Estimations of Total Energy and Impurity Formation Energy under Large Deformations Based upon Local Strain: Algorithms and Practices*

At large strains, it is difficult to estimate the total energy and impurity formation energy of materials, although at small strains, linear fits from equilibrium can give good estimates. In this report, we define a local perturbation for any strain as local strain, use it to perform Taylor expansion on the above energy, and then use a series of such Taylor expansions to characterize the situation under any large strain. Then taking the incorporation of indium atoms, magnesium atoms, and nitrogen vacancies into gallium nitride as examples, we found that the errors of the results obtained by the new algorithm are an order of magnitude smaller than that of the linear fitting. In addition, during the fitting process, we confirmed that the volume ratio before and after doping under equilibrium conditions is a conserved quantity, which greatly simplifies and accelerates the corresponding estimations.