Theoretical Study of the Photoinduced C− H Bond Cleavage in

9914

J. Phys. Chem. C 2007, 111, 9914-9918

Theoretical Study of the Photoinduced C-H Bond Cleavage in Formaldehyde Adsorbed on the Ag(111) Surface Daria B. Kokh,* Robert J. Buenker, and Heinz-Peter Liebermann Fachbereich C-Mathematik und Naturwissenschaften, Bergische UniVersita¨t Wuppertal, Gaussstrasse 20, D-42097 Wuppertal, Germany

Jerry L. Whitten Department of Chemistry, North Carolina State UniVersity, Raleigh, North Carolina 27695-8204 ReceiVed: February 16, 2007; In Final Form: April 23, 2007

A theoretical study of the photoinduced C-H bond cleavage in H2CO adsorbed on Ag(111) surface is carried out by employing an ab initio embedding approach and multireference configuration interaction method. Pathways for one- and two-step fragmentation into CO + 2H are investigated as well as adsorption properties of the H and HCO products. The π* electron-attachment state, H2CO-(a), formed due to photoinduced electron transfer from the surface to an adsorbate, serves as intermediate for the dissociation process. An effective reaction pathway includes initial nuclear relaxation of the H2CO-(a) anion followed by electron detachment and subsequent dissociation of the neutral H2CO(a) molecule. The present calculations also show that, in contrast to gaseous H2CO, cleavage of the C-H bond in adsorbed H2CO needs higher excitation energy than the C-O bond. The corresponding energy difference is obtained to be about 1.6 eV.

I. Introduction Photodissociation is a first step in the formaldehyde polymerization process on the Ag(111) surface that has been observed experimentally under UV irradiation with a photon energy threshold of 3.1 ( 0.2 eV.1 Although H2CO is weakly bound to silver (experimental binding energy is only about 0.27 eV),2 its polymerization threshold on the surface is notably lower than in the gas phase (∼3.75 eV)3 and the observed dissociation products are significantly different than those in the gas phase.4,5 Dissociation of formaldehyde on silver, therefore, is an example of photon-driven reactions on metals where the gas-phase approximation for an adsorbate cannot be satisfactorily applied. Experimental6 and our recent theoretical7 analysis have shown that, in contrast to gaseous H2CO, whose photoexcited H2CO (S1) state serves as an intermediate for photodissociation, formaldehyde on the silver surface can effect dissociation only through an electron-attachment state. This ensures a difference in reaction mechanisms and, therefore, distinctions in the energetics and products for gaseous and adsorbed H2CO reported in experimental studies.4,5 Unfortunately, there are no systematic experimental data available on formaldehyde photodissociation products that would provide an unambiguous description of the dissociation mechanism. Either adsorbed or gas-phase species have been observed, and only several fixed excitation wavelengths have been used. Specifically, adsorbed species have been analyzed only at the excitation wavelength of 287 nm (4.32 eV).4 The latter study has shown that CH2 and presumably O are formed due to photodissociation of formaldehyde on silver. On the other hand, only CO molecules have been detected as gas-phase products at an excitation wavelength of 266 nm (4.66 eV) in measurements carried out at 266 and 355 nm.7 These data make clear * Corresponding author: e-mail [email protected].

that the lowest formaldehyde photodissociation channel on the Ag (111) surface must be C-O bond breaking with formation of adsorbed O and CH2, but at an excitation energy above 4.66 eV, CO + 2H and/or CO + H2 dissociation presumably takes place as well. Recently, we reported a detailed investigation of formaldehyde dissociation into O + CH2 on Ag (111).7 According to this study, C-O bond cleavage occurs in two key steps: (1) excitation of the formaldehyde anion due to electron transfer from the surface to the adsorbate, whereby the anion gains an excess of vibrational energy and nuclear relaxation can then take place, and (2) subsequent reneutralization of the vibrationally excited anion via a Franck-Condon (FC) transition to the H2CO ground state, whereby a distorted molecule that is strongly bonded to the surface can be formed. Molecules that possess enough energy to overcome a C-O bond cleavage barrier can then dissociate. The computed threshold of the dissociation process has been obtained to be about 3.6 eV. In addition, it has been shown that both the ground and S1 excited states of H2CO are weakly bound to the surface. The latter state serves as an intermediate for formaldehyde dissociation in the gas phase, and its relaxation leads to formation of the vibrationally excited H2CO ground state that can then dissociate. Since the vibrational excitation of H2CO needed for its dissociation is notably larger than the binding energy of the H2CO molecule and very likely leads to molecular desorption, the gas-phase channel cannot be effective on the surface. Moreover, the H2CO (S1) state lifetime (∼10-7-10-9 s)8 is significantly longer than the typical time for adsorbate excitation quenching on the surface (∼10-13-10-15 s),9 and therefore, a gas-phase channel for the energy transfer to the H2CO ground state and its subsequent dissociation are unlikely. In the present work we extend our recent analysis of formaldehyde O + CH2 fragmentation7 to the C-H bond-

10.1021/jp071334e CCC: $37.00 © 2007 American Chemical Society Published on Web 06/12/2007

Photoinduced C-H Bond Cleavage in Formaldehyde breaking channel, and we make an attempt to derive a general picture of photoinduced dissociation of formaldehyde adsorbed on silver. First, it is worthwhile to consider some general assumptions that can be made before a computational treatment is undertaken. Specifically, on the basis of experimental findings (such as the absence of products usually observed in gas-phase dissociation of formaldehyde or notably higher threshold for their formation,5 as well as the observed electron-induced formaldehyde polymerization6) and our study of O + CH2 dissociation summarized above, we can expect that the most probable intermediate for the H2CO dissociation on silver is an electron-attachment state, H2CO-(a). On the other hand, H2CO-(a) should be neutralized by electron transfer back to the surface (although some nuclear relaxation could occur), and subsequent redistribution of H2CO(a) vibrational energy may take place, including a possible dissociation reaction. Therefore, in addition to the H2CO-(a) relaxation pathway, one has to consider possible channels of the C-H bond cleavage along the potential energy surface (PES) of neutral H2CO adsorbed on the silver surface. They are as follows: (1) dissociation into H2 + CO and (2) simultaneous or sequential C-H bond breaking leading to formation of 2H + CO products. In the former case, however, both fragments, H2 and CO, are weakly bound to Ag(111) and formaldehyde dissociation cannot be facilitated by the surface. A vibrationally excited molecule would rather desorb in this case, and dissociation is doubtful. This conclusion is supported by experiment, since no H2 has been found either in the gas phase or on the surface. Therefore, we can rule out this channel. By contrast, the energy of the H + HCO products and, therefore, the corresponding reaction barrier may be significantly lowered by the surface due to strong binding of atomic hydrogen (up to 2.4 eV10) and presumably also HCO to Ag(111). For the same reason, simultaneous breaking of two C-H bonds might also be quite effective. The subsequent H + CO dissociation of HCO is quite probable since the barrier for C-H bond breaking in HCO is only ∼0.2 eV in the gas phase.11 On the basis of this preliminary analysis, we have limited our investigations by considering only two model processes: (1) the breaking of two C-H bonds in adsorbed H2CO simultaneously and symmetrically, and (2) sequential dissociation with formation of adsorbed H/HCO as a first step (one C-H bond is fixed) and subsequent dissociation of the HCO radical. Both dissociation channels occur through formation of a substrate-mediated electron-attached intermediate state. Our purpose is to describe the reaction pathway, including nuclear rearrangement on both the anion and neutral PES, and to determine the corresponding fragmentation threshold. Finally, we will compare the C-H and C-O bond-breaking processes for adsorbed formaldehyde. II. Computational Procedure The silver-adsorbate system has been described by use of an embedded cluster method that allows us to carry out an accurate many-electron treatment of the adsorbate/surface portion of a system as well as to describe coupling in this region to the bulk lattice. Details of this method and reference to its previous applications to processes on metal surfaces involving ground and excited electronic states are reported in refs 7, 12, and 13. Briefly, there are 37 silver atoms in the surface layer and 27 each in the middle and bottom layers of the Ag91 cluster employed in the present study. Depending on the adsorbate, up

J. Phys. Chem. C, Vol. 111, No. 27, 2007 9915 to five of the seven central silver atoms that are located on the surface layer nearest to the adsorbed molecule have been described with a 28-electron Ag core and 4s, 4p, two 4d, 5s, and 5p atomic basis functions (AOs). All other silver atoms have either a 46-electron core plus a 5s function or a 47-electron core, depending on their remoteness from the central atom. Relativistic core potential functions are placed on all silver atoms, as discussed in ref 13. Each hydrogen atom of the adsorbate is described by two s and one p functions; carbon and oxygen have four s (10 primitive gaussians), two p (five primitives), and one d functions. An additional diffuse p function has been included in the AO basis sets of carbon and oxygen (with an exponent of 0.08 in each case) in order to afford a more accurate description of the binding. A similar p function has been added to the AO set of the Ag atoms with a 28-electron core, which provides a balance between the surface and adsorbate AO basis sets. Self-consistent field (SCF) calculations of appropriate multiplicity have been carried out for an adsorbate-cluster system. Then localization and the partitioning procedure described in ref 14 have been applied to the SCF molecular orbitals (MOs) to obtain pseudocanonical localized MOs (confined to the adsorption site). This transformation changes the SCF MOs of the system and allows us to have the electronic wave function localized on the adsorbate and surrounding cluster. In addition, this procedure usually reduces the configuration interaction (CI) expansion size, allowing one to obtain a more accurate energy for a given adsorbate electronic state. The localized MOs have been employed then as basis in the ab initio multireference CI (MRD-CI) calculations15 with a selection energy threshold of T ) 0.1 µHartree. The resultant total energies have been extrapolated to the full CI limit by employing the generalized Davidson correction.16 Substrate-mediated electron attachment to the formaldehyde molecule has been described as an electron transfer from Ag91 to the lowest unoccupied MO originating mostly from an adsorbate due to the localization procedure (it is, for example, π* at the equilibrium geometry of formaldehyde). This corresponds to the lowest charge-transfer state of the clusteradsorbate system, Ag91+-H2CO- (we do not consider states corresponding to internal Ag91 excitations in our study). Preliminary results for the adsorbate geometry along the reaction pathway have been optimized by use of the SCF energy for a state of the cluster-adsorbate system of an appropriate multiplicity as criterion. These data have then been refined in the MRD-CI calculations. Some restrictions have been made on the degrees of freedom varied: (a) the C-O distance and HCO internal geometry have been fixed over the whole pathway for dissociation into 2H + CO and HCO + H, respectively, and (b) H2CO has been considered to be symmetric with respect to the C-O axis for 2H + CO bond breaking. The binding energy of an adsorbed molecule has been determined with respect to the supermolecule (the neutral cluster plus the ground state of the separated adsorbate at its equilibrium geometry) at a cluster-adsorbate distance of ∼15a0. III. Results and Discussion A. Adsorption of H and HCO Fragments on Ag(111). Atomic hydrogen forms a polar covalent bond with surface atoms of the silver cluster in which the electronic charge is shifted toward the adsorbate. This is in fact similar to Ag(111)adsorbate bonds formed by molecular fragments with one open p-shell at the atom bound to the surface (as for the NH2 and OH species considered in ref 17). Specifically, an open shell of

9916 J. Phys. Chem. C, Vol. 111, No. 27, 2007 the Ag91-H doublet ground state changes its character from hydrogen AO at large adsorbate-surface distance R to Ag91(5s) as the equilibrium value of R is reached, whereas a set of doubly occupied hybrid Ag91-H MOs are formed instead. The Ag91-H ground state, therefore, correlates diabatically with ionic products Ag+91-H-. This also means that adsorbed hydrogen does not have open shells, and the complete pathway of the simultaneous C-H bond cleavage can be calculated on the closed-shell singlet ground-state PES. The binding energy of atomic hydrogen has been computed to be about 1.9 eV for the 3-fold hollow site (according to experimental data, it has been estimated to be ∼2.4 eV10) and the equilibrium value of R to be ∼2.5a0. In contrast to atomic hydrogen, HCO is weakly bound to Ag(111) mostly because of the small electron affinity of the formyl radical (0.313 eV).18 The computed binding energy of HCO is ∼0.5 eV and the equilibrium cluster-adsorbate distance is ∼7a0, which is typical for physisorption. The HCO-Ag(111) bond is so weak that the singly occupied MO of adsorbate-cluster system still keeps its HCO character upon adsorption, despite some hybridization of the doubly occupied HCO-Ag91 MOs. Due to its physisorption, HCO exhibits only small energy variations as it changes its position relative to the surface: the tilting angle of the CO axis away from the surface normal can be varied between θ ) 60° and 90° and the orientation angle of the HC axis relative to the surface normal can be varied from γ ) 90° up to γ ) 140° without notable change in binding energy (where γ ) 0° corresponds to HCO lying in a plane perpendicular to the silver surface with hydrogen tilted away from the surface). Since HCO still has an open shell upon adsorption and H does not, the H2CO(a) f HCO(a)-H(a) pathway has been computed on the closed-shell ground-state PES when the geometry of the H2CO molecule is close to equilibrium and only on the open-shell triplet-state PES when the C-H bond is about to be broken, rCH >3.8a0 (in our calculations, one singly occupied MO belongs to adsorbed HCO and the other to the Ag91 cluster). In the gas phase the HCO dissociation pathway into H + CO fragments has a small energy barrier of about 0.17 eV.11 On the surface, a hydrogen atom readily forms a chemical bond with silver upon increasing the C-H bond length by only ∼0.5a0 (γ ∼ 90°). Exploratory calculations of the HCO-Ag91 energy variation with increasing C-H distance, obtained without pathway optimization, give an upper limit for the HCO(a) f H(a) + CO reaction barrier of ∼0.2 eV, which is smaller than the HCO(a) binding energy. Therefore, it seems clear that HCO(a) can effectively dissociate into gas-phase CO and atomic hydrogen adsorbed on the silver surface. B. H2CO Photoinduced Dissociation on Ag(111). The energy variation of the Ag91-H2CO system is shown in Figure 1 as a function of the vertical cluster-adsorbate distance R. In this case H2CO is fixed parallel to the surface plane for the sake of simplicity. Since the formaldehyde molecule is only physisorbed, tilting of the CO axis relative to the surface normal within ϑ ) 60°-110° as well as variation of the molecular plane angle with respect to the surface plane within ∼0°-30° cause only minor changes in adsorption energy, although the tilted geometry may be slightly more favored. A pathway for an H2CO(a) f H(a) + HCO(a) reaction that is located entirely on the PES of the neutral adsorbate is shown by the dotted line in Figure 2 (it starts from the equilibrium H2CO geometry shown by point 1), where the contour plot of the Ag91-H2CO ground-state PES is given with respect to the rCH and R coordinates. A one-dimensional representation of the

Kokh et al.

Figure 1. Computed potential energy curves of ground and chargetransfer states as a function of the vertical distance R of the adsorbed molecule to the cluster surface: (b, O) -H2CO(a) has its gas-phase equilibrium geometry; (2, ]) -H2CO(a) is on the way to H(a) + HCO(a) dissociation (rC-H ) 3.2a0 for the C-H bond that is to be broken). Solid arrows show the reaction pathway for H(a) + HCO(a) dissociation. The molecule at its equilibrium rC-H value and for rC-H ) 3.2a0 has a different orientation with respect to the surface (see text).

Figure 2. Contour plot of the potential energy surface of the H2CO-Ag91 ground state representing the H2CO f H + HCO dissociation reaction. The reaction pathway shown by the solid line is also given in Figure 3 in a one-dimensional representation. Initial points (1)-(3) represent H2CO(a) formed from H2CO-(a) due to electron detachment.

same pathway along the rCH coordinate is also shown in Figure 3, as well as the dissociation pathway into CO-2H(a). In the same figure, the energy variation of gas-phase formaldehyde is shown for both fragmentation channels by dashed lines. It can be seen that the energy barrier is about 2.2 and 1.7 eV for dissociation into CO-2H(a) and HCO(a)-H(a), respectively, in contrast to values of 4.4 and 3.5 eV for the same reactions in the gas phase. Therefore, the silver surface notably reduces the formaldehyde dissociation energy due to binding of the distorted molecule to the surface. Strong adsorbate-surface binding becomes possible only when molecular distortion significantly weakens the C-H bond so that chemical bonds can be formed between the open-shell fragments (H and HCO) and the surface. In addition, in the case of HCO-H fragmentation, the lowest state of the Ag91-H2CO system becomes a triplet at rCH > 3.8a0, as has been noted in the previous section.

Photoinduced C-H Bond Cleavage in Formaldehyde

Figure 3. Reaction pathways of the H2CO(a) f H(a) + HCO(a) and H2CO(a) f 2H(a) + CO processes. Photoinduced electron transfer from the silver surface to an adsorbate excites H2CO to the π* electronattachment state. Subsequent reneutralization of H2CO-(a) leads to formation of vibrationally excited H2CO(a) that can then dissociate into H(a) + HCO(a) or 2H(a) + CO. Projections of the adsorbate positions [H2CO(a); H(a) + HCO(a); 2H(a)] are shown in the small panels. Distances between adsorbed hydrogen atoms and between H(a) and carbon atom of HCO(a) are rHH ) 5.1a0 and rCH ) 4.6a0, respectively.

One should point out, however, that excitation of neutral H2CO(a) to energies that would be above the dissociation barrier is hardly possible since the molecule is weakly bound to the surface and can easily desorb. Instead, as shown below, an intermediate anion state can enable the molecule to gain energy for overcoming a dissociation barrier. Photoinduced formation of the adsorbed H2CO-(a) anion is described in the present calculations by an electron transfer from the Ag91 cluster to the adsorbed H2CO molecule (Ag+-H2COstate, see Figure 1). In contrast to the neutral molecule, the anion is well stabilized on the surface due to an image charge (modeled by a positive hole of Ag91 in our calculations) and has a larger equilibrium C-O distance. This ensures that there is an excess of vibrational energy of H2CO-(a) during formation. Since a typical lifetime of an excited adsorbate on a metal surface (∼10-13-10-15 s)9 is comparable with the period of nuclear motion in H2CO (10-14 s), nuclear relaxation of formaldehyde may start on the anion PES. Subsequent anion neutralization can be described as a FC transition from Ag91+-H2CO- to the Ag91-H2CO state. Distorted H2CO(a) formed as a result of anion neutralization may desorb from the surface or dissociate if its energy is above the reaction barrier. Relative efficiency of these two reactions depends strongly on the geometry of H2CO(a) (that can be described as a starting point for the dissociation reaction on the Ag91-H2CO PES). An example of the dissociation process that is energetically possible, but nevertheless unlikely, is demonstrated in Figure 2 by a dotted arrow starting at point 2 and shown in the direction of H(a) + HCO(a) products. In this case H2CO(a), formed due to neutralization of the anion, possesses an excess of energy that is sufficient to overcome the dissociation barrier. However, the rapid gradient of the PES directed toward large R makes C-H bond breaking much less effective than desorption from the surface. And on the contrary, dissociation would very likely occur if the energy of the distorted H2CO(a) formed as a result of the FC transition is below its

J. Phys. Chem. C, Vol. 111, No. 27, 2007 9917

Figure 4. Reaction pathway of formaldehyde dissociation into CH2(a) + O(a) from ref 7. Projections of the positions of the adsorbates [H2CO(a); O(a) + CH2(a)] are shown in the small panels. Distance between carbon and oxygen atoms in adsorbed O(a) + CH2(a) is rCO ) 5.9a0.

desorption threshold but above the dissociation barrier. The latter case is illustrated by the pathway starting from point 3 and shown by a solid line in Figure 2. The total CH dissociation pathway is marked by the solid arrows in Figure 3. Although the energy variations shown in Figures 1-3 are only functions of the C-H and R distances, the molecular orientation relative to the surface and some other internal coordinates have also been optimized along the fragmentation pathway. In particular, the formaldehyde molecule inclines toward the surface as the C-H distance increases, since hydrogen atoms form stronger bonds than either the CO or HCO fragments. This result is consistent with the interpretation of experimental data suggested in ref 5, namely, that H2CO changes its tilting angle with respect to the surface upon dissociation. According to the present calculations, successful dissociation may take place at rC-H > 3.2a0 and rC-H > 2.7a0 for the H + HCO and 2H + CO reactions, respectively. The computed excitation energy thresholds are around 5.2 eV (5.1 and 5.3 eV for H + HCO and 2H + CO reactions, respectively), and their difference lies within the limits of uncertainty of our calculations. This indicates that both symmetric and antisymmetric stretch vibrations may initiate C-H bond cleavage. In addition, one should note that the excitation threshold computed in the present study does not mean that the dissociation process is forbidden at lower energies (because H2CO-(a) can already be formed at a photon energy of about 3.2 eV) but rather only that the reaction does not occur to a significant degree unless this value has been reached. This agrees with the interpretation of the experimental dependence of the C-O cross section on excitation wavelength proposed in ref 5, where the experimental data have been interpreted as corresponding to a large increase in CO formation in going from 355 to 266 nm excitation wavelength. C. Comparative Characteristics of Photoinduced C-H and C-O Bond Cleavage of H2CO on Ag(111). Finally, it is of interest to compare the dissociation processes leading to C-O and to C-H bond cleavage in H2CO(a). The pathway of the former reaction that has been analyzed in our prevous study7 is given in Figure 4. Upon comparing Figures 3 and 4, one can see a strong difference in the potential energy variation of adsorbed anion along the rC-O and rC-H coordinates. Since the

9918 J. Phys. Chem. C, Vol. 111, No. 27, 2007 formaldehyde anion is formed upon electron attachment to the π* antibonding orbital, the natural relaxation pathway of the H2CO- nuclei is directed toward increased C-O distance. This makes breaking of the C-O bond much more effective than C-H. Indeed, CH2 + O fragmentation needs about 1.6 eV excitation energy less than 2H + CO, even though the dissociation barrier on the ground-state PES for the former reaction is more than 1 eV higher than for the latter. One should also note that the difference of the computed excitation thresholds for C-O and C-H bond cleavage (∼1.6 eV) is in excellent agreement with the experimental results (3.1 eV1 and 4.66 eV,5 respectively), which indicates that underestimation of the stability of the adsorbed anion state is the main reason for the overestimation of the computed energy thresholds in both reactions. IV. Conclusion Photoinduced dissociation of formaldehyde adsorbed on Ag(111) through simultaneous or sequential C-H bond breaking has been analyzed by an embeded cluster theory and MRD-CI methods. The present calculations lead to the following overall picture of the dissociation process: The intermediate state for this process is an adsorbed formaldehyde anion formed by photoinduced electron transfer from the Ag(111) surface to the π* MO of the adsorbed molecule. As a result of the strong binding, the anion gains an excess of vibrational energy upon formation. This enables it to reach a critical geometry that causes an internal bond to be weakened and surface-fragment chemical bonds are formed. Electron detachment back to the surface leads to formation of distorted H2CO that is strongly bound to the surface. The subsequent fragmentation occurs along the PES of the neutral adsorbate. Because of the natural weakening of the C-O bond in the formaldehyde anion that serves as an intermediate in formaldehyde photodissociation on the surface, the energy threshold for the C-O bond breaking is lower than that of C-H, with the energy difference being about 1.6 eV. Finally, the binding energies of the dissociation fragments, hydrogen atom and HCO, on Ag(111) have been computed to be ∼1.9 and ∼0.5 eV, respectively. Acknowledgment. We thank the Deutsche Forschungsgemeinschaft (Grant BU 450/15-1) and the U.S. Department of

Kokh et al. Energy for their support of this work. We also thank Professor M. G. White for bringing this interesting problem to our attention. Most of the calculations have been performed on the Division of Natural Sciences, International Christian University of Osawa computer facilities, and we especially thank Dr. Luka´sˇ Pichl for affording this possibility. References and Notes (1) Fleck, L. E.; Feehery, W. F.; Plummer, E. W.; Ying, Z. C.; Dai, H. L. J. Phys. Chem. 1991, 95, 8428. (2) Fleck, L. E.; Ying, Z. C.; Feehery, M.; Dai, H. L. Surf. Sci. 1993, 296, 400. (3) Chuang, M.-Ch.; Foltz, M. F.; Moore, C. B. J. Chem. Phys. 1987, 87, 3855. (4) Fleck, L. E.; Howe, P.-T.; Kim, J.-S.; Dai, H.-L. J. Phys. Chem. 1996, 100, 8011. (5) Rao, R. M.; Dvorak, J.; Beuhler, R. J.; White, M. G. J. Phys. Chem. B 1998, 102, 9050. (6) Fleck, L.; Kim, J.-S.; Dai, H.-L. Surf. Sci. 1996, 356, L417. (7) Kokh, D. B.; Buenker, R. J.; Liebermann, H.-P.; Pichl, L.; Whitten, J. L. J. Phys. Chem. B 2005, 109, 18070. (8) Shibuya, K.; Fairchild, P. W.; Lee, E. K. C. J. Chem. Phys. 1981, 75, 3397. (9) Zhou, X.-L.; Zhu, X.-Y.; White, J. M. Surf. Sci. Rep. 1991, 13, 73. (10) Ertle, G. In The Nature of the Surface Chemical Bond; Rhodin, T. N., Ertl, G., Eds.; North-Holland: Amsterdam, 1979. (11) Werner, H.-J.; Bauer, C.; Rosmus, P.; Keller, H.-M.; Stumpf, M.; Schinke, R. J. Chem. Phys. 1995, 102, 3593. (12) (a) Whitten, J. L. J. Phys. Chem. A 2001, 105, 7091. (b) Whitten, J. L. J. Vac. Sci. Technol. A. 1999, 17, 1710. (c) Sremniak, L.; Whitten, J. L. Surf. Sci. 2002, 516, 254. (13) (a) Whitten, J. L.; Yang, H. Int. J. Quantum Chem. Quantum Chemistry Symposium 1995, 29, 41. (b) Whitten, J. L.; Yang, H. In Transition State Modeling for Catalysis; American Chemical Society: Washington, DC, 1998. (14) (a) Whitten, J. L.; Yang, H. Surf. Sci. Rep. 1996, 24, 55. (b) Buenker, R. J.; Liebermann, H. P.; Kokh, D. B.; Izgorodina, E. I.; Whitten, J. L. J. Chem. Phys. 2003, 291, 115. (15) (a) Buenker, R. J.; Peyerimhoff, S. D. Theor. Chim. Acta. 1974, 35, 33. (b) Buenker, R. J.; Peyerimhoff, S. D. Theor. Chim. Acta. 1975, 39, 217. (c) Buenker, R. J.; Peyerimhoff, S. D.; Butscher, W. Mol. Phys. 1978, 35, 771. (d) Krebs, S.; Buenker, R. J. J. Chem. Phys. 1995, 103, 5613. (16) Knowles, D. B.; Alvarez-Collado, J. R.; Hirsch, G.; Buenker, R. J. J. Chem. Phys. 1990, 92, 585. (17) Kokh, D. B; Buenker, R. J.; Whitten, J. L. Surf. Sci. 2006, 600, 5104. (18) Murray, K. K.; Miller, T. M.; Leopold, D. G.; Lineberger, W. C. J. Chem. Phys. 1986, 84, 2520.