Spin-adapted open-shell time-dependent density functional theory: towards a simple and accurate method for spin-flip-down excitations

A major challenge in using spin-flip time-dependent density functional theory (SF-TD-DFT) for spin-flip-down excitations is the presence of spin contamination. While several improved methods have been developed in the past, a simple and accurate method remains elusive. Here, based on our previous development on spin-adapted open-shell TD-DFT for spin-conserving excitations (X-TD-DFT) [Z. Li and W. Liu, J. Chem. Phys. 135, 194106 (2011)], we introduce a method termed as XSF-TDA for modeling spin-flip-down excitations, and provide an in-depth comparison of different methodologies for mitigating spin contamination in SF-TDA. Pilot applications to prototype systems demonstrate the promise of XSF-TDA over existing SF-TDA methods, including unrestricted SF-TDA (USF-TDA) and mixed-reference SF-TDA (MRSF-TDA), in describing bond breakings and inverted singlet-triplet gap systems.