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PreprintCC BYChemRxiv

Revisiting Spin Contamination in Mixed-Reference Spin-Flip Time-Dependent Density-Functional Theory

  • Samuel Dier1,2
  • Linus Bjarne Dittmer3
  • Anton Rikus1
  • Andreas Dreuw3
  • Johannes Neugebauer1
  1. 1Organisch-Chemisches Institut and Center for Multiscale Theory and Computation, University of Münster, Corrensstraße 36, Münster, Germany, 48149
  2. 2Theoretical Chemistry, Ruhr Universität Bochum, Universitätsstr. 150, Bochum, Germany, 44801
  3. 3Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205A, Heidelberg, Germany, 69120
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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.

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Cite

BibTeXRIS
BibTeX
@misc{dier2026revisiting,
  title = {{Revisiting Spin Contamination in Mixed-Reference Spin-Flip Time-Dependent Density-Functional Theory}},
  author = {Samuel Dier and Linus Bjarne Dittmer and Anton Rikus and Andreas Dreuw and Johannes Neugebauer},
  howpublished = {ChemRxiv},
  year = {2026},
  month = oct,
  doi = {10.26434/chemrxiv.15010307/v1},
  url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010307/v1},
  note = {CC BY},
}
RIS
TY  - UNPB
TI  - Revisiting Spin Contamination in Mixed-Reference Spin-Flip Time-Dependent Density-Functional Theory
AU  - Samuel Dier
AU  - Linus Bjarne Dittmer
AU  - Anton Rikus
AU  - Andreas Dreuw
AU  - Johannes Neugebauer
PY  - 2026
DA  - 2026/10/12
PB  - ChemRxiv
DO  - 10.26434/chemrxiv.15010307/v1
UR  - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010307/v1
AB  - 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.
ER  -