The hybrid halide perovskite ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$ exhibits a complex structural behavior, with successive transitions between orthorhombic, tetragonal, and cubic polymorphs around 165 and 327 K. Herein we report first-principles lattice dynamics (phonon spectrum) for each phase of ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$. The equilibrium structures compare well to solutions of temperature-dependent powder neutron diffraction. By following the normal modes, we calculate infrared and Raman intensities of the vibrations, and compare them to the measurement of a single crystal where the Raman laser is controlled to avoid degradation of the sample. Despite a clear separation in energy between low-frequency modes associated with the inorganic (${\mathrm{PbI}}_3{}^{-}{)}_n$ network and high-frequency modes of the organic ${\mathrm{CH}}_3{\mathrm{NH}}_3{}^{+}$ cation, significant coupling between them is found, which emphasizes the interplay between molecular orientation and the corner-sharing octahedral networks in the structural transformations. Soft modes are found at the boundary of the Brillouin zone of the cubic phase, consistent with displacive instabilities and anharmonicity involving tilting of the ${\mathrm{PbI}}_6$ octahedra around room temperature.

Forming a four-component compound from the first 103 elements of the periodic table results in more than 1012 combinations. Such a materials space is intractable to high-throughput experiment or first-principle computation. We introduce a framework to address this problem and quantify how many materials can exist. We apply principles of valency and electronegativity to filter chemically implausible compositions, which reduces the inorganic quaternary space to 1010 combinations. We demonstrate that estimates of band gaps and absolute electron energies can be made simply on the basis of the chemical composition and apply this to the search for new semiconducting materials to support the photoelectrochemical splitting of water. We show the applicability to predicting crystal structure by analogy with known compounds, including exploration of the phase space for ternary combinations that form a perovskite lattice. Computer screening reproduces known perovskite materials and predicts the feasibility of thousands more. Given the simplicity of the approach, large-scale searches can be performed on a single workstation.

Cu₂ZnSnS₄ (CZTS) is a promising material for photovoltaic and thermoelectric applications. Issues with quaternary semiconductors include chemical disorder (e.g., Cu–Zn antisites) and disproportionation into secondary phases (e.g., ZnS and Cu₂SnS₃). To provide a reference for the pure kesterite structure, we report the vibrational spectra—including both infra-red and Raman intensities—from lattice-dynamics calculations using first-principles force constants. Three-phonon interactions are used to estimate phonon lifetimes (spectral linewidths) and thermal conductivity. CZTS exhibits a remarkably low lattice thermal conductivity, competitive with high-performance thermoelectric materials. Transition from the sulfide to selenide (Cu₂ZnSnSe₄) results in softening of the phonon modes and an increase in phonon lifetimes.