ARES-Phonon: Phonon Calculation Package using Nondiagonal Supercell Finite Displacement Method with Machine Learning

We have developed a phonon calculation software based on the supercell finite displacement method: ARES-Phonon. It can perform phonon and related property calculations using either non-diagonal or diagonal supercell approaches. Particularly for the non-diagonal supercell method, for phonons with wave vectors $(\frac{n_1}{m_1},\frac{n_2}{m_2},\frac{n_3}{m_3})$, only a non-diagonal supercell of size equal to the least common multiple of $m_1{m}_2{m}_3$ needs to be constructed, significantly reducing the computational burden. We have tested this method on Diamond, $Mo{S}_2$, and $S{i}_3{O}_6$ systems, and the results indicate that this approach can achieve the same level of accuracy as density functional perturbation theory. Speed tests were conducted for systems of different sizes, varying symmetries, and sampling densities of Brillouin zone $\mathit{\text{q}}$ points, showing that compared to the diagonal supercell method, the non-diagonal approach is approximately an order of magnitude faster and becomes even more efficient with increasing system complexity. Combining this method with machine learning potentials based on synchronous learning techniques, a further reduction of approximately $90\mathrm{\%}$ in computational cost can be achieved while maintaining reliable accuracy.