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Abstract Ensemble density functional theory (EDFT) is a generalization of ground-state DFT, which is based on an exact formal theory of finite collections of a system’s ground and excited states. EDFT in various forms has been shown to improve the accuracy of calculated energy level differences in isolated model systems, atoms, and molecules, but it is not yet clear how EDFT could be used to calculate band gaps for periodic systems. We extend the application of EDFT toward periodic systems by estimating the thermodynamic limit with increasingly large finite one-dimensional ‘particle in a box’ systems, which approach the uniform electron gas (UEG). Using ensemble-generalized Hartree and local spin density approximation exchange-correlation functionals, we find that corrections go to zero in the infinite limit, as expected for a metallic system. However, there is a correction to the effective mass, with results comparable to other calculations on 1D, 2D, and 3D UEGs, which indicates promise for non-trivial results from EDFT on periodic systems. 

Abstract Maximum overlap methods are effective tools for optimizing challenging ground‐ and excited‐state wave functions using self‐consistent field models such as Hartree‐Fock and Kohn‐Sham density functional theory. Nevertheless, such models have shown significant sensitivity to the user‐defined initial guess of the target wave function. In this work, a projection operator framework is defined and used to provide a metric for non‐aufbau orbital selection in maximum‐overlap‐methods. The resulting algorithms, termed the Projection‐based Maximum Overlap Method (PMOM) and Projection‐based Initial Maximum Overlap Method (PIMOM), are shown to perform exceptionally well when using simple user‐defined target solutions based on occupied/virtual molecular orbital permutations. This work also presents a new metric that provides a simple and conceptually convenient measure of agreement between the desired target and the current or final SCF results during a calculation employing a maximum‐overlap method.