Revisiting Spin Contamination in Mixed-Reference Spin-Flip Time-Dependent Density-Functional Theory
Year: 2026
Type: preprint
Abstract: Mixed reference spin-flip time-dependent density-functional theory (MRSF-TDDFT) has achieved widespread adoption as a computational method for describing photochemistry beyond the Franck–Condon region, as it removes most of the spin contamination limiting previous spin-flip (SF-)TDDFT approaches. The C → V excitation space, in which an electron from a doubly occupied (closed) orbital is promoted to an unoccupied (virtual) orbital, remains spin-incomplete in MRSF-TDDFT. The contamination induced by this incompleteness has consistently been reported as negligible, since the missing configurations are expected to be high in energy, thus barely coupling to low-lying vertical excitations. We show that the expression for 〈Ŝ 2 〉, which these assessments are based on, is erroneous and misses a key contribution of C → V excitations in singlet states, while triplet states always remain spin-pure. We derive and implement a corrected equation for 〈Ŝ 2 〉 and show that low-lying excited states with significant spin contamination become unavoidable if the singly occupied orbitals (SOMOs) localize onto a subsystem, decouple by symmetry, or if the density of orbitals around the Fermi level is high. We find that these results are virtually independent of the choice of density-functional approximation, but do not seem to impact the accuracy of excitation energies and spectroscopic properties. Nonetheless, these results show that severe spin contamination in MRSF-TDDFT becomes unavoidable when describing extended systems or the collective behavior of many chromophores.
Source: ChemRxiv
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221601431