The unparalleled structural diversity of intermetallic compounds provides nearly unlimited poten-tial for the discovery and optimization of materials with useful properties, such as thermoelectricity, superconductivity, magnetism, hydrogen storage, superelasticity, and catalysis. This same diversity, however, creates challenges for understanding and controlling the unpredictable structure of interme-tallic phases. Moreover, the fundamental design principles that have proven so powerful in molecular chemistry do not have simple analogues for metallic, solid state materials. One of these basic principles is the concept of atomic size effects. Especially in densely packed crys-tal structures where the need to fill space is in competition with the atoms’ preferences for ideal intera-tomic distances, substitution of one element in a compound for another with similar chemical proper-ties yet different atomic size can have dramatic effects on the ordering of the atoms (which in turn af-fects the electronic structure, vibrational properties, and materials properties). But because the forces that hold metallic phases together are less easily understood from a local perspective than covalent or ionic interactions in other kinds of materials, it is usually unclear whether the atoms are organized to optimize stabilizing, bonding interactions or rather forced to be close together despite repulsive, steric interactions. This dissertation details the development of a theoretical method, called Density Functional Theo-ry-Chemical Pressure (DFT-CP) analysis, to address this issue. It works by converting the distribution of total energy density from a DFT calculation into a map of chemical pressure through a numerical ap-proximation of the first derivative of energy with respect to voxel volume. The CP distribution is then carefully divided into contact volumes between neighboring atoms, from which it is possible to deter-mine whether atoms are too close together (positive CP) or too far away from each other (negative CP). This technique is used in combination with the concept of structural plasticity (Berns, 2014) to demonstrate how complex intermetallic phases can be understood as a response of simpler structure types to the destabilizing buildup of CP. From this point of view, interfaces created in complex struc-tures relieve the CP manifest in the more basic, parent structures. This is shown specifically for Ca36Sn23 relative to a hypothetical W5Si3-type Ca5Sn3 phase, LnMnxGa3 (Ln = Ho-Tm, x < 0.15) com-pared to unstuffed AuCu3-type LnGa3 structures, and structural derivatives of CaCu5- and HoCoGa5-type compounds. As a direct result of the technical developments necessitated by these analyses on structural com-plexity in intermetallics, a further connection is made in this thesis between the calculated CP schemes and the frequencies of vibrational modes in MgCu2-type CaPd2, the Cr3Si-type superconductor Nb3Ge, and CaCu5-type CaPd5. Local chemical interactions revealed by DFT-CP analysis are used to identify structure-property relationships for the pseudogap in the phonon density of states (DOS) of CaPd2, the higher critical temperature of Nb3Ge vs. Nb3Sn, and the wide diversity of structures based on the CaCu5 type.