UT theoretical chemistry code forum

Dear Prof Henkelman,

I am looking at interstitial H diffusion through bulk CeO2; specifically, I am attempting to get rate prefactors of H moving from one site to another for various values of the U parameter for GGA + U. I am having trouble converging the prefactor with additional DoF further away from the interstitial H in the dynamical matrix with some of choices for U. I have attached an image that includes two tables that differ in U parameter values. The results in the first table seems to be converging to a reasonable prefactor (8 THz); whereas, the results in the second table seem to diverges to a questionably high prefactor (2,200THz). I am unsure if this is an issue with the displacement value I am using (0.001Ang) for different modes during the dynamical matrix calculation, or that convergence to the saddle point and relaxation at the energy minimum is insufficient, or something else completely. I got the saddle points by first running NEB until the max force < 0.05 eV/Ang, and then converged the results further to < 0.01eV/Ang with dimer calculations. The energy minimum was converged to max force< 0.01eV/Ang. I would appreciate any thoughts about the issue and/or a strategy of how to efficiently determine the problem.

-Jared

I think that there is definitely something wrong with the high prefactors in the high U_ox calculations.

But first, do you really want to add +U on oxygen? This is intended to correct for delocalization in d-states of metals, not p-elements.

Anyway, what I can say is that adding +U make the convergence of the electronic structure and can lead to convergence to metastable states on the electronic structure surface. If you are doing a prefactor calculation and even one displacement does not converge to the same electronic structure, this can completely throw off our prefactor values (a significant increase in energy over a small distance lead to a high curvature).

I recommend looking at each calculation and make sure that you are getting to the electronic ground state for each calculation.

Also, maybe reconsider your choice of using +U for O.

Thank you for the timely and thorough reply.

Regarding +U for O, it seems to be a controversial but there is some work suggesting it gives a better description in CeO2 (e.g. José J. Plata, Antonio M. Márquez, Javier Fdez. Sanz; Communication: Improving the density functional theory+U description of CeO2 by including the contribution of the O 2p electrons. J. Chem. Phys. 28 January 2012; 136 (4): 041101. https://doi.org/10.1063/1.3678309)

I appreciate the suggestion to check the electronic convergence; in fact, I had not noticed that the electronic stucture for the first displacement did not fully converge, but that does not seem to be the issue here. After redoing this calculation, ensuring convergence with EDIFF =1E-8, the prefactor did not significantly change.

Ok, do check not only convergence but that each displacement has converged to the same electronic structure (spin state and charge occupancy on the O and metal centers). It just takes one structure converging to a metastable (electronic) state to mess it all up. Also look at the frequencies and see which mode(s) are giving rise to the deviation in the prefactor, which may point to a problematic part of the calculation. One final suggestion: make sure there is not an issue with zero or near-zero modes - these can not be treated within the harmonic approximation.

And to the +U for O, remember that any additional empirical parameter can only keep things as good/bad as they are or improve them in the sense of fitting to what you want, but you have to ask yourself how ab-initio you are at that point. For the d-electrons there is a reasonable theoretical justification for +U; for O, not so much.