Electron affinity of rhenium (Z = 75) with augmented basis sets

[Cristian Ioniță]

Greetings,

We have been trying to calculate the electron affinity of Re (experimental value: 0.15 eV) using the relativistic coupled cluster approach. We are correlating all the electrons and utilize the cv4z and ae4z basis sets, as well as the augmented versions thereof, acv4z and aae4z. The electron configurations are [Xe] 4f14 5d5 6s2 for Re and [Xe] 4f14 5d6 6s2 for Re- respectively. We find it unlikely that the extra electron goes into a p orbital.

The results we obtain are way off: approx. 0.54 eV for the CCSD(T)-computed EA (259% deviation) with aae4z when the input files for both Re and Re- include the occupation number for the $\kappa$ value (.KPSELE). This is especially needed for the neutral atom, as DIRAC opens the 6s subshell otherwise. The closest value we obtained is 0.26 eV using acv4z/no KPSELE for Re and cv4z/no KPSELE for Re- (still CCSD(T)). That our most accurate result is based on calculations with different basis sets and an unphysical DHF result for Re (open s shell) is intriguing.

Is there anything amiss with the input? If not, it would be most interesting to learn what causes such poor estimates. I have attached to this message the output files for Re and Re- with KPSELE and aae4z basis sets—what we assumed would afford the most accurate calculations.

Thank you in advance for your help and time.

Best regards,

[Kenneth Dyall]

It is likely that there are no good single-determinant well-isolated reference states in a 4-component calculation (unlike spin-free calculations where there is a single-determinant high-spin reference). The d_3/2^4 d_5/2^1 determinant is a reasonable proposal for the neutral, but the d_3/2^3 d_5/2^2 determinant is not very far away and will mix strongly. You should consider checking the t1 diagnostic for the coupled-cluster calculations: likely it is quite large.

In addition, the dns2 and dn+1s1 states are in the same energy range and mix to some extent in any calculation for most J values. So likely you would need to use a multireference method to obtain a good electron affinity. 

On the use of basis sets, you should always use an augmented basis set for the negative ion. Results without diffuse functions are likely to artificially raise the energy of the anion, and then your electron affinity would be smaller for the wrong reason. If anything, comparing the result in the aae4z basis for the anion with the result in the ae4z basis for the neutral is more justifiable (or any axz basis for the anion with xz basis for the neutral). It may also be a good idea to do calculations at the tz and qz level and extrapolate to the basis set limit.

Given the small size of the differences you are seeing you might need to include the Gaunt or Breit interaction, which you can estimate from a DHF calculation, or a COSCI calculation, Estimates of QED effects (though the latter are often not large for electron affinities unless the s population changes. 

Best regards,

Ken.

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[Cristian Ioniță]

Thank you very much for your reply, Ken. The T1 diagnostic for CCSD is indeed large: approximately 0.111. Regarding the contribution of the Gaunt/Breit corrections, I have my doubts that they are going to account for the remaining 390 meV on their own at this stage.

It does appear that a multireference approach is the best course of action, but unfortunately, I am not at all familiar with their implementation in DIRAC. The information available on the website is also quite sparse. Could I please ask for some references or guidance in this regard? My project is focused on RELCCSD, but I am eager to attempt an alternative, albeit more accurate, approach.

Best regards,

[Kenneth Dyall]

You might want to talk to Lukas Pasteka, who is currently working on calculations for the 3d elements.

I'm not sure how useful Fock space CC would be here; it relies on a closed-shell reference, which for Re would have to be the Re+ ion, 5d_3/2^4 6s^2. This should work well for the IP, but it might also be OK for the EA.

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