Do the U values affect structure optimization with the DFT+U simulation to optimize crystal structure?

Question

I am trying to do structure optimization of TiO2, since titanium is a transition metal, I need to use DFT+U to simulate the right band structure, but the electronic band structure would also affect the force on atoms, so does this mean that I need to use DFT+U model during the structure optimization stage? How important would the inclusion of U values be?

Answer 1

This isn't possible to answer with any certainty without trying it. Strictly speaking, if you need a Hubbard U to correct for the spurious self-interaction, then you need it to model the material accurately - including modelling the forces, dynamical matrix etc.

Having said that, it is usually found that the forces are very similar with and without U, at least as long as the ground state is qualitatively similar (e.g. it keeps the same non-metallic character, same kind of magnetisation etc). The Hubbard U only affects a few states, so the effect on the forces is often fairly small. There are no guarantees with this, this is little more than a plausibility argument and empirical observation.

On a practical note, you don't have to do a full geometry optimisation to see what difference it makes. Why not do a single DFT and DFT+U calculation for the initial geometry and see how similar the forces are? If they are similar, then you could probably do the geometry optimisation without the Hubbard U. Once you've obtained the DFT ground state geometry, you can then do a DFT+U calculation at that optimised geometry and see whether the forces are within your force convergence tolerance or not.

As a final remark, I'm assuming that the reason you want to do the geometry optimisation without a Hubbard U is because the DFT+U is slower or less robust. If it's slower, it might be worth seeing whether there are quicker ways of applying it (some DFT programs have several methods implemented); if it's less robust, then it may be worth investigating more sophisticated density/potential mixing methods, or alternative fully-self-consistent methods which don't use mixing schemes.