It is documented in the Q-Chem manual that the FNO approximation can be used for EOM-IP calculations without losing much accuracy. I was wondering if it is applicable to EOM-EE-CCSD calculations. I tried to run a calculation like this and found that the job does run but (i) orbital symmetry is disabled and (ii) some of the states that were captured in a normal EOM-EE calculation are missing in the calculation using FNO, while some other states are actually reproduced in the FNO calculation with decent accuracy.
FNO procedure truncates the virtual orbital space based on the reference-state correlation criterion. Hence, for EOM states that live in the virtual space, such as EA (1p), DEA (2p), and EE (1h1p), this truncation may not be optimal – for example, diffuse orbitals are not very important for correlation, so they are likely to be excluded by FNO, which would affect the description Rydberg states (you may not even see them anymore). On the other hand, some excited states, such as low-lying valence excited states, should be captured reasonably well. I would expect that states like pi-pi* excitations in conjugate organic chromophores are described reasonably well by FNO. So you can use FNO for EOM-EE, but with a great caution.
In contrast, for EOM states that live in the occupied domain, such as IP (1h), DIP (2h), and SF, the truncation has the same effect as for the reference state - it does not affect the leading state character, only the correlation. That is why FNO works great for these states.
The current implementation does not properly tackle symmetry, so the computed FNOs may not be symmetry pure – that is why we turned symmetry off. We will eventually fix this issue. The actual symmetry of the many-body state is not affected by the FNO truncation.
Thanks for the explanation. That’s really helpful!