A MD-based method to calculate free energy for crystalline structures: from basic theory to application

Free energy calculation is a challenging problem in molecular dynamics (MD). Its key issue is to get entropy. However, entropy seems difficult to be obtained by MD directly, but requires support from other methods, such as phonon theory and cluster variation method, etc. In this work, we find a way to obtain free energy by a single MD task. It is derived from phonon theory and fluctuation theory first, and then we prove that it does not rely on phonon theory but can be independent. Finally, we use this method to study Si, find the results in agreement with experiment.