J . Phys. Chem. 1987, 91, 5558-5568
5558
FEATURE ARTICLE Adsorption of Rare-Gas Atoms on Microsurfaces of Large Aromatlc Molecules Samuel Leutwyler* Institut fur Anorganische, Analytische and Physikalische Chemie, Universitat Bern, CH-3012 Bern, Switzerland
and Joshua Jortner* School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel (Received: September 4, 1986; In Final Form: June I I , 1987)
The binding of rare-gas (R) atoms to large aromatic molecules (M) on the one hand and to the basal plane of graphite on the other hand represents two extremes of the interaction of rare-gas atoms with ordered arrays of sp2 hybridized carbon atoms. In this paper we discuss the analogies between the characteristics of large van der Waals M-R, complexes and R atoms on graphite surfaces, focusing on structure, packing, orientational registry effects, and the nuclear motion of R adsorbates on finite microsurfaces. The elucidation of the structure, energetics, and nuclear dynamics of large M-R, complexes rests on semiempirical model calculations of potential surfaces. These provide a quantitative account of the geometry, the existence of isomers, the dissociation energies, and the frequencies of out-of-plane and in-plane vibrational modes for large-amplitude intermolecular nuclear motion.
I. Prologue Large van der Waals (vdW) complexes, consisting of an organic aromatic molecule (M) bound to rare-gas (R) are expected to provide basic information on the structural, energetic, and dynamic manifestations of intermolecular interactions in well-characterized, large, chemical systems. As often happens in the area of modern chemical physics, the impetus for the elucidation of the characteristics of these interesting systems was
(1) Amirav, A.; Even, U.; Jortner, J. Chem. Phys. Lett. 1979, 67, 9. (2) Amirav, A.; Even, U.; Jortner, J. J . Chem. Phys. 1981, 75, 2489. (3) Amirav, A.; Even, U.; Jortner, J. J . Phys. Chem. 1981,85, 309. (4) Amirav, A.; Even, U.; Jortner, J. J . Chem. Phys. 1982,67, 1. (5) Leutwyler, S.; Even, U.; Jortner, J. Chem. Phys. Lett. 1982,815,439. (6) Leutwyler, S.;Even, U.; Jortner, J. J . Chem. Phys. 1983, 79, 5769. (7) Ondrechen, M. J.; Berkovitch-Yellin, Z.; Jortner, J. J . Am. Chem. SOC. 1981,103,6586. (8) Even, U.; Amirav, A.; Leutwyler, S.; Ondrechen, M. J.; BerkovitchYellin, Z.; Jortner, J. Faraday Discuss. Chem. SOC.1982, 73, 153. (9) Levy, D. H. Adv. Chem. Phys. Wiley Interscience: New York, 1981; Vol. 47, p 323. (IO) Hays, T. R.; Henke, W.; Selzle, H. L.; Schlag, E. W. Chem. Phys. Lett. 1980, 77, 19. (11) Henke, W. E.;Yu, W.; Selzle, H. L.; Schlag, E. W.; Wutz, D.; Lin, S.H. Chem. Phys. 1985, 92, 187. (12) Raitt, I.; Griffiths, A. M.; Freedman, P. A . Chem. Phys. Lett. 1981, 80,225. (13) Griffiths, A. M.; Freedman, P. A. Chem. Phys. 1981,63, 469. (14) Amirav, A.; Jortner, J. Chem. Phys. 1984,85, 19. (1 5) Amirav, A.; Sonnenschein, M.; Jortner, J. Chem. Phys. 1984,88,199. (16) Leutwyler, S . ; Schmelzer, A.; Meyer, R. J . Chem. Phys. 1983, 79, 4385. (17) Leutwyler, S . J. Chem. Phys. 1984,81, 5480. (18) Leutwyler, S. Chem. Phys. Lett. 1984, 107, 284. (19) Kettley, J. C.; Palmer, T. F.; Simons, J. P. Chem. Phys. Lett. 1985, 115, 40. (20) Doxtader, M. M.; Gulis, I. M.; Schwarz, S . A,; Topp, M. R. Chem. Phys. Lett. 1984, 112, 483. (21) Jortner, J.; Even, U.;Leutwyler, S . ; Berkovitch-Yellin, Z. J . Chem. Phys. 1981, 78, 309. (22) Even, U.;Jortner, J.; Berkovitch-Yellin, Z. Can. J . Chem. 1985,63, 2073.
0022-3654/87/2091-5558$01 SO10
initiated by progress in novel experimental methods. The advent of the modern techniques of spectroscopy in seeded supersonic made possible the exploration of the s t r u c t ~ r e , ~the "~~ e n e r g e t i ~ s , ~ , ~ the - * J ~excited-state electronic-vibrational level and the intramolecular dynamic^'-^*^*'^ of large vdW molecules. These studies provided new ways and means for the elucidation of solvent effects. Large vdW MR, complexes can be viewed as a guest molecule embedded in a well-characterized local solvent configuration.2 Studies of excited-state energetics and dynamics of such large vdW complexes establish the interrelationship between the level structure, the nuclear motion, and the relaxation paths of an isolated molecule and of a solventperturbed molecule, providing basic information on solvent perturbations, as explored from the microscopic point of view. A significant alternative description of large vdW complexes pertains to the characteristics of microsurfaces. These large complexes can be viewed as rare-gas atoms adsorbed on a finite "microsurface" of graphite. Attempts to elucidate the details of gas-surface interactions and the physisorption process have resulted in considerable experimental and theoretical effort directed toward the study of rare gases on the basal plane of g r a ~ h i t e . ~ ~ , ~ ' These studies deal with semiinfinite surfaces of graphite. The binding of raregas atoms to a large aromatic molecule will provide information concerning adsorption on a finite surface. To pursue further the analogies between the characteristics of large vdW (23) Levy, D. H. Annu. Rev. Phys. Chem. 1980,31, 197. (24) Beck, S. M.; Liverman, M. G.; Monts, D. L.; Smalley, R. J. J . Chem. Phys. 1979, 70, 232. (25) Smalley, R. E.;Wharton, L.; Levy, D. H.; Chandler, D. W. J . Chem. Phys. 1978,68,2487. (26) Kukolich, S. G.; Shea, J. A. J . Chem. Phys. 1982,77, 5242. (27) Fung, K. H.; Selzle, H. L.; Schlag, E. W. Z . Naturforsch. 1981,A36, 1338. (28) Haynam, C.A.; Brumbaugh, D. V.; Levy, D. H. J . Chem. Phys. 1983, 79, 1581. (29) Meerts, W.L.; Majewski, W. A. In Laser Spectroscopy; Weber, H. P., Luethy, W., Eds.; Springer: Berlin, 1983; Vol. 6,p 14. (30) S t e l e , W. A. The Interaction of Gases with Solid Surfaces; Pergamon: Oxford, 1974. (31) Bruch, L. W. Surf. Sci. 1983, 125, 194.
0 1987 American Chemical Society
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The Journal of Physical Chemistry, Vol. 91. No. 22, 1987 5559
complexes and adsorption on graphite surfaces, the following features are pertinent: 1. Packing of rare-gas adsorbents on microsurfaces. 2. Registry effect^,^^"^ originating in well-defined orientations of R 2 (and R,) species on the microsurface, which result from structural commensurability between the adsorbent vdW molecule and the finite substrate. 3. Nuclear motion of rare-gas adsorbate^^^ on microsurfaces emerging from the analysis of intermolecular M-R vibrations. 4. Order-disorder transitions and the melting34in finite twodimensional systems. In this article we shall dwell on some surface analogies of large vdW complexes, focusing on the structure, energetics, and nuclear motion on these finite microsurfaces. These studies will be helpful in bridging the gap between molecular and surface chemical physics. 11. Adsorbent-Molecular-Microsurface Interactions
The understanding of the structure, energetics, and dynamics of nuclear motion and intramolecular dynamics of large vdW complexes requires a different conceptual framework than that applied, so successfully, to small vdW molecules.36 In the latter case, very detailed spectroscopic information on realistic potential surfaces can be obtained, serving as central input data for the description of the energy levels and relaxation phenomena. This approach is prohibitively difficult for large vdW complexes in view of the huge dimensionality of the potential surface. The elucidation of the features of large vdW complexes rests on semiempirical model calculations of the potential surface^.^^^^'^ The potential energy surfaces for the nuclear motion of rare-gas atoms in M R complexes were modeled on the basis of the pairwise two-body interaction model,’989169’7921-22 which rests on the following assumptions: (1) a vibrationless intramolecular state of M in MR, is considered; (2) the nuclear motion of M within the MR, molecule is considered to be frozen; (3) the M-R and R-R pair interactions were considered; (4) the M-R interaction potential was represented in terms of pairwise atom-atom interactions between each C and H atom in the aromatic molecule and the rare-gas atom; ( 5 ) the atom-atom interactions are expressed in terms of a 6-12 Lennard-Jones potential. The potential energy for the MR, molecule is
(11.1)
V$2$ is the pairwise interaction between R, located at FI, and a C atom located at Fa in M, while V$’k is the atomatom interaction between R and an H atom located at Fs 62&(rIa)
= 4cRC[(aRC/rIa)’2
-
vk2k(rIb’)
= 4cRH((uRH/rIg)’2
- (‘RH/rIg)6)
(‘JRC/rIa)61
(11.2)
(II.3)
where rla = IFI - Fal and rIg = IFI - Fgl. The potential parameters cRC and u R C were taken from the physisorption of R atoms on graphite,37while t R H and uRH were derived7 from the combination is the pairwise potential between rare-gas atoms.7 rules. G2jR The following comments are in order regarding the simplifications inherent in the derivation of the pairwise two-body potential energy surface. Firstly, the consideration of a vibrationless state of M in MR, implies weak coupling between the intramolecular high-frequency M vibrational modes and the low-frequency intermolecular vdW M-R modes. Secondly, the rigid substrate approximation is similar to that utilized for semiinfinite graphite crystals plated with rare-gas atoms.33 Thirdly, the effect of (32) Ellis, T. H.; Scoles, G.; Valbusa, U. Chem. Phys. Lett. 1983, 94, 247. (33) Cardini, S.; OShea, S. F. Phys. Rev. 1984, 8 3 0 , 7177. (34) Dash, J. G. Phys. Rep. 1978, 38, 177. (35) Van der Waals Molecules”; Faraday Discuss. Chem. SOC.1982, 73. (36) Klemperer, W. Ber. Bunsen-Ges. Phys. Chem. 1974, 78, 127. (37) Crowell, A. D., Steele, R. B. J. Chem. Phys. 1961, 34, 1347. (38) Sage, M.; Jortner, J. J . Chem. Phys. 1985, 82, 5437.
three-body contributions to the total potential energy should be ~0nsidered.l~ These higher order terms, which may be significant for MR, (n 3 2) complexes, fall into the following categories: ( a ) M-M-R Terms. These have already been incorporated in the effective two-body potential. ( b ) R-M-R Terms. This contribution can be evaluated in an analogy to the three-body terms, which arise in the physisorption interaction of rare-gas atoms with the basal plane of graphite.3e42 calculation^^^^^^ of the three-body contribution AG3LG to the pair interaction potential between a pair of adatoms on graphite resulted in the following values for the decrease of the well depth relative to the pair potential of the R-R bare pair: A@AG/@2t\ = 21% for Ne-Ne, 13% for Ar-Ar, 12% for Kr-Kr, and 13% for Xe-Xe. An analysis of the experimental data43of rare-gas adsorption on graphite surfaces has resulted in the decrease of the pair binding energy by 10% for Ar-Ar and by 6.5% for Kr-Kr, due to surface interactions, which is in fair agreement with theory. These three-body R-M-R contributions amount to 1%-2% of the total binding energy of the MR2 vdW m01ecule.I~ (c) R-R-R Terms. For M-R, ( n 3 3) vdW complexes, with more than two atoms being located on the same side of M, a three-body contribution from the R-R-R triple dipole energy has to be incorporated. Three-body interactions in small rare-gas clusters have been evaluated44by using terms up to the fourth order. For R3 the ratio of the three-body interaction to the N 0.01, being repulsive as two-body interaction is V$3?R-R/@?R in bulk rare gases. This contribution does not exceed 0.1% of the total energy of MR, (n = 3-10) complexes and can safely be neglected. From the foregoing discussion, we infer that three-body contributions may be of importance for the determination of the relative stability of MR, (n 3 2) complexes. The dominating contribution to the higher order terms originates from the R-M-R terms, which have to be taken into account in the assessment of the relative stability of energetically close-lying isomers.17 111. Potential Energy Surfaces
The intermolecular potential energy surfaces, which characterize the nuclear motion of rare-gas atoms in M-R, complexes are expected to provide two classes of information: (1) chemical data concerning binding energies, structure, and the existence and nature of isomers; (2) spectroscopic data, which pertain to the intermolecular vibrations of the rare-gas atoms with respect to the large aromatic molecule. It is practical to consider the details of the potential surfaces only for moderately small M-R, (n < 3) complexes, as for larger (n 3 3) systems the proliferation of coordinates renders the representation rather cumbersome. For these larger systems, the chemical and spectroscopic information should be extracted from molecular dynamics calculations which, to the best of our knowledge, have not yet been performed on those large complexes. ZZZ.A. M - R Complexes. A comprehensive representation of the potential energy surfaces involves the dependence of the M-R interaction on the in-plane (x,y) coordinates at fixed z, which are where zOpt is the conveniently represented in the form V(x,y,.zopt), optimal averaged equilibrium distance, z,,, of the rare-gas atom from the microsurface (Figure 1). The variation of z,,, across the relevant parts of the M molecular plane is small, being typically f0.02 8,in the relevant range of x and y . Potential surfaces for the Ar complexes of the catacondensed aromatic hydrocarbons (Figures 2 and 3) reveal the following characteristics: 1. The motion parallel to the short molecular axis (y) is characterized by a single minimum for all polyacenes. 2. The potential parallel to the long molecular axis ( x ) is characterized by several minima or inflection points, whose number is equal to the number of aromatic rings. (39) Sinanoglu, 0. Pitzer, K. S . J. Chem. Phys. 1960, 32, 1279. (40) MacLachlan, A. D. Mol. Phys. 1964, 7 , 381. (41) Freeman, D. L. J . Chem. Phys. 1975, 62, 4300. (42) Rauber, S.; Klein, J. R.; Cole, M. W. Phys. Reu. 1983, 827, 1314. (43) Everett, D. H. Discuss. Faraday SOC.1965, 40, 177. (44) Etters, R. D.; Danilowicz, R. J . Chem. Phys. 1979, 71, 4767.
Leutwyler and Jortner
5560 The Journal of Physical Chemistry, Vol. 91 No. 22, I987 ~
PERVLENE -ARGON
TETRACENE -ARGON
[AI
y
3 0
3 0
2 0
2 8
I 0
I 0
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PERVLENE -XENON y
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6
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Figure 1. Contour maps of the peryleneAr and perylene-Xe intermolecular potential energy surfaces. The distances from the R atom to the perylene molecular plane are fixed at the optimized distances zOpt= 3.42 A (R = Ar) and z = 3.70 (R = Xe). The innermost contours are at -1.66 kcal/mol (Ar) and -2.50 kcal/mol (Xe), while the contour spacings are 0.04 kcal/mol (Ar) and 0.05 kcal/mol (Xe). Superimposed on the same figure are the geometrical positions of the R atoms at the minimum energy configuration of the P.R2 (2 0) vdW complexes.
+
3. The potential energy for the out-of-plane motion is conformal and exhibits the form close to the Lennard-Jones atom-surface 4-10 potential. The potential energy curve along the z axis is universal having a similar shape for all hydrocarbons, as is evident for the corresponding potential curves for pery1ene.R (R = Ne, Ar, Kr, and Xe), which are portrayed in Figure 3. The existence of multiple stable binding configurations in these systems gives rise to a number of interesting features: ( a ) Van der Waals Cortformers in h4.R Complexes. The pentaceneSR complexes provide the first example of the van der Waals (vdW) conformers for a binary complex. Because of the shallowness of the multiple minima in the potential energy surfaces, the existence of vdW conformers cannot be determined by inspection of the surface but hinges on the probability distributions of the associated intermolecular vibrations. The intermolecular
-1 B
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Figure 2. (a, top) Contour map of the tetracene-Ar intermolecular potential energy surface. The perpendicular distance of the Ar atom to the tetracene molecular plane is z = 3.42 A. The innermost contour is at V = -1.54 kcal/mol and the contour spacing is 0.04 kcal/mol. (b, bottom) Contour map of the pentaceneAr intermolecular potential energy surface. The perpendicular distance of the Ar atom from the pentacene molecular plane is z = 3.44 A. The innermost contour is at V = -1.53 kcal/mol and the contour spacing is 0.03 kcal/mol.
vibrational calculations show t h a t for pentacene-R (R = A r , Kr,
and Xe) the side minima support three to four localized vibrational eigenfunctions,16 giving rise to a second experimentally distinguished vdW isomer at finite temperatures. ( b ) Tunneling Motions between Symmetrically Equivalent Binding Sites. For those complexes which exhibit double minimum potentials, Le., naphthalene-R and tetraceneeR and larger polyacene complexes, such as pentacene-R, tunnel splitting will be exhibited as a consequence of the indistinguishability of the two equivalent binding sites (see sections V.F, G.). The case of pentaceneeR (Figure 2) demonstrates that tunneling behavior also occurs for a triple-minimum system containing two symmetrically equivalent minima. ( c ) The Dependence of Binding Configuration on R. For complexes with extremely shallow double minima, the structure
2
3
4
z
5
6
6,
Figure 3. Calculated intermolecular potential energy curves V ( z ) for perylene-R (R = Ne, Ar, Kr, and Xe) vdW complexes along the outof-plane z coordinate at the perylene center of symmetry ( x = y = 0.0
.hi). of the complex depends on the size of R or, alternatively, on the corrugation of the molecular microsurface. Typical examples of this effect are provided by the pyrene-R complexes (Figure 4). While the potential energy surfaces for R = Ne and Ar exhibit double minima leading to a C, symmetry binding configuration,
Feature Article
The Journal of Physical Chemistry, Vol. 91, No. 22, 1987 5561 PYRENE * Ne
(zoDt=3.11 A 1
TETRACENE,R2 l R = Ar.Kr.Xe)
Y
3 3 8
2 2 0
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Figure 4. Contour maps of the intermolecularpotential energy surfaces for the pyreneR (R = Ne, Xe) vdW complexes. The optimized average distances from the molecular plane are zOpt= 3.1 1 A (Ne), zOpt= 3.74 A (Xe). The innermost contours are at V = -0.72 kcal/mol (Ne) and at V = -2.5 kcal/mol (Xe), with spacings of 0.02 kcal/mol (Ne) and 0.05
-3 -L
. .
kcal/mol (Xe). Note the gradual transition from a double-minimum potential (Ne) to a single-minimum potential (Xe) with increasing size of R.
Figure 5. Contour maps for the tetraceneSR, (R = Ar, Kr, and Xe) total binding energies. The ( x y ) coordinates indicate the location of the center of mass of the R-R dimer, which is oriented parallel to the x axis, with a constant R-R distance corresponding to the gas-phase equilibrium bond distance (Ar-Ar; 3.76 A, Kr-Kr: 4.01 A, Xe-Xe: 4.36 A). The distance of the R-R dimer to the tetracene molecular plane is also held fixed.
the "collapse" to a single minimum for R = Kr and Xe indicates a transition to C2, geometry of the large M-R complex. While the features of the potential surfaces of linear catacondensed hydrocarbons reflect the topology of the aromatic microsurface, the situation is different for pericondensed aromatic hydrocarbons. Typical examples for such d system are given in Figure 1 for the potential surfaces of perylene-Ar and perylenemxe complexes. The potential energy surfaces exhibit a single strong binding site per side of the perylene molecule and do not reflect the geometrical structure of the perylene substrate. The potential energy surfaces of the pericondensed aromatic hydrocarbons (perylene, benzperylene, and coronene) are qualitatively similar to each other and also to that of benzene, exhibiting a single stable binding site above the center of the molecular plane. The binding topologies of rare gases to aromatic molecules may be classified as follows: Type I, a single binding site per side (e.g., benzene-R, perylene-R, coronene-R, and anthracene-R). Type 11, multiple binding sites per side. These fall into two subsets: II.A, two equivalent binding sites per side (e.g., naphthalene-R, tetracene-R, pyrene.R, and ovalene-R); ILB, two inequivalent binding sites per side (pentacene-R). Pericondensed aromatic hydrocarbons generally give M-R complexes of type II.A/b. III.B. M-R2 Complexes. We now proceed to discuss the potential energy surfaces, structure, and isomerism for van der Waals (vdW) complexes containing two rare-gas atoms. For M.R2 complexes there are two distinct spatial arrangements, which in the following will be termed isomers; the (2 + 0) geometry where both rare-gas atoms are bound to the same side of the aromatic
molecule, and the (1 1) geometry with the rare-gas atoms on opposite sides of the molecular plane. The potential energy hypersurfaces for M.R2 complexes are functions of six independent coordinates and one must resort to simplified representations. The (1 + 1) vdW complexes may be discussed to a very good approximation in terms of the (1 0) surfaces. For the (2 0) isomers, a suitable representation involves (a) holding the R-R distance constant at the gas-phase equilibrium distance, and (b) a fixed relative orientation of M and R2. Figure 5 shows the potential energy surfaces for tetracene-R2 (2 + 0) complexes with R = Ar, Kr, and Xe. The R2 distances are fixed at 3.76 8, (Ar,), 4.01 8, (Kr2), and 4.36 8, (Xe,), while the R-R axis is held parallel to the tetracene long axis ( x axis). The following interesting features should be noted: (a) For tetracene~Ar,,the ar2 subunit is located symmetrically above the tetracene molecular plane. (b) For the heavier tetracene-R2 complexes, double-minimum potentials are found, which are extremely shallow for R = Kr and pronounced for R = Xe. This size dependence of the vdW complex structure is inverse to that noted above for M.R complexes of naphthalene and pyrene. (c) The elongated, nearly flat, potential energy minima give rise to in-plane long-axis vibrations of R2relative to tetracene with extremely low frequencies and huge vibrational amplitudes; for R, = Ar and R2 = Kr2, the rms vibrational amplitudes are 1.4 respectively. and 2.8 (d) The tetracene-Xe, complex is expected to be asymmetric and will be localized on the typical experimental time scale. The
+
+
1,
+
5562 The Journal of Physical Chemistry, Vol. 91, No. 22, 1987 200
_-
600
-
7
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Leutwyler and Jortner
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1 / (number of C atoms1 Figure 6. Calculated dissociation energies D, [cm-’1 for a series of M.R vdW complexes (R = Ne, Ar, Kr, and Xe) as a function of the inverse number of C atoms in M.
localization of the Xe2 subunit may be understood in terms of registry effects, as they are known for R (R = Kr and Xe) graphite interaction. The Xe2 dimer is commensurate with the biphenyl subunit in the graphite hexagonal lattice, leading to a well-defined orientation for an Xe atomic monolayer adsorbed on graphite ( 4 3 X 43)R30°,45-46the driving force for this orientation being the surface corrugation of graphite. The same microscopic effect also leads to the stabilization of the asymmetric conformation of tetracene.Xe2.
IV. Ground-State Structure and Energetics I V A Geometry. The potential energy surfaces provide direct information concerning the equilibrium geometry of M-R, complexes. Some pertinent information is assembled in Table 111. These structural data reveal that (1) the equilibrium in-plane coordinates x,, and y,,, depend, of course, on the nature of the aromatic substrate; (2) the equilibrium distance, z,,,, of the rare-gas atom from the substrate is practically independent of the nature of the aromatic molecule. These universal distances are z,,, = 3.10 f 0.02 8, for Ne, z,,, = 3.44 f 0.04 8, for Ar, z,,, = 3.52 f 0.04 8,for Kr, and z,, = 3.75 f 0.05 A for Xe, where the variance reflects the spread of the calculated data for different substrates. These calculations predict the universality of the paranel R-microsurface distance. Experimental data on the equilibriumgeometry of some M-R complexes (with R = He and Ar) were obtained from the analysis of the rotational contour of the electronic origin of the So SI transition or by microwave spectroscopy: b e n ~ e n e . H e s-tetra,~~ ~ i n e . H e ,furane.Ar,26 ~~ ben~ene-Ar,~’ and f l ~ o r e n e . A r . ~The ~ existence of the “universal” parallel M-Ar distance seems to be borne out by the experimental data. The agreement between the calculated and experimental structure is excellent (Table I). The M-Ar distance normal to the molecular plane extrapolates smoothly from z,,, = 3.49 A for benzene to z,, = 3.37 A30 in graphite. W . B . Dissociation Energies. The binding energies, Do, of rare-gas atoms to aromatic molecules, which correspond to the heat of adsorption on a microsurface, are relatively large, being in the range of 300-1000 cm-’ for a single Ne, Ar, Kr, or Xe atom.
-
(45) Venables, J. A,; Kramer, H. M.; Price, G. L. Surf Sci. 1976,55,373. (46) Schabes-Retchkiman, P. S.; Venables, J. A. Surf:Sei. 1981,105,536. (47) Meyer, R. J. Mol. Spectrosc. 1979, 76, 266. (48) Carlos, W. E.; Cole, M. W. Surf.Sci. 1980, 91, 339.
TABLE I: Eouilibrium Coordinates‘ ~~
~
~~
R benzeneb tetraceneC pentacened fluoreneeJ Ne (0, 0, 3.11) (1.0,0, 3.08) (0, 0, 3.11) (0, -0.30, 3.15) Ar (0, 0, 3.47) (1.10, 0, 3.42) (0, 0, 3.44) (0, -0.40, 3.47) [O,0, 3.44 0.2019 [O,-0.47 f 0.1 1, 3.44 O.l]* Kr (0, 0, 3.56) (1.10, 0, 3.50) (0, 0, 3.52) (0, -0.55, 3.55) Xe (0, 0, 3.78) (1.00, 0, 3.72) (0, -0.65, 3.75)
*
*
Numbers in parentheses represent the results of model calculations, while numbers in square brackets correspond to experimental results. The numbers represent X,,,,Y,,, Z,,, (in A) for M-R complexes. bReference 21. CReferences 7 and 8. dReferences 8 and 16. CBerkovitch-Yellin,2.; Jortner, J.; Leutwyler, S.,to be published. fOrigin of coordinate system at center of mass. $Reference 27. *Reference 29.
The dissociation energy, which has to be corrected for the zeropoint vibrational contribution, is given by (1V.I) where De is the energy of the minimum of the potential surface and (w,] are the intermolecular M-R vibrational frequencies (see section V). Typical zero-point energy corrections for the M-R complexes are 30-40 cm-I. An overview of the dissociation energies is provided in Figure 6 . Pertinent experimental information regarding these binding energies was obtained from the following sources: 1. Resonant two-photon ionization of a M R I complex, proceeding via an intermediate excitation of an intramolecular vibration in s,,will result in the M+ ion when the vibrational predissociation (VP) channel is open to the intermediate state while, when the VP channel is closed, extensive production of the MR1+ ion is expected.6*8 2. The lack of VP from an electronic-vibrational excitation of a MR, vdW complex, as interrogated by energy-resolved emission, indicates that the reactive channel is presumably c l o ~ e d . ~ ~ ~ (3) The heavy-atom effect on the decay lifetime of the SI state of vdW complexes was adopted2,*to search for the onset of VP, establishing both a lower and an upper limit for Do. The experimental findings for the dissociation energies in the S1 electronically excited state are summarized in Table 11. The ground-state dissociation energy Do(So) D can be inferred by correcting the excited-state stabilization energy, whereupon
D(S0) = D ( S l ) - ldPl
(IV.2)
The Journal of Physical Chemistry, Vol. 91, No. 22, 1987 5563
Feature Article
TABLE II:
Experimental Estimates of Do [cm-'1
exptl tetracene.Ar" tetracene.Krb fluoreneNeC fluorene.ArC fluorene.Krc fluorene.XeC
styrene.Ard carbazoleAr' carbazoleKrf
>314 5 1200 1230 510 & 95 1717 2733 5420 571 & 6 764 & 28
2273 51140 2230 470 f 95 1657 2620 5395 525 & 6 696 f 28
502 520 250 501 597 756 366 454 629
I
0
'References 2 and 8. bReferences 2 and 8. 'Reference 6. dRademann, D.; Jortner, J., unpublished results. eBoesiger, J.; Leutwyler, S., to be published. fBoesiger, J.; Leutwyler, S. Chem. Phys. Lett. 1986, 226, 238.
-
where 6~ is the microscopic spectral shift2*8J8of the So SI origin of the complex relative to that of the bare molecule. The agreement between the results of the model calculation and the experimental estimates is satisfactory within the large uncertainty range of the latter. Interesting information regarding the dependence of the binding energies on the size of the microsurface is obtained from Figure 6, where we plot D vs. the inverse number of carbon atoms in M. The catacondensed series of aromatic hydrocarbons from benzene and naphthalene to pentacene give binding energies which lie on a straight line in this diagram and extrapolate to a hypothetical infinite chain hydrocarbon (upper dashed lines). The pericondensed substrate molecules yield a second series of binding energies, starting with anthracene via perylene and coronene and extrapolating to graphite.
V. Intermolecular Vibrations of Large Complexes The nuclear motion of large M.R, complexes reveals two major classes of vibrational modes: (1) intramolecular vibrational modes of the large molecule; (2) intermolecular vibrational modes, involving the motion of the ligands relative to the large molecule and relative to each other. Regarding class 1, the intramolecular vibrational frequencies may be slightly modified in the complex due to the static and dynamic interaction with the rare-gas atoms. Of considerable intrinsic interest are the intermolecular vibrational modes of the complex because of two reasons. First, these vibrations constitute the precursors of local phonon modes of an impurity in a condensed phase. Second, these vibrational modes in a M.R, complex with a small coordination number, which correspond to the motion of rare-gas atom(s) relative to an aromatic finite surface, provide an analogue of surface vibrational modes of rare gases on graphite. A reasonable starting point for the understanding of vibrational motion in large complexes rests on the notion of the separation of time scales for intermolecular and intramolecular motion.38 V.A. Classification. Upon complexation of an aromatic molecule M by a monoatomic solvent atom R, the three translational degrees of freedom of R go over into three intermolecular vibrational degrees of freedom of the vdW complex. Due to the special geometry presented by the microsurface of M, the intermolecular vibrations separate in a natural way into an "outof-plane" and two "in-plane" vibrational coordinates oriented normal and parallel, respectively, to the molecular microsurface. For a large set of M-R complexes, the three orthogonal molecule-fixed coordinates x , y , and z form a set of symmetry coordinates suitable for the description of the intermolecular vibrational motion. The z symmetry coordinate (out-of-plane) is the only coordinate of symmetry type a, for those M-R complexes with relatively high point-group symmetries (C,,, C3u,and C6u),.Accordingly, it represents the totally symmetric intermolecular normal coordinate for these cases. Also, in many complexes of C, symmetry, the z symmetry coordinate is a close approximation to the out-of-plane-type normal coordinate. The x (long axis) and y (short axis) symmetry coordinates form a basis for the description of the in-plane intermolecular motions. These vibrations
-. I
00
--_ I
/
I
/
0 05
I
I
I
,
,
,
,
0 10
,
,
0 15
I
,
,
,
0 20
1 / inumber 01 C ntomsl
Figure 7. Calculated fundamental out-of-planevibrational frequencies
(cm-') [Figure 9a] and corresponding force constants fiz (Nm-I) [Figure 9b] of M.R complexes. (M = benzene, naphthalene, anthracene, perylene, coronene, and graphite). Note that vibrational frequencies generally decrease (Kr and Xe) or remain almost constant (Ar) with increasing number of carbon atoms in M. On the other hand, the force constants increase smoothly with increasing size of the substrate molecule. uZ
exhibit large rms amplitudes on the order of several angstroms and hence are associated with continuous rotation-like reorientation of the whole M.R complex in space due to angular momentum conservation.'6 In the calculation of the level structure of the intermolecular vibrations, we shall invoke the following assumptions: (a) the intramolecular and intermolecular vibrations are separable; (b) even for the cases for which intramolecular modes of low-frequency approach or overlap the intermolecular frequencies, it is still convenient to maintain the separation between intramolecular/intermolecularmodes and, subsequently, calculate the shifts and couplings by a perturbative treatment;38 (c) the aromatic host molecule M behaves as a rigid body with no internal degrees of freedom. The potential energy surfaces for M.R complexes were utilized to extract the vibrational energy levels for M-R motion. Two methods of calculations, using a one-dimensional linear oscillator approximation and one-dimensional or two-dimensional flexible model treatment, were e m p l ~ y e d . ' ~ ~ ~ ' V.B. The Out-of-Plane Vibration. For all aromatic substrates M, the intermolecular M-R V ( z ) potential energy curves are conformal and close to a Lennard-Jones 10-4 potential. Hence, the out-of-plane vibrational frequencies and frequency spacings of M-R complexes with the same solvent atom R are expected to be systematically related. The calculated and observed z-mode fundamental frequencies turn out to be only weakly dependent on form and size of the aromatic substrate for the series ranging from benzene to graphite, as given in Figure 7. The v, fundamental frequencies of the M-Ar complexes are seen to be practically independent of M, while the series of M-Kr and M-Xe vdW complexes even exhibit a counterintuitive decrease of u, with increasing size of the substrate molecule and increasing binding energy (Figure 7). These trends originate from a sensitive balance
5564
Leutwyler and Jortner
The Journal of Physical Chemistry, Vol. 91, No. 22, 1987
,
45
v
c * C C '-
15
-
b)
6 :
v1
J
G 0 -
23 7
7
23 771
23.843
23.914
23.986
24.057
24,129
24.2
qWc[1000 cm-' ] Figure 8. LIF excitation spectra of perylenesxe, (n = 1-3) vdW complexes, synthesized in a seeded (2% Xe/98% He) supersonic expansion at po = 1.4 bar and D = 0.5 mm. The strongest bands are due to the perylene molecular electronic origin (Ox) and 95 cm-I intramolecular excitations (95). The perylenexe vdW complex exhibits a prominent progression in the excited-state v i mode. Note the two vdW isomers of the peryleneXe2complex denoted by (1 + 1) and (2 + 0), which are present at roughly equal concentrations in the beam.
2
Figure 9. LIF excitation spectra of tetracenexe, (n = 1-3) vdW complexes synthesized in a seeded supersonic expansion (2% Xe/98% He) at po = 2.0 bar and D = 0.5 mm. The dominant feature at the high energy of the spectrum is the tetracene electronic origin (Ox). The T-Xe vdW complex
exhibits both out-of-plane ( v i ) and in-plane ( v i ) excitations. Similar features are also clearly observed for T.Xe2 and T.Xe3. Note the appearance of a small amount of the T.Xe2 (1 + 1) isomer just to the red of the T.Xe2 (2 + 0) origin. between the out-of-plane force constantsf, =(d2V/dz2),, (Figure 7) and the reduced masses c((M-R),both of which increase concurrently with increasing size of M. The u, vibration of a M-R vdW complex bears a close analogy to the perpendicular atomic vibrations of a rare-gas monolayer on the surface of graphite.33 These atomic vibrations of a monolayer, which are normal to the plane, are determined almost completely by the adatomsurface potential. The motion normal to the surface behaves like an Einstein mode for a solid, with almost no dispersion over the Brillouin zone.33 The characteristic Einstein frequency evaluated for the perpendicular motion of a monolayer of Xe on graphite is wE = 33 cm-1,33with an uncertainty of f 3 cm-I, depending on the potential parameters. This value of wE is close to the calculated out-of-plane frequencies of a Xe atom bound to aromatic molecules, which fall into the range v, = 30-35 cm-'. To the best of our knowledge, the lateral vibrations
of a rare-gas monolayer on graphite surfaces have not yet been documented experimentally. On the other hand, the intermolecular vibrational frequencies of M-R molecules are amenable to experimental observation, providing direct information on the nuclear motion of adatoms on microsurfaces. V.C. Experimental Observation of Out-ofplane Vibrational Excitations of M-R Complexes. Out-of-plane (z-mode) intermolecular vibrational transitions are often prominent in electronic spectra of M-R, complexes. Figures 8 and 9 show parts of the laser-induced fluorescence excitation spectra of perylene-Xe, ( n = 1-3) and tetracene-Xe, ( n = 1-3) vdW complexes. These complexes were synthesized and cooled in supersonic expansions with a 2% Xe/98% He mixture at POD= 80 Torr cm, where Po is the stagnation pressure and D is the nozzle diameter. The spectra are dominated by the electronic origins of the S, So excitation of the bare aromatic molecule marked by 0; in Figures
-
The Journal of Physical Chemistry, Vol. 91, No. 22, 1987 5565
Feature Article TABLE III: A Comparison of Observed and Calculated Excited-State z-Mode Vibrational Frequencies v, [em-'] of Perylene-R and Tetracene-R vdW Complexes withR = Ar, Kr, and Xe'
exptl
vdW complex Zfi perylene.Ar 47.2 peryleneKr 38.7 perylenexe 37.1 tetraceneSAr tetraceneeKr tetraceneexe
33.9 3 1.8
ZA(95)b 46.3 38.7 36.8
calcd ZA 45.8 37.3 34.6 43.8 36.0 33.6
exptl Zi
70.2c 72.2
Zi(95)
74.6
(59.4) 59.9
calcd Za 89.2 73.3 67.8 85.2 70.6 66.2
'The calculated values were obtained with the linear oscillator method. Incombination with the perylene 95.5 cm-' intramolecular frequency. e Double band. 8 and 9. Bands due to perylene-Xe, and tetracene-Xe, complexes appear on the low-energy side of the bare molecular electronic origins. At the moment we focus on the perylene-Xe and tetracene-Xe 0; and associated 2;progression due to the excited-state (SI) Y, mode. In the case of perylene-Xe, quite prominent twomembered progressions with vibrational spacings Avz = 36-37 cm-' are associated with the 0; band and also with intramolecular excitations with 95 and 194 cm-' vibrational energy. Also, in the case of tetracene-Xe, a z-mode progression is observed built upon the tetracene-Xe 0; band. Weaker low-frequency transitions are observed as well in combination with the 000, ZA, and Zi bands. These are due to in-plane vibrational transitions, which are discussed in the subsequent section. In order to calculate the r-mode frequencies in the SIstates of perylene and tetracene, the welldepth parameters tRCand t R H (cf. Table I) were both scaled by the factor
D ~ ( S I ) / D ~ ( S=O1) + [Sij/De(So)I to bring the excited-state well-depths D e @ , ) into agreement with the calculated D,(So) values and the observed red shifts 6% uRC and uRH were kept constant. The v, frequencies were calculated as before and are compared with the experimental values in Table 111. The agreement between the calculated and the experimental values of ZA is excellent, the difference being of the order of 4%. It is apparent that the simple isotropic model yields results of astonishing accuracy. V.D. In-Plane Vibrations. W e have pointed out that in all of the large M-R van der Waals complexes two vibrational modes exist in which the motion of the rare-gas adsorbate relative to the substrate molecule is nearly parallel to the substrate molecular plane. Due to the weak in-plane restoring forces, the fundamental frequencies are extremely small, being typically of the order of 5-10 cm-I. For substrate molecules with D3hor higher symmetry (benzene, triphenylene, or coronene), the in-plane vibrations occur in degenerate pairs, while for the longer polyacenes a short-axis (y) and a long-axis (x) mode can be distinguished. Thus, in pentacene-R the ratio of fundamental frequencies is w ~ : w ,= 2: 1. The in-plane intermolecular vibrational motions are characterized by very large vibrational amplitudes, especially in excited vibrational states. Accordingly, it is important to assess the effects due to the continuous reorientation of the vdW complex in space that takes place during the vibrational motion (conservation of angular momentum). Sets of vibrational energies calculated for tetraceneAr and pentacene-Ar by the linear oscillator method and the flexible model t r e a t m e ~ ~ are t l ~ shown , ~ ~ in Figure 10. V.E. Tunneling Splittings. Van der Waals complexes, which can exist in the binding configurational, 1I.A or ILB, exhibit potential energy profiles V ( x ) ,which are symmetric, with at least two equivalent minima. As a consequence of the indistinguishability of the "left" and "right" minimum configuration of such an M-R complex, the vibrational levels for the long-axis motion, which are located below the barrier, will exhibit tunneling splitting. As an assessment of the spectroscopic effects to be expected, a number of tunneling splittings were calculated for the lowest energy x-axis vibrational states of naphthalene-Ar, tetracene-R
TABLE I V Calculated Tunnel Splittings of M.R van der Waals Complexes
vibrtnl
tunnel splitting, cm-'
quantum
species naphthaleneAr tetraceneeAr tetraceneeKr tetracenexe pentaceneaNe
pentaceneAr pentaceneeKr
no. u ,
1-dimb
011 01 1 213 4/5= 01 1 213 415' 01 1 213 4/54 112 415 213 516 314 617
2.31 0.014 0.37 2.18 0.0056 0.20 1.38 0.0042 0.16 1.20 0.005 0.56 0.0014 0.25 0.0003 0.049
'State above barrier. model treatment.
2-dim'
3-dimc
0.05 0.94 3.19
0.03 1.29 0.0055 0.39
Linear oscillator approximation. Flexible
TABLE V: A Comparison of Experimentally Observed and Calculated In-Plane (x-Mode) Vibrational Excitations (cm-I) for TetraceneR (R = Ar, Kr, Xe)
excitation
x2x:
(first tunnel doublet)
R
exutl
calcd
Ar Kr
8.5 4.7 4.3 17.1 7.6 7.2
7.718.0 4.915.1 4.214.4 13.5115.3 8.419.8 7.318.5
Xe Ar (second tunnel doublet)
Kr Xe
( R = Ar, Kr, and Xe) and pentacene-R ( R = Ne, Ar, and Kr). The results are gathered in Table IV and lead to the following conclusions: 1. For tetracene R and pentacene R (u, = 0/1, 2 / 3 ) , two pairs of tunneling vibrational states lie below the barrier independently of the nature of R. 2. The tunneling splitting of the lower pair of vibrational states is small, Le., in the range of 0.001-0.01 cm-I, increasing to 0.054.5 cm-' for the next pair and then to 1-2 cm-I for the pair of states immediately adjacent to the top of the barrier. We conclude that the tunneling splitting should be observable even at a moderate spectral resolution. Based on the ground-state splitting between the u, = O/ 1 pair of vibrational states, tunneling frequencies can be calculated by the relationship v = 2AE/h, yielding frequencies ranging from v = 5 X lo8 s-l to v = 2 X 1Olos-l for the various examples given in Table IV. These rates are typically 1-2 orders of magnitude faster than radiative relaxation rates of these M.R complexes. On the other hand, the tunneling frequencies are comparable to rotational frequencies of these huge molecular complexes, leading to interesting rotational-tunneling coupling phenomena. V.F. In-Plane Intermolecular Vibrations of Tetracene-R. The theoretical calculations and predictions outlined in the previous sections can be tested by electronic spectroscopy of an M.R complex of sufficiently low structural symmetry (point group C, or lower). In these cases,the long-axis in-plane (x) mode becomes totally symmetric and can be studied in single-quantum vibronic excitations. x-Mode excitations have been observed for tetracene-R (R = Ar, Kr, and Xe) and similar observations should also be possible for complexes such as pyreneeR and naphtha1ene.R. Figures 9, 11, and 12 show the laser-induced fluorescence excitation spectra of tetracene-Xe, ( n = 1-3), tetracene-Kr, (n = 1-4), and tetracene-Ar, (n = 1-2) from 400 cm-' below the tetracene bare molecule 0; band up to the tetracene electronic origin. The vibrational structure due to tetracene-R x-axis vibrations is clearly discerned. Both fundamental and overtone transitions are observable within 20-30 cm-' to the blue side of the respective tetracene-R 0; bands, and similar patterns of low-frequency ex-
Leutwyler and Jortner
5566 The Journal of Physical Chemistry, Vol. 91, No. 22, 1987 -I .42
-1.44
-I
46
-I
48
-
E?
2
3
3 Y
w - I .50
-1
52 2
I
0
-I
-2
X ( A ,
Puntacere . ‘ “ ~ i
-
500
-.c;
--s
-
3 dilnensional
1 dimens:orial
-lW
480
-
I&
-1 L5
11
-E
12
-
w
1
5 20
w
-1
50
-1
55
5 40
-L
-3
-2
-1
0 0
1
2
3
L
XCi)
Figure 10. (a, top) Energy levels of tetracene-Ar along the long molecular ( x ) axis at yo = 0.0 A and zo = 3.40 A. (b, bottom) Potential energy of pentacene.Ar as a function of x at yo = 0.0 A and zo = 3.44 A. The vibrational levels calculated by the LOA (one-dimensional)and by the FMT (two-dimensional)are given on the left and right of the diagram, respectively.
citations also occur in combination with the z-mode excitations discussed above. For tetraceneKr (Figure 11) the first and second excitations are weak and strong, respectively, and are observed at =4.5 and =7.5 cm-’ above the 0: band. The first band is interpreted as the pair of transitions X2and X: and the second The experimental and peak as the pair of transitions and calculated values are compared in Table V and show excellent agreement. However, the calculated D = 4/5 tunneling splittings of 1.3-1.4 cm-’ should appear as a splitting of the second and stronger band in the spectrum but no evidence of this tunneling splitting was found.
two-dimensional critical phenomena. They constitute a simple physical realization of king and Potts models with dimensionality a = 2 and order parameter n = 1-3, which are of considerable current interest for the study of two-dimensional phase transit i o n ~ . Related ~~ questions pertain to epitaxial effects, such as registry and commensurate-incommensurate transition^.^^ The rare-gas/graphite surface interaction has traditionally been probed by physisorption measurements based on gas-solid virial coefficient^.^' More recently, atomic beam scattering has proven to be a powerful tool for the elucidation of the interaction potential between low-mass atoms and crystal surfaces. For the He-gra-
VI. Microsurfaces and Macrosurfaces from Benzene to Graphite The binding of rare-gas atoms to large aromatic molecules on the one hand and to the (0001) surface of graphite on the other hand represent the two extremes of the interaction of rare-gas atoms with ordered arrays of sp2-hybridized carbon atoms. The properties of rare gases adsorbed onto the graphite basal plane at low (submonolayer) coverages are of considerable interest because of the occurrence of quasi-two-dimensional phases and
(49)Vilches, 0.E.Annu. Rev. Phys. Chem. 1980, 31, 463. (50) (a) Chinn, M. D.; Fain, S. C. Phys. Rev.Lett. 1977, 39, 140. (b) Hanson, F.; McTague, J. P. J. Chem. Phys. 1980, 72, 6363. (c) Moncton, D.;Stephens, P.; Birgenau, R.;Horn, P.; Brown, G. Phys. Reu. Lett. 1981, 46, 1533. (d) Nielson, M.; Als-Nielsen, J.; Bohr, J.; McTague, J. P. Phys. Rev. Lett. 1981, 47, 582. (e) Abraham, F. F.; Koch, S. W.; Rudge, W. E. Phys. Rev. Lett. 1982,49, 1830. (0 Abraham, F. F.; Rudge, W. E.; Auerbach, D. J.; Koch, S. W. Phys. Rev. Lett. 1984, 52, 445. (51) (a) Sams, J. R.; Constabaris, G.; Halsey, G. D. J . Phys. Chem. 1960, 64, 1689;1%1,65, 367. (b) Yaris, R.;Sams, J. R. J . Chem. Phys. 1962, 37, 571.
2.
The Journal of Physical Chemistry, Vol. 91, No. 22, 1987
Feature Article
5567
T 0 :
-
-
-
2 2 12
2 2 16
22 2
22 24
22 28
2 2 32
2 2 36
22 4
Figure 11. LIF excitation spectra of tetracene-Kr, (n = 1-4) vdW complexes synthesized in a seeded supersonic expansion (5% Kr/95% He) at p o = 2.0 bar and D = 0.5 mm. Note the out-of-plane (vi) progression for T-Kr. Progressions with similar frequency intervals are also found for n = 2-4.
I!
3 1 e .-
o:
I I
I
TABLE VI: Comparison between Several Theoretical Potential Forms for the Laterally Averaged Graphite-Helium Interaction, V , ( z ) , and a Comparison between Calculated and Experimental Bound-State Resonances (BSR) anisotropic" isotropic Yuk-6" (12-61' Tommasinib (12-6)' z ( V = 0), 8, Z " f 8,
cm-'
-V,,,
1.76 2.10 128.5
2.34 2.57 132.1
2.58 3.04 126.6
2.48 2.93 125.7
97.8 51.3 22.3 7.6 1.8
97.8 49.8 22.4 8.5 2.6
96.5 51.3 23.0 7.7 1.3
95.4 51.1 24.1 9.3
exptl d
e
96.6 51.0 23.0 8.0 1.4
97.3 51.3 23.0 8.2 1.4
BSR, cm-I
v=o u u v v
= = = =
l 2 3 4
I
-100
-75
-50
-25
Relative energy Vvoc [I".
0
25
]
Figure 12. LIF excitation spectrum of tetracene-Ar, (n = 1, 2) vdW complexes synthesized in a seeded supersonic expansion (5% Ar/95% He) at po = 1.75 bar and D = 0.5 mm. Note in-plane ( v i ) and out-of-plane (v;) excitations of tetraceneaAr.
phite interaction especially, extensive data are now available,5z which give information about bound-state resonances, Le., Hegraphite vibrational energy levels in the molecular physics terminology, of the laterally averaged potential normal to the graphite surface, V,(z). The magnitude of the first Fourier component of the potential is also obtained, yielding the corrugation amplitude to a good a p p r ~ x i m a t i o n . ~ ~ On the other hand, spectroscopic information on bond lengths and intermolecular vibrational frequencies is also available for the interaction of H e with simple aromatic molecules, such as benzenez4and s - t e t r a ~ i n e . Obviously, ~~ it would be extremely important to find a unified description of both the He-benzene (52) (a) Elgin, R. L.; Greif, J. M.; Goodstein, D. L.Phys. Rev. Lett. 1978, 41, 1723. (b) Boato, G.; Canthi, P.; Tatarek, R. Phys. Rev. Lett. 1978, 40, 887. (c) Boato, G.; Cantini, P.; Guidi, C.; Tatarek, R.; Felcher, G. P. Phys. Rev. 1979, B20, 3957. (d) Derry, G. D.; Wesner, D.;Carlos, W. E.; Frankl. D.R. SurJ Sci. 1979, 87, 629. (53) Carlos, W. E.; Cole, M. W. Phys. Rev. Lett. 1979,43,691; Surf: Sri. 1980, 91, 339.
"Carlos, W. E.; Cole, M. W. Surf. Sci. 1980, 91, 339. bBoato, G.; Cantini, P.; Guidi, C.; Tatarek, R.; Felcher, G. P. Phys. Reu. B 1979, 20, 3957. The model potential used was V ( z ) = D(((1 + X Z ) / ~ ) - ~ , 2((1 + X,)/n)-"). CPresentwork. dExperimental values of ref b adjusted to the u = 4 value of ref e; experimental accuracy *0.8 cm-'. 'Derry, G.; Wesner, D.; Carlos, W. E.; Frankl, D. R. Surf. Sci. 1979, 87, 629. fPotential energy minimum. and Hegraphite interaction in terms of a universal potential. The He-graphite interaction V(r)may, of course, be written as a sum of He-C interactions, Le. V(r) = CU(r - R,) i
where the H e atom is at position r and the C atoms are located at their (RJequilibrium positions. Carlos and Cole@' have analyzed the experimental atomic beam scattering dataSZin terms of various isotropic pair potentials, U(lr - RJ),as well as anisotropic potentials, U(r - R,),and find good agreement for anisotropic Yukawa-6 and Lennard-Jones 12-6 pair potentials. The inclusion of anisotropy is physically reasonable and reflects the nonspherical atomic charge distribution and anisotropic dielectric function of graphite. However, the application of the Carlos-Cole parameters to the He-benzene interaction leads to unrealistically short bond distances with zmin= 2.80 k, and the vibrationally averaged distance ( z ;u = 0) = 2.99 A. These values are about 10% smaller than the experimentally observed distances for s-tetrazineHe, ( z ) = 3.284 f 0.019 and for benzeneHe, (z) = 3.17 A 0.37
J . Phys. Chem. 1987, 91, 5568-5573
5568
We suggest a parametrization based on an isotropic Lennard-Jones 12-6 potential for the He-C pair interaction, which predicts quite accurate bond distances and vibrational energy levels for both the He-benzene and He-graphite intermolecular potentials (see Table I): (a) The vibrationally averaged benzene-He bond length is (z; v = 0) = 3.18 A, which is in good agreement with the experimental value of Smalley et a1.24 (b) The fundamental out-of-plane frequency is w, = 35.3 cm-I, while a value of w = 38 cm-' has been observed for the s-tetrazine-He complex in the SI excited state.25 (c) The calculated bound-state resonances for the Hegraphite interaction compare well with both the experimental valuess0 and also with the previously calculated bound-state resonance energies53%54 (see Table VI). (54) Carneiro, K.; Passell, L.; Thomlinson, W.; Taub, H. Phys. Rev. 1981, B24, 1170.
(d) The predicted graphite-He distances are zmin= 2.92 A and
( z ;v = 0 ) = 3.08 A. Neutron scattering experiments have been
performed on He films adsorbed on Grafoil flakes at approximately monolayer coverage.54An approximate measurement of the height of the first helium layer above the graphite basal plane yields ( 2 ) = 2.85 A. The simple potential advanced by us, which rests on the properties of large vdW molecules, allows for a remarkable accurate description of the experimental data for graphite-helium, implying that a unified description of the H e interaction with ordered sp2-hybridized carbon atom arrays is feasible for any size of the ordered arrays. Registry No. Xe, 7440-63-3; Ar, 7440-37-1; Kr, 7439-90-9; Ne, 7440-01-9;graphite, 7782-42-5;perylene, 198-55-0;tetracene, 92-24-0; pentacene, 135-48-8;pyrene, 129-00-0;naphthalene, 91-20-3;coronene, I9 1-07-1 ; anthracene, 120-12-7. (55) Leutwyler, S.;Meyer, R., to be published.
ARTICLES Theoretical Analysis of the Vibrational Spectra of Ferricyanide and Ferrocyanide Adsorbed on Metal Electrodes Carol Korzeniewski,t M. W. Severson,*P. P. Schmidt,*Stanley Pons,* and Martin Fleischmanna Department of Chemistry, University of Utah, Salt Lake City, Utah 84112, Department of Chemistry, Oakland University, Rochester, Michigan 48063, Department of Chemistry, The University, Southampton. Southampton SO9 SNH, England, and Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109 (Received: November 4, 1986; In Final Form: June 10, 1987)
The vibrational frequencies of ferricyanide and ferrocyanide adsorbed on metal electrodes have been calculated by expansion of the potential to second order with the Cartesian form of the Taylor series. The vibrational frequencies are a strong function of electrode-adsorbate orientation and binding energy. Ion pairing with alkali-metal cations has a minimal effect on the vibrational frequencies; however, ion-pairing interactions may be important in stabilizing the adsorbate-surface orientation. Calculated vibrational frequencies are compared with surface enhanced Raman and in situ infrared spectra.
Introduction The influence of cation type and electrode material on the homogeneous and heterogeneous electron-transfer rates of the ferricyanide/ferrocyanide redox couple has received a great deal of attention. In the homogeneous reaction, it has been shown that the rate of electron transfer depends upon the nature and concentration of cations in solution.' The heterogeneous mechanism has been studied by electrochemical methods. In these systems the reaction rate depends upon electrode material as well as the nature and concentration of cations in solution.2" In both cases proposed mechanisms involve association of a cation with the reacting species. Several models of the molecular environment have been suggested to explain the kinetic behavior at electrode surfaces. Schleinitz et al. have proposed the formation of dimeric species in which a cation bridge is formed between the reacting specie^.^^^ Sohr et al. have proposed a similar species and have suggested *Address correspondence to this author at the University of Utah. 'University of Michigan. 'Oakland University. 5The University, Southampton.
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that stabilization by the surface is involved.' Radiotracer and voltammetric studies of the redox couple indicates adsorption of [Fe(CN),I3- on platinum electrodes and that the interaction most likely involves one or two cyanide ligands bonded to the surface through the nitrogen atom.* Other workers have presented ion-pairing arguments to explain the diverse reaction rates. Peter et al. have studied the kinetics of the reaction at gold electrodes as a function of the concentration of various alkali-metal cation^.^ (1) Shprer, M.; Ron, G.; Loewenstein, A,; Navon, G. Inorg. Chem. 1%5, 4, 361.
( 2 ) Kuta, J.; Yeager, E.J . Electroanal. Chem. Interfacial Electrochem.
1975, 59, 110.
(3) Bindra, P.; Gerischer, H.; Peter, L. M. J . Electroanal. Chem. Interfacial Electrochem. 1974, 57, 435. (4) Schleinitz, K.; Landsberg, R.; Lowis von Menar, G. V. J . Electroanal. Chem. Interfacial Electrochem. 1970, 28, 279. ( 5 ) Schleinitz, K.; Landsberg, R.; Lowis von Menar, G. V. J . Electroanal. Chem. Interfacial Electrochem. 1970, 28, 287. (6)Sohr, R.; Muller, L.; Landsberg, L. J . Electroanal. Chem. Interfacial Electrochem. 1974, 50, 5 5 . (7) Sohr, R.; Muller, L. Electrochim. Acta 1975, 20, 451. (8) Wieckowski, A.; Szklarczyk, M. J . Electroanal. Chem. Interfacial Electrochem. 1982, 142, 157.
0 1987 American Chemical Society
