Calculation problem of body-centered cubic uranium

[quanfu_han]

We planned to calculate the vacancy formation energy of bcc structure uranium, but during the calculation process we found that when we introduced a single vacancy into the structure of uranium, the overall structure showed a tendency of phase change. Obviously, such a result is unreasonable. We tried using the pseudopotential of uranium PBE and PW91, and changing the size of the lattice, but none of these could solve this problem. We searched the literature and found that many researchers also have related problems in the calculation of bcc structure U, such as ''Beeler B, Good B, Rashkeev S, et al. First principles calculations for defects in U[J]. Journal of Physics : Condensed Matter, 2010, 22(50): 505703.'' and "Jiang P, Qiu R, Cao J, et al. Development of U-Zr-Xe ternary interatomic potentials appropriate for simulation of defect and Xe behaviors in U- Zr system[J]. Journal of Nuclear Materials, 2023: 154824." We did a series of tests and found that uranium with the bcc structure is particularly unstable when defects or doping are introduced into the supercell. Do you know what causes this problem and how to fix it?

[jonathan_lahnsteiner2]

Dear quanfu_han,

Welcome to the vasp forum. This post is very physics-related and not directly related to the usage of vasp. Therefore, the post was moved
to the users-for-users forum. Here any kind of question can be discussed with other vasp users.

Related to your question, I wonder how large is your supercell in which you study the defect formation energy. Is there
data about a finite-size analysis available? Maybe the size of the supercell is related to the stability of the bcc structure of uranium
when defects are introduced.

All the best Jonathan

[quanfu_han]

Dear Jonathan，

Thank you very much for your reply. In my calculations, I tested 3*3*3 (54 atoms), 4*4*4 (128 atoms) and 5*5*5 (250 atoms) supercells. We believe that for normal structural optimization, the introduction of monovacancy should not lead to chaos in the supercell structure. Therefore we suspect that the pseudopotential of U is unreasonable for body-centered cubic uranium.
In the paper "Beeler B, Good B, Rashkeev S, et al. First principles calculations for defects in U[J]. Journal of Physics: Condensed Matter, 2010, 22(50): 505703.'' the authors mentioned:
“One issue that arises when calculating defects in U is due to the large cutoff radius of the pseudopotential used. When a defect is present and the atoms are relaxed, adjacent pseudopotential cores may overlap. A large enough core overlap can make the supercell unstable, yielding unrealistic results for the relaxed structure. Another source of anomalous structural lattice relaxation around defects is the inherent mechanical instability of the bcc allotrope of U at 0 K.”
Apparently we have the same problem. I would like to confirm whether the author's explanation in this paper is correct? Did you find this problem in your tests to develop uranium pseudopotentials?

Best wish!
Quanfu Han

[jonathan_lahnsteiner2]

Dear Quanfu Han,

You can check benchmarks of VASP with respect to AE calculations of Fleur and Wien2K at
https://acwf-verification.materialscloud.org/
For the bcc EOS, the results are virtually identical, with eps=0.018 (eps<0.06 is "excellent agreement").
According to the Materials Project, bcc Uranium bonds are ~2.9 Angstroms long.
The core radius for the projection operator in the U potential is RMAX=2.901, and the one for the radial grids is RDEP= 2.950, so
let's be generous and say the core has a radius of 3 a.u., which corresponds to ~1.6 Angstroms.
So cores seem to be indeed slightly overlapping even in the undisturbed case.

I hope this is of help

All the best Jonathan