We develop a projector-based formulation of the coherent potential approximation (CPA) within a pseudopotential Hamiltonian in the framework of density functional theory. In the pseudoatomic-sphere scheme, the projectors are constructed from corelike orbitals localized near each pseudoatomic site, which enables a systematic treatment of element-dependent site scattering in pseudized Hamiltonians without relying on explicit atomic-sphere boundaries or intermediate effective model Hamiltonians. In the unit-cell scheme, by contrast, the projectors are defined by window functions that extract the potential contribution at individual mesh points over a unit cell. This generalizes the single-site scattering picture to a unit-cell scattering picture that incorporates the full potential within each unit cell, and fits naturally into a plane-wave-based framework. We assess both schemes by computing the density of states for a one-dimensional Gaussian-well chain with the orthogonalized plane wave method. Because the pseudized potential has a small contribution inside the pseudoatomic sphere, the pseudoatomic-sphere scheme yields results almost indistinguishable from the virtual crystal approximation. In contrast, the unit-cell scheme successfully reproduces the split-band feature characteristic of CPA in strongly disordered alloys. The present work paves the way for extending plane-wave-based ab initio methods to chemically disordered alloy systems.

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• Crystal structure
• Electrical properties
• Electronic structure
• Phonons
• Disordered alloys
• Density functional theory
• First-principles calculations
• Plane-wave expansion