Efficacious symmetry-adapted atomic displacement method for lattice dynamical studies

Small displacement methods have been successfully used to calculate the lattice dynamical properties of crystals. It involves displacing atoms by a small amount in order induced forces on all supercell for computation force constants. Even though these are widely use, our knowledge, there is no systematic discussion optimal directions from crystal's symmetry point view nor rigorous error analysis such methods. Based group theory and crystal, we propose directions, with an equivalent concept $k$, deduced directly Cartesian coordinates rather than usual fractional coordinates, that maintain theoretical maximum triple product $V$ spanned three displacements avoid possible severe roundoff errors. The proposed generated minimal set irreducible atomic keep required independent calculations minimum. We find calculated constant explicitly depends inverse inaccuracy forces. Test systems as Si, graphene, orthorhombic Sb2S3 illustrate method. Our method shown be very robust treating low-symmetry cells large `aspect ratio' due huge differences parameters, use vacuum height, or oblique unit cell unconventional choice primitive vectors. expected strategy can address higher-order interatomic interactions achieve good accuracy efficiency.