These errors are particularly prevalent in geometrically strained and spin-polarized systems, such as transition structures and transition metal clusters. Nevertheless, in certain cases symmetry breaking yields an improved treatment of static correlation at single-reference cost, though static and dynamic correlation can become poorly balanced in such cases. To correct spin contamination error, spin projection methods can be used to remove the contaminating spin states from a broken-symmetry determinant. When projection is carried out after a spin-contaminated determinant is fully converged, this approach is referred to as projection-after-variation (PAV). PAV schemes often maintain mean-field cost and recover static correlation without needing to explicitly rely on multi-reference methods. In contrast, variation-after-projection (VAP) methods variationally optimize a projected determinant, which will obtain static correlation and some dynamic correlation contributions as well.