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The bond length of silver dimer
Volume 186, number 4,s
CHEMICAL PHYSICS LETTERS
15 November 1991
The bond length of silver dimer * Benoit Simard, Peter A. Hackett Steacie Institutefor Molecular Sciences, National Research Council of Canada, 100 Smex Drive, Ottawa. Ontario, Canada KIA OR6
Andrew M. James ’and Patrick R.R. Langridge-Smith Universityof Edinburgh, WestMains Road, Edinburgh EH9 3JJp Scotland, UK Received 30 July 1991
The spectroscopy of the A-X system of disilver in a supersonic jet has been studied at 120 MHz resolution. The lowest rotational levels were observed and an unequivocal J-numbering was established for the first time. The following bond lengths were derived: r, (X, 107Ag~09Ag)=2.53350(48)A, r,(A)=2.6549( 10) A. The ground state bond length is compared with previous experimental and ab initio determinations.
1. Introduction The electronic structure of unligated metal clusters is of importance in many areas of chemistry
ranging from organometallicchemistry to catalysis and surfacescience. Small silver clusters are of particular interest because of their role in the formation of the latent photographic image [ 11. Previous work on the spectroscopy of disilver has suffered from serious limitations due to the presence of three isotopomers: lo7Ag2,26.85W, ‘07Ag’0gAg, 49.93%, logAg2,23.32Oh.This causes severe complications due to the blending of spectral lines. In addition, disilver is typically made in high temperature sources and in such sources the population of lowlying levels is much reduced via the Boltzmann factor, and it has proven difficult to establish an unequivocal rotational line numbering. Recently, new spectroscopic techniques have been applied to the study of the electronic spectroscopy of the refractory metal dimers and trimers [ 21I The success of these methods is largely due to their abil* Issued as NRC No. 32838. ’ Current address: Steacie Institute for Molecular Sciences, National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario, Canada KIA OR6.
ity to prepare these high temperature molecules in a low temperature, yet, isolated environment. Typically, laser vaporisation and supersonic expansion techniques have been used to produce intense, low temperature beams of these molecules. Spectroscopic interrogation of these species is normally accomplished by pulsed laser-induced fluorescence, LIF, or multiphoton ionisation methods. The latter approach permits mass selective detection so that the spectrum of individual isotopomers can be recorded. This can reduce the problem of spectral blending, which can complicate LIF spectra when more than one isotopomer is present. In this study, we have overcome the difficult problem of spectral blending in the spectrum of disilver by using a narrow bandwidth, continuous wave ring dye laser to excite fluorescence in expansion cooled silver dimers. The resulting excitation spectrum contains rovibronic lines due to all three dimer isotopomers but the 120 MHz resolution is sufficient to resolve all three systems. As a consequence of the supersonic expansion all low-lying rotational states are observed and a unequivocal Jnumbering has been established. We report analyses for the O-Oand 2-O bands of the A(Oz )-X ( ‘El ) system of Agz.The recent analysis reported by Pesic and Vujisic [3] is shown to be in error.
0009-2614/9 I /$ 03.50 0 199I Elsevier Science Publishers B.V. All rights reserved.
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2. Silver dimer spectroscopy Several electronic band systems of silver dimer have been studied in both absorption and emission using high temperature sources [ 3-71. As a consequence of spectral congestion only lines with J> 30 have been resolved [ 31 and the rotational line numbering is in some doubt. Semi-empirical relationships and the known rotational constants for dicopper and digold have been used to estimate a bond length for Ag, [ 61. These results should be viewed with some caution. The lowest energy band system of Ag,A(O: )-X( ‘C.$) with origin at 435.22 nm has been the subject of two-colour, two-photon resonance enhanced multiphoton ionisation experiments [ 8,9] and isotope shifts and rotational constants have been determined with moderate precision. Studies of disilver isolated in rare gas matrices have been reported [ 21. In matrices, the A-X system is blue-shifted to 390 nm. A magnetic circular dichroism study confirms that both states participating in the transition are orbitally nondegenerate [ lo]. More recently, Montano et al. [ 111 used synchrotron radiation to record EXAFS spectra of silver microclusters isolated in solid argon. The interatomic distance in the dimer was reported as 2.47(2) 8, (lu error bound). Numerous theoretical studies of diatomic silver have been reported [ 12-281. In the main, these have sought an accurate description of the ground state. Calculations indicate that the ground state has ‘El symmetry, with a o bond formed by overlap of two singly occupied 5s atomic orbitals. The fully occupied 4d” cores play little part in the bonding. Basch [ 121 has calculated a bound excited state (T,=2.59 eV) with ‘1: symmetry, consistent with the experimentally observed A state. Grinter 1131 has also assigned the A state as ‘Zz, formed by 5so*-5sd promotion. Extended Htickel [ 141 and Xa calculations [ 151 are in agreement with this assignment.
3. Experimental setup The molecular beam containing silver dimer molecules was generated by laser vaporisation of a silver target rod in a pulsed supersonic source of helium (50 psi backing pressure). The apparatus has been 416
I5 November 199I
described in detail previously [29]. In these experiments a 25 mm long, 1.5 mm diameter tube was used to enhance dimer formation prior to supersonic expansion. Laser-induced fluorescence was excited perpendicular to the molecular beam axis 4.3 cm downstream from the point of expansion. Emission was collected along a third, orthogonal axis by a biconvex 5 cm focal length lens and imaged through a small monochromator. The spectroscopic resolution of these experiments due to the residual Doppler width of the molecules in the viewing zone was 120 MHz. Low resolution excitation spectra were recorded using an excimer-pumped pulsed dye laser (Lumonits EPD 300). High-resolution spectra over the range 22945-22978 cm-’ were obtained using a computer driven, cw ring dye laser (Coherent CR699-29 ) operating on stilbene 3 dye and pumped by the multiline ultraviolet output of an argon-ion laser. The spectra scanning rate was typically 30 MHz per second. Absolute laser wavenumbers were determined with the wavemeter incorporated in the 699-29 system. A coarse calibration was provided by a Burleigh WA-20 wavemeter whose accuracy is 0.02 cm-‘. Finer calibration was achieved using the manufacturer supplied routine. The overall calibration accuracy is 200 MHz. The laser’s internal wavemeter was constantly checked against the external wavemeter to verify proper functioning of the auto-scanning system.
4. Results and rotationalanalysis Fig. 1 shows a portion of the LIF spectrum of the A-X origin band showing resolved rotational lines from all three isotopomers of disilver. Fig. 2 shows the spectrum in the region of the null gap and Rbranch bandhead. The intense P and R branches due to io7AgiogAgcould be followed out to low and high J with relative ease, although the identity of the first P and R branch lines was not immediately clear. Absolute line numbering in this spectrum was established utilising the nuclear spin intensity alternation which is present for the homonuclear isotopomers “‘Ag* and ‘OgAg2.Disilver has a ground state of ‘C: symmetry and both the “‘Ag and “‘Ag nuclei have I= l/2. Thus an even : odd rotational line in-
Volume 186, number 4,5
CHEMICAL PHYSICS LETTERS
15 November 1991 P(J)-‘erAg-‘09Ag
P(J)-‘e”Ag2 I
II
P(J)-“-Ag
2
22970.9
22969.9 Wavenumber Fig. 1. A portion of the fluorescence excitation spectrum of the (O-O) band oft& 4(f):)-X( alternation between odd and even P(J) lines.
I 22976.0
I
I 22916.~
22977.0
tC: ) system of Ag, showing the intensity
I 22977.5
Wavenumber Fig. 2. A portion of the fluorescence excitation spectrum of the (O-O) band of the A(O: )-X( ‘Z: ) system of A& in the region of the band origin.
tensity alternation in the ratio 1: 3 is predicted for the homonuclear dimers. The positions of the homonuclear satellites to a particular ‘07Ag109Ag ro-
vibronic line were calculated using the rotational constants and isotope shifts available from the earlier pketoionisation study of Butler et al. [ 91. The 417
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observation of weak or strong homonuclear satellites at the calculated positions confirmed the identity of the ‘“‘Ag’09Agline in question. The remote possibility that our assignment could be in error by 2 quanta of J in either direction was also tested. in this case, the rotational constants obtained upon least squares fitting firstly did not agree with those determined earlier [91, and secondly were not physically realistic: with the line numbering changed by 2 the bond length changes by 0.20 A. However, the rms deviation of the tit was still of the order of 120 MHz. Further confirmation of our assignment comes from the spectrum of the 2-O band, shown in fig. 3. Here, due to the large vibrational isotope shift, a portion of the spectrum due to Io7Ag2is displaced to the blue, clear of the neighbouring 107Ag’09Ag R-branch bandhead. This greatly facilitates the assignment. The first member of the P branch is clearly discernible and an unequivocal assignment may be made utilising nuclear spin considerations. The fact that the average of the ground state bond length for dicopper, 2.2 197 A [ 301 and our derived value for disilver, 2.53350 A, vide infra, differs from the value of the bond length for the heterodimer CuAg, 2.370 A, [ 31,321 by only 0.005 A, also supports our assign-
23282
15 November 1991
ment. This ground state bond length agrees well with the values obtained from resonant two photon ionisation spectra of the B-X and A-X systems [ 9 1, but is more accurately determined. The EXAFS bond length determination by Montana et al. [ 111, 2.47 A, is in reasonable accord with our result. Due to unresolved congestion in some portions of the O-Oband, it was not possible to assign as many lines arising from the homonuclear isotopomers as from ‘07Ag109Ag.Thus for this band we report the results of the analysis for the heteronuclear isotopomer spectrum alone, For the 2-O band, our analysis was restricted to lo7Ag2. Accurate rotational constants were obtained from the LIF data by fitting the observed P and R line positions using a nonlinear least squares procedure, which employed a modified Levenberg-Marquardt algorithm with a finite difference Jacobian I33 1. The line positions were calculated using the well-known expression [ 34 ] u(J)=v,,tF(Jti)-F”(J))
(1)
where i= - 1 and i= + 1 refer to the P and R lines, respectively. The rotational term values for both the upper and lower states are assumed to be well represented by the simple expression
Wavenumber
23284
Fig. 3. A portion of the fluorescence excitation spectrum of the (Z-O) band of the A(O:)-X( ‘Xl ) system of A&, showing uncongested rotational structuredue to lo7Agz.
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CHEMICAL PHYSICS LETTERS
Volume 186, number 4,5
I;(J)=BJ(J+l)-DJ2(J+1)*.
(2)
table 3. The random measurement error is 120 MHz, well below the experimental accuracy of 200 MHz.
Tables 1 and 2 give the observed and calculated line positions and residuals from the fit. The molecular constants derived from the analysis are presented in
Table 1 Observed line wavenumbers and residuals (in parentheses) for the (O-O) band of ‘07Ag’09Ag ‘)
P(J)
J 0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
22976.7306( -28) 22976.6336(64) 22976.5125(5) 22976.3867(-11) 22976.2533( - 15) 22976.1107(-22) 22975.9689(69) 22975.8074(52) 22975.6389(54) 22975.4580(21) 22975.2715(22) 22975.0723( - 16) 22974.8744(49) 22974.6573( 11) 22974.4327( -13) 22974.2033(5) 22973.9686(58) 22973.7184(46) 22973.4542( - 17) 22973.1920(29) 22972.9183(50) 22972.6289(3) 22972.3308( -42) 22972.0264( -60) 22971.7211(l) 22971.3976( -30) 22971.0662( -50) 22970.7363(34) 22970.3877(20) 22970.0265(-31) 22969.6650( 5) 22969.2876(-28) 22968.9097( 23) 22968.5186(31) 22968.1161(15) 22967.7120( 72) 22967.2927(67) 22966.8637( 54) 22966.4243(27) 22965.9768(a) 22965.5225( 1I ) 22965.0553( -25)
NJ)
J
P(J)
R(J)
22976.9177(-15) 22976.9988(O) 22977.0636( -58) 22977.1365(54) 22977.1744( -95) 22977.2318(41) 22977.2538(-88) 22977.2837( - 50) 22977.3025(-32) 22977.3112(-27) 22977.3112(-20) 22977.3025(-10) 22977.2837(-12) 22977.2538( -36) 22977.2213(4) 22977.1744(-11) 22977.1280(68) 22977.0534( -46) 22976.9866(a) 22976.9043( -4) 22976.8140( -7) 22976.7137( -20) 22976.6093( 15) 22976.4908( - 1) 22976.3626( -25) 22976.2289( - 15) 22976.0833( -34) 22975.9358( 17) 22975.7764(39) 22975.6076(56) 22975.2347(7) 22975.0332( - 35) 22974.834I (38) 22974.6166( 16) 22974.3885( -22) 22974.1563(-IL) 22973.9172(20) 22973.6624( - 16) 22973.4009( -30) 22973.1333(-14) 22972.8571(5) 22972.5689( -6)
43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83
22964.5834( - 19) 22964.1025( - 13) 22963.6098( -35) 22963.1045( -93) 22962.6098( 44) 22962.0888( 8) 22961.5694(78) 22961.0283(21) 22960.4856( 37) 22959.9264( -2 1) 22959.3612(-50) 22958.7919( -29) 22958.2093( -52) 22957.6200(-51) 22957.0175(-93) 22956.4168( -26) 22955.8031(l) 22955.1713(-63) 22954.5414( - 18) 22953.9003(6) 22953.2454( - 19) 22952.5822(-36) 22951.9180(28) 22951.2337( - 19) 22950.5496(26) 22949.8510(17) 22949.1438( 13) 22948.4289(22) 22947.7018( - I ) 22946.9719(39) 22946.2267( 17) 22945.4773(44)
22972.2687( -47) 22971.9706(23) 22971.6524( -18) 22971.3248(-63) 22970.9934( -56) 22970.6619(39) 22970.3096( 17) 22969.9488(O) 22969.5790( - 17) 22969.1990( -45) 2296X.8207(33) 22968.4267(45) 22968.0203(23) 22969.6123(75) 22967.1832(7) 22966.7580(68) 22966.3147(38) 22965.8627( 12) 22965.4069(39) 22964.9359(4) 22964.4616(27) 22963.9735(2) 22963.4612( - 174) 22962.9669( - 79) 22962.4641(21) 22961.9430(30) 22961.4226( 136)
_
22960.3252(56) 22959.7619(5) 22959.1903( -36) 22958.6168( -6) 22958.0284( -34) 22957.4344( -26) 22956.8354(23) 22956.2159(41) 22955.5987(g) 22954.9668( 2) 22954.3238(23) 22953.6754( I I) 22953.0177(O)
‘) rms=0.0041 cm-‘= 123 MHz.
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CH&MttiAk !%YsICS LETTERS
Table 2 Observed line wavenumbers atidresiduals (in parentheses) for the (2-O) band of ‘“‘A&*)
J 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
P(J)
R(J)
23283.1650(-39) 23283.0566( -42) 23282.9439(12) 23282.8142(-6) 23282.6757( - 11) 23282.5287(-3)
23283.4322(-20)
23283,3568(131 --
23282.2003(- 34) 23281.8459(70) 23281.4352(7) 23281.2215(41) 23280.9918(14) 23280.7545(9) 23280.5041(- 27) 23280.2475(-27)
13283.4925( - 103) 23283.5656(41) 23283.6103(O) 23283.6550(58) 23283.6804(22) 23283.6979(6) 23283.7088(22) 23183.788k[29) 23283.6979(26) 23283.6697( -51) 23283.6457( 12) 23283.6043( I ) 23283.5576(35) 23283.4942(2) 23283.4239( -2) 23283.3402( -40) 23283.2524( -21) 23283.1526( -22) 23283.0424(-29) 23282.9282(24) 23282.79?5( 10) 232&2.6594(2 1) 23282.5091(IO) 23282.1782( -20) 23281.8154(28) 23281.4060(f) 23281.1849(-22)
n) rms=0.0030 cm-‘z 90 MHz.
15November 199I
5. Discussion Pesic and Vujisic [ 31 analysed specira of the B-X a)pbt@m of Bilverdirhiix generat6d in a I&g’s furnace Bt 2100 K. The bond length they derived for the ground state, 2.47 A, is seriously at odds with our value of 2.5310 A, We attribute the discrepancy to an erroneous assignment by Pesic and Vujisic, The Doppler width of their 8~urce is 1.5 OH% Due to congestion near the band origin, they fCi;e litl&bletD resolve any rotational structure below j= 30: fiiilure to identify the first members of the P and R bran&$ leads to considerable ambiguity concerning the absolute line numbering. Preparing silver dimers, as we have done, in a rotationally cold, molecular beam environment, arid probing them with sub-Doppler resolution, permits the observatiofi 0f the fully r@ solved lines P ( 1) and R ( 0). An unequivodi rlSB& ment of all lines is thus possible. The ass&nri.l&ti~ 0f PC& KndVtijisiZffas described as “unequivocal” ofi the basis that it gave the smallest rms error when subjected to least-squaresfitti@: However, this is not necessarily a valid criterion for e$ia%ii$ing Ebii’&t assignments. For example, in our analysis of th&8;; 0 band, altering the line numbering by 2 changes the rms of the fit by ~2 MHz, The fact that we recorded no spectra due to vibrational hot bands precluded a dir&t determination of (Y,for the ground state. Therefore the P&w-is relation [ 35 ] was employed to calculate an @pf0%* imate Q, value, using the vibrational constant9 d& termined by Kiemtla atid Lindqvist [ 5 1, and the rotationai constants from this work. Since the precision
Table 3 Spectroscopic constants for the A(@)-X( ‘Cl ) system of Agl *I
‘07W09Ag A (v=O) B, (cm-‘) D, (cm-‘) r,(A)
0.044224(19) b, 10.3(24)x lO-9 2.65815(56)
cu, (cm-‘) B, (cm-‘) r,(A)
2.15(3O)x1O-4 0.04433l(34) 2.6549( 10)
‘O’Agz A (u=2)
i“Ag’OgAg x (u=O)
‘O’A& x (UEO)
0.044200(40)
0.048682( 19) 7.6(24)x10-9 2.53350(48)
0.049149(44)
2.6711(12)
l.9520(15)x10-4c’ 0.048780( 19) 2.53096(48)
*) vm(‘07Ag’09Ag)=22976.8308(12) cm-‘. b1Numbers in parentheses are the uncertainties (2~) in the units of the last quoted decimal place. c’Calculated from the Pekeris relation [ 351.
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2.5331(12)
Volume 186, number 4,5
CHEMICAL PHYSICS LETTERS
Table 4 Comparison of theoretical and experimental determlnations of the bond length in the X (‘C: ) state of Aga Theory a1
Experiment
HFtCl HFtCt RECP RECP RECP RECP RECP RECP RECP PP RECP RF-HFS PP PP LIF RZPI EXAFS
r,(A)
Ref.
2.79 2.75 2.71 2.68 2.68 2.65 2.62 2.62 2.60 2.54 2.52 2.52 2.51 2.50
1161 1171 [I81 [I21 IL91
2.5310 2.529 2.47
1201 1211 1221 ~231 ~241
I251 WI 1271 1281 this work 191 IllI
a) HF+CI: nonrelativistic all electron.RECP: relativistic effective core potential. PP: pseudopotential. RP-HFS: relativistic perturbational HFS.
of even the most sophisticated theoretical treatment is less than that of our experiment, comparison of these values with theory is permissible. Many recent ab initio theoretical studies on the silver dimer molecule are in close agreement with our experimental value. The results of selected calculations are compared with experiment in table 4. Nonrelativistic all electron cal ulations by McLean [ 161 and Shim and Gingerich F 171 derived ground state bond lengths of 2.79 and 2.75 A respectively. Incorporating an estimated relativistic contraction of 0.15 A [26] would bring these values into reasonable agreement with experiment. Other groups have used relativistic effective core potentials to describe the inner electrons in silver dimer. The best agreemeent with experiment using this method was provided by a study due to Martin [25] in which a bond length of 2.52 A was obtained. As is made clear by table 3, pseudopotential methods have proven quite successful in describing the bonding in the ground state of silver dimer, with the results of a number of such calculations clustering around our experimentally determined bond length, 2.53 10 A. It appears that
15 November 199I
the bonding in the ground state of silver dimer is described by current theory. It is worth noting that the bond length in disilver is actually longer than that determined for digold, 2.47 19 A [ 36,371. This rather striking result arises because the relativistic contraction in digold, 0.3 1 A [38], is substantially greater than that in disilver, 0.15 A [26]. Any detailed discussion of the bonding in the A(O: ) excited state must await the results of detailed ab initio calculations, but it appears that this state derives substantial character from the configuration d”(so)’ (~8)‘. It appears that the A state is bound by 2.46 eV relative to the lowest excited atomic asymptotes (2S+2P). This unusually strong binding is surprising in light of the fact that the bond length is substantially lengthened and the vibrational frequency is reduced from 192.4 to 154.6 cm-’ following excitation. The reason for this may bc that the configuration d2’(so) ’(~a*) ’formally correlates with the lowest ion pair limit. Ag+ (‘So) tAg-( ‘So). The Coulombic attractive limb of the ion pair potential closely follows the A state curve and could be responsible for enhancing the bond strength in this region. The long bond is consistent with an ion pair state. Clearly, this is an oversimplification; other valence configurations of the same symmetry will also contribute.
6. Conclusion We have reported here the first unequivocal rotational analysis of the A( 0:)-X( ‘Z: ) system of silver dimer. A number of ab initio determinations of the ground state bond length are found to be in agreement with our experimental result.
Acknowledgement AMJ would like to thank the National Research Council of Canada for their support and hospitality during his visit.
References [ I ] M.R.V. Sayhun, Phot. Sci. Eng. 22 ( 1978) 317.
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[Z] M.D. Morse, Chem. Rev. 86 (1986) 1049. [j] D.S. Pesic and B.R. Vujisic, J. Mol. Spectry. 146 (1991) 516. [4] J. Ruamps, Compt. Rend. Acad. Sci. (Paris) 238 (1954) 1489. [ 51B. IUeman and S. Lindqvist, Arkiv Fysik 8 (1954) 333. [ 61 V.I. Srdanov and D.S. Pesic, J. Mol. Spectry. 90 ( 1981) 27. [ 71 CM. Brown and M.L. Ginter, J. Mol. Spectry. 69 (1978) 25. [8] J.B. Hopkins, P.R.R. Langridge-Smith, M.D. Morse and R.E. Smalley, unpublished results. [9] A.M. Butler, Ph.D. Thesis, University of Edinburgh (1989); A.M. Butler, A.M. James, G.W. I&mire, J.W. MacDonald and P.R.R. Langridge-Smith, in preparation. [lo] R. Grinter, S. Armstrong, U.A. Jayasooriya, J. McCombie, D. Norris and J.P. Springall, Faraday Symp. Chem. Sot. 14 (1980) 94. [ 11) P.A. Montana, J. Zhao, M. Ramanathan, G.K. Shenoy, W. Schulzeand J. Urban, Chem. Phys. Letters 164 ( 1989) 126. [l2] H. Basch, J. Am. Chem. Sot. 103 (1981) 4657. [ 131R. Grinter, Chem. Phys. 102 (1986) 187. [ 14J G.A. Gzin and W.E. Klotzbucher, Inorg. Chcm. 18 (1979) 2101. [IS] G.A. Ozin, H. H&r, D. McIntosh, S. Mitchell, J.G. Normal and L. Noodleman, J. Am. Chem. Sot. 101 (1979) 3504. [ 161A.D. McLean, J. Chem. Phys. 79 (1983) 3392. [ 171I. Shim and K.A. Gingerich, J. Chem. Phys. 79 (1983) 2903. [ 181R.B.RossandW.B.Ermler,J. Phys.Chem. 89(1985) 5202. [ 191K. Balasubramanian and M.Z. Liao, Chem. Phys. 127 (1988) 313. [20] W.C. Ermler, R.B. Ross and R.M. Pitzer, private communication. [2l]P.J.HayandR.L.Martin,J.Chem.’Phys. 83 (1985) 5174.
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[22] H. Basch, Faraday Symp. Chem. Sot. 14 (1980) 149. [231&P. Walch, C.W. Bauschlicher Jr. and S.R. Langhoff, 5. Chem. Phys. 85 (1986) 5900. [24] H. Stall, P. Funetealba, M. Dolg, J. Flad, L. von Szentpaly and H. Preuss, J. Chem. Phys. 79 (1983) 5532. [ 25 ] R.L. Martin, J. Chem. Phys. 86 ( 1987) 5027. [26] T. Ziegler, J.G. Snijders and E.J. Baerends, J. Chem. Phys. 83 (1981) 4573. [27] J.L. Martins and W. Andreoni, Phys. Rev. A 28 (1983) 3637. [28] J. Andzelm, E. Radzio and D.R. Salahub, J. Chem. Phys. 83 (1985) 4573. [ 291 B. Simard, S.A. Mitchell, L.M. Hendel and P.A. Hackett, Faraday Discussions Chem. Sot. 86 ( 1988) 163. [ 301 J. Lochet, J. Phys. B 11( 197%)LSS. [31] G.A. Bishea, N. Marak and M.D. Morse, J. Chem. Phys., submitted for publication. [ 321 A.M. James, Ph.D. Thesis, University of Edinburgh ( 1990); A.J. James, G.W.Lemire, J.F. Mi1lerandP.R.R. LangridgeSmith, in preparation. [ 331 K. Lcvenberg, Q. Appl. Math. 2 (1944) 164. [ 34 ] G. Henberg, Molecularspectra and molecularstructure, Vol. 1. Spectra of diatomic molecules (Van Nostrand, Princeton, 1950). [35] CL. Pekeris, Phys. Rev. 45 (1934) 98. [ 36 ] L.L. Ames and R.F. Barrow, Trans. Faraday Sac. 63 ( 1967) 39. [37] B. Simard and P.A. Hackett, J. Mol. Spectry. 142 (1990) 310. [38] P. Schwerdtfeger, M. Dolg, W.H.E. Schwarz, G.A. Bowmaker and P.D.W. Boyd, J. Chem. Phys. 91 (1989) 1762.
CHEMICAL PHYSICS LETTERS
15 November 1991
The bond length of silver dimer * Benoit Simard, Peter A. Hackett Steacie Institutefor Molecular Sciences, National Research Council of Canada, 100 Smex Drive, Ottawa. Ontario, Canada KIA OR6
Andrew M. James ’and Patrick R.R. Langridge-Smith Universityof Edinburgh, WestMains Road, Edinburgh EH9 3JJp Scotland, UK Received 30 July 1991
The spectroscopy of the A-X system of disilver in a supersonic jet has been studied at 120 MHz resolution. The lowest rotational levels were observed and an unequivocal J-numbering was established for the first time. The following bond lengths were derived: r, (X, 107Ag~09Ag)=2.53350(48)A, r,(A)=2.6549( 10) A. The ground state bond length is compared with previous experimental and ab initio determinations.
1. Introduction The electronic structure of unligated metal clusters is of importance in many areas of chemistry
ranging from organometallicchemistry to catalysis and surfacescience. Small silver clusters are of particular interest because of their role in the formation of the latent photographic image [ 11. Previous work on the spectroscopy of disilver has suffered from serious limitations due to the presence of three isotopomers: lo7Ag2,26.85W, ‘07Ag’0gAg, 49.93%, logAg2,23.32Oh.This causes severe complications due to the blending of spectral lines. In addition, disilver is typically made in high temperature sources and in such sources the population of lowlying levels is much reduced via the Boltzmann factor, and it has proven difficult to establish an unequivocal rotational line numbering. Recently, new spectroscopic techniques have been applied to the study of the electronic spectroscopy of the refractory metal dimers and trimers [ 21I The success of these methods is largely due to their abil* Issued as NRC No. 32838. ’ Current address: Steacie Institute for Molecular Sciences, National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario, Canada KIA OR6.
ity to prepare these high temperature molecules in a low temperature, yet, isolated environment. Typically, laser vaporisation and supersonic expansion techniques have been used to produce intense, low temperature beams of these molecules. Spectroscopic interrogation of these species is normally accomplished by pulsed laser-induced fluorescence, LIF, or multiphoton ionisation methods. The latter approach permits mass selective detection so that the spectrum of individual isotopomers can be recorded. This can reduce the problem of spectral blending, which can complicate LIF spectra when more than one isotopomer is present. In this study, we have overcome the difficult problem of spectral blending in the spectrum of disilver by using a narrow bandwidth, continuous wave ring dye laser to excite fluorescence in expansion cooled silver dimers. The resulting excitation spectrum contains rovibronic lines due to all three dimer isotopomers but the 120 MHz resolution is sufficient to resolve all three systems. As a consequence of the supersonic expansion all low-lying rotational states are observed and a unequivocal Jnumbering has been established. We report analyses for the O-Oand 2-O bands of the A(Oz )-X ( ‘El ) system of Agz.The recent analysis reported by Pesic and Vujisic [3] is shown to be in error.
0009-2614/9 I /$ 03.50 0 199I Elsevier Science Publishers B.V. All rights reserved.
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2. Silver dimer spectroscopy Several electronic band systems of silver dimer have been studied in both absorption and emission using high temperature sources [ 3-71. As a consequence of spectral congestion only lines with J> 30 have been resolved [ 31 and the rotational line numbering is in some doubt. Semi-empirical relationships and the known rotational constants for dicopper and digold have been used to estimate a bond length for Ag, [ 61. These results should be viewed with some caution. The lowest energy band system of Ag,A(O: )-X( ‘C.$) with origin at 435.22 nm has been the subject of two-colour, two-photon resonance enhanced multiphoton ionisation experiments [ 8,9] and isotope shifts and rotational constants have been determined with moderate precision. Studies of disilver isolated in rare gas matrices have been reported [ 21. In matrices, the A-X system is blue-shifted to 390 nm. A magnetic circular dichroism study confirms that both states participating in the transition are orbitally nondegenerate [ lo]. More recently, Montano et al. [ 111 used synchrotron radiation to record EXAFS spectra of silver microclusters isolated in solid argon. The interatomic distance in the dimer was reported as 2.47(2) 8, (lu error bound). Numerous theoretical studies of diatomic silver have been reported [ 12-281. In the main, these have sought an accurate description of the ground state. Calculations indicate that the ground state has ‘El symmetry, with a o bond formed by overlap of two singly occupied 5s atomic orbitals. The fully occupied 4d” cores play little part in the bonding. Basch [ 121 has calculated a bound excited state (T,=2.59 eV) with ‘1: symmetry, consistent with the experimentally observed A state. Grinter 1131 has also assigned the A state as ‘Zz, formed by 5so*-5sd promotion. Extended Htickel [ 141 and Xa calculations [ 151 are in agreement with this assignment.
3. Experimental setup The molecular beam containing silver dimer molecules was generated by laser vaporisation of a silver target rod in a pulsed supersonic source of helium (50 psi backing pressure). The apparatus has been 416
I5 November 199I
described in detail previously [29]. In these experiments a 25 mm long, 1.5 mm diameter tube was used to enhance dimer formation prior to supersonic expansion. Laser-induced fluorescence was excited perpendicular to the molecular beam axis 4.3 cm downstream from the point of expansion. Emission was collected along a third, orthogonal axis by a biconvex 5 cm focal length lens and imaged through a small monochromator. The spectroscopic resolution of these experiments due to the residual Doppler width of the molecules in the viewing zone was 120 MHz. Low resolution excitation spectra were recorded using an excimer-pumped pulsed dye laser (Lumonits EPD 300). High-resolution spectra over the range 22945-22978 cm-’ were obtained using a computer driven, cw ring dye laser (Coherent CR699-29 ) operating on stilbene 3 dye and pumped by the multiline ultraviolet output of an argon-ion laser. The spectra scanning rate was typically 30 MHz per second. Absolute laser wavenumbers were determined with the wavemeter incorporated in the 699-29 system. A coarse calibration was provided by a Burleigh WA-20 wavemeter whose accuracy is 0.02 cm-‘. Finer calibration was achieved using the manufacturer supplied routine. The overall calibration accuracy is 200 MHz. The laser’s internal wavemeter was constantly checked against the external wavemeter to verify proper functioning of the auto-scanning system.
4. Results and rotationalanalysis Fig. 1 shows a portion of the LIF spectrum of the A-X origin band showing resolved rotational lines from all three isotopomers of disilver. Fig. 2 shows the spectrum in the region of the null gap and Rbranch bandhead. The intense P and R branches due to io7AgiogAgcould be followed out to low and high J with relative ease, although the identity of the first P and R branch lines was not immediately clear. Absolute line numbering in this spectrum was established utilising the nuclear spin intensity alternation which is present for the homonuclear isotopomers “‘Ag* and ‘OgAg2.Disilver has a ground state of ‘C: symmetry and both the “‘Ag and “‘Ag nuclei have I= l/2. Thus an even : odd rotational line in-
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15 November 1991 P(J)-‘erAg-‘09Ag
P(J)-‘e”Ag2 I
II
P(J)-“-Ag
2
22970.9
22969.9 Wavenumber Fig. 1. A portion of the fluorescence excitation spectrum of the (O-O) band oft& 4(f):)-X( alternation between odd and even P(J) lines.
I 22976.0
I
I 22916.~
22977.0
tC: ) system of Ag, showing the intensity
I 22977.5
Wavenumber Fig. 2. A portion of the fluorescence excitation spectrum of the (O-O) band of the A(O: )-X( ‘Z: ) system of A& in the region of the band origin.
tensity alternation in the ratio 1: 3 is predicted for the homonuclear dimers. The positions of the homonuclear satellites to a particular ‘07Ag109Ag ro-
vibronic line were calculated using the rotational constants and isotope shifts available from the earlier pketoionisation study of Butler et al. [ 91. The 417
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observation of weak or strong homonuclear satellites at the calculated positions confirmed the identity of the ‘“‘Ag’09Agline in question. The remote possibility that our assignment could be in error by 2 quanta of J in either direction was also tested. in this case, the rotational constants obtained upon least squares fitting firstly did not agree with those determined earlier [91, and secondly were not physically realistic: with the line numbering changed by 2 the bond length changes by 0.20 A. However, the rms deviation of the tit was still of the order of 120 MHz. Further confirmation of our assignment comes from the spectrum of the 2-O band, shown in fig. 3. Here, due to the large vibrational isotope shift, a portion of the spectrum due to Io7Ag2is displaced to the blue, clear of the neighbouring 107Ag’09Ag R-branch bandhead. This greatly facilitates the assignment. The first member of the P branch is clearly discernible and an unequivocal assignment may be made utilising nuclear spin considerations. The fact that the average of the ground state bond length for dicopper, 2.2 197 A [ 301 and our derived value for disilver, 2.53350 A, vide infra, differs from the value of the bond length for the heterodimer CuAg, 2.370 A, [ 31,321 by only 0.005 A, also supports our assign-
23282
15 November 1991
ment. This ground state bond length agrees well with the values obtained from resonant two photon ionisation spectra of the B-X and A-X systems [ 9 1, but is more accurately determined. The EXAFS bond length determination by Montana et al. [ 111, 2.47 A, is in reasonable accord with our result. Due to unresolved congestion in some portions of the O-Oband, it was not possible to assign as many lines arising from the homonuclear isotopomers as from ‘07Ag109Ag.Thus for this band we report the results of the analysis for the heteronuclear isotopomer spectrum alone, For the 2-O band, our analysis was restricted to lo7Ag2. Accurate rotational constants were obtained from the LIF data by fitting the observed P and R line positions using a nonlinear least squares procedure, which employed a modified Levenberg-Marquardt algorithm with a finite difference Jacobian I33 1. The line positions were calculated using the well-known expression [ 34 ] u(J)=v,,tF(Jti)-F”(J))
(1)
where i= - 1 and i= + 1 refer to the P and R lines, respectively. The rotational term values for both the upper and lower states are assumed to be well represented by the simple expression
Wavenumber
23284
Fig. 3. A portion of the fluorescence excitation spectrum of the (Z-O) band of the A(O:)-X( ‘Xl ) system of A&, showing uncongested rotational structuredue to lo7Agz.
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CHEMICAL PHYSICS LETTERS
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I;(J)=BJ(J+l)-DJ2(J+1)*.
(2)
table 3. The random measurement error is 120 MHz, well below the experimental accuracy of 200 MHz.
Tables 1 and 2 give the observed and calculated line positions and residuals from the fit. The molecular constants derived from the analysis are presented in
Table 1 Observed line wavenumbers and residuals (in parentheses) for the (O-O) band of ‘07Ag’09Ag ‘)
P(J)
J 0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
22976.7306( -28) 22976.6336(64) 22976.5125(5) 22976.3867(-11) 22976.2533( - 15) 22976.1107(-22) 22975.9689(69) 22975.8074(52) 22975.6389(54) 22975.4580(21) 22975.2715(22) 22975.0723( - 16) 22974.8744(49) 22974.6573( 11) 22974.4327( -13) 22974.2033(5) 22973.9686(58) 22973.7184(46) 22973.4542( - 17) 22973.1920(29) 22972.9183(50) 22972.6289(3) 22972.3308( -42) 22972.0264( -60) 22971.7211(l) 22971.3976( -30) 22971.0662( -50) 22970.7363(34) 22970.3877(20) 22970.0265(-31) 22969.6650( 5) 22969.2876(-28) 22968.9097( 23) 22968.5186(31) 22968.1161(15) 22967.7120( 72) 22967.2927(67) 22966.8637( 54) 22966.4243(27) 22965.9768(a) 22965.5225( 1I ) 22965.0553( -25)
NJ)
J
P(J)
R(J)
22976.9177(-15) 22976.9988(O) 22977.0636( -58) 22977.1365(54) 22977.1744( -95) 22977.2318(41) 22977.2538(-88) 22977.2837( - 50) 22977.3025(-32) 22977.3112(-27) 22977.3112(-20) 22977.3025(-10) 22977.2837(-12) 22977.2538( -36) 22977.2213(4) 22977.1744(-11) 22977.1280(68) 22977.0534( -46) 22976.9866(a) 22976.9043( -4) 22976.8140( -7) 22976.7137( -20) 22976.6093( 15) 22976.4908( - 1) 22976.3626( -25) 22976.2289( - 15) 22976.0833( -34) 22975.9358( 17) 22975.7764(39) 22975.6076(56) 22975.2347(7) 22975.0332( - 35) 22974.834I (38) 22974.6166( 16) 22974.3885( -22) 22974.1563(-IL) 22973.9172(20) 22973.6624( - 16) 22973.4009( -30) 22973.1333(-14) 22972.8571(5) 22972.5689( -6)
43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83
22964.5834( - 19) 22964.1025( - 13) 22963.6098( -35) 22963.1045( -93) 22962.6098( 44) 22962.0888( 8) 22961.5694(78) 22961.0283(21) 22960.4856( 37) 22959.9264( -2 1) 22959.3612(-50) 22958.7919( -29) 22958.2093( -52) 22957.6200(-51) 22957.0175(-93) 22956.4168( -26) 22955.8031(l) 22955.1713(-63) 22954.5414( - 18) 22953.9003(6) 22953.2454( - 19) 22952.5822(-36) 22951.9180(28) 22951.2337( - 19) 22950.5496(26) 22949.8510(17) 22949.1438( 13) 22948.4289(22) 22947.7018( - I ) 22946.9719(39) 22946.2267( 17) 22945.4773(44)
22972.2687( -47) 22971.9706(23) 22971.6524( -18) 22971.3248(-63) 22970.9934( -56) 22970.6619(39) 22970.3096( 17) 22969.9488(O) 22969.5790( - 17) 22969.1990( -45) 2296X.8207(33) 22968.4267(45) 22968.0203(23) 22969.6123(75) 22967.1832(7) 22966.7580(68) 22966.3147(38) 22965.8627( 12) 22965.4069(39) 22964.9359(4) 22964.4616(27) 22963.9735(2) 22963.4612( - 174) 22962.9669( - 79) 22962.4641(21) 22961.9430(30) 22961.4226( 136)
_
22960.3252(56) 22959.7619(5) 22959.1903( -36) 22958.6168( -6) 22958.0284( -34) 22957.4344( -26) 22956.8354(23) 22956.2159(41) 22955.5987(g) 22954.9668( 2) 22954.3238(23) 22953.6754( I I) 22953.0177(O)
‘) rms=0.0041 cm-‘= 123 MHz.
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Table 2 Observed line wavenumbers atidresiduals (in parentheses) for the (2-O) band of ‘“‘A&*)
J 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
P(J)
R(J)
23283.1650(-39) 23283.0566( -42) 23282.9439(12) 23282.8142(-6) 23282.6757( - 11) 23282.5287(-3)
23283.4322(-20)
23283,3568(131 --
23282.2003(- 34) 23281.8459(70) 23281.4352(7) 23281.2215(41) 23280.9918(14) 23280.7545(9) 23280.5041(- 27) 23280.2475(-27)
13283.4925( - 103) 23283.5656(41) 23283.6103(O) 23283.6550(58) 23283.6804(22) 23283.6979(6) 23283.7088(22) 23183.788k[29) 23283.6979(26) 23283.6697( -51) 23283.6457( 12) 23283.6043( I ) 23283.5576(35) 23283.4942(2) 23283.4239( -2) 23283.3402( -40) 23283.2524( -21) 23283.1526( -22) 23283.0424(-29) 23282.9282(24) 23282.79?5( 10) 232&2.6594(2 1) 23282.5091(IO) 23282.1782( -20) 23281.8154(28) 23281.4060(f) 23281.1849(-22)
n) rms=0.0030 cm-‘z 90 MHz.
15November 199I
5. Discussion Pesic and Vujisic [ 31 analysed specira of the B-X a)pbt@m of Bilverdirhiix generat6d in a I&g’s furnace Bt 2100 K. The bond length they derived for the ground state, 2.47 A, is seriously at odds with our value of 2.5310 A, We attribute the discrepancy to an erroneous assignment by Pesic and Vujisic, The Doppler width of their 8~urce is 1.5 OH% Due to congestion near the band origin, they fCi;e litl&bletD resolve any rotational structure below j= 30: fiiilure to identify the first members of the P and R bran&$ leads to considerable ambiguity concerning the absolute line numbering. Preparing silver dimers, as we have done, in a rotationally cold, molecular beam environment, arid probing them with sub-Doppler resolution, permits the observatiofi 0f the fully r@ solved lines P ( 1) and R ( 0). An unequivodi rlSB& ment of all lines is thus possible. The ass&nri.l&ti~ 0f PC& KndVtijisiZffas described as “unequivocal” ofi the basis that it gave the smallest rms error when subjected to least-squaresfitti@: However, this is not necessarily a valid criterion for e$ia%ii$ing Ebii’&t assignments. For example, in our analysis of th&8;; 0 band, altering the line numbering by 2 changes the rms of the fit by ~2 MHz, The fact that we recorded no spectra due to vibrational hot bands precluded a dir&t determination of (Y,for the ground state. Therefore the P&w-is relation [ 35 ] was employed to calculate an @pf0%* imate Q, value, using the vibrational constant9 d& termined by Kiemtla atid Lindqvist [ 5 1, and the rotationai constants from this work. Since the precision
Table 3 Spectroscopic constants for the A(@)-X( ‘Cl ) system of Agl *I
‘07W09Ag A (v=O) B, (cm-‘) D, (cm-‘) r,(A)
0.044224(19) b, 10.3(24)x lO-9 2.65815(56)
cu, (cm-‘) B, (cm-‘) r,(A)
2.15(3O)x1O-4 0.04433l(34) 2.6549( 10)
‘O’Agz A (u=2)
i“Ag’OgAg x (u=O)
‘O’A& x (UEO)
0.044200(40)
0.048682( 19) 7.6(24)x10-9 2.53350(48)
0.049149(44)
2.6711(12)
l.9520(15)x10-4c’ 0.048780( 19) 2.53096(48)
*) vm(‘07Ag’09Ag)=22976.8308(12) cm-‘. b1Numbers in parentheses are the uncertainties (2~) in the units of the last quoted decimal place. c’Calculated from the Pekeris relation [ 351.
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2.5331(12)
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Table 4 Comparison of theoretical and experimental determlnations of the bond length in the X (‘C: ) state of Aga Theory a1
Experiment
HFtCl HFtCt RECP RECP RECP RECP RECP RECP RECP PP RECP RF-HFS PP PP LIF RZPI EXAFS
r,(A)
Ref.
2.79 2.75 2.71 2.68 2.68 2.65 2.62 2.62 2.60 2.54 2.52 2.52 2.51 2.50
1161 1171 [I81 [I21 IL91
2.5310 2.529 2.47
1201 1211 1221 ~231 ~241
I251 WI 1271 1281 this work 191 IllI
a) HF+CI: nonrelativistic all electron.RECP: relativistic effective core potential. PP: pseudopotential. RP-HFS: relativistic perturbational HFS.
of even the most sophisticated theoretical treatment is less than that of our experiment, comparison of these values with theory is permissible. Many recent ab initio theoretical studies on the silver dimer molecule are in close agreement with our experimental value. The results of selected calculations are compared with experiment in table 4. Nonrelativistic all electron cal ulations by McLean [ 161 and Shim and Gingerich F 171 derived ground state bond lengths of 2.79 and 2.75 A respectively. Incorporating an estimated relativistic contraction of 0.15 A [26] would bring these values into reasonable agreement with experiment. Other groups have used relativistic effective core potentials to describe the inner electrons in silver dimer. The best agreemeent with experiment using this method was provided by a study due to Martin [25] in which a bond length of 2.52 A was obtained. As is made clear by table 3, pseudopotential methods have proven quite successful in describing the bonding in the ground state of silver dimer, with the results of a number of such calculations clustering around our experimentally determined bond length, 2.53 10 A. It appears that
15 November 199I
the bonding in the ground state of silver dimer is described by current theory. It is worth noting that the bond length in disilver is actually longer than that determined for digold, 2.47 19 A [ 36,371. This rather striking result arises because the relativistic contraction in digold, 0.3 1 A [38], is substantially greater than that in disilver, 0.15 A [26]. Any detailed discussion of the bonding in the A(O: ) excited state must await the results of detailed ab initio calculations, but it appears that this state derives substantial character from the configuration d”(so)’ (~8)‘. It appears that the A state is bound by 2.46 eV relative to the lowest excited atomic asymptotes (2S+2P). This unusually strong binding is surprising in light of the fact that the bond length is substantially lengthened and the vibrational frequency is reduced from 192.4 to 154.6 cm-’ following excitation. The reason for this may bc that the configuration d2’(so) ’(~a*) ’formally correlates with the lowest ion pair limit. Ag+ (‘So) tAg-( ‘So). The Coulombic attractive limb of the ion pair potential closely follows the A state curve and could be responsible for enhancing the bond strength in this region. The long bond is consistent with an ion pair state. Clearly, this is an oversimplification; other valence configurations of the same symmetry will also contribute.
6. Conclusion We have reported here the first unequivocal rotational analysis of the A( 0:)-X( ‘Z: ) system of silver dimer. A number of ab initio determinations of the ground state bond length are found to be in agreement with our experimental result.
Acknowledgement AMJ would like to thank the National Research Council of Canada for their support and hospitality during his visit.
References [ I ] M.R.V. Sayhun, Phot. Sci. Eng. 22 ( 1978) 317.
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[Z] M.D. Morse, Chem. Rev. 86 (1986) 1049. [j] D.S. Pesic and B.R. Vujisic, J. Mol. Spectry. 146 (1991) 516. [4] J. Ruamps, Compt. Rend. Acad. Sci. (Paris) 238 (1954) 1489. [ 51B. IUeman and S. Lindqvist, Arkiv Fysik 8 (1954) 333. [ 61 V.I. Srdanov and D.S. Pesic, J. Mol. Spectry. 90 ( 1981) 27. [ 71 CM. Brown and M.L. Ginter, J. Mol. Spectry. 69 (1978) 25. [8] J.B. Hopkins, P.R.R. Langridge-Smith, M.D. Morse and R.E. Smalley, unpublished results. [9] A.M. Butler, Ph.D. Thesis, University of Edinburgh (1989); A.M. Butler, A.M. James, G.W. I&mire, J.W. MacDonald and P.R.R. Langridge-Smith, in preparation. [lo] R. Grinter, S. Armstrong, U.A. Jayasooriya, J. McCombie, D. Norris and J.P. Springall, Faraday Symp. Chem. Sot. 14 (1980) 94. [ 11) P.A. Montana, J. Zhao, M. Ramanathan, G.K. Shenoy, W. Schulzeand J. Urban, Chem. Phys. Letters 164 ( 1989) 126. [l2] H. Basch, J. Am. Chem. Sot. 103 (1981) 4657. [ 131R. Grinter, Chem. Phys. 102 (1986) 187. [ 14J G.A. Gzin and W.E. Klotzbucher, Inorg. Chcm. 18 (1979) 2101. [IS] G.A. Ozin, H. H&r, D. McIntosh, S. Mitchell, J.G. Normal and L. Noodleman, J. Am. Chem. Sot. 101 (1979) 3504. [ 161A.D. McLean, J. Chem. Phys. 79 (1983) 3392. [ 171I. Shim and K.A. Gingerich, J. Chem. Phys. 79 (1983) 2903. [ 181R.B.RossandW.B.Ermler,J. Phys.Chem. 89(1985) 5202. [ 191K. Balasubramanian and M.Z. Liao, Chem. Phys. 127 (1988) 313. [20] W.C. Ermler, R.B. Ross and R.M. Pitzer, private communication. [2l]P.J.HayandR.L.Martin,J.Chem.’Phys. 83 (1985) 5174.
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[22] H. Basch, Faraday Symp. Chem. Sot. 14 (1980) 149. [231&P. Walch, C.W. Bauschlicher Jr. and S.R. Langhoff, 5. Chem. Phys. 85 (1986) 5900. [24] H. Stall, P. Funetealba, M. Dolg, J. Flad, L. von Szentpaly and H. Preuss, J. Chem. Phys. 79 (1983) 5532. [ 25 ] R.L. Martin, J. Chem. Phys. 86 ( 1987) 5027. [26] T. Ziegler, J.G. Snijders and E.J. Baerends, J. Chem. Phys. 83 (1981) 4573. [27] J.L. Martins and W. Andreoni, Phys. Rev. A 28 (1983) 3637. [28] J. Andzelm, E. Radzio and D.R. Salahub, J. Chem. Phys. 83 (1985) 4573. [ 291 B. Simard, S.A. Mitchell, L.M. Hendel and P.A. Hackett, Faraday Discussions Chem. Sot. 86 ( 1988) 163. [ 301 J. Lochet, J. Phys. B 11( 197%)LSS. [31] G.A. Bishea, N. Marak and M.D. Morse, J. Chem. Phys., submitted for publication. [ 321 A.M. James, Ph.D. Thesis, University of Edinburgh ( 1990); A.J. James, G.W.Lemire, J.F. Mi1lerandP.R.R. LangridgeSmith, in preparation. [ 331 K. Lcvenberg, Q. Appl. Math. 2 (1944) 164. [ 34 ] G. Henberg, Molecularspectra and molecularstructure, Vol. 1. Spectra of diatomic molecules (Van Nostrand, Princeton, 1950). [35] CL. Pekeris, Phys. Rev. 45 (1934) 98. [ 36 ] L.L. Ames and R.F. Barrow, Trans. Faraday Sac. 63 ( 1967) 39. [37] B. Simard and P.A. Hackett, J. Mol. Spectry. 142 (1990) 310. [38] P. Schwerdtfeger, M. Dolg, W.H.E. Schwarz, G.A. Bowmaker and P.D.W. Boyd, J. Chem. Phys. 91 (1989) 1762.