J . Phys. Chem. 1990, 94, 8329-8333
8329
Structures and Vibrational Frequencies of Acetylene in Three Binding Sites on the Pd( 111) Surface Harrell Sellers National Center for Supercomputing Applications, Beckman Institute for Advanced Science and Technology, University of Illinois, Urbana, Illinois 61801 (Received: March 27, 1990; In Final Form: May 21, 1990)
The structures and vibrational frequencies for acetylene in the on-top position, the three-atom hollow, and the diamond-shaped hollow on the Pd( 1 1 1 ) surface have been computed at the RECP Hartree-Fock + PT2 (second-order perturbation theory) level of theory. The metal surface was modeled with clusters of metal atoms having up to IO atoms and two layers. Our calculations indicate that acetylene decomposes as it binds in the diamond-shaped hollow (which is very probably the site of CH production on the Pd( 11 1) surface); and, they confirm the postulation that the acetylene molecule exists in a rehybridized conformation in the three-atom hollow. On the basis of our computed vibrational spectra we propose that there is evidence in the published HREELS spectra suggestive of all three situations including acetylene in the on-top position. Our computed structure and vibrational frequencies for the three-atom hollow chemisorption confirms the proposed literature structure and assignments of HREELS data and represents a success of the Stockholm rule cluster modeling of chemisorption on an infinite metal surface.
Introduction The structure(s) and vibrational spectra of acetylene on the (1 I 1) surface of palladium have been studied experimentally with UV photoemission, LEED, and HREELS techniques.'-' The experimental research has led to a proposed structure and bonding scheme (referred to as "di-u/d') for acetylene in what we herein refer to as the three-atom hollow.7 However, there has not been any previous confirmation of this proposed structure from highquality ab initio calculations. There has also not been any conformation from high-quality ab initio calculations of the assignment of the vibrational spectra. The interpretation of the experimental data is not wholely agreed upon. The question of benzene formation at low temperatures on the Pd( 11 I ) surface is addressed in the current literature The low-temperature energy loss feature seen at 660 cm-l by Timbrell et aL7 and at 690 cm-l by Marchod has been attributed to a negative ion resonance enhancement of the symmetric C H wagging vibration of chemisorbed acetylene7 as well as to a flat-lying benzene molecule.6 Timbrell et aL7 have shown that the 660-cm-' loss feature demonstrates the dependence on incident beam energy characteristic of a resonance enhanced feature, and Marchon6 has demonstrated that this peak vanishes when the crystal is flashed to 273 K. While it is not possible for us to resolve this question, we can add another piece of information, namely, the energy difference between the neutral system having the acetylene fragment in its equilibrium conformation and the monoanion at that same geometry. It is also very likely that other molecules exist bound to the metal ~ u r f a c e . ~It, is ~ possible that energy loss features might be misassigned and it is clear that high-quality ab initio calculations can contribute to the understanding of systems of this type. Toward this goal we present structures and vibrational frequencies of acetylene adsorbed on models of the Pd( 1 1 1) surface in the on-top position, in the diamond-shaped hollow, and in the three-atom hollow obtained from high-quality ab initio calculations. ( I ) Tysoe, W. T.; Nyberg, G. L.; Lamber, R. M. Swj. Sci. 1983,132, 128. (2) Demuth, J. E. Surf. Sci. 1979, 84, 315 (3) Gates, J. A.; Kesmodel, L. L. Surj. Sci. 1982, 76, 4281. (4) Gates, J. A.; Kesmodel, L. L. Surf. Sci. 1983, 124, 68. ( 5 ) Kesmodel, L. L.; Waddill, G. D.; Gates, J. A. Surf. Sci. 1984, 138, 464. (6) Marchon, B. Surf. Sci. 1985, 162, 382. (7) Timbrell, P. Y.; Gellman, A. J.; Lambert, R. M.; Willis, R. F. Surf. Sci. 1988, 206, 339. (8)Sesselmann, W.; Woratschek, B.; Ertl, G.; Kiippers, J.; Haberland, H. Surf. Sci. 1983, 130, 245. (9) Gentle, T . M.; Muetterties, E. L. J. Phys. Chem. 1983, 87, 2469.
Calculations This work was performed with the DISCO programi0 on the Cray-2 at the National Center for Supercomputing Applications. We employ the model potential ECP method of Bonifacic and Huzinaga" because this method preserves the nodal structure of the metal atom valence orbitals. In our calculations presented here we have used two representations for the metal atoms. The metal atoms that are binding directly to the acetylene molecule, which then defines the chemisorption site, were 18-electron atoms. In the 18-electron Pd atoms the electron density below and including the 3d electron density is replaced by the relativistic effective core potential (RECP) and the 4s and 4p electron density is kept "frozen" at the relativistic S C F shape.I2*l3 Keeping the 4s and 4p electron density, rather than including it with the core, fixes up the description of the short-range repulsion and allows for a correct description of the Coulomb and exchange interactions with the valence orbitals. Then 10 electrons are kept fully variational at the S C F level and included in the correlation space in the PT2 (second-order perturbation theory) calculations. The second-layer metal atoms, and in the case of acetylene in the on-top position, the distant top layer atoms, were one-electron atoms. Hence, the on-top, three-atom-hollow, and diamond-shaped-hollow situations employed one, three, and four of the 18-electron RECP palladium atoms, repsectively. Figure 1 depicts a fragment of the Pd( 11 1) surface having an acetylene molecule in each of the three sites considered herein. Table I contains the RECP parameters and metal atom basis sets employed in this work. The palladium core orbital projection operators that impose the valence orbital nodal structure were described with the Pd atom basis set of Hyla-Krispin et aLi4 The carbon and hydrogen basis sets were the DZP basis sets. The on-top calculations were performed with the larger of the two 18-electron and I-electron RECP basis sets, but computer time constraints required that we reduce the size of the Pd basis set in the three-atom-hollow and diamond-shaped-hollow calculations, since these latter systems need three and four of the 18-electron Pd atoms, respectively. However, as will be seen from the results ( I 0) Almlof, J.; Faegri Jr., K.; Feyereisen, M.; Korsell, K. Disco is a direct SCF and PT2 computer program. The closed-shell PT2 is MP2 perturbation theory and the open-shell PT2 is the method of Hubac and Carsky described in: Phys. Reu. 1980, 22, 2392. (1 I ) Bonifacic, V.; Huzinaga, S. J. Chem. Phys. 1974, 60, 2779. (12) Pettersson, L.; Wahlgren, U. Chem. Phys. 1982, 69, 185. (13) Almlof, J.; Faegri Jr., K.; Grelland, H. H. Chem. Phys. Left. 1985, 114, 53. (14) Hyla-Krispin, 1.; Demuynck, J.; Strich, A.; Benard, M. J . Chem. Phys. 1981, 75, 3954.
0022-3654/90/2094-8329$02.50/0 0 1990 American Chemical Society
Sellers
8330 The Journal of Physical Chemistry, Vol. 94, No. 21, 1990
Q
00
0:o
O0*O0
00
O O Y O O
O.oO
000000 0. OO 00 00
*
0
0
0
0
Figure 1. Acetylene in the on-top position, diamond-shaped-hollow, and three-atom-hollow binding sites.
of our Pd lo-acetylene calculations (which model the chemisorption in the three-atom-hollow site), this Pd basis set reduction did not impact the accuracy of the results significantly. The RECP parameters were fit to the orbital energies and orbital shapes of atomic Pd orbitals that were obtained from SCF calculations that include the Darwin and mass-velocity relativistic correction^.'^ So, the orbital energies and the orbital shapes reproduced by our RECPs include the effects of the Darwin and mass-velocity relativistic corrections. Panas et al.I5 have demonstrated that results (binding energies) can be obtained that are essentially converged with respect to cluster size (and therefore are germane to the infinite surface case) from small clusters provided that the cluster is in a proper bonding state. This proper bonding state of the cluster is very often not the ground state. We have referred to this as the Stockholm rule,16 and we have applied this rule in calculations of the atomic adsorption of H, N, 0, and S on the Pd( 11 1) surface.I6 In order to use the Stockholm rule successfully one must know the bonding scheme involved between the adsorbate and the metal surface. For example, a lone sulfur atom bonds to the threefold site of the Pd( 1 1 1) surface with a purely n scheme, and a cluster with as few as 10 Pd atoms that obeys the Stockholm rule can give a binding energy very nearly the same as much larger clusters.16 In atomic cases such as this one, it is clear that the open-shell (atomic) electrons will form bonds and the cluster can be prepared to receive them by choosing a particular electronic state. In our present situations with acetylene on the Pd( 1 1 1) surface the adsorbate is a closed-shell molecule at large distances from the metal surface, and it would seem that the Stockholm rule does not have much to offer in this case. However, the spirit of the Stockholm rule is to provide the adsorbate with ample opportunity to interact with the cluster by removing obstacles that may exist. In modeling the adsorption of acetylene on the Pd( 1 1 1) surface with metal cluster systems, we proceeded under the notion that the primary bonding would occur, at least initially, via the T systems of the acetylene and the metal d orbitals of the proper symmetry (A” in C,symmetry). Hence, in the spirit of the Stockholm rule we then chose a cluster MO occupancy that put these cluster orbitals closer to the Fermi level than the symmetric MOs that could cause an unphysical r e p u l ~ i o n . ~For ~ *the ~ ~larger clusters we employed, for example, the Pdl0cluster, this choice of MO occupancy yielded low-lying electronic states for the cluster, but not the ground state.15*16So there is a cluster promotion energy associated with putting the cluster in the states we employed, as is the usual Also, in the open-shell systems such as the PdIoand Pdlo-acetylene systems, we chose the half-filled MO(s) to minimize the open-shell electron density in the region of the chemisorption site. ~~
(15) Panas, 1.; Schule, J.; Siegbahn, P. E. M.; Wahlgren, U. Chem. Phys. Lett. 1988, 149, 265. (16) Sellers, H. L. Chem. Phys. Leu. 1990, 170, 5.
O.oO Figure 2. Three views of cluster-adsorbate system employed to model the acetylene in the on-top position. The central atom of the metal cluster is an 18-electron RECP atom and the other metal atoms are 1-electron atoms. The acetylene fragment is shown in its equilibrium conformation.
6 Q
P
Figure 3. Two views of the cluster-adsorbate system employed to model the acetylene in the three-atom hollow. The three top-layer metal atoms are 18-electron RECP atoms and the seven second-layer atoms are 1electron RECP atoms. The acetylene fragment is shown in its equilibrium conformation.
Our goal here, however, is not to compute binding energies, which are considered to be a more sensitive indicator of the fitness of a cluster to model infinite surface Bauschlicher et aI.l7 have pointed out that the computed harmonic frequencies and adsorbate structures converge more rapidly with respect to cluster size (ignoring the Stockholm rule) than do the binding energies. It is exactly these less sensitive quantities on which we are concentrating in this work. We believe that our computed structures and harmonic frequencies should be of high quality as we are computing properties less sensitive to cluster size than binding energies and we have imposed the Stockholm rule on the cluster models of the Pd( 1 1 1) surface. (17) Bauschlicher, Jr. C. W. Chem. Phys. Lett. 1986,129,586. Bauschlicher, Jr. C. W.; Bagus, P. S.; Schaefer 111, H. F. IBM J . Res. Dev. 1978, 22, 213. Bagus, P. S.; Schaefer, 111, H. F.; Bauschlicher, Jr., C. W. J . Chem. Phys. 1983, 78, 1390.
The Journal of Physical Chemistry, Vol. 94, No. 21. 1990 8331
Structures of Acetylene on the Pd( 11 1) Surface
9
TABLE I: Effective Core Potential Parameters and Basis Sets for RECP Pd Atoms
9
~
contraction coefficients'
exponents
18-Electron Atom Parameters s-Orbital Basis 4sb
746.474 7 1 -0.076 786 5 0.357 3374 42.568 152 6.398 31 6 9 -0.96 1 102 6 1.4061058 0.679 0340 0.683 773 7 0.595 536 7 0.1192827 0.029 487 8 0.040635 0 -0.008 195 2
124.183 70 9.208 866 9 1.747706 6 0.676 336 0 0.030
21.175 493 1.400 522 8 0.363 037 7
0.09
1 .O
1.o
1.o
p-Orbital Basis 4Pb 0. I44 485 3 -0.479 005 2 1 .O 1.o 0.560511 8 0.563 768 0 1.o 0.0
1.o
1 .o
1 .o
Figure 4. Views of two cluster-adsorbate systems used to model the acetylene in the diamond shaped hollow system. The acetylene fragment is in the equilibrium conformation obtained from the single-layer cluster system. The four toplayer metal atoms are 18-electron RECP atoms and the second-layer atoms are 1-electron RECP atoms.
1.o
d-Orbital Basis 4d 0.215 916 7 -0.591 1750 1.0 -0.504675 1 1 .o -0.129 2 14 6 I .o
RECP ParametersC 18-electron-atom RECP parameters for use with full basis set: Ai = 0.759608, 0.105196, 0,133746: (yi = 464.400965, 31.668681, 2.491 399 18-electron-atom RECP Parameters for use with trunctated basis set:d Ai = 2.190314, 0.189452, 0.234099: ai = 307.663650, 20.729119, 1.635598 I -Electron Atom Parameters
+Orbital Basis 5s
745.133 29 42.665 655 6.41 3 543 1 1.468 842 1 0.695 I90 7 0.1 I3 764 1 0.040 635 0
-0.01 8 002 6 0.085 346 3
-0.254 759 3 0.238 742 4 0.322 607 4 -0.507 699 3 -0.642 007 2
1 .O
1 .o
1 .o
1.o
1 .o
1 .o
RECP Parameters I-electron-atom RECP parameters fur use with full basis set: Ai = 14.808991, 3.423574, 0.892869: = 2.741977, 0.643796, 0.191998 I-electron-atom RECP parameters for use with truncated basis set:d Ai = 18.225569, 4.199475, 1.09448: ai = 2.352505, 0.5523388, 0.164713 PThe contraction coefficients are given in general contraction format. *Contraction coefficients for a frozen orbital. cThe form of the RECP is Ze&l + x i A i exp[-a$]I/r. dThe basis set is truncated by discarding all but the first and last contracted functions in the p and d spaces of the 18-electron atom and in the s space of the I-electron atom. In the s space of the 18-electronatom the 4s is retained and the 5s contraction (from the I-electron atom) is added. We rsfit the RECP parameters for the truncated basis sets. For example, the truncated basis set for the 18-electron atom is a 2s, 2p, 2d basis set containing the contracted (frozen in the case of 4s and 4p) function and the most diffuse function in the cases of the p and d spaces and the 4s and 5s in the s space. Figures 2-4 are views of the acetylenecluster systems actually used in the structure optimization of the acetylene fragment. The acetylene fragment is shown in its equilibrium geometry in each of the figures. For the case of acetylene in the on-top position six I-electron Pd atoms and one 18-electron Pd atom were used in the cluster model of the Pd(l11) surface. In all our calculations the Pd-Pd nearest-neighbor distance was fixed to the bulk value of 5.2 bohr. In the three-atom-hollow and diamond-shaped-hollow calculations, the three and four top layer metal atoms, respectively,
were 18-electon Pd atoms. In the case of the acetylene in the three-atom hollow, the structure of the acetylene fragment was optimized pointwise (DISCO does not yet have a gradient routine) without the seven I-electron Pd atoms of the second layer. When a reasonable estimate of the acetylene structure on the Pd, cluster was obtained, we added the second layer and refined the structure of the acetylene fragment to equilibrium on the resulting Pdlo two-layer cluster. This process saves computer time and demonstrates the importance of the second layer in this system. The CC stretching frequency is used most often in the literature as the indicator of a particular C,H, species on the Pd( 1 1 1) surface. For this reason we are particularly interested in the computation of this band. Since the symmetric vibrations (with respect to the acetylene fragment) are the only ones that can contribute to this computation, we limited our force constant calculations to the symmetric representation in the cases of the acetylene in the on-top position and in the diamond-shaped hollow. We point out here that the interaction force constants between the CC stretch and HCC bending modes are very important. For the three-atom-hollow case (Figure 3) we did calculate the C H wagging force constants (out of plane with respect to the acetylene fragment), since the assignment of one of these modes is currently in This is the only case in which we computed outof-plane modes (symmetric and asymmetric). In our vibrational analysis we considered the acetylene fragment to be moving against an infinite mass. We did not try to compute barriers to adsorption because this is a separate optimization problem. We also did not calculate any binding energies because it is known that at the DZP SCF + PT2 level of theory the quality of the binding energy prediction is not as good as the frequency and structural predictions and would not be useful for our purposes here.16J8J9 Simandiras et aI.l9 have shown that very high quality structures PT2 and force constants can be obtained at the Hartree-Fock level of theory for hydrocarbon systems. We cannot claim with certainty the kind of accuracy demonstrated previo~sly,'~ since we have introduced the additional approximations of the RECP metal atoms, the cluster models, and numeric differentiation of the energy (as opposed to analytic second derivatives). However, the same computational trends noted by Simandiras et al.I9 regarding the results of SCF PT2 calculations employing the DZP basis set in free acetylene are apparent in our results as will be discussed below, One should keep in mind that ours are harmonic frequencies and the anharmonicity is another source of discrepancy between our computed harmonic frequencies and the observed
+
+
(18) (19)
Rohlfing, C. M.;Hay, P. J . J . Chem. Phys. 1985,83, 4641. Simandiras, E. D.; Rice, J. E.; Lee, T. J.; Amos, R. D.; Handy, N .
C.J . Chem. Phys. 1988.88, 3 1 8 7 .
8332 The Journal of Physical Chemistry, Vol. 94, No. 21, 1990 TABLE 11: Structures of Adsorbed Acetylene Molecules" coordinate On-tOD 3-atom hollow diam hollow 1.290 1.420 2.053 CC dist (c) CH dist (ch) 1.074 1.089 1 090 145 117 91 CCH (cch) 2.029 1.402 0 958 perp dist 0 22 tilt angle 0 Distances are given in Angstroms and angles in degrees
Sellers TABLE 111: Harmonic Vibrational Analysis of Acetylene in the On-Too Position freq 254 608 1669 3411
C2H2 motiono p cch c ch
C2D2 motion p 250 432 ccd 0.85 c 1557 2597 cd freq
freq
250 355 1434 2316
C2T2 motion 0.85 p CCt
0.7 c, 0.3 cct ct
energy loss features. The discrepancy between our computed frequencies and the observed frequencies due to the anharmonicity effect is particularly prominent in the C H stretching modes. Also the HREELS observations are dependent on surface loading and the observed energy loss features under similar conditions can differ from lab to lab by as much as 30-50 wavenumbers.
"In Tables Ill-VI the notation p, cch, (cct), c, ch, (ct, cd), and w denote the perpendicular stretching, CCH (CCT) bending, CC stretching, CH (CT, CD) stretching, and CH wagging motions, respectively. The number preceding indicates the fraction of the kinetic energy of the mode contained in the indicated vibrational coordinate. Frequencies are in cm-I.
Results Table IJ contains the equilibrium structures for the acetylene fragments in the three binding sites considered in this work. The acetylene in the on-top position has gained about 0.06 A in the CC bond and the hydrogens are bent up by 35O. The rotation of the molecule about the axis perpendicular to the surface and the CC bond is for all practical purposes a free rotation. Simandiras et aI.l9 find that the DZP basis set at the Hartree-Fock + PT2 level predicts the CC bond in free acetylene to be too long by 0.023 A. This correction could be applied to the bond length we compute for acetylene in the on-top position to get a more accurate CC distance, but this correction is less than the experimental error in LEED structural determinations. The acetylene in the diamond-shaped hollow is foi all practical purposes dissociated. The acetylene hydrogens are bent up by 88.7' (the HCC angle is 91.3') and CC distance is 2.05 A. The carbons are sitting quite low in the diamond-shaped hollow with a perpendicular distance of 0.958 A. When we put in the four-atom second layer it became clear that the second layer could be important in the diamond-shaped-hollow system. We did not reoptimize this structure with a second layer because, in order to do a good job, one should relax the symmetry requirement we imposed on the two CH groups and employ a more extensive second layer. The presence of the second layer makes the two carbon binding pockets of the top layer unequivalent and may allow some interesting chemistry to take place there. We consider that the primary result from the diamond-shaped-hollow calculations we performeu is that the diamond-shaped hollow is a site at which the CC bond undergoes cleavage, and we do not believe that the second layer will change this result. However, there may be a substantial barrier to this process since low-temperature HREELS studies exist that do not see evidence of C H formation.' Gates and Kesmode14have concluded that C H production on the Pd surface is the result of CC bond scission of acetylene rather than from ethylidyne dehydrogenation. Our calculations on the diamond-shaped-hollow system support their conclusion. The picture of adsorbed acetylene currently in vogue in the literature has the molecule in a three-atom-hollow site in a rehybridized state.7 This picture is very similar to the structure we obtain for acetylene in the three-atom hollow. From our two-layer Pdlo-acetylene calculations we obtain a value of 1.420 A for the CC bond length which is nearly the midpoint between the CC double and single bonds. The HCC angle we obtain is 117O, and the distance from the carbon atoms to the plane of the top layer of the metal atoms is 1.402 A. The presence of the second layer causes a lengthening in the perpendicular distance of 0.15 A but has suprisingly little effect on the other structural parameters of the acetylene fragment. The C H bonds are tilted from the vertical as shown in Figure 3 by 21.7O. The acetylene fragment is not in the center of the three-atom hollow, but the CC bond is shifted in the same direction that the C H bonds point by 0.19 A. The structural parameters of the acetylene fragment are very much in line with the notion that the carbon atom hybridization is sp25.7 However, our computed CC bond length and HCC angle are outside the range estimated by Demuth2 for the Pd( 1 1 1) surface and more resemble his estimates for acetylene on Ni. Demuth
TABLE IV: Harmonic Vibrational Analysis of Acetylene in the Three-Atom Hollow freq 429 678 890 I151 1389 3340
C2H2 motion" 0.95 p w asym w 0.65 cch, 0.3 c 0.6 c, 0.35 cch ch
C2D2 fres motion 406 0.8 p 536 w 687 asym w 842 0.9 ccd 1324 0.8 c 2472 cd
frea 380 489 605 693 1292 2118
-
C2T2 motion 0.7 p, 0.3 0.3 p, 0.65 w asym w cct 0.85 c ct
"See text and Table 111 footnote.
finds two catagories of acetylene structures, one strongly ( s p 2 3 and one weakly distorted, and does not find the strongly distorted acetylene on Pd. More recent literature7 is more in line with our results. Our structure for the acetylene in the three-atom hollow confirms the proposed strongly distorted, rehybridized acetylene bound in the three-atom hollow.7 Table I11 contains the frequencies for the in-plane modes of C2H2-doand C2D2( d 2 )in the on-top position and a description of the modes according to the kinetic energy distribution among the internal coordinates. No experimental data yet exists for the tritium compounds, but we give the frequencies for the tritium compounds in all cases studied herein. The notation "p, cch, c, ch, and, w" used in Tables 111-VI denotes perpendicular stretching, CCH bending, CC stretching, CH stretching, and the CH wagging motions, respectively. The numbers appearing before the letters are the fraction of the total kinetic energy of the vibration that is contained in the motion of the indicated coordinate. If no number is given before the letter then the vibration is essentially 100% of the indicated motion. The harmonic CC stretching frequency appears at 1669 and 1557 cm-I in the doand dt systems. It is reasonable to expect to see acetylene in the on-top position at high coverages and low to moderate temperatures. From the results of Simandiras et obtained for free acetylene with the DZP basis set at the SCF PT2 level, it is seen that the computed harmonic CC stretching frequency is too low by about 55 cm-' (see Table VI). The anharmonicity lowers the energy of the stretching vibration by about 25 cm-1.20 So, the DZP S C F + PT2 harmonic CC stretching frequency we obtain should reasonably be about 25-30 cm-' lower than the observed value. Adding this much energy to our computed CC stretching frequency gives a value right at 1700 cm-'. The CC stretching frequency of acetylene in the on-top position could very well be a contributor to the feature that is routinely attributed to carbon m o n o ~ i d e . ~The , ~ . ~CH , ~ stretching vibration is much more affected by anharmonicity than are the slower phonon modes and, therefore, the computed value should be too high. Also, the C H vibrations are much lighter phonons and are sensitive to phonon-phonon correlation effects including Fermi resonances and near resonances. However, the differences between the CH frequencies of acetylene in the different sites should be meaningful. The case for the presence of acetylene in the on-top position is
+
(20) Pulay, P.;Meyer, W. Mol. Phys. 1974, 27, 473. ( ? I ) Strey, G.; Mills, 1. M . J . Mol. Sfrucr. (THEOCHEM)1976, 59, 103.
The Journal of Physical Chemistry, Vol. 94, No. 21, 1990 8333
Structures of Acetylene on the Pd( 1 1 1) Surface TABLE V: Harmonic Vibrational Analysis of Acetylene in the Diamond-Shaped Hollow C2H2 freq motion" 555 0.4 c, 0.6 p 724 0.56 c, 0.4 p 1088 cch 3204 ch
freq 539 697 791 2363
C2D2 motion 0.35 c, 0.65 p 0.4 c, 0.4 p 0.6 ccd cd
freq 519 618 725 2011
C2T2 motion 0.3 c, 0.7 p cct c ct
"See text and Table 111 footnote. TABLE VI: Harmonic Frequencies of Free Acetylene ab initio" experimental" freq motionb freq motion .1956 C 201 1 C 3555 ch 3497 ch ~
" Values quoted in ref 19. Experimental values from ref 21. Ad hoc basis set corrections to the acetylene CC distance and CC and CH harmonic stretching frequencies are -0.023 A, 55 cm-I, and -58 cm-I, respectively. bSee text and Table 111 footnote. not conclusive, but loss features are present in published HREELS studies where they would have to be in order for acetylene to be present in this site. The frequencies for acetylene doand d2 in the three-atom hollow are given in Table IV. We obtain the values of 1389 and 1324 cm-' for the frequencies of the CC stretching vibrations or C2H2 (do)and C2D2(d2),respectively. The energy loss features accepted as the CC stretching frequencies in acetylenedo and -d2 from As in HREELS data are 1400 and 1359 cm-', re~pectively.~.~ the case of the on-top adsorption, we expect our computed CC frequencies to be slightly too low as they are. We obtain band centers at 678 and 890 cm-' for the symmetric and asymmetric CH wagging vibrations, respectively, for acetylene in the threeatom hollow. These features have been seen at 690 and 880 cm-' by Marchon,6 and at 660 and 880 cm-I by Timbrel1 et aL7 We consider that this is very good agreement with the accepted frequencies and assignments. The M O s of this system are consistent with the di-a/?r description in the 1iteratu1-e.~This is strong evidence supporting the current view of the bonding of acetylene in the three atom h01low.~ The computed vibrational frequencies for the acetylene fragment in the diamond-shaped hollow should be somewhat different upon the inclusion of a more extensive second layer and the relaxation of the symmetry. However, it is still possible to see in the computed frequencies of this system bands that are normally attributed to the motion of CH such as the loss feature reported for CH at around 750 ~ m - ' . Since ~ CH formation is seen in the 400-500 K temperature range4 and not at very low temperatures, it is reasonable to assume that there is a significant barrier to the adsorption of acetylene in the diamond-shaped hollow. In our geometry optimization of acetylene in the diamond-shaped hollow the initial structure for the acetylene fragment was taken as the on-top-site equilibrium structure. The initial distance above the surface was also taken from the on-top-site equilibrium structure. Although we did not check for structures with shorter CC bond lengths than 1.29 A, we did not see any evidence of a bound state in the diamond-shaped hollow in which the acetylene fragment was intact. Addressing the anion resonance selective mode enhancement question,' we computed the energy difference between the neutral Pdlo-acetylene system (acetylene in the three atom hollow, Figure 3) having the acetylene fragment in its equilibrium nuclear configuration and the anion in the same nuclear configuration constructed by adding an electron in the LUMO of A' symmetry. We also computed the force in the direction of the symmetric CH
n
n
W Figure 5. The di-a/?r bonding scheme employed by the acetylene fragment in the three-atom hollow.
wagging vibration numerically. At the Hartree-Fock level the anion is 2.67 eV higher in energy than the neutral and 2.97 eV higher in energy at the Hartree-Fock + PT2 level of theory. The experimental value of about 3.0 eV is in good agreement with these calculations. While the absolute magnitude is not important, the computed force in the direction of the symmetric CH wagging motion is significant and indicates that the equilibrium geometry of the anion should be significantly different from that of the neutral. These data support the finding7 that the peak at 660 (690) cm-I is likely due to a negative ion resonance enhancement rather than the presence of benzene. The Mulliken populations of the acetylene anion in the three-atom hollow indicate that the two carbons are each supporting about half an electron of excess negative charge. In the neutral, however, the carbons are also significantly carbanionic supporting net negative charges of -0.35 each. The d-orbital populations of the three toplayer Pd atoms shift significantly upon electron capture and are telling of a significant rearrangement of the bonding electron density in going from the neutral to the cation. The LUMO of A' symmetry in C, is antibonding with respect to the ?r attachment part of the di-a/?r bonding scheme (Figure 5). The addition of an electron to this orbital significantly weakens or breaks the ?r part of the attachment which, as our force calculation indicates, tends to push the molecule up toward the higher bridging di-a attachment. This movement of the acetylene fragment toward the bridging position is a very similar motion to the symmetric CH wagging vibration. It is reasonable to think that the anion should lead to an ethylene-like C2H2fragment, but this is speculation and the calculation has not been done. This description is very much in line with the idea that the negative ion resonance enhances the symmetric CH wagging vibration.
Conclusion The agreement between the HREELS data and our computed harmonic frequencies of acetylene in the three-atom hollow is a successful application of the Stockholm rule and the cluster modeling of the metal surface chemisorption. Our results for the on-top adsorption of acetylene suggest that acetylene may be present under certain conditions and contributing to the loss feature usually attributed to carbon monoxide. Our calculations support the notion that the 660 (690)-cm-' loss feature is due to an anion resonance enhancement of the symmetric CH wagging vibration. The primary result we draw from the diamond-shaped hollow calculations is that this is very probably the site (or one of the sites) of CH production on the Pd( 1 11) surface. Acknowledgment. The author thanks the National Center for Supercomputing Applications and the Beckman Institute for Advanced Science and Technology, and Dr. Roger Ove for support of this work. The author thanks Professor A. Gellman for many discussions. We thank Mr. Pierre Dewey La Fontaine, Jr., for his contributions and dedicate this work to the occasion of his 60th birthday in July 1990. Registry No. C2H4,74-86-2; Pd, 7440-05-3.
