Searching for the optimum conditions for silicene growth by calculations of the free energy

Very recently we developed an efficient method to calculate the free energy of 2D materials on substrates and achieved high calculation precision for graphene or $\gamma$-graphyne on copper substrates. In the present work, the method was further confirmed to be accurate by molecular dynamic simulations of silicene on Ag substrate using empirical potential and was applied to predict the optimum conditions based on \emph{ab initio} calculations for silicene growth on Ag (110) and Ag (111) surface, which are in good agreement with previous experimental observations.