A new framework is presented for evaluating the performance of self-consistent field methods in Kohn-Sham density functional theory. The aims of this work are two-fold. First, we explore the properties of Kohn-Sham density functional theory as it pertains to the convergence of selfconsistent field iterations. Sources of inefficiencies and instabilities are identified, and methods to mitigate these difficulties are discussed. Second, we introduce a framework to assess the relative utility of algorithms in the present context, comprising a representative benchmark suite of over fifty Kohn-Sham simulation inputs, the scf-xn suite. This provides a new tool to develop, evaluate and compare new algorithms in a fair, well-defined and transparent manner. CONTENTS

The exact exchange-correlation (xc) kernel f xc (x, x , ω) of linear response time-dependent density functional theory is computed over a wide range of frequencies for three canonical one-dimensional finite systems. Methods used to ensure the numerical robustness of f xc are set out. The frequency dependence of f xc is found to be largely due to its analytic structure, i.e., its singularities at certain frequencies, which are required in order to capture particular transitions, including those of double excitation character. However, within the frequency range of the first few interacting excitations, f xc is approximately ω independent, meaning the exact adiabatic approximation f xc (ω = 0) remedies the failings of the local density approximation and random phase approximation for these lowest transitions. The key differences between the exact f xc and its common approximations are analyzed, and cannot be eliminated by exploiting the limited gauge freedom in f xc . The optical spectrum benefits from using as accurate as possible an f xc and ground-state xc potential, while maintaining exact compatibility between the two is of less importance.

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