Slave Mode Expansion for Obtaining Ab Initio Interatomic Potentials and its Applications

Having an interatomic potential overcomes limitations within DFT since it has a negligible cost in computing material properties while DFT is severely restricted by its computational cost when carrying out such tasks. In this thesis, we propose a new approach for creating an interatomic potential based on the Taylor series expansion of the crystal energy as a function of its nuclear displacements. We enlarge the dimensionality of the existing displacement space and form new variables (ie. slave modes) which transform like irreducible representations of the point group and satisfy homogeneity of free space. Standard group theoretical techniques can then be applied to deduce the non-zero expansion coefficients a priori. At a given order, the translation group can be used to contract the products and eliminate terms which are not linearly independent, resulting in a final set of slave mode products. By the end of the day, one ends up with an expansion that satisfies lattice symmetry and its number of coefficients is much smaller than that of a common Taylor series expansion. While the expansion coefficients can be computed in a variety of ways, we demonstrate that finite difference is effective up to fifth order. On the other hand, we demonstrate the power of the method in the strongly anharmonic systems PbTe and graphene. All anharmonic terms within an octahedron are computed up to fourth order for PbTe, while those within a hexagon are computed up to fourth order and dimer terms are computed at fifth order for graphene. In addition, for PbTe, a proper unitary transformation of its potential demonstrates that the vast majority of the anharmonicity can be attributed to just two terms, indicating that a minimal model of phonon interactions is achievable. The ability to straightforwardly generate polynomial potentials will allow precise simulations at length and time scales which were previously unrealizable.