figure 1. Time-of-flight mass spectra of water cluster ions, formed by electron attachment at 7 eV (top spectrum) and near-0 eV (middle spectrum), and by electron impact ionization at 20 eV (bottom spectrum). The composition of the main product ions given in the figure is different in each case. The expansion conditions (Po = 195 Torr, neat D,O expansion), and therefore the distribution of the neutral water clusters before ionization, were the same. Note the logarithmic intensity scale.

of cluster ions24as well as electron detachment in the drift tube. Those ions which pass the grids are postaccelerated by a potential drop of 2.5 kV onto the conversion dynode of an electron multiplier. The time elapsed between the leading edge of the ion extraction pulse and the detector signal is digitized in a home-built time-to-digital converter with multistop capability and a maximum channel resolution of 30 ns; the events are stored in a multichannel analyzer. The repetition rate of the electron gun is adjusted according to the time-of-flight of the largest ions being observed; it is on the order of 10 kHz. Results Composition and Size Distributions of Anions. The composition and the size distribution of the water cluster anions crucially depends on the energy of the incident electrons. Between 5 and 10 eV, ions with the composition (D20),]0D- ( n 2 1) are the main product from electron attachment. The distribution of these ions is displayed in Figure 1, top, using a logarithmic intensity 150 for a stagnation scale. The cluster size extends up to n pressure of p o = 195 Torr. The first part of this spectrum is displayed with a linear intensity scale in Figure 2 (top). Close inspection of the spectrum reveals the occurrence of a very weak signal corresponding to (D20),10- ( n 1 1). Below 5-eV incident electron energy, very few cluster anions are produced, but the intensity rises again for energies below 1 eV. The composition of these ions, however, is (D20);. A spectrum, recorded with an electron energy close to 0 eV, is displayed in the middle of Figure 1 (logarithmic intensity scale) and in the middle of Figure

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(24) Kreisle, D.; Echt, 0.;Knapp, M.; Recknagel, E. Phys. Rev. A 1986, 33, 768. Surf. Sci. 1985, 156, 321. Echt, 0.; Kreisle, D.; Knapp, M.; Recknagel, E. Chem. Phys. Lett. 1984, 108, 401.

The Journal of Physical Chemistry, Vol. 91, No. 10, 1987 2603

Electron Attachment to Water Clusters Ee=7eV

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t i m e o f flight (psec) Figure 3. Attachment of low-energy electrons to a beam of undeuteriated water clusters gives rise to (H20)”-, n 2 11.

0

-, 5

10

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20

25

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time o f flight (psecl Figure 2. Mass spectra of water cluster anions, formed by electron attachment. The top and middle spectra are replotted from Figure 1,

using a linear intensity scale. The bottom spectrum displays the intensity distribution of neutrals, arising from cluster anions (distribution as shown in the middle spectrum) in the drift tube. The detachment reaction given in the figure appears to be the main source for the detected neutrals.

2 (linear intensity scale, small clusters only). Most notable is the abrupt increase, by two orders of magnitude, in the ion intensity between the 11-mer (which is barely detectable) and (approximately) the 18-mer. The expansion conditions and therefore the size distribution of the neutral clusters were the same as used for recording the top spectra. The spectrum is very clean at these low energies. The only ion that does not belong to the homologous series of “pure” water cluster anions occurs at 46 amu; it is labeled “I” in the mass spectra. It is possibly due to NO2-, formed by pyrolysis of N 2 0 (impurity from preceding experiments) at the filament of the electron gun or the ionization gauge.25 For comparison, the bottom spectrum in Figure 1 displays the distribution of positively charged water clusters. Their composition is (D20)F,D+. Again, the spectrum was obtained with the same expansion conditions as used for the other spectra. The electron emission current was also the same, but the electron energy was set to 20 eV. All three spectra in Figure 1 show the same degree of falloff in the intensity of large cluster ions ( n > 50). Figure 3 displays a spectrum obtained by electron attachment to clusters to undeuteriated water; the electron energy was close to 0 eV. The spectrum is very similar to the corresponding spectra obtained with deuteriated water at low electron energies. Note, however, that the intensity of (H20)11-is an order of magnitude larger than that of (D20)ll-,if the spectra are normalized to the most intense ion peak (which occurs at about n = 20). The minimum cluster size and the steep rise in ion intensity do not depend on the expansion conditions. Under milder expansion conditions, though, the maximum intensity is reached at slightly smaller cluster size, and the intensity levels off much faster for large clusters. This trend is to be expected from the well-known dependence of neutral cluster size distributions upon expansion conditions, as monitored ( 2 5 ) Chantry, P.J. J . Chem. Phys. 1969, 51, 3380.

e l e c t r o n energy

(eV)

Figure 4. Bottom: energy dependence of selected cluster ions formed by

electron attachment to a beam of deuteriated water clusters. The yield being displayed for the solvated hydroxyl anions has been summed up over several cluster sizes. For a given cluster size n, their maximum intensity is only -8% of that for ( D 2 0 ) , f . Top: yield curves of SFC and SF< produced from SF6,recorded for the purpose of electron energy ~alibration.’~ by electron impact ionization.I6 Pronounced intensity anomalies are observed for large cluster anions: The 51-mer and the 53-mer stand out particularly strong in the distributions of (H,O); (Figure 3) and (D,O),- (Figure 1, middle). These anomalies do not occur in the spectra of hydroxygenated cluster anions (Figure 1, top) nor do they occur in the cluster cation spectra (Figure 1, bottom). Intensity anomalies like these often arise from prompt or metastable decay; the intensity of relatively strongly bound cluster ions will be enhanced by the preferential decay of more weakly bound species.24 This conjecture is supported by the fact that water cluster ions other than (H20),- or (D,O); do not show the same anomalies: The geometrical arrangement of the water molecules in the cluster or, at least, in the cluster core, will depend on the kind of charge distribution and/ or on the kind of chemical bonding of the charged species. We are, however, puzzled by two observations: (1) The intensity anomalies at n = 51, 53, 55, and 57 do not become more pronounced by excluding from the spectrum all possible product ions from metastable decay in the drift tube. This is in stark contrast to the behavior of anomalies in the distributions of, e.g., Xe,+ or ( H ~ O ) , _ ~ H + . ~ ~ (2) The intensity anomalies observed in our spectra of water cluster anions are absent in the spectra recorded by Haberland

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The Journal of Physical Chemistry, Vol. 91, No. 10, 1987

and c o - ~ o r k e r s . ~We ~ * cannot ~~ offer an explanation for this. Dependence of Anion Intensity on the Electron Energy. The yield of selected cluster anions vs. energy of the incident electrons is displayed in Figure 4 (bottom). The intensity of hydroxygenated cluster anions has been summed up over cluster sizes 2 In I 9 in order to reduce the statistical fluctuations of the data. The cross section peaks at 7 eV and forms a shoulder at 9 eV. Within the statistical error, the shape of this yield curve is the same for all cluster ions (D20),,0D-, 2 I n I 50, between 5 and 10 eV. Above 10 eV, the yield of large hydroxygenated cluster anions is essentially zero. The yield of 0- (not shown in Figure 4) features a low intensity a t about 7 eV, a maximum at 9 eV, and a broad second maximum at about 11 eV. The shape of this curve agrees with the results obtained from dissociative attachment to water

As described above, cluster ions with the stoichiometry (D20); are observed only for very low electron energies. Figure 4 (bottom) displays the yield curve of the 18-mer. Within the statistical accuracy, the shape and the position of the resonance for other clusters in this homologous series is the same; only the 1 1-mer and 12-mer were not included in this comparison because of their low intensities. The intensity of (D20),f is approximately 10 times larger than that of (D20),10D-, 2 I n I20, at their respective resonance energies. In order to calibrate the energy scale of the electrons and to measure the electron energy distribution, we have also recorded the yield curves of SF, and SF 2.50 Also, the calculated dipole moment of the octamer is zero for most interaction potentials being tested.51 Attraction will then only arise from the interaction between the electron and the long-range polarization field. Antoniewicz et al. use a continuum model to calculate the adiabatic EA of a water droplet.52 They attain about 0.1 eV for a cluster radius of 10 A; the electron remains in a very diffuse orbital (surface state). Given the estimated temperature of the water clusters in our experiment, T 180 K, binding energies of 10 meV are certainly not sufficient to prevent autodetachment from the anions on the time scale of the mass analysis. Injection of electrons into the condensation zone of a jet of neat water ~ a p o r ’gave ~ . ~rise ~ to the same size distributions as observed by us, i.e. no cluster anions below n = 11 were observed. In a seeded expansion, however, Haberland and co-workers could form cluster anions as small as the dimer.49s53 Beyond n = 10, the anion intensity rose steeply, again. This behavior possibly indicates a sudden increase in the adiabatic EA, due to the fact that t k s e clusters are big enough to solvate an electron; but the electrdn affinity of a dielectric sphere is also calculated to increase rather abruptly beyond a certain cluster size.52 According to various model calculations, eight water molecules (the largest system being investigated) could solvate an electron such that the cluster anion would be stable with respect to complete decomposition into molecules and a free e l e ~ t r o n . ~ ”The . ~ ~energy of this cluster anion, however, would still be about 2 eV above the energy of (H20), (relaxed) and a free e l e ~ t r o n .Thus, ~ an ensemble of hot, metastable clusters in this size range might trap low-energy electrons, but cold, relaxed water clusters would not. Their vertical EA would be even more negative than -2 eV.

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(45) Wiesenfeld, J. M.; Ippen, E. P. Chem. Phys. Lett. 1980, 73, 47. Walker, D. C. J . Phys. Chem. 1980, 84, 1140. (46) Tachiya, M.; Mozumder, A. J . Chem. Phys. 1974, 61, 3890. (47) de Koning, L. J.; Nibbering, N. M. M. J . Am. Chem. SOC.1984,106, 7971. (48) Wallqvist, A.; Thirumalai, D.; Berne, B. J. preprint. (49) Haberland, H.; Ludewigt, C.; Schindler, H.; Worsnop, D. R. Z . Phys. A 1985, 320, 15 1 . (50) Kay, B. D.; Castleman, A. W., Jr. J . Phys. Chem. 1985, 89, 4867. (51) Brink, G.; Glaser, L. J . Phys. Chem. 1984, 88, 3412. (52) Antoniewicz, P. R.; Bennett, G . T.; Thompson, J. C. J . Chem. Phys. 1982, 77, 4573. (53) Haberland, H.; Ludewigt, C.; Schindler, H.-G.; Worsnop, D. R. J . Chem. Phys. 1984,81, 3742.

Knapp et al. The high cross section for the formation of (H20);, n I11, or (D20);, n I12, by attachment of low-energy electrons indicates that another mechanism provides initial localization of the electrons. The vertical EA is strongly negative only if the electron is assumed to occupy a state similar to that of the solvated electron. An initial shallow trap could be provided by a surface state, which would present no energy barrier to the incoming electron.52 Efficient trapping of electrons at van der Waals clusters for energies close to 0 eV seems to be a rather general phenomenon.22933,54*55 A comparison with carbon dioxide clusters might be especially illuminating. Small cluster ions (C02),-, n 1 1, feature a resonance at about 3-eV electron energy. It corresponds to the 4.4-eV resonance in the 0- yield from C 0 2 molecules and reflects the strongly negative vertical EA of the monomer.21 For cluster sizes n I2, however, an additional resonance appears at or close to 0 eV, it becomes the dominant resonance for n 2 We speculate that the interaction being responsible for the high attachment probability at low energy is the same as in case of water. This does not imply, of course, that theflnal state of the excess electron in water and C 0 2 clusters are of the same nature: (C02); is probably best characterized as C02- being solvated in the cluster,56whereas the corresponding state does not seem to occur in liquid water. Also, it remains unknown whether the sudden onset in the intensity of “pure” water cluster anions beyond n = 11 reflects the onset of efficient prelocalization, or of sufficient stability of the final, relaxed cluster anion. The high detachment probability found for (D20),-, n = 12, 13, 14, and its rapid decline for larger sizes indicates that the metastability of the relaxed cluster anion causes the characteristic shape of the size distribution, because the time scale for the analysis is of the order of 10 p s after attachment. We cannot rule out, however, that the electron detachment is partly induced by collisions. This seems unlikely because, under comparable background gas pressures and beam densities in the ionizer and the drift tube, the detachment probability of (SF,),- is found to be negligible in this size range. But if the electron in the water cluster anions does indeed reside in a diffuse, weakly bound surface state, its cross section for collision-induced detachment may be much larger than for SF, cluster anions, which probably consist of a solvated SF6-. The main conclusion, though, would be the same: The adiabatic electron affinity of water cluster anions, n 12, appears to be rather small. “Small” means that it will be comparable to the sublimation energy of a neutral water cluster (taken at its estimated temperature) in this size range. A rough estimate of this quantity may be obtained from the heat of vaporization of liquid water at its boiling temperature, which is 0.42 eV. The sublimation energy provides a meaningful criterion, because sublimation from these clusters does occur on the time scale of 0.1 ms: it is these decompositions which determine the final temperature of the clusters in the neutral beam.35 Recently, Bowen and co-workers have analyzed water cluster anions by photoelectron spectro~copy.~’They find detachment energies which increase from 0.75 eV for the 1 1-mer to 0.97 eV for the 15-mer. These energies are upper bounds to the adiabatic electron affinity, because photodetachment is a vertical process. A final remark should be made concerning the isotope effect in the size distributions of (H20); and (D20),,-, respectively. In the latter case, the 11-mer is barely visible, but in the former case, it is already quite strong. There is an effective shift in the onset of cluster anion intensity by An = 1. The same phenomenon was observed by Haberland and co-workers,13J4who actually observed a trace of (H20)10-in some of their experiments with a nonseeded beam.26 This shift is probably related to an isotope effect reported by Hamill and co-workers in aqueous glasses.58 They observed 5.22s33354

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(54) Stamatovic, A.; Leiter, K.; Ritter, W.; Stephan, K.; Mark, T. D. J . Chem. Phys. 1985, 83, 2942. (55) Mark, T. D.; Leiter, K.; Ritter, W.; Stamatovic, A . Phys. Reu. Lett. 1985, 55, 2559. ( 5 6 ) Rossi, A. R.; Jordan, K. D. J . Chem. Phys. 1979, 70, 4422. (57) Bowen, K., private communication. ( 58) Stradowski, Cz.; Hamill, W . H . J . Phys. Chem. 1976, 80, 1431.

J. Phys. Chem. 1987, 91, 2607-2626 that the yield of matrix-trapped excess electrons in D 2 0 is larger than in H20 and concluded that D 2 0 is less efficient in the initial electron localization (to yield the solvated electron) than HzO. The reason for this difference is ascribed to the lower vibrational frequency of D 2 0 . Therefore D 2 0 is more prone to autodetachment, and this process can compete more favorably with the transfer of the excess energy (electron affinity) to the lattice, which is required for prelocalization.

Conclusion Our experiments demonstrate that efficient mechanisms exist for the trapping of low energy electrons at cold, preexisting water clusters in the size range n 5 12. Thus, the initial localization of an electron at a cluster does not require large configurational fluctuations or molecular reorientation. Similar mechanisms seem to exist for other systems as well. The vertical electron affinity of COz, e.g., is strongly negative, because the geometry of COzin its ground-state deviates appreciably from the geometry of neutral COz. Nevertheless, a COz cluster anion can be formed efficiently by attachment of near-0-eV electrons.

2607

Our results do not, however, answer the question whether a solvated electron represents the ground state of a cluster anion comprised of as few as 12 water molecules.

Note Added in Proof. From a recent molecular dynamics simulation of electrons in liquid water6' it has been concluded that the concentration of preexisting deep traps is much higher than thought previously. Thus, electron solvation might proceed very rapidly, without significant structural relaxation. Acknowledgment. It is a pleasure to thank K. Bowen, H. Haberland, and T. D. Mark for stimulating discussions, and C. E. Klots for critical comments on the manuscript. This work was financially supported by the Deutsche Forschungsgemeinschaft. Registry No. HzO,7732-18-5. (59) Krohn, C. E.; Antoniewicz, P. R.; Thompson, J. C. Surf.Sci. 1980, 101, 241. (60) Kestner, N. R., private communication. (61) Schnitker, J.; Rossky, P. J.; Kenney-Wallace, G. A. J. Chem. Phys. 1986, 85, 2986. Schnitker, J.; Rossky, P. J., preprint.

Generalized Valence Bond Studies of Metallic Bonding: Naked Clusters and Applications to Bulk Metals Mark H. McAdont and William A. Goddard III* Arthur Amos Noyes Laboratory of Chemical Physics,$ California Institute of Technology, Pasadena, California 91 125 (Received: June 17, 1986)

Using the generalized valence bond (GVB) method, we have examined the bonding in numerous small clusters of Li atoms (Li, and Li,', n I13). Our conclusion is that the optimum bonding involves interstitially localized singly occupied orbitals, e.g., (1) bond-centered orbitals for one-dimensional clusters (e.g., rings such as Lid, Lis, Lis, and Li,, and linear chains such as Li3+,Cu3+, Lis+, Lis. Lis-, and Li13+),(2) equilateral-triangle-centered orbitals for planar close-packed clusters (e.g., Lila, Lil;+, and Li13+),and (3) tetrahedron-centeredorbitals for three-dimensional clusters (examples here include three high-symmetry [icosahedral (Ih), face-centered cubic (fcc), and hexagonal close-packed (hcp)] Li,,' structures and three low symmetry [y-brass-like] Li13+structures. Of the three high symmetry Li13+clusters, Ih has the lowest energy while total energies for fcc and hcp are 0.26 and 0.56 eV higher, respectively. GVB wave functions for these three clusters suggest a set of rules predicting structures even more stable than the icosahedron. These lower energy structures [denoted as OPTET (optimum tetrahedral)] maximize the number of tetrahedra under the restrictions of the rules (e.g. minimizing the number of occupied tetrahedra sharing corners) and lead to relatively low symmetry, e.g. C2,, C,. These OPTET clusters coincide with truncations of the y-brass structure. The lowest energy Li13+OPTET cluster [y-(4,4,5), C,,] has a total energy 0.58 eV lower than that of the icosahedron. Suggestions are given on the relevance of these results for stability and reactivity of small clusters and on the extension of these ideas to infinite systems.

I. Introduction The valence bond (VB) principles of structural chemistry,' based on spin pairing of hybridized atomic orbitals on various atoms, lead to excellent rationalization of the geometries and bonding for nonmetallic molecules and solids; e.g., bulk Si and Ge are tetrahedrally coordinated, Se and Te have helical chains in their solid forms, the As4 molecule has a tetrahedron structure with a single bond along each edge, etc. These simple VB ideas of nonmetallic systems have been confirmed by ab initio generalized valence bond (GVB) calculations2 that lead directly to localized spin-paired atomic orbitals corresponding to various bond pairs. Valence bond principles have also proven valuable in understanding defects and surface reconstruction in nonmetallic solids, e.g. the Si vacancy3 and the GaAs( 110) ~ u r f a c e . ~ For metallic systems, there has not been an analogous set of simple principles to predict a priori the optimum geometries and structures of clusters, defects, or interfaces. In order to lay the A.R.C.S. Foundation Predoctoral Fellow, 1985-1986. 'Contribution No. 7413.

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foundation for developing chemical concepts for metallic systems, we have employed GVB approaches to examine the bonding in various one-dimensional (1D),5 two-dimensional (2D), and three-dimensional (3D) clusters of Li atoms. The results of this study have led directly to a new generalized valence bond model of metallic bonding63' based on electrons localized in interstitial regions such as bond midpoints (1D clusters), triangular faces (2D clusters), and tetrahedral hollows (3D clusters). This model is (1) Pauling, L. The Nature of the Chemical Bond, 3rd ed.; Cornell University Press: Ithaca, New York, 1960. (2) Goddard 111, W. A.; Dunning,Jr., T. H.; Hunt, W. J.; Hay, P. J. Arc. Chem. Res. 1973, 6, 368. Goddard 111, W. A,; Harding, L. B. Annu. Reu. Phys. Chem. 1978, 29, 363. (3) Surratt, G. T.;Goddard 111, W. A. Solid State Commun. 1977, 22, 413. Phys. Rev. B 1978, 18, 2831. (4) Barton, J. J.; Goddard 111, W. A.; McGill, T. C. J . Vac. Sci. Technol. 1979, 16, 1178. Swarts. C. A,; McGill, T. C.; Goddard 111. W. A. Surf Sci.

1981, (5) (6) (7) 149.

110, 400.

McAdon, M. H.; Goddard 111, W. A,, unpublished results. McAdon, M. H.; Goddard 111, W. A. Phys. Rev. Lett. 1985,55, 2563. McAdon, M. H.; Goddard 111, W. A. J . Non-Cryst. Solids 1985, 75,

0 1987 American Chemical Society