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.

GRAPHICAL ABSTRACT

KEYWORDS:

• Approximate projection
• spin contamination
• spin projection
• unrestricted SCF

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

We gratefully acknowledge support from UC Merced and computing time on the Multi-Environment Computer for Exploration and Discovery (MERCED) cluster which is supported by National Science Foundation (Division of Advanced Cyberinfrastructure) grant number ACI-1429783. H.P.H. also acknowledges support from the American Chemical Society Petroleum Research Fund (ACS-PRF No. 56806-DNI6) and the Hellman Fellows Fund for a faculty fellowship.