2904
J. Phys. Chem. 1981, 85,2904-2912
The UV-Visible Spectra of Copper Atoms Isolated in Various Matrices M. Moskovits” and J. E. Hulse Lash Miller Chemical Laboratories and Erindale College, University of Toronto, Toronto M5S 1A 1, Canada (Received November 21, 1980; In Final Form: May 26, 1981)
-
The UV-visible absorption spectra of Cu atoms isolated in solid alkane and N2 matrices are presented. The triplet structure of the 2P 2Sabsorption is attributed to a dynamic Jahn-Teller effect in the cubooctahedral (Oh),exciplex-like CuAr12local molecule. This is shown to explain the triplet structure as well as its temperature dependence in the rare-gas matrices. The behavior of this triplet with increasing chain length mimics that observed for Cu in Ar with increasing temperature. This is attributed to an increase in the Jahn-Teller stabilization energy resulting from a nonspecific interaction between the Cu atom and the alkane carbons which are shown to become increasingly more tightly packed about the copper with increasing alkane chain length. A ground-state static distortion is suggested to be unlikely as a contributor to the triplet structure. Such a distortion is shown to be important, however, in producing the spectrum of Cu isolated in ethane which, after annealing, adopts a noncubic structure. The intense absorption near 206 nm which is normally attributed to a transition to a state formed from the 3d94s4pconfiguration is assigned to a (3d’O5~)~P 2Stransition which is the first member of a Rydberg series red shifted, unlike the valence transition, as a result of the polarizability of the matrix or interactions with the conduction band of the matrix. The isolation efficiencies of the various matrices are considered in terms of a heat conduction model. The observed ability of Ne, Ar, Kr, and Xe to isolate atoms with increasing efficiencies is predicted, as is the observation that the short alkanes isolate with approximately equivalent efficiencies. With longer alkanes (C12and up) the isolation abilities are predicted to decline. +-
Introduction The UV-visible spectroscopy of matrix-isolated Cu atoms has produced a voluminous literature1 partly devoted to the understanding of the 2P 2S absorption. In this paper we report the changes in that spectrum with matrix support for a series of hydrocarbon matrices. In so doing we consider also the isolating capabilities of those matrices. The spectroscopy of metal atoms in hydrocarbon matrices has been the subject of previous articles.2
were focused onto the same photomultiplier tube (Hamamatsu R955). Two lock-in amplifiers set at the appropriate frequency and phase extracted the two separate signals from which the ratio or the log of the ratio was generated on a PAR Model 188 ratiometer. When the log ratio was used the output was the base-10 absorbance directly. The instrument had among its advantages the ability to suppress the rapidly increasing baselines in the high-energy part of the spectrum resulting from scattering by translucent matrices.
Experimental Section The apparatus has been described el~ewhere.~ Briefly, copper was vaporized from a tantalum hairpin filament heated directly with alternating current. Metal vapor and research-grade alkane or Nz were cocodensed on a CaFz window cooled to 11K by a Displex refrigerator. Cu/alkane spectra were recorded on a Techtron UV-visible spectrometer. The Cu/N2 spectrum was recorded on a home-built spectrometer which operated as follows. The light of either a D2 or tungsten-iodine lamp was dispersed in a Heath EU700 monochromator. A quartz lens collimated the output. The parallel beam passed through a rotating chopper perforated with two sets of holes so that the upper part of the beam was interrupted at 210 Hz while the lower part was chopped at 330 Hz. A baffle was positioned in such a way that the lower portions of the CaF2 deposition substrate received no metal while the upper portion received a full complement of metal. Both portions, however, received the full dose of gas. When rotated so as to intercept the spectrometer beam, the metal-free half which served as a reference was traversed by the 330-Hz beam, while the upper half containing metal was crossed by the 210-Hz beam. Both halves of the beam
Results The UV-visible spectra of copper atoms isolated at 11 K in matrices of argon, nitrogen, methane, ethane, npropane, n-butane, n-pentane, and n-octane appear in Figure 1. The line positions and intensities in the gas phase along with the bands in the various matrices are collected and compared numerically in Tables I and 11. These spectra all belong to freshly deposited, unannealed samples. For every host but ethane, annealing at temperatures up to 30% of the melting temperature had only the effect of narrowing and sharpening the bands slightly. Annealing of a copper-atom-containing ethane matrix to temperatures above 30 K resulted in an irreversible change in the spectrum (Figure 2) to which the discussion will return below. The area under the triplet (near 300 nm) was found to be approximately constant for the Cz to C8 alkanes when normalized to the same total quantity of metal and with the same metal/gas ratio, while for Cu in CHI the area was somewhat less than the others. The relative magnitude of this absorbance will be taken as a measure of the isolating efficiency of a matrix gas. The larger the area the better the isolation. A series of spectra of Cu in solid CHI at varying Cu/ methane ratios is shown in Figure 3. The experiments were carried out so that the total quantity of metal deposited was approximately constant while the quantity of CHI decreased from one experiment to the next. Interference fringes in the spectrum of Cu in octane indicate
-
(1)D.M. Gruen, “Cryochemistry”, M. Moskovita and G. A. Ozin, Ed., Wiley-Interscience, New York, 1976,Chapter 10. (2) (a) M. Moskovits and J. E. Hulse, J. Chem. Phys., 67,4271(1977); (b) W. E.Klotzbiicher, S. A. Mitchell, and G. A. Ozin, Inorg. Chem., 16, 3063 (1977). (3)M.Moskovits and J. E. Hulse, J. Chem. Phys., 66,3988 (1977). 0022-3654/81/2085-2904$01.25/0
0 1981 American Chemical Society
The Journal of Physical Chemistry, Vol. 85, No. 20, 1981 2005
Spectra of Copper Atoms in Various Matrices
TABLE I: Observed Cu Line Positions (cm-I) in Various Matrices term 3d1"('S)4p( 'Po)
gas 30 535 30 784
Ar 32680 33146 33568
N2 31666 32020 32733
3d94s(3D)4p(4Po)
40 114 40 944 44 916 45 821 45 879 46 173 49 383
41841 42680 45851 46598
41203 42017 45269 46125
31250 31817 32248 32 733 33 190 41322 42194 45249 46296
47192 48100
46751 47755
47170 47619
3d94s('D)4p( 4D0) 3d94s(3D)4p(2P") 3d94s('D)4p('D0) 3d10(1S)5p(ZP")
CH4
C2H6
C3H8
C4H10
CSH12
C6H14
C8H18
30404 31221 32383
30130 31046 32289
29595 30779 32258
29446 30590 32237
29377 30553 32175
41408
41339
41288
41339
41034
47733
47574
47755
47664
29053 30404 32103
45372
47687
47483
TABLE 11: Line Intensities Relative t o the Lowest Energy Line for Cu Isolated in Various Matrices
term
gas 1.00 2.05
0.06 0.01 3d94s(3D)4p(4Do) 0.018 0.054 3d94s(3D)4p(zPO) 0.084 3d94s(3D)4p(zDo) 0.071 1.74 3d1"( S)5p(,Po) 3d94s(3D)4p(4P")
200
300 nrn
400
200
Ar 1.00 1.05 0.80
N* 1.00 1.06 0.92
0.03 0.01 0.01 0.02
0.03 0.01 0.05 0.16
0.10 0.63
0.19 0.57
300 n m
CH4
1.00 0.90 0.70 0.30 0.05 0.02 0.01
C2H6
C3H8
C4H10
C5H12
C6H14
1.00 1.08 0.88
1.00 1.09 0.92
1.00 1.14 0.99
1.11 1.00
1.00 1.11 0.99
0.02
0.02
0.02
0.02
0.03
0.52
0.53
0.49
0.52
1.00
C8H18
1.00 1.14 1.05
0.07 0.20
0.20 0.50
400
Flgure 1. Portions of the UV-visible spectra of Cu atoms isolated at 12 K in various matrices: (A) octane: (B) hexane; (C) pentane: (D) butane: (E) propane: (F) ethane; (G) methane; (H) Ar; (J) nitrogen (note scale change in the case of the latter).
that the matrix was 4 pm thick if a refractive index of 1.4 is assumed for solid octane. Discussion Three aspects of the results will be discussed: the effect of Cu/CH4 ratio on the formation of aggregates as gauged by the decrease in the Cu atom absorption in matrices; the influence of chain length and melting point of the matrix
0.63
1
1
1
200
3 0
400
0.37
nm Figure 2. Portions of the UV-visible spectra of Cu atoms isolated in ethane at 12 K: (A) immediately after codeposition of Cu and gas; (B) after annealing to 35 K and recooling to 12 K.
--
on the isolation efficiency;and, most importantly, the cause of the triplet structure in the 2P 2S absorption. The decline of the Cu 2P 2S peak with increasing metal-to-gas ratio is shown in Figure 4 (normalized for a constant total quantity of copper). The trend is well accounted for by the scheme proposed in ref 4 in which copper atoms react to form dimers and higher polymers in a stepwise reaction process in the soft, fluid region of the matrix still in the process of condensing. In that model the aggregation process proceeds for a length of time and at a rate given by the product k r where It is proportional to D, the diffusion constant of 6 u atoms in the (liquid) matrix host while T~ is the mean lifetime during which the
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The Journal of Physical Chemistry, Vol. 85, No. 20, 1981
Moskovlts and Huise
TABLE 111: Calculated Isolation Efficiency of Several Matrix Materials Together with Various Phvsical ProDerties (W/mK) X 103
TPCplq! csg units 10-6
117 (25) 121 (91) 88 (125) 70 (170) 212 ( 9 9 ) 200 1 8 0 (157) 146 (204) 152 (194) 1 3 1 (260) 1 2 9 (277) 126 (307)
351 416 421 540 511 246 177 339 382 581 612 791
K,
C,, J mol-’ K “
Ne
T Y bK p , g ~ m - ~q , ’ C p
TM,K
35.35 (24.5)‘ 42.05 i 8 3 . 8 j 44.85 (116.0) 44.69 (161.3) 55.44 (90.6) 68.2 (89.9) 84.31 (85.4) 113.0 (134.9) 140.6 (180) 171.5 (200) 201.3 (200) 237.4 (250)
24.5 8318 116.0 161.3 90.6 89.9 85.4 134.9 143 178 182 216
25.8 8517 118.7 163.7 99.92 137.2 157.3 203.7 226.3 260.1 277.0 397.6
1.44 1.62 2.92 3.51 0.47 0.57 0.58 0.60 0.63 0.66 0.68 0.70
0.16 (26)‘ 0.29 (86) ~, 0.50 0.52 (164) 0.15 (100) 0.36 (137) 0.55 (157) 0.48 (204) 0.48 (226) 0.45 (260) 0.48 (277) 0.45 (308)
9
In [ (TR- To)/ “ ( T M- Toll 3.30 1.62 1.25 0.89 1.53 1.54 1.59 1.09 1.02 0.79 0.77 0.58
akTqd
1160 674 528 480 781 380 282 370 390 459 471 457
a Num-ars in parentheses are the temperatures (in ur...s of K) at wt.-h C, was measured, chosen so as to be as close as was available in the literature for the liquid at its melting point. The mean temperature of the liquid during the condensation process, taken to be the mean between the boiling and melting points. The numbers in parentheses in the columns marked q and K are the temperatures (in units of K) which these measurements refer to. These were chosen so as to be as close as possible to T. A number proportional to the product of the numbers in the previous two columns which, in turn, is proportional to k T q as defined in the text. e C,, T M ,p , q , and K values were taken from Landoldt Borstein, Vol. 2.
0
IO0
50
metal / g a s
ratio
Figure 4. The intensity of the 2lBnm absorption of Cu atoms isoiated in solid methane (ordinate in arbitrary units) as a function of the metal-to-gas mole ratio (abscissa in arbitrary units) for a series of matrices each containing the same total quantity of metal.
I
,
200
I
,
300
/
,
400
nm
Figure 3. Three representative UV-visible spectra of Cu atoms isolated In solid methane, obtained by cocodenslng the same quantity of Cu with methane buy varying the metailgas mole fraction. For a to c this mole fraction varies in the ratio 1:0.72:0.35.
reaction can take place before the freezing front overtakes the reacting species. The influence upon k7q of the nature of the matrix material was not considered in ref 4. An analysis of the dependence of T~ on various physical properties of the matrix is presented in the Appendix where the expression rq = ( ~ C Z ~ / T ~ K In ) [ ~ ( T-RT 0 ) / r ( T M - To)]
(1)
is derived, assuming that the condensation process is almost independent of the concentration of metal, which is almost always small, and that the condensation takes place in a region of width 1 bounded by T oon the cold side. rq is the time required for the mean temperature of the layer to reach the immobilization temperature TM, taken to be ~~~~
~
~
(4) M. Moskovita and J. E. Hulse, J . Chem. SOC.,Faraday Trans. 2,
73,471 (1977).
the freezing point of the matrix material. (One should distinguish here between the immobilization temperature pertinent to our case and the temperature defined through Taman’s rule,5 which sets the temperature at which noticeable diffusion takes place within a matrix at TM/3.The diffusion spoken of in the context of Taman’s rule is, of course, a substantially slower one than that operative in generating clusters in a condensing matrix.) For want of a better alternative, k is taken to be that given by Smoluchowski6 k = 16rRD 2R being the mean distance for the aggregation reaction to take place (here assumed to be approximately the diameter of a copper atom) and D the diffusion constant of Cu in the liquid matrix. Using the Stokes-Enstein relation for D one has
D = kBT/6avR
(3)
which when substituted in (2) yields k = 8kBT/37
(4)
(5) H. E. Hallam, Ed., “Vibrational Spectroscopy of Trapped Species”, W h y , New York, 1973. (6)M. V. Smoluchowski, Z. Phys. Chem. ( L e p i z g ) , 92, 192 (1917).
Spectra of Copper Atoms In Various Matrices
\ \ \
I
\
metal / g a s
ratio
-. I
Flgure 5. The twelfth root of the spectral absorption of Cu atoms as a function of metal-to-gas mole ratio. Points are experimentally determined. Solid line is the expected trend if copper clusters form statistically.
Estimates of the product Tqk/12 are given in Table I11 for the noble gases and for the first eight alkanes. When kTq is large, cluster formation is favored. In Table I11 we see that cluster formation is predicted to be greatly favored in Ne matrices as compared to the other three noble gases which in turn are expected to produce clusters with decreasing efficiency on going from Ar to Xe. This is as ~ b s e r v e d . ~This trend results mainly from the proportionality to the diffusion rate (i.e., inverse proportionality to the viscosity) since T~ is more or less constant for the rare gases. According to the data of Table 111, the normal alkanes C2to c8 (Le., C2H6 to C8H16) are predicted to be roughly equivalent in their isolating capabilities and approximately on a par with Kr and Xe while methane is predicted to be somewhat better than Ar in promoting clusters. This is what the present results and those of ref 2b indicate. This comes about as a result of the offset of the decreasing logarithmic term with increasing T M of the longer alkanes by an increasing prelogarithmic term with increasing chain length. The latter term will begin to dominate for alkanes with very long chains for which TM levels off with chain length while C, increases monotonically. In long-chain alkane matrices, the isolation of atoms is therefore predicted to become progressively more difficult as the rate at which energy can be extracted from the condensed paraffin layer comes to dominate rq. This is indeed what is observed with Cu in dodecane& and Ag in docosane.8 The observed similarity in the isolating capabilities of the normal alkanes C2to c8 also tends to indicate that the aggregation processes take place when the matrix material is liquid rather than gaseous. For an ideal gas the quantity DPC/Kis approximately unitySg Hence in that limit the higher alkanes should be considerably more efficient isolators than the lower ones on account of the decrease in the logarithmic term with chain size, contrary to what is observed. The degree of isolation as gauged by the area under an absorption of Cu in CHI as a function of metal-to-gas ratio also indicates that cluster growth as a result of stochastic encounters of Cu atoms placed on fccub lattice sites and remaining immobile thereafter is not the dominant mechanism for cluster growth at higher metal concentrations. The statistical concentration of isolated copper atoms is given by [CUI = a(l - a)lZ,lowhere a is the (7)W.Schulze, Abstracts of 1st International Matrix Isolation Symposium, Berlin, 1977. (8)H. Huber, P. Mackenzie, and G. A. Ozin, J. Am. Chem. SOC., 102, 1548 (1980). (9)R. D.Present, “Kinetic Theory of Gases”,McGraw-Hill, New York, 1958.
The Journal of Physical Chemlstfy, Vol. 85, No. 20, 7981 2907
probability that a particle condensing on the matrix is Cu. a is therefore approximately equal to the metal-to-gas ratio Mo.The absorbance of the 217-nm band, Ac,, has been normalized to a common quantity of copper so that Acu [CUI/Mo. Hence AC;/l2 should be linear with Mo with decreasing slope. Figure 5 shows that this is true at low values of Mo. At high values of Mo the isolated fraction drops well below this line, indicating that considerably more cluster formation occurs than predicted by the stochastic model. The spectrum of copper isolated in argon has been reported several timed’ and in methane once.2a These articles have treated almost exclusively the (3d1°4p)(2Po) (3~lO4s)(~S) transition (Table I) with little attention paid to the higher energy transitions. In all of the articles quoted above the method of correlating matrix and gasphase spectra that is developed in ref l l c has been given straightforward application. Briefly, the strength of an absorption from the ground state is proportional to the oscillator strength, f, and the degeneracy of the upper state, g. The gas-phase-to-matrix correlation is made by comparing the products gf and the positions of the gas-phase lines with the observed band intensities and positions in the spectrum of the matrix-isolated material. Tables of the gas-phase values for some 64 elements are provided in ref llc. The data included in these tables were garnered from the monograph of Corliss and Bozmanlb which is a compendium of oscillator strengths of most of the elements derived from the best values of spectral line intensities available at the time of its publication (1962). These were the measurements of Meggers et In 1975, a new set of measurements was issued by Meggers et a1.120 which superceded their earlier monograph. Since gf is proportional to intensity, the gas-phase values reported in this article were corrected from ref 12a by multiplying by the ratio 1(1975)/1(1962). The Cu in Ar absorption at 208 nm (48000 cm-l) is normally attributed to a 2P(3d94s14p1) 2S1/2transition. The small gf value for this transition in the gas phase (Table 11) compared with its much larger intensity in the matrix makes this assignment unlikely. We assign this absorption instead to the 2P(3d105p) 2S1/2transition and note in so doing that this becomes the only band to be red shifted on going from the gas phase to the matrix. A possible explanation for this is offered below. The Triplet Structure. The triplet structure of the 2P112,3/~ 2S1/2absorption was attributed in ref 2a to an exciplex formation between the excited Cu atom and one of its argon neighbors. While Anderson has shownls that decreasing the Cu-Ar distance of one of the ligands in a cubooctahedral, electronically excited CuAr12cluster produces a lowering of its energy, it is clear that that process does not lead to the deepest minimum possible for a distorted CuAr12structure. Triplet structures similar to the 2P 2S structure of isolated copper have been observed in the F-center spectra of Cs halides14and the impurity spectra of In+-doped Cs
-
-
-
-
-
~
(10)R.E. Behringer, J.Chem. Phys., 29,537(1958);J. E.Hulse, Ph.D. Thesis, University Microfilms, Ann Arbor, MI, 1978. (11) (a) F. Forstmann, D. M. Kolb, D. Leutloff, and W. Schulze, J. Chem. Phys., 66,2806((1977);(b) L.Brewer and B. King, ibid., 53,3981 (1970); (c) D. H. W. Carstens, W. Brashear, D. R. Eslinger, and D. M. Gruen, Appl. Spectrosc.,26, 184 (1972),and ref 2a. (12) (a) C. H. Corliss and W. R. Boman, Natl. Bur.Stand. (US.), No. 53 (1962); (b) W.F. Meggers, C. H. Corliss, and B. F. Scribner, ibid., No. 48 (1961);(c) W.F.Meggers, C. H. Corless, and B. F. Scribner, ibid., No. 145 (1975). (13)A. B. Anderson, J. Chem. Phys., 68, 1744 (1978). (14)P. R. Moran, Phys. Rev. A, 137, 1016 (1965),and references therein.
2908
The Journal of Physical Chemistry, Vol. 85, No. 20, 1981
halides.15 In the latter the absorption band structure has been successfully explained in terms of the dynamical Jahn-Teller effect15J6which produces a triplet structure even in the absence of spin-orbit coupling when a T 8 tz upper state potential energy surface is considered (as described below). For F centers the large spin-orbit interaction expected has prompted Moran to take a different a p p r 0 a ~ h . l ~He considers interactions between the Fcenter electron and a~ and eglattice vibrations, neglecting the tzp.In the local cubic symmetry the excited F-center electronic state is a T1, orbital triplet. The degeneracy of this triplet is removed in Moran’s treatment as a result of purely electrodynamic interactions with the doubly degenerate, noncubic vibrations and the symmetric vibration of the surrounding lattice and a concurrent strong spinorbit coupling. Moran distinguishes between his treatment and the dynamical Jahn-Teller effect but although the mathematic formalism is indeed different from that used by, for example, Longuet-Higgins et a1.,16 physically the two approaches are closely related, leading to the same form for the upper state potential energy surfaces. In the absence of strong spin-orbit coupling the e modes alone does not produce a triplet. Despite the similarity between the fate of the excited electronic state of an F center and an impurity center there is a conceptual difference between them. In the former the motion of the light electron does not influence greatly the vibrations of the lattice around it. This is partly the reason that Moran used an approach which ultimately views the electron’s excited state as being modulated by the lattice’s motion. For an impurity center the local molecule is more akin to a central ion with ligands. The vibrations of the “ligands” about the central ions are split off the phonon band, becoming localized on the molecule. Clearly an isolated Cu atom approximates the latter situation more closely than the former. Moreover, Cho” has recently criticized Moran’s treatment, showing that a more rigorous approach does not produce clearly resolved triplets for values of the coupling parameters used by the latter. For simplicity we will refer to the Cu atom and its 12 surrounding host atoms or molecules as a “molecule”. The “molecule” CuAr12belongs to point group Oh. The “molecular” state arising from C U ( ~ P ) has A ~2Tlu ~ symmetry.18 The Jahn-Teller theorem dictates that the minimum in the energy of C U * A ~ ~ ~ (will ~T~ be, )found when the “molecule” distorts along one (with the exception of alg) or a combination of the normal coordinates alg + (15)A.Fukuda, J. Phys. SOC.Jpn., 27,96 (1969);Phys. Reu. B, 1,4161 (1970). (16)For a summary, see for example R. Englman, “The Jahn-Teller Effect in Molecules and Crystals”, Wiley-Interscience, New York, 1972. (17)K. Cho, J. Phys. SOC.Jpn., 25, 1372 (1968). (18)Experimental evidence quoted in ref 2a indicates that the solidphase disposition of the rare gas about an impurity copper atom is close packed. Thus the symmetry group of the immediate environment of the foreign atom is either O,, (in fccub) or Da (in hcp). The electronic ground state is 2 S l p , a Kramers doublet. The wave function of this state transforms aa the El,% representation of the extended point group Oh or the Ell2 representation of D%’. Classification within the double groups is necessary because the total angular momentum is half-integral. The excited state in question is the lowest valence state which in the free molecule is split by spin-orbit coupling into a 2P$z and a 2Pp/2state. The wave functions of these states transform as El/% and G32~ in oh‘ and E3/2, Esp, and E6p in D3,,’. In principle a 2Postate can splil into three states in a D% enwronment. However, a P state (L= 1)will only be split if the electrostatic potential of the environment has a quadrupole or lower moment. The quadrupole moment of an hcp environment with ideal c/a ratio vanishes, the leading term in the multipole expansion being an octupole. Hence the orbital degeneracy of an excited Cu atom (2P)will not be lifted in an hcp environment. In a fccub environment, moreover, one may in the limit of weak spin-orbit coupling deal with the orbital wave functions representing the Cu (ZP) alone. These belong to the TI, representation in 0, symmetry. It is this approach which we have chosen to take.
Moskovits and Hulse I
I
I
I
I
I
1
Ar
.
1
O.O5t-
t
1
-
Flgure 6. The energy interval between the outer two components of the *P *S trlplet in the absorption spectrum of Cu atom Isolated in the solid rare gases shown. After Forstmann et al.”’
eg + tag. This process has been studied at length for a variety of systems, among them heavy metal-doped phosphors.16 If ?Flu 8 egcoupling dominates, the upper state potential surface splits, in the absence of spin-orbit coupling, into three equivalent intersecting surfaces when plotted in qe, qespace, these being the two normal coordinates associated with the egvibration. It has been shown, however,16that in this case the T A absorption band consists of a single Gaussian. Coupling with b,on the other hand, causes the upper state potential energy surface to split into a hypergeometric structure with four equivalent minima in q,,, qf, qEspace (these being the normal coordinates spanning b)which produces a triplet in absorption,16with a spacing S between the outer two maxima given by
-
s = 2[3/2Ej~hWtcoth (hWt/2kT)]1/2
(5)
where E j T is the Jahn-Teller stabilization energy and ut the frequency of the localized phonon of symmetry tzg along whose normal coordinates the distortion takes place. The outer two maxima are also predicted to straddle the middle one more or less symmetrically in frequency but not in intensity. Such triplets have been observed in several systems. The C band for CsBr:In+, for example,16 looks almost identical with the 2P 2S band observed with Cu in rare gas and alkane matrices. The progress with increasing temperature of the three components of the (CsBr:In+) triplet also behaves almost identically with what was reported by Forstmann et al.l’* for Cu in solid rare gases, namely, the frequency of the high-energy component changes little with temperature while the frequencies of the two lower-energy maxima decrease with temperature. The total spacing obeys eq 5 quite well (Figure 6) when the parameters (0.38 eV, 41.5 cm-l), (0.26 eV, 31.1 cm-l), and (0.19 eV, 22.5 cm-l) were used for (EjT, hot) corresponding to Cu in Ar, Kr, and Xe, respectively. Moreover, the ratios of hot for Ar, Kr, and Xe are approximately in the ratios of the square root of their masses as would be expected in first order for vibrators of different mass but approximately equivalent force constants. We conclude that the triplet structure seen in the absorption spectra of Cu isolated in solid rare gases is adequately explained by invoking an exciplex between the excited (2P)Cu atom and its host atom neighbors whose geometry is distorted trigonally along normal coordinates of the tze; vibrations. The distortion is a dynamical one and
-
The Journal of Physical Chemistry, Vol. 85, No. 20, 1981 2909
Spectra of Copper Atoms In Various Matrices
of ethane, which is hexagonaLZ0 After crystallization the site symmetry about a Cu atom is no longer isotropic; hence a static, distortional component will exist in the 2P state of Cu in addition to a possible E 8 e Jahn-Teller effect. In this case the T1, will be split into a 2A1(2P)and 2E(2P)state by the static distortion while E 8 e JahnTeller effect will cause the 2E(2P) 2A1(2S)transition to become a doublet as expected16 and observed in the spectra of several Co salts.21 The expected splitting in the two absorption maxima of an E 8 e system id6
3 3 0 0 0 1 , 1 v
32000
1-
-
34
31000
30 !6
-
v/n
!2
30000
hw&’
8
“1
1/2
coth 2kT
4
0
Flgure 7. The frequencies of the three components of the *P *S triplet in the absorption spectrum of Cu atoms isolated In the various normal alkanes (extend to n = 8); the alkane molar volume per carbon a t o m (extends to n = 12); as a function of the chain length of the alkane. +-
no static distortion of the ground state need be invoked. The splitting may also be accounted for entirely in the absence of spin-orbit coupling, which may be quenched to a greater or lesser extent in these systems. Our data do not allow us to determine the magnitude of spin-orbit coupling present in the “exciplex”. This may be determined from MCD measurements. Such a study on alkaline earth atoms isolated in rare gas matrices by Schatz et concluded that there is some mixing of the orbitals of the excited metal atom with those of its neighbors, especially with Xe, indicating that the label “exciplex” is merited to some extent in that case. In the presence of spin-orbit coupling, distortions along eg alone do produce triplets as shown by the calculations of Moran14 and Cho,17 and in general the excited state surface would be generated by vibronic coupling to alg,.eg, and tzgmodes. Our discussion in terms of tzgcoupling alone should not be construed to imply the total absence of contributions from eg coupling. We do note, however, that the rather symmetrical form of the 2P 2S triplet more closely represents the line shapes calculated by Cho17 for cases in which coupling to tZgmodes dominated. The portions of the spectra of copper atoms isolated in the alkanes CHI to C8H18corresponding to the 2P ‘5 transitions look very similar to those of Cu in Ar taken at increasing temperatures. That is, as the size of the alkane increases the frequency of the center of the triplet shifts to lower frequencies, the splitting between the highest and lowest components of the triplet increases and the frequency of the highest-frequency component is almost independent of chain length (Figure 7). Increasing the alkane chain length, then, mimics an increase in the matrix temperature. The observed triplet structure remains almost unchanged on warming to 35 K, then recooling the matrix in all cases except for that of ethane in which an irreversible change occurred in the 2P 2Sspectrum (Figure 2). After warming and recooling, the two outer Components of the triplet were no longer symmetrically disposed about the middle component; instead, one member split off from the other two. We propose that this arises from a transition from a glassy, isotropic matrix to the crystalline form
-
-
-
(19) R.L. Mawery, J. C. Miller, E. R. Krausz, P. N. Schatz, and L. Andrews, J. Chem. Phys., 70, 3920 (1979).
where the meaning of the symbols may be deduced by comparison with eq 1. When wt = we and Em’ the doublet splitting in the E 8 e situation is expected to be 1.2 times smaller than in T 8 t2; the observed twofold reduction in the splitting implies that either or both of these equalities do not obtain. The crystal structure of methane is fccub; hence, the triplet structure is not expected to change on heating (the 2p 2Sband of Cu in methane is actually a quintet which consists of an intense triplet whose profile resembles closely the triplet observed with solid noble gases or the other alkanes as hosts with two weaker absorptions on the high-energy side of this. When we speak of “the triplet structure” of Cu in methane we are referring to the intense portion of the band), while for the longer alkanes crystallinity is achieved with more difficulty,22thereby explaining the lack of change in the spectrum on warmup. The increase in the overall splitting of the 2P 2Striplet with increasing chain length may come about as a result of an increase in either EJT or nu,. We attribute the increase to the former, since it is unlikely that the vibrations of the matrix molecules would increase in frequency as the chain length is increased. The Jahn-Teller stabilization energy, on the other hand, is expected to increase since in the longer alkanes the carbons are packed more closely to the Cu atom. This is illustrated in Figure 7 in which the mean volume per carbon atom (molar volume divided by the number of carbon atoms) is plotted against chain length. This curve resembles the progress of the triplet splitting with chain length quite nicely. The emission spectrum of matrix-isolated Cu is expected to be Stokes shifted from the absorption spectrum as a result of nonradiative relaxation within the upper state. Considering for a moment the C U ( ~ Patom ) and its immediate host atoms (or molecules) as a large molecule, the excited molecule may rapidly lose vibrational quanta which will, in turn, excite phonons in the solid host before reemitting. In the process the upper state “molecule” will find itself at a point in normal coordinate space corresponding to a steeply rising portion of the ground-state potential. This will contribute further to the Stokes shift, as illustrated in Figure 8. The calculations of EnglmanZ3 indicate that the emission spectrum which proceeds from a T, 8 tzpsurface to the lA, ground state may display as many as six peaks. This situation may be complicated further by the possibility that emission from the E 8 e
-
-
(20) R. W. G. Wyckoff, “Crystal Structures”, 2nd ed, Interscience, New York, 1963. (21) F. A. Cotton and M. D. Meyers, J. Am. Chem. SOC.,82, 5023 (1960). (22) R.W.Douglas and B. Ellis, Ed., “Amorphous Materials”, Wilep Interscience, New York, 1972. (23) R. Englman, M. Caner, and S. Toaff, J.Phys. SOC.Jpn., 29,306 (1970).
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The Journal of Physical Chemistty, Vol. 85, No. 20, 1981
Moskovlts and Hulse
eV
-*
8-
-*
12-
-* -* -* -*
-* 16--*-*
20
,
I
I
I
I
Flgure 8. A cross section through the *S and *P surfaces of the CuAr,, “molecule” illustrating an absorption and emission process.
TABLE IV: Jahn-Teller Parameters for CuAr,,‘ EJT, eV 41.6 0.38 Kr 31.2 0.26 Xe 22.6 0.19 ’Based on the data of Forstman et al.’la hw,, cm-’
Ar
surface may contribute significantly even when the absorption bandshape is dominated by the T @ t2 surface, as has been previously reported for KBr:Sn2+.2i If sufficient vibrational energy is lost into the matrix, local softening can occur, a process considered in some detail by DeMore and Davidson26and observed by several authors.26 Reported emission spectra for Ag,27Na,28and KZ9are in general agreement with the above remarks, which will be expanded further in a separate article discussing emission spectroscopy of matrix-isolated Cu atoms.30 The model we propose above contrasts with that of Forstmann et al.lla in which an exciplex formation is invoked only to explain the presence of a fourth band in Xe-isolated Ag. The triplet structure is attributed by them to a static distortion producing a local tetragonal site symmetry about the atom. It is clear from our discussion above that the triplet structure may come about in s1 atoms isolated in fccub solids even in the absence of a static distortion (and even in the absence of spin-orbit coupling). We maintain that in fact no static distortion occurs with the rare gas solids as evidenced by the similarity with the spectra of impurities in solids cited above and other corroborative arguments cited previously in ref 2a. Although the term “exciplex” was used in this paper to emphasize the similarity between the excited Cu atom and (24)A. Fukuda, S.Makishima, T. Mabuchi, and R. Onaka, J. Phys. Chem. Solids,28,1763 (1967). (25)W. B. DeMore and N. Davidson, J. Am. Chem. SOC.,81,5869 (1959). (26)W. Weltner, D. MacLeod, and P. H. Kasai, J. Chem. Phys., 46, 3172 (1967);L. C. Balling, M. D. Harvey, and J. F. Dawson, ibid.,69,1670 (1978);G. A. Ozin and H. Huber, Inorg. Chem., 17,155 (1978). (27)D. Leutloff and D. M. Kolb, Ber. Bunsenges. Phys. Chem., 83,666 (1979). (28)L.C. Balling, M. D. Harvey, and J. J. Wright, J. Chem. Phys.,70, 2404 (1979). (29)L. C. Balling, M. D. Harvey, and J. F. Dawson, J. Chem. Phys., 69, 1670 (1978). (30)R. H.Lipson, MSc. Thesis, University of Toronto; M. Moskovits and R. H. Lipson, manuscript in preparation.
its immediate “ligands” and that of a molecule, the values of EJT obtained for Cu in Ar, Kr, and Xe (Table IV) indicate that the interaction between guest and host is quite weak, so that it would not be entirely incorrect to describe it as “nonspecifi~”.~~ This last statement must be tempered, however, by the observation that Em decreases on going from Ar to Xe while a nonspecific (polarizability) effect would be expected to display the reverse trend. This may be rationalized by noting that the 4p level of Cu and the 4s (empty) level of Ar have similar energies while the 5s and 6s levels of Kr and Xe are further removed in energy from the first. This implies that a certain measure of chemical bonding (albeit small) exists between C U ( ~ P ) and its noble gas environment. With the alkanes the nonspecific portion of the interaction between excited (2P)copper and the carbons is an important one as shown by the increasing Jahn-Teller stabilization energy with chain length. Had the chemical interaction played a significant role in these cases one would have expected the opposite trend to be observed since the mismatch in energy between Cu 4p and the first excited Rydberg state of the alkanes (which is essentially a carbon 3s state) increases as one proceeds from C1 to C6 (Figure 9). Likewise a changing polarizability with chain length would also not provide a likely explanation for the shifts, since the polarizability of the Cu-atom environment is not expected to change much with chain length. If anything, tighter packing ought to decrease the polarizability of the environment. Recently Forstmann and O ~ s i c i n have i ~ ~ successfully calculated the average blue shifts of the valence level lines of noble metals isolated in noble gas matrices by orthogonalizing the free metal atom wave functions to the wave functions of the 12 surrounding rare gas atoms. Calculation of such a nonspecific effect of the matrix cage would most likely reveal the formation of the exciplex which we are discussing. With Cu in solid N2the splitting is about that observed in Ar. However, the triplet structure is not as symmetric as that reported for Cu in the noble gases or in the (isotropic) alkanes. The high-energy component of the 2P 2S triplet of Cu in N2 is split off from the other two com-
-
(31)A recent, careful magnetic circular dichroism study of copper atoms isolated in solid, rare gas matrices (S.Armstrong, R. Grinter, and J. McCombie) shows the Cu-Ar interaction to be essentially nonspecific and not in disagreement with the Jahn-Teller interpretation. (32)F. Forstmann and S. Ossicini, J. Chem. Phys., 73, 5997 (1980).
Spectra of Copper Atoms in Various Matrices
ponents. The nitrogen molecules in solid N2 are placed on fccub lattice points. Each molecule is inclined33in such a way, however, that the site symmetry about a substitutional site is lowered to C2. The triplet structure is therefore expected to be modified somewhat by the small perturbation brought about by the alignment of N2 molecules about a Cu atom. Excitons and the 2P(3d105s) 2S1/2 Transition. The electronic excited states of molecular solids are most satisfactorily treated in the exciton formulation, an exciton being an excitation of an excited state of the system.34 The key characteristic of these excitations is their mobility; they can propagate through the solid, transporting energy. The theory has been treated in depth by Dexter and Kn~x.~~ Two limiting cases are presented. The simplest is that of a convex parabolic valence bond and a concave parabolic conduction band, both with extrema at the center of the first Brillouin zone (unit cell). In an optical absorption, an electron is excited into the conduction band, leaving a positive hole at the top of the valence band. The electron and the hole will interact to an extent which depends upon the spatial extent of the conduction band state involved. If it is spread out over a large volume of the crystal, then the electron-hole interaction may be described in a manner analogous to that applied to a hydrogen atom with the Coulomb potential reduced by an effective dielectric constant representing the screening of the intervening charge distribution. Thus a Rydberg series of exciton states arises, each with a principal quantum number and each possessing a characteristic radius. The energies of these states converge to the band gap as the principal quantum number increases. This is the Wannier model of the exciton. In the limit of a vanishingly small exciton radius, the exciton takes on the characteristics of an atomic excited state with the proviso that the excitation is mobile. This is the Frenkel model of the exciton. Situations uncovered experimentally usually lie somewhere between these two extremes. Such intermediate cases are more difficult to treat and cannot be given such a general physical description. The rare gas solids provide a full range of examples of excitons,36 each substance having two Rydberg series converging to the bottom of the conduction band. Xenon is the best behaved. The n = 1 number of each series coincides almost exactly with a transition of the free atom which is characteristic of a Frenkel exciton. The n = 1 excitons of krypton, argon, and neon which are blue shifted by 0.3, 0.5, and 1.1 eV, respectively, from the free atom positions are typical of the intermediate case. Moreover, the bands in argon and krypton are split further by a few tenths of an electronvolt into doublets. Thus there is a secondary complicating interaction with the surrounding solid. The higher members of the series for all of these elements have large radii and are excellent instances of Wannier excitons. If an impurity present in a molecular solid lattice has an excited state much lower than any such state of the host, then an excitation of this state will not be able to move readily through the crystal. Such an excitation is known as a trapped exciton and the Frenkel model is appropriate to this case. It is on this basis of a great disparity between the energies of the states that optical spectra of
-
(33) R. W. G. Wyckoff, “Crystal Structures”, Vol. 7, Interscience, New York, 1963, p 29. (34) D. L. Dexter and R. S. Knox, “Excitons”, Interscience, New York, 1965. (35) B. Sonntag in “Rare Gas Solids”, M. L. Klein and J. A. Venables, Ed., Academic, London, 1976, Chapter 17.
The Journal of Physical Chemistry, Vol. 85, No. 20, 198 1 29 11
matrix-isolated species may be compared meaningfully with gas-phase spectra. Ideally, the energy levels of the host crystal and of the impurity atom could be plotted on the same energy scale and correlated with the levels of the separated species. This would be achieved by subtracting the energy required to remove an electron to infinity from the energies of the observed transitions in each case. Unfortunately this is not as yet possible in as much as the vacuum-ultraviolet absorption and photoemission spectra of transition metal impurities in the molecular solids under investigation here have not been measured. Indeed, even the spectra of the pure solids are not well understood. Difficulties might arise in assembling such a diagram even if the data were available. For example, examining the electronic properties of argon, the ionization potential of the free atom is known, 15.755 eV.36 The experimental band gap is 14.15 eV.= The vacuum level of the solid, that is, the energy required to remove an electron, is known, 13.8 eV.36 Notice that it takes less energy to remove an electron from the solid than to excite it into the conduction band. The choice of a common point for comparing the energy levels of gas-phase copper atoms and solid argon is clearly not straightforward. We have therefore decided to proceed in the simplest fashion and refer the energy levels of the separated atoms and molecular building blocks of the crystals to their respective first ionization potentials. Figure 9 was constructed in that fashion. The horizontal dashed line represents the location of the bottom of the conduction band in solid argon. For the sake of discussion, and in the absence of the information, we assume that the dashed horizontal line represents the energy of the bottom of the conduction band in every one of the solids appearing in the figure. The 3d1°4p1 state of Cu is well below the conduction band. Hence its status as a trapped (Frenkel) exciton; by contrast the copper 3d1°5p Rydberg orbital is within 1eV of the bottom of the conduction band. (Rydberg orbitals of impurities are best described as Wannier excitons in molecular solid^.^') We therefore conjecture that the transition to the (3dlO5~)~P level of copper is the lowest, n = 1, member of a Rydberg series of Wannier excitations and the red shift in the level comes about as a result of the weakening of the Coulombic potential between the electron and the Cut core by the intervening dielectric. Verification must await the appropriate vacuum-ultraviolet spectroscopic measurements. Acknowledgment. We thank NSERC, the Atkinson Foundation, and Imperial Oil for financial support. J.E.H. thanks the National Research Council of Canada for a scholarship. Appendix When the vapor which eventually forms the matrix condenses it initially forms a dense fluid layer at the surface of the matrix whose temperature decreases as a function of time until it freezes. During this time span the fluid is both dense enough to allow the concentration of metal atoms which may now be construed to be a solute in solution to attain a substantial value and fluid enough to allow the metal atoms to diffuse with considerable ease. This leads to the formation of aggregates. In the analysis below we wish to obtain an expression for the mean time during which the matrix remains fluid so that the aforementioned aggregation process may take (36) C. E. Moore, Natl. Bur. Stand. (U.S.),No.467 (1949). (37) J. Jortner in “Vacuum Ultraviolet Radiation Physics”, E. Koch, Ed., Braunschweig: Pergamon Vieweg, 1977.
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The Journal of Physical Chemistry, Vol. 85, No. 20, 1981
place. The actual freezing process involves the motion of the freezing front outward from the solid through a liquid region which is constantly being replenished. We will model this process by a static fluid layer of thickness 1 which is initially at a temperature TR,taken to be room temperature, and finally reaches the matrix temperature T,,.We define the time, 7q,required to immobilize a metal atom as the time it takes for the center of this layer to achieve the immobilizationtemperature Th.Although this is a crude approximation of the true state of affairs, it will likely give values of rq which are at least in the correct relative order for a set of matrix materials. The partial differential equation governing heat flow is given in ref 37 as cp(aT/at) = Ka2T/ax2
(Al) in which c, p, and K are, respectively, the heat capacity in cal g-l K-l, the density in g cm4, and the heat conductance in cal cm-l s-l K. The quantities t and x are, respectively, the time, the distance into the fluid layer defined such that x = 0 is at the gas-fluid interface while x = 1 is the fluid solid interface. T is the temperature at x and t. The solution of (Al) is obtained in the customary fashion by setting T(x,t)to be the product of a space-dependent and a time-dependent function and separating the partial differential equation into a space-dependent part and a time-dependent part. The solution iss8 T(x,t) = D + Cx + Ex2 + Ft + E[A, cos ax + B, sin a x ] exp(-t/T,) (A2)
Moskovits and Hulse
T R - To = C(A, cos ax
+ B, sin a x )
This is a Fourier expansion for the constant TR - Toover [0,1] for which it suffices to keep either the sine or cosine expansion. We choose the sine expansion and set a = nn/l, n being an integer running from unity to infinity; hence TR - To= C B, sin n r x / l (A3) n=l
in which the values of B, are obtained from B, = ( 2 / 1 )
x’
(TR- To) sin nnx/l dx
In particular B, = 4(TR - To)/?r (A4) The complete solution for T(x,t) with the above boundary conditions is, therefore T(x,t) = TO+ C (B, sin ? m x / l ) exp(-t/.,) (A5) n=l
where = pC12/n2n2K (A61 Assuming that after a time 7q the temperature at x = 112, that is, the temperature in the center of the fluid layer, reaches Tim,A5 yields 7,
a
where T , = (pc/Ka2). A,, B,, C, D , E, F, and a are constants. By back differentiating one may relate E and F as follows: E = pcF/2~ Boundary Conditions: (i) A t t = a,F must be zero for T to be finite; hence E is also zero. We are therefore left with
T(x,-) = D + Cx which we take to equal Tofor all x . Hence C = 0 and D =
To.
(ii) At t = 0, T(x,O) = TR for all x . Hence (38) H. Margenau and G. M. Murphy, “The Mathematics of Physics and Chemistry”, Van Nostrand, New York, 1956.
For T~ sufficiently large, terms with n > 1will contribute negligibly since Tq/7, a: n2 and the n = 2 terms is identically zero. Under such circumstances it suffices to keep only the n = 1term in (A7). Upon substituting for B1and T~ from (A4) and (A6), the expression for Timbecomes Ti,= To ~ ( T- RTo)/?rexp(-Tqa2K/pc12) (A8) In the main part of the paper we assumed that Timmay be set equal to TM, the melting point temperature of the matrix material, in which case we may solve A8 for r9 in terms of the parameters p, c, 1, K , TR,To,and TM of which only 1 is in principle unknown. The expression thus obtained is Tq = (PCl2/X2K)In [4(!fR - TO)/T(TM - TO)](A9) which is the required result.
