On approximate projection models

Abstract

Approximate projection (AP) schemes are widely used in computational studies of diradicals and transition metal systems to remove spin contamination in unrestricted density functional theory and Hartree–Fock results. Spin contamination results from an inability of single-reference descriptions to correctly model orbital degeneracies. Spin projection methods, including AP, avoid more expensive approaches using multi-reference wave functions to rectify the spin contamination error. Efficient derivations of the AP derivatives have allowed the computation of improved geometries and properties. In this work, we establish a connection between AP and formulations developed using Löwdin's projection operator to obtain an understanding of where the method will work and highlight situations in which caution should be exercised.