The Self-Consistent Field in Kohn-Sham Density Functional Theory: A Review of Methods and Algorithms*

Software that computes the electronic structure of a material by searching for an infimum of the Kohn-Sham energy functional - achieving self-consistency - requires the use of an algorithm that iterates an initial estimate of the particle density toward the self-consistent particle density. We present a review of methods and algorithms that solve this problem in the context of plane-wave, pseudopotential density functional theory.

This review involves first identifying features intrinsic to the Kohn-Sham framework that produce sources of numerical difficulty for self-consistency algorithms. A test suite of over fifty Kohn-Sham inputs is then designed in order to exploit these difficulties and target weaknesses in contemporary algorithms. In order to utilise this test suite, a sample of methods from literature are then implemented in the plane-wave, pseudopotential density functional theory code, CASTEP. These methods are then benchmarked on the test suite, and a novel set of analysis tools allow us to determine the effectiveness of each method. We believe this study will not only elucidate the current state of the literature, but also assist future method development by providing a systematic work-flow for presenting new methods and assessing their effectiveness.