MOs and occupations for a calculated spin-flip TD-DFT singlet ground state?

Using collinear spin-flip(SF) TD-DFT with the Tamm-Dancoff approximation, BHanHLYP and a simple test molecule (ethene, with a singlet ground state).

It’s my understanding, using ethene as an example, that spin-flip DFT starts with a unrestricted Kohn-Sham single-reference triplet reference state, then generates the other TD-DFT ‘excited’ states using the MOs and occupancies from that reference state and a calculated excitation vector. The relative energy of the ground state can be calculated, and the molecular geometry can be optimized on this ground-state PES. So far, so good.

My question is: can the wavefunction of the resulting singlet SF ground state, which appears as an effective negative-energy ‘excited’ state, have its electron density distribution represented (and written in machine-readable form), as another set of only MOs and occupancies?

It doesn’t matter if this output set is single-reference or multi-reference, for my purposes, just so long as it can be output as only MOs and occupations.

Can Q-Chem do this? Does the Tamm-Dancoff approximation need to be dropped in order to achieve this?

I’m not sure what you mean by “only” MOs and occupancies. Like normal TDDFT, spin-flip starts from a single-determinant reference state with spin S+1 (high-spin triplet in your example) then generates target states of spin S (singlets, in your example), essentially as CI expansions. This means that the S0 state has multiconfigurational character in principle, even if it’s nominally (meaning mostly) just a single closed-shell determinant. See Fig. 4 here: 10.26434/chemrxiv-2022-gj75d

Hello John,
Yes, when I say ‘only’ , I mean ‘nothing else is needed’. Also yes, I expected that the multireference set of MOs and occupations representing the total density would be almost entirely dominated (in terms of weighting) by the ground state singlet S0. What I’m looking for is the complete set of MOs and occupations representing not just the reference state density, but the total density (i.e. all states), in .fchk, MOLDEN or WFX format. Is there a way to get this?

The ground-state density (of the SF-TDDFT ground state) can be exactly represented by the natural orbitals and their occupations computed for the SF-TDDFT state (this can be done using libwfa). You can use these orbitals and their (fractional) occupations to analyze bonding pattern (e.g., compute the number of effectively unpaired electrons) and to compute some one-electron properties (e.g., dipole moments). However, this density is not sufficient to compute properties that require full density matrix (e.g., kinetic energy).

This paper shows possible uses of natural orbitals and their occupations in the context of multi-configurational wave-functions: