Thermodynamics of Interacting Phonons

Many thermodynamic properties of materials can be attributed to phonons and their interactions, also known as the Taylor series of the Born-Oppenheimer (BO) energy surface. In this the- sis, we present several novel approaches to computing phonons and their interactions, as well as implementations to predict thermodynamic properties of materials from phonons and phonon interactions. First, we implemented the symmetry analysis technique that allows us to write the Taylor series of the BO energy surface for a material at arbitrary order N using the space group irreducible derivatives, guaranteeing the symmetry of the crystal by construction. Second, we derived the minimum supercell multiplicity equation with which we can compute the smallest possible supercells that can accommodate N given wave vectors, greatly improving the computational efficiency for finite displacements calculations. Third, we implemented 2 branches of finite displacements methodologies, lone irreducible derivatives (LID) and bundled irreducible derivatives (BID), with the former sacrificing efficiency for accuracy and the latter emphasizing on using the least amount of calculations to extract all irreducible derivatives. Additionally, we implemented algorithms to predict materials properties including Grüneisen parameters, phonon linewidth, phonon frequency shift and thermal conductivity using our space group irreducible derivatives. We applied our methods on a wide range of materials, and the comparison against literature demonstrated massive gain on efficiency while maintaining high quality results.