I am interested in calculating IPs (cationic states) corresponding to ionization out of deeply lying orbitals, in particular L-shell orbitals, i.e. 2s of C, N or O, for a large system (about 30 atoms). Specifying very large (for instance 70) number of states to be calculated doesn’t help, as the 2s ionized states lie deeper, and further increasing the number of states leads to a crash of the calculation. Specifying the initial guess also does not help much. I wonder if there is some way/trick to reach those states? Can one use CVS-IP-EOM in this case?
Many thanks for your reply! I did try to use CVS-IP-EOM-CCSD to get ionization out of a C 2s orbital in benzene, having used example 7.66 in section 7.10.8 in the on-line manual, as a test. I first changed
CVS_IP_STATES = [2,1,0,0,0,0,1,2]
to
CVS_IP_STATES = [3,1,0,0,0,0,1,2]
hoping to get ionization out of the lowest C 2s of Ag symmetry. However, what I got was a C 1s-ionized satellite state (corresponding to ionization out of a C1s plus excitation involving C1s core orbitals) rather than ionization out of a C 2s orbital. If I understand it right, to get ionization out of a C2s orbital one should include C 2s orbitals in the “frozen core” set, that is, increase the number of “n_frozen_core”, which is 6 by default. I tried n_frozen_core=8 to include two C 2s orbitals. This indeed gave me the states with ionization out of a C 2s orbitals. However, the increased number of frozen core orbitals also affected the CCSD (ground state) calculation, in a way, that the lowest C 2s orbitals were not included in the correlation for the CCSD ground state, which is not good.
I wonder if it is possible to keep the number of core-frozen orbitals for the CCSD calculation by default, i.e. n_frozen_core=fc, but then increase it for the CVS-IP-EOM-CCSD calculation?
The FC-CVS method, by definition, excludes the “core” orbitals you are interested in exciting / ionizing for the ground state correlation, so there’s no way around that. I believe a different CVS scheme (https://doi.org/10.1063/1.4935712) which allows for what you want to do was just implemented in 6.3.1 although I dont see it documented in the release log…
Thanks very much for your response! Yes, that nice extension of the CVS scheme would solve my problem. It’s a pitty if it is not in 6.3.1. Is it possible to check out for certain if it is there or not?
FYI, this is feasible using TD-DFT, which allows for arbitrary active spaces amongst the occupied MOs, so can implement the CVS approach that you need. For example, used here recently for L-edge XAS:
@kaushik : could you please detail your suggesting as for what kind of “proper CVS approach” you mean?
@jherbert : Can this also be used to calculate ionized states, i.e., IPs? I mean, TDDFT is usually for excited (not ionized) states. Such flexibility of selecting “active orbitals” is not possible for IP-EOM-CCSD, I guess?
TD-DFT for excitation energies. For ionization energies, I would use a Delta-SCF approach or a Slater transition method, https://doi.org/10.1063/5.0134459
That’s the publication from Coriani and Koch in the context of CC-based methods. The FC-CVS-EOM-CC is its variant and not the other way around. For benzene with just 2s and 2p C orbitals, I don’t think separating 2s and 2p orbitals makes sense (sp2 hybridization and all). CVS makes sense for excitations from “relatively” inner shells, which isn’t the case for 2s orbitals in benzene. So, CVS approaches are unreliable for isolating excitations from 2s orbitals of benzene (if such excitations even exist in benzene). For your original system with C, N, and O atoms, if the 2s orbitals of O and/or N don’t mix with higher valence orbitals, even the FC-CVS variant will be fine. How different are the CCSD and low-lying excitation energies with and without including the 2s orbitals of O and/or N in the frozen core for your system? For your original system, assigning 2s orbitals on C to be frozen could potentially run into the same problem with CVS as that in benzene.
@jherbert : Yes, Delta-SCF (Delta-DFT) does work pretty well for K-shell (1s) orbitals due to very good energetic separation of the 1s orbitals from other, higher-lying orbitals. But I am not sure it will work if there are severalclose-lying 1s orbitals, for instance, several C 1s orbitals. The same is for the L-shell (2s) orbitals (ionized or excited), that is there are several energetically close-lying L-shell orbitals. Furthermore, the energy separation of the L-shell orbitals from the outer-valence orbitals is not so good compared to the K-shell orbitals. All this will make Delta-SCF difficult to converge for a particular L-shell ionized (excited) state in the case of polyatomic molecules. But it should/could be feasible for atoms and small molecules I guess. I have a polyatomic molecule, sort of uracil. I am not familiar with STM, but I guess it is similar to Delta-SCF.
@kaushik : As Juanes mentioned above, the method of Coriani and Koch could be more suitable for L-shell orbitals. The FC-CVS variant in Q-Chem freezes the specified core orbitals in the CCSD (ground-state) calculation. So, if I freeze one or several 2s orbitals to calculate ionization out of them, they will also be frozen at the CCSD step, which I consider too inaccurate. So, it suites exceptionally for the K-shell (real core) orbitals.
Well, I disagree to your comment to some extent (and also correcting my earlier comment that you need the proper CVS approach). If 2s orbitals are indeed well separated energetically from the higher valence occupied orbitals, even FC approximation to CVS should work fine. For benzene, 2s orbitals are not well separated from higher occupied orbitals; in fact, they mix with 2p orbitals resulting in the textbook sp2 hybridization. So, you shouldn’t separate any 2s orbitals from valence orbitals using any CVS approach for benzene. For most cases that work well with “proper” CVS approach, the FC variant should also work fine. For clarity, please specify for which system, benzene or your original ~30-atom system, are you inquiring or commenting about. You can verify this with some quick test calculations.
Many thanks for your quick reply!
To make it as clear as possible, at the moment, I am trying to assess the IPs for 2s of C, N and O of uracil (12 atomic molecule, 4 carbons, 2 nitrogens, 2 oxygens, 4 hydrogens). My idea was (is) to estimate the error related to use of the FC-CVS approximation. For that I performed FC-CVS IP-EOM-CCSD calculations for uracil with n_frozen_core = 12 and obtained four IPs associated with ionization out of 2s orbitals of 2 oxygens and 2 nitrogens. As I wrote before, in the calculation, 12 orbitals are frozen already at the step of CCSD ground-state calculation, that is, in addition to eight 1s frozen orbitals (which is fine) also four 2s orbitals are frozen (not correlated) at the CCSD step, which introduces additional error in the accuracy, in my view. To estimate how large is the overall error in the 2s IPs values obtained I need reference values calculated faithfully, that is, without the FC-CVS approximation. So far, I didn’t manage to get these reference data. I tried to get them by doing IP-EOM-CCSD calculation (without FC-CVS) having specified 50 states to be calculated. But I could not reach/access the 2s orbitals (the number of states was not large enough to reach them). If I increase the number of states further, the calculation crashes.
Here are the HF orbital energies of 2s of two oxygens and two nitrogens in uracil (in a.u.):
-1.434 -1.399 -1.309 -1.241
The next HF orbital energies (2s of four carbons):
-1.086 -0.928 -0.895 -0.802
So, in my view, they are all energetically quite close.
DeltaSCF should work well for several energetically-close 1s orbitals provided they dont mix spatially. For example, the two oxygen 1s orbitals are localized despite being energetically close. As for the carbon 1s in uracyl I cannot be so sure. You can always localize them (Boys localization) to make Delta SCF work but that comes with its caveats.
For the ionization of inner-valence hybrid 2s-2p orbitals in a molecule like uracil, yeah I’m not sure DeltaSCF would work… I imagine the way to go for this situation would be a sort of IP-EOM-CC or IP-ADC that allows you to target a specific set of active orbitals to ionize from while allowing configurations with different hole states to mix. Dont know if that exists (yet)!