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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.