Optimization of c-parameter in MGGA

[beauyy]

Dear sir,
     How can I optimize c-parameter in MGGA when the experimental or HSE06 values of bandgap are unavailable?

[Anders Blom]

If it's a bulk material you can just let it be computed self-consistently. If it's not (which I suspect; I'm guessing you are looking at some 2D material perhaps), that's a harder question. Probably you have to bite the bullet and attempt some HSE06 calculations, you could use FHI-aims in ATK 2015 for that (requires a separate license though).

[beauyy]

I am comparing the bandgaps of a series of Molybdenum dichalcogenides (MoX2; X=S, Se, Te). Should they be compared with the same c-paramter value? Or should their c-parameters be optimized respectively?
 If they are optimized respectively, does their bandgaps can be compared to each other?

[Anders Blom]

No, there is no reason to assume the same c-parameter will work for different materials. What you should do is manually optimize the value of c for each one. It's not difficult to find literature references for computed band gaps with advanced methods like GW for MoS2 and probably the other X too, to fit against.

[beauyy]

So in the situration that the bandgap of  other 2D material that has no  literature value, I can only use GGA  to get the relative value when they are compared between different Xes, or under different uniaxial stresses, altuhough the result caculated by GGA is underestimated?

[Jess Wellendorff]

So, you are in the situation where you would like to calculate and compare the band gaps of a range of different materials. However, you only have experimental band gaps for a few of them. If using MGGA, you can choose between using self-consistent c-values or fitted c-values.

If you were considering fully periodic bulk systems, I would recommend using self-consistently determined c-values for all materials. That's a simple and clean approach. However, you are considering 2D materials with large vacuums, for which the c-parameter probably diverges if you try the self-consistent option. Therefore, I would use for all the materials a c-value that was fitted to match the experimental band gap of MoS2. This would give you a good foundation for seeing which material has larger or smaller gap, and the general trend of the gaps under applied strains.

However, MGGA might just not be the best way to get correct band gaps for TMDs. Probably the only real option for a scientifically correct approach is to use HSE06 or similar. FHI-aims could do that.