4824
J. Phys. Chem. 1992,96.4824-4829
Purchase of equipment through the Productivity Capital Investment Program is gratefully acknowledged. We thank Dr. M. J. McQuaid (BRL)for numerous stimulating discussions and Drs. W. R. Anderson and D. C. Dayton (BRL) for critical reiriew of the manuscript. We also thank Dr. A. J. Kotlar for providing us with a PC-AT computer program for the interconversion of wavelength (air) and wavenumber (vacuum). Support from the NRC Postdoctoral Associate Program is acknowledged (G.W.L.). Registry No. Kr, 7439-90-9; hydroxyl, 3352-57-6.
References and Notes (1) Smith, D. B.; Miller, J. C. J . Chem. Soc., Faraday Trans. 1990,86, 2441. (2) Miller, J. C. J . Chem. Phys. 1989, 90, 4031. (3) Miller, J. C. J. Chem. Phys. 1987, 86, 3166. (4) Mills, P. D. A.; Western, C. M.; Howard, B. J. J . Phys. Chem. 1986, 90, 4961. ( 5 ) Sato, K.; Achiba, Y.; Kimura, K. J . Chem. Phys. 1984, 81, 57. ( 6 ) Langridge-Smith, P. R. R.; Carrasquillo, E.; Levy, D. H. J . Chem. Phys. 1981, 74, 6513. ( 7 ) Berry, M. T.; Brustein, M. R.; Lester, M. I.; Chakravarty, C.; Clary, D. C. Chem. Phys. Lett. 1991, 178, 301. (8) Goodman, J.; Brus, L. E. J. Chem. Phys. 1977,67,4858. (9) Bramble, S. K.; Hamilton, P. A. Chem. Phys. Lett. 1990, 170, 107. (10) Fawzy, W. M.; Heaven, M. C. J . Chem. Phys. 1988,89, 7030.
(11) Berry, M. T.; Brustein, M. R.; Adamo, J. R.; Lester, M. I. J . Phys. Chem. 1988, 92, 5551. (12) Berry, M. T.; Brustein, M. R.; Lester, M. I. Chem. Phys. Lett. 1988, 153. 17. (13) Beck, K. M.; Berry, M. T.; Brustein, M. R.; Lester, M. I. Chem. Phys. Lett. 1989, 162, 203. (14) Berry, M. T.; Brustein, M. R.; Lester, M. 1. J . Chem. Phys. 1989, 90, 5878. (15) Berry, M. T.; Brustein, M. R.; Lester, M. I. J . Chem. Phys. 1990,92, 6469. (16) Schleipen, J.; Nemes, L.; Heinze, J.; ter Meulen, J. J. Chem. Phys. Lett. 1990, 175, 561. (17) Fawzy, W. M.; Heaven, M. C. J . Chem. Phys. 1990.92, 909. (18) Ohshima, Y.; Lida, M.; Endo, Y . J. Chem. Phys. 1991, 95, 7001. (19) Chann. B.-C.: Yu.L.: Cullin. D.: Rehfuss. B.: Williamson. J.: Miller. T. A,; Fawzy,k'. M.;'Zheng, X.;Fei,'S.; Heaven, M. C. J. Chem. Phys. 1991; 95, 7086. (20) Lin, Y.; Kulkarni, S. K.; Heaven, M. C. J. Phys. Chem. 1990, 94, 1720. (21) Chang, B.; Cullin, J.; Williamson, J.; Dunlop, J.; Rehfuss, B.; Miller, T. J. Chem. Phvs. 1992. 96. 33416. (22) ChakrAarty, C.'; Ciary, D. C.; Degli Esposti, A.; Werner, H.-J. J. Chem. Phys. 1990, 93, 3367. (23) Chakravarty, C.; Clary, D. C.; Degli Esposti, A,; Werner, H.-J. J. Chem. Phvs. 1991. 95. 8149. (24) Dedi Eswsti. A,: Werner. H.-J. J . Chem. Phvs. 1990. 93. 3351. (25) Daidigiin, P.'J.; Anderson,'W. R.; Sausa, R. C.; Miziolek, A: W. J . Phys. Chem. 1989, 93, 6059. (26) Lemire, G.W.; Sausa, R. C., to be published.
Electronlc Spectroscopy of Ag2-Xe D.L.Robbins, K.F. Willey, C. S. Yeh, and M. A. Duncan* Department of Chemistry, University of Georgia, Athens, Georgia 30602 (Received: January 28, 1992; In Final Form: March 2, 1992)
-
A vibrationally resolved electronic spectrum is reported for the metal dimer-rare gas complex Agz-Xe. The spectrum is obtained using resonant two-photon photoionization in the energy region near the Ag, B X electronic transition (292-280 nm). The complex exhibits extensive activity in three vibrational modes, making it possible to determine vibrational constants, anharmonicities, and cross-mode couplings. An unusual cancellation of factors results in the Agz-Xe complex having nearly the same rare gas stretching frequency (u: = 79.9 cm-I) as the corresponding krypton (0: = 72.6 cm-I) and Ar complexes (0: = 73.9 cm-l) which have been studied previously. Progressions extending over a significant range of the excited-state potential surface make it possible to derive the excited-state dissociation energy (Do' = 2761 cm-I). Combination with the red-shifted electronic state origin yields the corresponding ground-state dissociationenergy (D,," = 1233 cm-I). These binding energies, when compared to those for similar argon and krypton complexes with Ag,, are greater than would be expected on the basis of the rare gas polarizability trend.
Introduction Spectroscopic studies of weakly bound complexes have been described recently for a number of metal-rare gas and metalmolecular These studies probe the unique set of fundamental interactions and the resulting potential surfaces which these complexes exhibit. Weakly bound metal complexes provide zeroth-order models for the study of metal-ligand interactions or the interactions present in adsorption on metal surfaces. We have recently described the first such sptctroscopic studies of metal dimer complexes, in the form of silver dimer-rare gas systems (Ag2-Ar, AgZ-Kr).l7 The increased complexity of these systems over metal atom complexes studied previously provides the opportunity to probe additional vibrational coordinates and their interactions. In the present report, we extend the series to include the complex of silver dimer with xenon, i.e., Ag,-Xe. We compare the vibrational frequencies and binding energy measured for this complex to those measured before for the corresponding argon and krypton complexes. *To whom correspondence should be addressed.
0022-3654/92/2096-4824$03.00/0
The electronic spectroscopy of silver dimer is well-characterized.18-zz It is a ciosed-sheli diatomic bound by a single u bond through the 5sI electrons (DO" = 1.66 eV).,O Therefore, the interaction of this system with rare gas atoms is expected to be purely van der Waals in nature. Consistent with this idea, the dissociation energies measured for Ag2-Ar and Ag,-Kr are a few hundred wavenumbers, and the vibrational frequencies of these complexes indicate that they contain a weakly perturbed Ag, moiety." The strength of the Ag,-RG van der Waals bond in these complexes should depend on the polarizability of both Ag, and the respective rare gas atom involved. While rare gas polarizabilities are well-known, that of silver dimer has not been measured. However, if the binding energies for the series of rare gas atoms are studied with Ag,, and if the structures of the complexes are the same, the relative dissociation energies should depend only on the rare gas polarizability trend. We find here that the xenon complex also has vibrational frequencies characteristic of a van der Waals system. As expected, it is more strongly bound than the argon and krypton complexes. However, its binding energy is significantly-greater than would be expected on the basis of the polarizability differences between the different 0 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 12, I992 4825
Electronic Spectroscopy of Ag2-Xe TABLE I: Observed and Calculated Vibrational Bands for l'Agtqe (UI,U*,U1) obsd freq calcd freq diff
0.0 25.4 50.9 54.4 79.2 106.2 134.6 155.9 162.3 183.0 188.7 211.6 217.2 232.3 243.0 259.5 269.5 307.5 317.6 324.1 334.9 343.5 351.4 363.7 371.2 381.7 393.2 404.1 408.7 420.0 430.8 437.3 448.9 454.0 467.0 475.7 480.8 485.1 493.8 501.8 509.8 522.9 524.4
0.0 26.8
0.0 1.4
55.0 78.5 105.5 133.8 155.9 163.2 183.0 189.5 211.4 217.1 232.1 241.1 259.3 267.5 307.2 317.8 325.2 334.5 344.3 350.8 363.2 372.1 381.1 393.3 402.3 408.6 419.9 428.1 437.4 447.9 453.9 467.7 478.3 48 1.5 485.7 494.5 504.2 510.5 522.6 525.5
0.6 -0.7 -0.7 -0.8 0.0 0.9 0.0 0.8 -0.2 -0.1 -0.2 -1.9 -0.2 -2.0 -0.3 0.2 1.1 -0.4 0.8 -0.6 -0.5 0.9 -0.6 0.1 -1.8 -0.1 -0.1 -2.7 0.1 -1 .o -0.1 0.7 2.6 0.7 0.6 0.7 2.4 0.7 -0.3 1.1
(Mass Channel 343) Relative to the origin at 34281 f 10 cm-' (Vacuum)' (UlP2,UI)
obsd freq
calcd freq
diff
529.5 540.4 553.5 565.1 568.1 579.7 595.8 608.2 614.1 623.6 625.8 634.5 640.4 645.5 652.8 660.9 665.3 669.0 680.0 685.1 669.8 712.3 725.5 733.6 738.8 754.2 711.2 784.5 792.6 798.5 809.6 818.5 823.7 826.6 836.2 842.9 85 1.8 857.7 870.3 883.7 891.8 897.0 912.7
53 1.5 541.0 553.2 562.2 567.9 579.2 596.0 606.6 613.1 623.9 626.9 637.5 640.1 644.9 653.1 662.8 665.4 668.5 680.6 684.0 699.5 711.7 725.8 733.6 737.1 753.8 770.9 784.7
2.0 0.6 -0.3 -2.9 -0.2 -0.5 0.2 -1.6 1 .o 0.3 1.1 3.0 -0.3 -0.6 0.3 1.9 0.1 -0.5 0.6 -1.1 -0.3 -0.6 0.3 0.0 -1.7 -0.4 -0.3 0.2
'The solvated Ag-Ag stretch is indicated by q,the Xe bending mode is w2, and the Xe van der Waals stretching mode is w3. Calculated frequencies are obtained with the equation and vibrational constants given in the text. Uncertainties in band positions are determined by the line widths (f1.0cm-l). rare gas atoms. There is evidence that the Ag,-Xe complex has a different structure than its argon and krypton counterparts. Experimental Section
Silver clusters are produced by pulsed-nozzle laser vaporization at 532 nm in a molecular beam apparatus described previ0usly.2~ The laser vaporization source is specially modified with a short cluster growth channel to optimize van der Waals complexes with metal atoms and dimers, rather than larger metal clusters. For production of the Ag2-Xe complex, vaporization of a I/.,-in,-diameter silver tube sample (Aesar) occurs in an expansion of about 1-10% xenon in argon. A NdYAG-pumped dye laser (Spectra-Physics PDL-2) is frequency doubled to produce the required radiation near 290 nm. This laser is used for one-color resonant two-photon ionization spectroscopy (R2PI), selectively detecting each of the different Ag,Xe+ isotopic mass channels in a timeof-flight mass spectrometer. Wavelengths are calibrated relative to the origin of the B X electronic transition of Ag,.
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Results pad Discussion Vibronic Spectra. Sharp spectral features are observed in the Ag2-Xe+ mass channel via R2PI when a molecular beam containing silver clusters is prepared with a xenon/argon expansion gas mixture. The resonances are observed to the red of the B X Ag2 origin (35 809 cm-l for 107J09Ag2).Both the total mass and the isotope pattern in the mass spectrum are consistent with
-
the identity of the molecular ion Ag,-Xe+. However, fragmentation of larger complexes containing additional metal or rare gas atoms could also produce this molecular ion. Fragmentation is possible because the second photon in the onecolor R2PI process populates states more than 1.2 eV in excess of the Ag, ionization potential (7.656 eV).,' The parent ion identity, combined with a convincing assignment of the spectrum, as described below, establishes that the Ag2-Xe+ signal results from ionization without fragmentation of Ag,-Xe. The wavelength dependence of the Ag2-Xe+ mass channel produces a spectrum of approximately 200 vibrational bands beginning 1528 cm-' to the red of the Ag, origin and extending for about 1500 an-I. A portion of this spectrum is shown in Figure 1 for the 107Ag,129Xe isotope. The lowest energy band is assigned to the electronic origin of the complex, and band positions relative to this reference point are given in Table I. Using the electronic origin of 107J09Ag2 as a reference,'" the frequency of the complex origin is determined to be 34 281 f 10 cm-l (vacuum). In spectra such as this, it is difficult to be certain of the exact quantum numbering because the true electronic origin may not be observed. Isotopically selected scans may be used under certain circumstances to establish the exact quantum numbering. However, while it is possible to obtain mass-selected scans of the spectrum, most of the various mass channels do not contain pure isotopomers. For example, mass channel 343, which is shown in Figure 1, can be assigned uniquely to the species 107Ag2129Xe, but mass channel 347 contains contributions from the species
4826 The Journal of Physical Chemistry, Vol. 96, No. 12, 1992 TABLE 11: Hot Vibrational Bands Observed to the Red of the Ag,-Xe Origin Band"
Robbins et al. TABLE HI: Spectroscopic Constants for Ag2-Ar, Ag,-Kr, and Ag,-Xe Complexes"
0,.u,.v2
obsd frea
calcd freu
diff
Ag2-Ar
Ag2-Kr
Ag2-Xe
i07JosAg2
o,o,o
0.0 -6.3 -10.5 -14.1
0.0 -6.1 -10.7 -14.0
0.0 -0.2 0.2 -0.1
35329 156.3 -0.7 1 28.3 -2.73 73.9 -1.72
34998 157.7 -0.64 27.9 -1.76 72.6 -1.06
35808.7 151.3 -0.70
755 275
1205 394
3428 1 165.3 -0.68 25.7 0.68 79.9 -0.57 7.45 -0.69 2761 1233
0,1,0 0,2,0 0,3,0
"The spectra of these bands (not shown) are a factor of 20-30 weaker than the vibrational cold bands shown in Figure 1. These band positions were measured in a scan without isotopic selection to increase the signal levels. However, isotope shifts are expected to be small for these low frequencies. Positions are measured relative to the electronic origin band cited above and are assigned to bending mode levels populated in the ground state. The vibrational constants determined from this fit are w2/1 = 7.45 cm-' and x p = -0.69 cm-l.
1wAg21z9Xe and lo7JosAg2'31Xe.Only channels 343 and 354 (109Ag2136Xe) can be assigned uniquely to single isotopomers. As indicated below, we have obtained spectra for the 343 and 354 mass channels. These two data sets are consistent with the origin indicated, but they are not sufficient to achieve a definitive origin assignment. Isotope shifts in polyatomic molecules with simultaneous changes in isotopes of two atoms are difficult to calculate except for certain symmetric s t r u c t ~ r e sand , ~ ~our attempts to do this were inconclusive. However, no spectral features are observed in the region 200 cm-I toward lower energy from the origin indicated with intensity within a factor of 30 of the origin assigned here. The abrupt onset and the consistent isotope data suggest that the lowest energy peak is in fact the true origin. The large red shift of this origin indicates that the complex is more strongly bound in its excited state than it is in its ground state. As indicated by the vibrational line assignments in Table I, essentially all of the bands observed are assigned to progressions and combinations of only three vibrational modes. As discussed below, however, a few additional bands not shown in Figure 1 are observed in other scans, and these are believed to be vibrational hot bands. The positions of these extra bands, which appear to the red of the origin, are given in Table 11. The pattern of the vibronic lines recorded here is quite similar to that observed for the corresponding argon and krypton complexes, making it straightforward to obtain assignments. The "solvated" Ag-Ag stretch should have about the same frequency as isolated Agl. As expected, there are both progressions and combination bands involving a frequency near 150-160 cm-I. Motions involving the rare gas atom are expected to be at lower frequency than the Ag-Ag stretch because of the weaker bonding. The frequencies observed near 80 and 25 cm-l are therefore reasonable. A triatomic species such as this should have rare gas stretching and bending modes, and the stretching mode should have the higher frequency. As indicated in Table I, we assign the Agz-Xe stretch as the intermediate frequency, and the low frequency is assigned to the Agz-Xe bending mode. The most prominent mode in the spectrum is the rare gas stretch, present in a pure progression of 10 members and in combination with one, two, or three quanta of the silver stretch. The silver stretch exhibits four members in a pure progression and is present in numerous combination bands. The bend exhibits a pure progression of only two members, but additional twomember bend progressions are found in several other combinations. In all, there are over 70 vibronic bands assigned in the first 800 cm-I of the spectrum. The full spectrum extends to about 1500 cm-l above the origin. However, vibrational assignments are difficult to obtain at higher vibrational energy because of increasingly severe overlap of the bands. We therefore include only the first 70 or so vibrational bands in the fit described below. Table I contains the bands included in the fit and additional lines whose positions are measured but which are not assigned. The spectrum has also been measured without isotopic selection up to energies about 600 cm-' beyond the bands listed. However, the line intensities are significantly weaker and so isotope-specific data like those presented in Table I have not been obtained in this energy region.
"f
WI XIf
w2/
x2/ w3'
x3' w2/1 Xa"
Do'
D/
"All entries are given in cm-' units. The lo7Ag2'29Xeisotope is compared to data obtained earlier for a composite of silver (in Ag,Ar) and silver-krypton (in Ag2Kr) isotopes.
To quantitatively check these assignments, we fit the observed lines to an energy level equation for triatomic molecules:24
+ Y2) + w2(uz + Yz) + wj(u3 + Yz) + + Yd2 + x2(uz + XI2 + x3(u3 + 1/2Y + XI2(UI + t/2)(uZ+ t/2) + x13(uI + t/2)('3 + Y2) + xZ3(u2 + YZ>(u3+ YZ)
G(UI,UZ,UJ) = wI(ui XI(UI
These terms represent three harmonic frequencies, each of their respective individual anharmonicities, and cross-mode or off-diagonal anharmonicities which reflect the couplings between the different vibrational modes. Although this fit involves nine parameters, the number of data points is large enough to make it meaningful. The vibrational constants obtained by least-squares fitting of the 107Ag2-129Xe data to this equation are w1 = 165.3, ~2 = 25.7,a3 79.9,X I = -0.68,~2 = 0.68,~3 = -0.57, ~ 1 2 0.60,xi3 = -0.68,and ~ 2 =3 0.13cm-I. In this analysis, wIis the solvated Ag-Ag stretch, w2 is the Xe bend, and w3 is the Xe stretch. The Ag-Ag stretching frequency obtained here (165.3cm-I) is significantly higher in energy than the corresponding stretch in the bare dimer (1 5 1.8 cm-l) in its excited B state. All three modes have about the same absolute value for the anharmonicity, but the bending mode has opposite the normal sign for this parameter. In other words, the vibrational bands in the bending mode progression become more widely spaced, rather than closer together, at' higher quantum numbers. The values of the cross-mode anharmonicities indicate that the Ag-Ag stretch is coupled more strongly to both xenon motions than those motions are coupled to each other. Calculated and experimental band positions are compared in Table I. We have also measured the vibronic band positions for a portion of the 1osAgz-136Xe isotopomer (masschannel 354). As expected, the band positions deviate significantly from those of the lo7Agz-129Xe isotopomer at higher vibrational quantum numbers. The vibrational constants obtained by a least-squares fit of this data to the nine-parameter equation above are oI= 158.1,w2 = 24.6,w3 = 78.9,X I = 0.83,X Z 0.71,~3 = -0.67, = 0.14,xi3 = 0.25,and ~ 2 =3 0.11 cm-l. The quality of this fit is not as good as that above because only 30 vibrational bands were included. However, as expected, all three of the vibrational frequencies in the heavier isotope species shift toward lower energy. The reversed sign of the anharmonicity in the Ag-Ag stretch is believed to arise because of the limited number of lines included in this mode and the importance of Fermi resonance in the early members of this progression (see below). Table I11 provides a comparison of the vibrational constants obtained here for the xenon complex to those reported earlier for the corresponding argon and krypton complexes. As indicated, the frequencies in all three vibrational modes are quite similar for the different complexes. However, on closer consideration, this similarity is not too unreasonable. As discussed previ~usly,~' the heavier rare gas atoms cause their complexes to have a greater reduced mass, which tends to produce lower vibrational frequencies. On the other hand, the heavier rare gas atoms are more polarizable, and they are therefore bound more strongly to the silver dimer, which tends to produce increased vibrational fre-
The Journal of Physical Chemistry, Vol. 96, No. 12, 1992 4821
Electronic Spectroscopy of Ag,-Xe v3
I
I
I
I
1
I
4
P
3
0
100
200
Relative Frequency (cm-1)
0
200
400
Relative Frequency (cm-1) Figure 1. R2PI excitation spectrum obtained for Ag,-Xe in the wavelength region near 280-290 nm. This spectrum was obtained by monitoring the 1mAgz129Xet ion in the mass spectrometer (mass channel 343) while the ionization laser was scanned. The spectrum shown represents a composite of scans spanning several dye laser tuning curves. The origin indicated is at 291.7 nm (air). Progressions are observed for the Ag-Ag stretch (Y,), the Xe-Ag2 bend (YJ, and the Xe-Ag, stretch (YJ, and there are numerous combination bands.
quencies. These two factors approximately offset each other, and the three rare gas systems have about the same vibrational frequencies. While the Ag-Ag stretch and Ag,-Xe stretch here have higher frequencies than in the lighter complexes, the bend has a lower frequency than before. Apparently, the bend is more influenced by the increased mass of the system, while the stretching modes are more influenced by the increased binding energy. The quality of the fit obtained here is noticeably worse than that reported in ref 17 for our argon and krypton complexes with Ag,. Several of the differences between calculated and observed band positions here are greater than 1 cm-l, while a few exceed 2 cm-I. One likely explanation for this is the increased importance of Fermi rmnance in the xenon complex spectra. The increased silver stretch and rare gas stretch frequencies in this spectrum compared to those for argon and krypton complexes bring these two modes into almost an exact 2: 1 resonance. At the first possible coincidence, the band corresponding to two members of the xenon stretch (0,0,2) has a frequency only 7 cm-'different from one silver stretch (l,O,O). This near coincidence occurs throughout the spectrum where these modes are involved. Not only are there the obvious coincidences at any even multiple of u3, but all the odd progression members except the first overlap with a u1u3 combination band. Toward higher quantum numbers, the uj and u1 progression members get further apart because vj has a larger anharmonicity. However, at even higher members, the difference in these two modes corresponds to a bending mode frequency. For example, 0,0,6and 3,0,0 are about 31 cm-l apart, but 0,1,6 and 3,0,0 are separated by only 4 cm-'. This interesting vibrational dynamics accounts for the difficulty in assigning lines at high vibrational energies, and it must also influence the mode coupling constants we derive. It is unusual in van der Waals complex spectroscopy to observe activity in all vibrational coordinates like that described here. Rare gas stretching modes are most often observed, while there are fewer examples of bending activity. In many complexes vibrational activity in the primary chromophore occurs at high enough energy to predissociate the complex (e&, rare gas complexes of the hydrogen halide~).~ In the present systems, the relatively high binding energy (discussed below) and the low Ag-Ag stretching frequency make it passible to observe multiple bound levels of Ag, below the dissociation limit of the complex. In addition to favorable energetics, these spectra are also the result of fortuitous Franck-Condon factors. The observation of long vibrational progressions suggests that there is a significant geometry change between the ground- and excited-state complexes. As indicated
Figure 2. R2PI excitation spectrum obtained for Ag2-Xe without isotope selection in the low-energy region of the spectrum. This spectrum was also taken at higher laser power than that used in Figure 1. Higher l a m power (resulting in partial saturation) and no isotope selection cause broadening of vibrational lines, but these conditions increase the signal on weak spectral features. As shown here, it is possible to observe a multiplet structure for the second member in the bend progression under these conditions.
below, the rare gas binding energy is greater in the excited state, and therefore the excited state is expected to have a shorter metal-rare gas bond distance. In other spectra taken under slightly different conditions, we have observed a number of vibrational lines with weaker intensities than those shown in Figure 1. For example, spectra obtained without isotope selection show the second member of the bending progression (0,2,0) with a much better signal-tc-noise ratio. As shown in Figure 2, there is a smaller peak just to the red (3.5 cm-') of the main (0,2,0) peak, perhaps due to a multiplet splitting at this level. It is therefore interesting to consider the nature of this peak. We have discussed in our earlier work on these complexes how single quantum levels in bending vibrational progressions are not usually expected for symmetric ("T"-shaped or linear) structures." Multiplet levels in the bending progression, however, are easily explained if there is an unusually shaped potential surface (e.g., a double-minimum well) or if the complex is linear. Linear complexes would have a doubly degenerate bending vibration. Each level in a linear bending progression has a u 1 degeneracy, which arises because of the possible combinations of the degenerate motions.24 For a linear complex, the bend has a ?r symmetry. The u = 2 level is 3-fold degenerate, with two members having u symmetry and the third having 6 symmetry. If these levels have slightly different energies (and they often do), two bands with a 2 1 intensity ratio should be observed, consistent with our spectrum. If a more extended bend progression were observed, the expected multiplet splittings at higher levels could be investigated to determine the actual source of this apparent multiplet pattern. However, the higher levels (O,n,O) for n = 3, 4,5, ... are not observed, presumably due to poor Franck-Condon factors. Likewise, even the other (0,2,n) combination levels, which should also exhibit this splitting pattern, are not observed with significant intensity. Other weak features are also observed throughout the spectrum which may be assigned to hot vibrational bands. Assignments are difficult to obtain for most of these bands because of their overlap with other peaks and their weak intensity. However, a series of bands occurring to the red of the origin have been observed and can be assigned convincingly to hot bending vibrations (Le., u; # 0). These bands cannot be assigned to vibrational sequences; sequence bands of the form ufl- ',Y = 1 1,2 2,... should appear to the blue of the origin band when the excited state is more strongly bound. The only progression possible to the red of the origin band involves transitions of the form Y? = 1,2,3, ... v i = 0. It is therefore straightforward to assign this series of bands to a ground-state progression in the bending mode and to determine the ground-state constants in this mode. Table
+
- -
-
4828 The Journal of Physical Chemistry, Vol. 96, No. 12, 1992
I1 lists the band positions observed and their calculated values. The constants determined are wZr‘ = 7.45 cm-’ and x2“ = -0.69 cm-l. Unfortunately, there are no corresponding hot band data for the other Ag, complexes to compare to these ground-state frequencies. lksochtion Eoergies. The observation of extensiveprogressions in vibronic spectra such as these makes it possible to investigate the shape of the potential surfaces and the dissociation energies in these complexes. The simplest treatment, which has a wellfounded tradition in molecular spectroscopy, approximates potential surfaces by Morse functions. If this assumption is made, a Birge-Sponer extrapolation of the vibronic band positions in the rare gas stretching coordinate allows calculation of the dissociation energy, D,,’, in that coordinate. Linear extrapolation of AGu+I12vs u to AG = 0 for the lo7Ag2’29-Xevibrational bands determines the dissociation limit to be at u = 68. Insertion of this quantum number into the vibronic energy level equation, and neglecting off-diagonal anharmonicity terms, gives a dissociation energy in the excited state (D,,’) of 2761 cm-l. Adding in the zero-point energy in the rare gas stretching coordinate gives Dd = 2801 cm-l. While the assumption of a Morse potential allows a simple determination of dissociation limits, this kind of treatment is not expected to be extremely accurate because it involves extrapolation to energy levels well beyond those actually observed in the experiment. The extrapolation error should be 5% or less. However, since the actual potential may deviate from the Morse form, the exact error in these dissociation energies cannot be estimated. Nevertheless, the dissociation energies obtained here are expected to be good enough for comparisons of the Ag, complexes with different rare gas atoms. With this information on the excited-state dissociation energies, it is possible to estimate the ground-state energetics. The observed origin for the complex and the known B X electronic origin for the Ag, molecule can be combined with the excited-state binding energy to give the ground-state dissociation energy, DO”:
Robbins et al. TABLE IV: Rare Cas Properties and Trends Predicted for Interactions with Silver Dimer Using the Drude Polarizability Model Described in the TexP rare C Y c6 Do” gas IP (eV) (xi044 cm3) ( ~ 1 cm-’ 0 ~ A6) (cm-I)
He Ne Ar
Kr Xe
Dorr = lJoo(Ag2-RG) + Do’ - lJoo(Ag2) This analysis produces a ground-state dissociation energy of 1233 cm-’ . Despite the limited accuracy in determining the dissociation energy, it is useful to compare the data for the xenon complex to those obtained for similar krypton and argon complexes with Ag,. As shown in Table 111, the xenon complex is more strongly bound than the other complexes. The order of D,”(Ag2-Xe) > D,”(Ag2-Kr) > D{(Ag2-Ar) follows the relative trend expected from the rare gas polarizabilities. Additionally, all three systems exhibit significantly greater dissociation energies in their excited states than in their ground states. This effect, which may be caused by either the orbital distribution or the polarizability of Ag, in its excited state, was discussed in our earlier papers.I7 It is interesting to note that the dissociation energies measured for the argon and krypton complexes are about half the binding energies of these atoms on a bulk Ag( 111) surface (530 and 870 cm-l, respectively), while the xenon complex dissociation energy is nearly the same as its Ag( 111) surface binding energy (1355 ~m-l).*~ It is possible to predict the magnitude of the dispersive interactions in van der Waals complexes such as these using a simple model first proposed by Dr~de.,~.,’ According to this model, the dispersive interaction, pabr is given by a single term, (Pab = -C6/16The coefficient c6 can be calculated by c 6
= 72/z[(EIa)(EIb)/(EIa + E1b)laaab
where the respective a’s are average polarizabilities of the interacting species and the EI’s are approximated by the ionization potentials. In the current systems, IPS are well-known for the rare gases and for silver dimer and so are the rare gas polarizabilities.21J8Unfortunately, the polarizability of Ag, is not known. However, we can estimate this parameter using the silver atom value, which has been calculated as (7.2-8.56) X cm3.28929 For a variety of alkali metals whose atomic and diatomic polarizabilities have been measured, the average dimer value is about
0.201
(39)
0.376
(73)
1.424
275 394 1233
2.071
3.198
“Ground-state C6 coefficients are compared for the rare gases. Dissociation energies predicted with the ratio of c6 values are given in parentheses.
+
-
0.204956 0.3956 1.6411 2.4844 4.044
24.586 21.564 15.759 13.999 12.130
-
::
CI
.
.
Xe
o DrudeModel 1120
o
0.0
w
Ex~erimental
’
0.9
1.8
2.7
Rare Cas Polarizability ( X l O - 2 4
3.6
1
4.5
cm3)
Figure 3. Plot of the complex dissociation energy versus the rare gas polarizability for the Ag, complexes studied here. The experimental dissociation energies, indicated by solid squares, were determined by a Birge-Sponer extrapolation of the vibrational levels in the rare gas stretch coordinate. The open circles indicate values predicted for helium, neon,
and xenon assuming a linear proportionality with polarizability. As indicated,the experimentally determined value for the xenon complex is significantly greater than predicted. 70% greater than that of the atom.28*29Using this ratio for Ag,, we obtain an estimate of 14 x cm3. c6 values can therefore be calculated for the silver dimer complexes studied here. These are ground-state values which should be proportional to ground-state well depths. Table IV summarizes the results of c6 calculations for Ag2 with the rare gases. For comparison to these calculated c6 values, Table IV also contains the ground-state dissociation energies derived for the three complexes. By inspection of the data in Table IV, it is therefore possible to consider the relative binding energies of Ag,-RG complexes in a somewhat quantitative fashion. There are two ways to do this. On the one hand, if the Drude model is valid for these complexes, the ratios of their measured dissociation energies should follow the same trend as the ratios of their calculated c6 coefficients. Taking the argon and krypton data as an example, the ratio of their ground-state binding energies (1.45) is closely predicted by the ratio of their C6coefficients (1.43). Thus, the Drude model provides a reasonable estimate of the relative dissociation energies in these complexes. Its success confirms that the bonding is van der Waals. Comparing the xenon and argon complexes gives a quite different result. The D,,” ratio is 4.52, while the corresponding c6 ratio is 2.25. The xenon complex is about a factor of 2 more strongly bound than expected. An equivalent way of presenting the data is to plot the binding energy of the complex versus the rare gas polarizability. This is valid because the Drude equation is dominated by the polarizability term. Figure 3 shows such a plot for the argon, krypton, and xenon complexes studied here. As shown, the experimental data for argon and krypton fall on a straight line whose slope indicates that their ground-state dissociation energies are linearly prop o r t i o ~to l the polarizability. The open circles on the plot indicate the dissociation energies expected for the xenon, neon, and helium complexes assuming that they are all proportional to the polarizability. This plot also shows that the xenon complex dissociation
Electronic Spectroscopy of Ag2-Xe energy is a factor of 2 greater than expected. Estimates of the C, coefficients and relative binding energies for the respective helium and neon complexes, obtained assuming this same polarizability dependence, are given in Table IV. These estimates are expected to be crude, but it will be interesting to test them with further experiments on other rare gases. It is clear from this discussion that the xenon complex is more strongly bound than would be expected by comparison to the other Ag2-RG complexes. It is important to reiterate, however, that the binding is still van der Waals in character. The total binding energy (1233 cm-I) and the Ag-Ag stretching frequency observed here (165 cm-I) are inconsistent with any inserted structure (Le., Ag-XeAg) for this complex. Why, then, should the xenon binding energy be so high? The answer may be that it has a different binding site on the Ag, substrate. Polarizability trends like those described here can only be applied if the complexes with different rare gases have the same structure. If they do not, the effective polarizability of the silver dimer, which also influences the binding, cannot be assumed to be constant for the different complexes. In particular, a metal dimer like Ag, should be more polarizable along its axis than perpendicular to it. If complexes with some rare gas atoms are “T”-shaped and those with others are linear, then it is not fair to make the comparisons described above. The linear complexes should, in general, be more strongly bound than their T-shaped counterparts. One scenario that is consistent with these binding energy trends, therefore, is that the argon and krypton complexes have the same structure, while the xenon complex has a different one. Since the linear complexes should be more strongly bound, the xenon complexes may be linear, with a T-shaped, or even an asymmetric structure likely for the argon and krypton complexes. The doublet structure observed for the second member in the xenon bend progression is also consistent with a linear structure for this complex. However, none of these data are conclusive proof of these structures. It is also not clear why the different rare gases should bind in different sites on Ag2. Another possible scenario is that the structures for the different complexes are the same, but our description of their binding is oversimplified. For example, repulsive interactions are not included in the Drude model, and these interactions may well be affected by the physical sizes of the atoms and their optimized bonding distances. However, there are no previous data to suggest anomalous behavior for xenon complexes in similar bonding situations. In previous spectroscopic studies on indium and aluminum metal atom rare gas complexes, binding energy trends for argon, krypton, and xenon were accurately described with the rare gas polarizabilities.” It is apparent that a direct method of probing structures is desirable to resolve this issue and to complete the characterization of these complexes. However, their rotational constants are likely to be too small for rotationally resolved spectroscopy with pulsed dye lasers. Experiments with continuous-wave dye lasers, or perhaps some form of “rotational coherence spectroswpy,”30may be required ultimately to measure the structures of these complexes.
Conclusions We describe vibrationally resolved electronic spectra for the complex Ag2-Xe and compare this complex to the Ag,-Ar and Ag2-Kr systems studied previously. These three systems represent the only examples of metal dimer van der Waals complexes studied spectroscopically. In each case, extensive vibrational activity is observed in all vibrational coordinates. The activity in the rare gas stretching mode makes it possible to investigate the potential energy surfaces for these complexes in their excited states and to obtain dissociation energies. Red-shifted spectral origins make
The Journal of Physical Chemistry, Vol. 96, No. 12, 1992 4829 it possible to estimate corresponding ground-state dissociation energies. Excited-state binding energies in these complexes are more than double the ground-state values, while even the ground-state values (250-1250 cm-’) are greater than “typical” for van der Waals complexes with closed-shell nonmetal molecules. The large polarizability of the silver dimer, particularly in its excited state, is at least partially responsible for this trend. In spite of the detailed data on vibrational activity and dissociation energies, no conclusions can be reached on the structure of these complexes. However, circumstantial evidence suggests that the xenon complex has a different structure than the argon and krypton complexes.
Acknowledgment. We gratefully acknowledge support for this work from the US. Department of Energy through Contract No. DE-FG09-90ER14156.
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