J. Phys. Chem. 1981, 85,621-623
02 1
in the micellar surface,l0was investigated. No appreciable change was observed in the line width of the spin probe in Cl6C2VZf-CTACmixed micelles under various molar ratios. As a consequence, the microviscosity around the pyridinium ring is suggested to be the same. Therefore, broadening of the ESR spectra must be due to an electron exchange reaction. The line width of each spectrum was estimated by computor simulation. The electron-exchange rate constant ( k )was evaluated from eq 41° by use of line
width values ( H ) where T is mean lifetime of c1&2v+’and
Ho is line width without electron exchange. A [c&2v2+] vs. ( H - Ho) plot is shown in Figure 4. The estimated k value from the slope of Figure 4 was -5 X lo9 M-l s-l,
Flgure 4. Effect of C16C2V2+concentration on the relative ESR line width. The H, value, 1.0 G, was estimated by extrapolating qto zero in a plot of the ESR line width vs. q.
shown in Figure 3. The hyperfine structures of the spectra showed appreciable broadening with increasing mole fraction of C&2v2+, and a single line signal without hyperfine structure was observed above 30%. One might suspect that the variation of line shape is due to motional broadening accompanied by increased viscosity. Then, the ESR spectra of 2,4-dinitrophenylhydrazone-2’,2’,6’,6’tetramethyl-4’-pyperidin-l’-oxy, as a spin probe solubilized
which indicated that electron migration was unexpectedly fast. The relatively high population of the bipyridinium group, as well as the orientation at the micellar surface, may be in favor of electron migration.
Acknowledgment. This work was supported in part by a fund from the Ministry of Education of Japan (Grant No. 505046). The authors are grateful for the financial aid. (9) The spin probes were found to be located near the surface of the sodium dodecyl sulfate micelle: J. Oakes, J. Chem. SOC.,Faraday Trans. 2, 68, 1464 (1972). The same conclusion was also obtained with the cetyltrimethylammonium bromide (CTAB) micellar system: T. Mateuo, K. Yudate, and T. Nagamura, submitted for publication to J. Colloid Interface Sci. (10) R. L. Ward and S. I. Weissman, J. Am. Chem. SOC.,79, 2086 (1957).
Electric Field Gradient Effects on the Spectroscopy of Adsorbed Molecules J. K. Sass, H. Neff, Fritz-Haber-Institut der Max-Planck-Gesellschaft, D- 1000 Berlin 33, West Germany
M. Moskovits,’ and S. Holloway Department of Chemistry and Erlndale College, University of Toronto, Toronto MSS 1A 1, Canada and Institut fiir Theoretlsche Physik der Freien Universitat Berlin, D I O O O Berlin 33, West Germany (Received: November 19, 1980; In Final Form: February 3, 1981)
The large electric field gradients which exist near a metal surface are shown to cause those vibrational modes of an adsorbed molecule which are hyper-Raman active to become Raman active, while quadrupole-allowed vibrations are shown to become infrared allowed under some circumstances. The restriction upon the above selection rules which comes about when the conjugate-chargeimage of the molecule is considered is also discussed.
Light scattering by molecules near metal surfaces has become, almost catastrophically, a subject of immense interest to a polyglot group of chemists and physicists partly as a result of the discovery that enormous Raman signals1are at times obtained from such systems. This in turn has created a surge in the study of the effects of electromagnetic fields near metal surfaces, a subject with a considerable previous literature mainly in the context (1) R. P. Van D u p e in “Chemical and Biological Applications of Lasers”, Vol. 4, C. B. Moore, Ed., 1978, Chapter 5; W. F. Murphy, Ed., “Proceedings of the VIIth International Raman Conference, Ottawa”, North Holland Publishing Co., 1980.
0022-3654/81/2085-0621$01.25/0
of photoemission.2 In this communication we consider in a general way some of the consequences of the inhomogeneity of the electric field, produced when an electromagnetic wave is caused to impinge upon a metal surface, on the selection rules of the Raman and infrared spectra of a molecule placed near the surface. Raman Scattering. The dipole moment induced in a molecule placed in an inhomogeneous electromagnetic field is given by3 (2) See, for example, B. Feuerbacher, Ed., “Photoemission and the Electronic Properties of Surfaces”, Wiley-Interscience,New York, 1978. (3) A. D. Buckingham, Adu. Chem. Phys., 12,107 (1967).
0 1981 American Chemical Society
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The Journal of Physical Chemistry, Vol. 85, No. 6, 1981
Letters
TABLE I: Elements of p , a , and A of Point Group D a h and Its Resolution in C,, ( ~ d ) ~
In (l),(cu,&r) stand for {x,y,z) and the tensor convention on repeated subscripts is assumed. The quantities CY,,, A,,,, and G,, are given by aafi
= CWu)((ilp,lj) (jlwplf))/h j
A,,, = CWw)((ilr,lj)(jl 6,,lf))/h j
(2)
where H(w) = wji/(uj?- w 2 ) ; p, 6, and m are the molecular electric dipole, quadrupole, and magnetic dipole operators and i and f a r e the initial and final states of the system. Consequently the ratio IAasrl/laaslwill be of the order of the ratio of the quadrupole moment of the molecule to its dipole moment, which has units of length and is of the order of a molecular dimension which we will call uM. The ratio IGaal/laasl is likewise of the order of the ratio of a molecular magnetic dipole to a molecular electric dipole moment. For Raman spectroscopya,A, and G should be understood to represent d a / d Q , d A / d Q , and d G / d Q where Q is a normal coordinate of vibration of the molecule. For molecules excited by an electromagnetic wave under vacuum the quantity dE,/dr produces terms of the order of i(27r/X)E, so that the ratio 11/3AdE/d~I/IaEl will be of the order of u M / X , which is approximately when aM is of the order of 1 A and X of the order of 5000 A. The ratio of the lGBl term to laEl is likewise small. The contributions of the last two terms are therefore normally ignored when discussing Raman intensities except when Raman optical activity is ~onsidered.~ The situation is somewhat different near a metal surface. When an electromagnetic wave impinges upon a metal, the field strength is found to vary in an interesting manner both just outside and immediately within the metal. Feibelman,5for example, considered the spatial behavior of an electromagnetic field near a jellium-vacuum interface and has shown that the real and imaginary parts of the vector potential can vary from their minimum to nearly their maximum values over a 2-A region just outside the metal. The magnitudes of these field gradients were found to depend on the energy of the incident radiation, in general decreasing as one progressed to lower photon energies (below the surface plasma energy). The gradient of the potential along a direction normal to the surface will clearly manifest its largest values in that region of space as well, as was also shown by Feibelman. Moreover, because the field varies from near its minimum to near its maximum values in a region of space of molecular dimensions, the order of magnitude of JdE/dzl near the surface will be roughly IE[/uM.The quantity 11/3AdE/dzl will now be of the order of 11/3(A/aM)lEll and A / U Mis of the same order of magnitude as a, so that near the surface the first two terms in eq 1 will contribute about equally to the Raman intensity. The third term, the magnetic field term, will, however, remain small. The importance of the dE/& term in photoemission has been recognized for some time. Specifically KlieweP has shown that momentum conservation in electron-hole pair creation may occur via this term, giving rise to a new class of surface interband transitions. (4) L. D. Barron, Adu. Infrared Raman Spectrosc., 4, 271 (1978);A. D. Buckingham and L. D. Barron, Mol. Phys., 20,1111 (1971);T. Brocki, M. Moskovits, and B. Bosnich, J. Am. Chem. SOC.,102,495(1980). (5)P. J. Feibelman, Phys. Rev. B , 12,1319 (1975). (6)K. L.Kliewer, Chapter 3 of ref 2.
a The modes which remain active when image charges are considered are marked with a n asterisk. ( R ) signifies Raman active.
Since the transformation properties of the tensor A are different from those of a,one expects the Raman selection rules for a molecule near a metal surface to be different, in general, from those operating under vacuum. This difference should not be confused with either that which comes about as a result of image charge considerations or those which arise from the lowering of the symmetry of an adsorbed molecule resulting from the formation of a chemical bond with one or several of the metallic surface atoms. The field gradient effect could manifest itself even when the surface-molecule interaction is very weak. We will now consider the new selection rules for Raman scattering which arise from both the a and the A terms in eq 1. Two situations will be considered. The first is for scattering by the ad-molecule alone, the second for scattering by the ad-molecule together with its conjugate-charge image in the metal. The latter is the situation generally thought to obtain for adsorbed molecule^,^ although there is evidence that in the case of surface-enhanced Raman scattering the former describes the situation better.8 The tensor A transforms like the product of three translations and therefore has the same transformation properties as the tensor /3 which gives rise to second-order, nonlinear effects such as hyper-Raman scattering. (One should state clearly at this point that the tensor A does not produce the hyper-Raman effect but simply transforms like the tensor which does.) The symmetry properties of the tensor /3 were discussed by Cyvin et aLe Let us illustrate the above comments with an example. Consider the point group D& such as that of benzene. Table I shows that normally vibrations spanned by alg, elq, and e2 are Raman active while all others are Raman silent. $hen strong Raman scattering occurs through tensor A as well as through a,one would see in addition to the above vibrations those of symmetry a%, bl,, b2,, el,, and e2, which include the infrared-active modes (of symmetry a2, and el,) as well as modes which are both infrared and Raman i n a ~ t i v e .If ~ one were unaware of the fact that the field gradient term were operative one might interpret the ap(7)H.A. Pearce and N. Sheppard, Surf. Sci., 69, 205 (1976). (8)M.Moskovita and D. P. DiLella, Chem. Phys. Lett., 73,500(1980). (9)S.J. Cyvin, J. E. Rauch, and J. C. Decius, J. Chem. Phys., 43,4083 (1965).
Letters
The Journal of Physical Chemistry, Vol. 85, No. 6, 1981
pearance of these otherwise unobserved modes in the surface Raman spectrum of benzene as arising from the lowering of the symmetry of the molecule due to bonding to a metallic site of a particular geometry. So for instance the collection of irreducible representations of D6h which are Raman active when both a and A contribute to the Raman signal resemble closely the set of representations which are Raman active through a alone (i.e., a1 and e) in the point group CSu(Ud) when the proper correlation is performed (see Table I). A recent SERS experiment involving benzene on silver in fact shows this behavior.1° In that study it was noted that the frequencies of the surface benzene molecule were shifted only a few wavenumbers, indicating a weak interaction, while at the same time seven vibrations which are normally not Raman active appeared with intensities about equal to those which are normally active. Moreover with the exception of vibrations belonging to bl,, which were not observed, only those which were spanned by both a and A appeared, Le., vibrations belonging to azgand bz remained silent. If one assumes that t i e scattering system is comprised of both the molecule and its conjugate-charge image, one must determine which elements of the tensors a and A remain “active”. This has been worked out for a by Albrecht and Hexterl’ who showed that on taking a surface-fixed coordinate system XYZ where Z is the surface normal, only axx,a y y , azz, and axy remain active upon inclusion of image charges. This result may be obtained directly if one observes that under charge conjugation Z goes to Z while (X,Y) (-X,-Y); hence in a composite tensor made up of the sum of the molecular tensor and its conjugate-charge image only those elements will survive which do not change sign upon making the transformation (X,Y,Z) (-X,-Y,Z). So for the vector 1.1 which transforms as (X,Y,Z) only pz remains active. For the tensor a,22,X2, y2 and XY do not change sign upon making the above transformations while XZ and YZ do; the latter two are therefore “surface inactive”. Similarly for the tensors B and A which transform as a product of three translations, Azzz, AYYZ, and Axyz are “surface active” since Z3, VZ, P Z , and X Y Z do not change sign upon making the “image charge transformation”, while A y y y , Axxx, Axxy, Axyy, AYzz,and Axzz produce “surface-inactive’’vibrations. The vibrations of a D6h molecule expected to be “surface-Raman active” when both a and A contribute to the intensity are limited to those spanned by alg, eZg,aZu,and eZuas shown in Table I. (In general for tensors which transform as odd order products of displacements (e.g., those which produce IR, hyper-Raman, etc.), those elements which transform as a” in the point group C, will be “surface active” when image charges are taken into account while for those tensors which transform as even products of displacements (e.g., ordinary Raman) only the elements
-
-
(10)M. Moskovits and D. P. DiLella, J.Chern. Phys., 73,6068(1980). (11) R.M. Hexter and M. G. Albrecht, Spectrochim. Acta, Part A, 35, 233 (1979);H.Nichols and R. M. Hexter, J. Chem. Phys., in press.
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which transform as a’ in C, will be “surface active”.) Infrared and Specular EELS. Ordinary infrared absorption occurs through modes of vibration which produce a change in the molecular dipole moment. Quadrupolar absorption is normally weaker by a factor of the order of a M / X . The induced quadrupole moment of a molecule is given by3 ea@ = + Ca@76(dE7/d6) (3) where, as before, {a,&y,6]stand for any of {x,y,z]. Near the metal surface where the electric field gradient is about (h/aM)times larger than usual those modes which under normal circumstances are merely quadrupole-momentallowed absorptions will appear with comparable intensity to dipole-allowedtransitions. Since Baa transforms as the product of two translations, some modes which are normally only Raman active will become infrared active and, to the extent that specular EELS mimics infrared, EELS active as well. For a D6h molecule, for instance, Table I shows that modes of symmetry alg,elg,and eZgmay appear. If, in addition, one demands that the selection rule be modified to include image-charge effects, then the surface-IR-active modes will be restricted to those marked with an asterisk in Table I. Of course the field gradient effect may not be as important in the infrared due to the aforementioned decrease in the magnitude of the field gradient at low photon energies. Vibrations of symmetry alg of benzene on platinum have been reported.12 These have been interpreted, however, as arising from the decrease of the site svmmetrv of benzene on the surface from D6h to c 3 u (gd). Finally one should point out that the above discussion, based as-it is on eq 1,is necessarily only an approximation. Equation 1 is based on a multipolar expansion which assumes that the fields vary slowly across the collection of charges (the molecule). This is clearly not the case here. A more correct approach would solve for the dynamics of a collection of charges (the adsorbed molecule) held together by springs of known force constants moving under the influence of the time-varying, self-consistent electric field resulting from the incident electromagneticfield, and the local fields due to the metal surface and the molecule itself. The resulting nuclear motion would be expanded in a basis of the normal coordinates of the molecule with the magnitude of the coefficients indicating which modes are “dowed”. Clearly this is a very difficult problem. The simpler approach which constitutes the substance of this note should, nevertheless, provide an indication at least of the symmetries involved.
Acknowledgment. M.M. thanks the Natural Sciences and Engineering Research Council of Canada and Imperial Oil for support. The hospitality of Professor Gerischer while visiting the Fritz Haber Institute is also gratefully noted. J.K.S. thanks the D.F.G. for support. (12)S.Lehwald, H. Ibach, and J. E. Demuth, Surf. Sci., 78,577(1978).
