This article addresses a fundamental problem faced by the ab initio community: the lack of an effective formalism for the rapid exploration and exchange of new methods. To rectify this, we introduce a novel, basis-set independent, matrix-based formulation of generalized density functional theories which reduces the development, implementation, and dissemination of new ab initio techniques to the derivation and transcription of a few lines of algebra. This new framework enables us to herein provide complete instructions for the construction of fully functional, highly efficient production codes for ab initio calculations employing arbitrary basis sets. Within this framework, we also discuss in full detail a variety of leading-edge ab initio techniques, minimization algorithms, and highly efficient computational kernels for use with scalar as well a
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