Toward the Systematic Design of Complex Materials from Structural Motifs

With first-principles calculations based on density functional theory, we can predict with good accuracy the electronic ground state properties of a fixed arrangement of nuclei in a molecule or crystal. However, the potential of this formalism and approach is not fully utilized; most calculations are performed on experimentally determined structures and stoichiometric substitutions of those systems. This in part stems from the difficulty of systematically generating 3D geometries that are chemically valid under the complex interactions existing in materials. Designing materials is a bottleneck for computational materials exploration; there is a need for systematic design tools that can keep up with our calculation capacity. Identifying a higher level language to articulate designs at the atomic scale rather than simply points in 3D space can aid in developing these tools.Constituent atoms of materials tend to arrange in recognizable patterns with defined symmetry such as coordination polyhedra in transition metal oxides or subgroups of organic molecules; we call these structural motifs. In this thesis, we advance a variety of systematic strategies for understanding complex materials from structural motifs on the atomic scale with an eye towards future design.In collaboration with experiment, we introduce the harmonic honeycomb iridates with frustrated, spin-anisotropic magnetism. At the atomic level, the harmonic honeycomb iridates have identical local geometry where each iridium atom octahedrally coordinated by oxygen hosts a $J_{eff}=1/2$ spin state that experiences interactions in orthogonal spin directions from three neighboring iridium atoms. A homologous series of harmonic honeycomb can be constructed by changing the connectivity of their basic structural units.Also in collaboration with experiment, we investigate the metal-organic chalcogenide assembly [AgSePh]$_\infty$ that hosts 2D physics in a bulk 3D crystal. In this material, inorganic AgSe layers are scaffolded by organic phenyl ligands preventing the inorganic layers from strongly interacting. While bulk Ag$_2$Se is an indirect band gap semiconductor, [AgSePh]$_\infty$ has a direct band gap and photoluminesces blue. We propose that these hybrid systems present a promising alternative approach to exploring and controlling low-dimensional physics due to their ease of synthesis and robustness to the ambient environment, contrasting sharply with the difficulty of isolating and maintaining traditional low-dimensional materials such as graphene and MoS$_2$.Automated density functional theory via high throughput approaches are a promising means of identifying new materials with a given property. We automate a search for ferroelectric materials by integrating density functional theory calculations, crystal structure databases, symmetry tools, workflow software, and a custom analysis toolkit. Structural distortions that occur in the structural motifs of ferroelectrics give rise to a switchable spontaneous polarization. In ferroelectrics lattice, spin, and electronic degrees of freedom couple leading to exotic physical phenomena and making them technologically useful (e.g. non-volatile RAM). We also propose a new neural network architecture that encodes the symmetries of 3D Euclidean space for learning the structural motifs of atomic systems. We describe how these networks can be used to speed up important components of the computational materials discovery pipeline and generate hypothetical stable atomic structures.Finally, we conclude with a discussion of the materials design tools deep learning may enable and how these tools could be guided by the intuition of materials scientists