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Full control of spin symmetry using complex conjugation and time-reversal (spin-flip) projection

Ascertain whether complex conjugation projection combined with spin-flip projection (equivalently time-reversal projection) can fully control spin symmetry at short bond lengths for tetrahedral H4 within projected coupled cluster theory, given that this combination amounts to half-spin projection and was insufficient to achieve full control in the reported calculations.

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Background

Tetrahedral H4 exhibits spin frustration and multiple mean-field solutions, many breaking time-reversal symmetry. The authors restore complex conjugation and time reversal by projecting complex conjugation and spin-flip.

They report that at short bond lengths this combined projection only achieves half-spin projection and does not fully control spin symmetry, implying the need to assess whether full spin projection must be integrated or whether enhanced half-spin strategies could suffice.

References

However, at sufficiently short bond length we are unable to fully control spin symmetry just by complex conjugation and time reversal projection since, as we noted, this amounts to only half-spin projection.

— Combining complex conjugation, time-reversal, and spin symmetry projection of coupled cluster wave functions (2405.06776 - Song et al., 10 May 2024) in Section "H4"