Sato parameters

The substrate in these studies was restricted to be rigid, and Morse functions were used for the hydrogen-surface and two-body interactions. The parameters in the Morse functions were determined for single hydrogen atoms adsorbed on the tungsten surface by fitting to extended Huckel molecular orbital (EHMO) results, and the H2 Morse parameters were fit to gas-phase data. The Sato parameter, which enters the many-body LEPS prescription, was varied to produce a potential barrier for the desorption of H2 from the surface which matched experimental results. 

The Dlatomics-ln-Molecules Approach. The simple version of the DIM method that we employ is based on the Heitler-London approximation (28). In spirit, it is similar to the London-Eyring approach except that we use accurate diatomic potential curves (29a) rather than an approximate form for the diatomic triplet curve (e.g. the Sato parameter for LEPS surfaces) (29b). 

Assume that the binding curves for the asymptotic fragments are available and have been used to determine the relevant parameters (7>ab> ab> ab)> (Das, Kas. l As) (Dj,s, bs. bs)- The parameters for the interaction with jellium, (Dah, ah. ah) and (Dbh, bh. bh). are not adjustable, being determined by the SCF-LD values. Thus, the remaining variables in the PES, the so-called Sato parameters, Aab>A s, and A s, are undetermined and available for flexible representation of the full molecule-solid reactive PES. We consider the effect of these on the PES later. At this point, we do want to emphasize that the basic physics and chemistry— (1) interactions with localized and delocalized metal electrons and (2) nonadditive chemical bonding—are correct. We should also note that the representation of an interaction in metals in terms of an embedding function (in jellium) plus two-body terms is identical in spirit to the embedded atom method (EAM) (Daw and Baskes 1984, 1988). The distinction here is that we do not use the EAM for the A-B interaction and explicitly incorporated nonadditive energies via the LEPS prescription, both of which are important for the accurate representation of the reactive PES. 

First, consider variation of the two Sato parameters with the results shown in Fig. 23. The curves correspond to fixed A w as a function of Ann (=Agg)-In panel a, note that as either of the Sato parameters approaches 1, the barrier energy increases and the molecular well depth decreases. This is easy to understand since as either A-> — 1, the antibonding interaction increases to 00 and it is the separation between the bonding and antibonding... 

Figure 23. (a) Activation barrier and molecular well depth as function of the N-N and N-W Sato parameters (b) same as (a) except for the height of the barrier location above the surface plane (c) same as (a) except for the N-N bond length at the barrier location. The figure is reprinted with permission from Kara and DePristo (1988a). 

Next, consider the location of the barrier as shown in panels b and c. Some of the curves extend over a limited range because the barriers exist only over a small range. It is possible to place the barrier in either the entrance channel or the exit channel by variation of the Sato parameters. 

Next, we consider a LEPS PES for the FIj/NiflOO) system (Kara and DePristo, 1989), which is based upon recent ab initio calculations (Siegbahn et al. 1988) along with dynamically adjusted Sato parameters. Since the H—Ni binding energy is 2.7 eV while D h is 1.8 eV, the two-body terms do not dominate for this system. Contour plots in Fig. 25 demonstrate that there are small activation barriers of a 0.035 eV and 0.045 eV in the entrance channel of the bridge - center and atop center PES, respectively. The dependence of the entrance channel barrier on the orientation of H2 has not been determined quantitatively, but the dependence on r is quite weak. The variation with position in the unit cell is also weak. In addition, for the atop -> center dissociation there is also a barrier in the exit channel. The exit channel barrier obviously has a strong dependence upon bond length. Thus, the PES is quite complex. 

Instead of performing the normal mode analysis we have used a more approximate method to take the qr- -coordinates into account. For the Cl - - CH4/CD4 reactions wc have in some work used a tanh-function in the breaking bond to interpolate between the saddle point and the product asymptote to get both the reaction thermicity and AfA" consistent with the ah initio calculations[18]. In addition, if the effective potential energy surface of the system is modeled by the semiempirical London-Eyring-Polanyi-Sato (LEPS) function, the correction is made directly in the Morse parameters for the two reactive bonds by adjusting the Sato parameters) , 19]. 

In making adjustments to the Raff surface we found that while we are indeed able to make localized changes, the changes caused by varying individual Sato parameters are not nearly as independent of each other as was the case with the atom-diatom reaction F + H2. To raise the saddle point to approximately the height of the PolCI one, all three Sato parameters need to be adjusted simultaneously in order to prevent other local maxima and minima from occurring. 

We have calculated [53], the full photodissociation spectrum for the dissociation of H2 0 into OH(X tt)+H on the first absorption band, the A state. A LEPS potential was used for the dissociating state in which the Sato parameters were made 0 dependent and were varied to obtain a good fit to the ab initio data of Staemmler and Palma [43]. 

The parameters entering these equations are then the Sato parameter A =... 

We shall present results for several kinds of potential energy surfaces. Many of the surfaces are obtained by the London-Eyring-Polanyi-Sato (LEPS) method, involving a single adjustable (Sato) parameter, or by the extended LEPS method, in which different Sato parameters are used for different atomic pairs. These methods are reviewed elsewhere.For other calculations we used rotated Morse curves (RMC),semiempirical valence bond (VB) surfaces, and rotated-Morse-bond-energy-bond-order (RMBEBO) surfaces. 

Results for the Cl 4- CH system with an RMBEBO surface were included in Table 4, and Table 5 gives results for this system for both LEPS and extended LEPS surfaces. For these two surfaces we use the same set of equilibrium geometries, range parameters, and dissociation energies for the input Morse curves as we did for the RMBEBO surface, and we present results for two sets of Sato parameters. The first choice, a LEPS surface with all Sato parameters zero, yields a saddle point whose location and height are close to those obtained from the RMBEBO surface. The saddle point location is 3.42 ag, Tq = 3.22 ag, and the intrinsic barrier height... 

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