Conclusion

By our "driven" KMC method, we were able to get reasonable values of the Soret coefficient in comparison to the previous MD simulations. To our knowledge, application of KMC to this problem has not yet been attempted. Starting from relative ignorance forced us to make non tested approximations. Thus, the only criterion of judging these assumptions is our results. Some of these assumptions are that, transition state theory is still valid in presence of a temperature gradient, the use of a local temperature dependent transition probability is valid, the frequency factor of transition probability is not temperature dependent, the use of large temperature gradients ($\sim$ 1 K / lattice constant) is justified in KMC simulations, and lattice relaxation processes can be neglected.
In comparison to MD simulations, in MD there is an added uncertainty due to the thermostats used and the mechanisms (mostly artificial particle exchanges or fictitious forces) used to impose such temperature gradients. Since the system size used in MD is usually small, this forces the concentration gradient (measured usually by counting the number of particles in a slab) to have large random errors. This might make the measured concentration gradient, which is a small magnitude, unreliable. We feel that if it is possible MC studies in these cases have more reliability than MD studies since there is no temperature uncertainty and there is no need for elaborate artificial schemes to impose temperature fields.