Generalized Langevin Treatment of Gas-Surface Dynamics

As discussed in the previous section a brute-force molecular-dynamics simulation of gas-surface dynamics, although simple in principle, is a large computational problem. Though these direct methods will continue to be of use, particularly in providing numerical benchmarks for the calibration of more approximate methods, it will prove useful to search for more efficient methods. The chief defect of direct methods when applied to gas-solid scattering is that the essentially harmonic chatracter of the lattice is not fully exploited. We expect that the strong, direct interaction with the solid will involve a relatively small number of lattice 

In the present context it is important to emphasize that the above discussion applies equally well to situations where the original lattice is either finite or infinite. All that is required for the present analysis is that the background lattice be harmonic and that it be harmonically coupled to the primary zone. Obviously if the entire lattice consists of only a few atoms, direct molecular-dynamics simulations are appropriate. However, even submicron-size particles contain a sufficiently large number of constituent atoms to make the present approach advantageous. 

The present section outlines the approach discussed above. Detailed developments are given elsewhere [3.36-40]. This approach is an outgrowth of previous work along these lines, principally by ZWANZIG [3.4] and by GOODMAN [3.1,5]. Recently SHUGARD et al. [3.41] have presented related but independent developments. 

Here X denotes the gas coordinate and x the lattice displacements, the latter in some suitably chosen mass weighted units. We assume that the gas particle interacts 

Since the gas does not interact directly with x, we write 

---