"Choosing" between degenerate lower-symmetry relaxed structures

[tsmidt]

Hello,

This is a symmetry related question. Given BaTiO3 in the cubic perovskite structure in space group 221 (high symmetry) -- if one performs a structural relaxation in VASP with ISYM=0, is it possible to relax into the tetragonal space group 99? If so, what aspect of the relaxation "chooses" which of the 6 degenerate tetragonal structures to relax to? Is it numerical error and if so from what aspect of the algorithm? Does the structure always relax to the same "choice"?

I apologize for not running these calculations myself -- I am still in the process of installing VASP on my cluster!

Thanks very much!
Tess

[fabien_tran1]

Hi,

A few comments:
-If the initial structure (221) is a (local or global) minimum, then nothing will happen at a temperature T=0 K.
-If the starting structure is close to a local minimum, then the optimization may be trapped and converge to this local minimum.
-In the POSCAR, T or F indicates which atoms will be allowed to change during the ionic relaxation or not.

[tsmidt]

Thank you for your reply.

I'm most interested in the following situation: suppose a high symmetry structure is locally an energy maximum and there are symmetrically degenerate energy minima, for example, that could be achieved by the displacement of a single atom in any of 6 directions in cubic unit cell (+/-x or +/-y or +/-z).

If ISYM=0, would the high symmetry structure "relax" to one of the 6 structures and if so, what was the source of the "noise" in VASP (numerical due to FFT grid, floating point, or something else) that "chooses" which direction the relaxation went. Will this source of noise always result in the same relaxed structure or will it sample all 6 structures equally?

Thanks again!
Tess

[fabien_tran1]

If the high symmetry structure really corresponds to a maximum, then what I would expect is that if it was previously properly optimized, then in principle no further relaxation (even by switching to ISYM=0) should occur provided that the same setting is used (ENCUT, EDIFFG, etc.).

If the high symmetry structure was not previously optimized with the same setting, then some residual forces/stress may be present and possibly trigger (if the condition with EDIFFG is not satisfied) the relaxation to another structure. Which one of the 6 structures is chosen depends on the direction of the residual forces.

[tsmidt]

That's very helpful. Thank you!