meta-GGA is not recommended for geometry optimizations！Why?

[Yue-Wen Fang]

In the morning, I found some information about meta-GGA from ATK manual.
It was stated that "A noteworthy detail about the meta-GGA exchange potential is that it can usually not be written as a derivative of an exchange functional. Therefore, meta-GGA is not recommended for geometry optimizations; for that, one should use standard GGA."
The question is why meta-GGA is not recommended fro geometry optimizations?
What's the relation between the exchange functional and geometry optimizations?

Thank you!

[Nordland]

In order for a geometric optimization to be good, the total energy and forces ( the derivative with respect to the total energy) needs to be proper correlated. The exchange-correlation is part of this energy.
For the TB09 metaGGA which the one currently supported in ATK, it is not possible to define a proper derivative of the TB09 potential, and hence the total energy and the forces is not well correlated any more.
In the worst case, it can end up with having non-zero forces in the minimum or having zero forces in a non-extreme.

[kstokbro]

The TB09 was constructed by the authors for giving accurate bandstructure (i.e. band gaps) of insulators and semi-conductors, it was never intended for giving good total energies and forces.

[Yue-Wen Fang]

In order for a geometric optimization to be good, the total energy and forces ( the derivative with respect to the total energy) needs to be proper correlated. The exchange-correlation is part of this energy.
For the TB09 metaGGA which the one currently supported in ATK, it is not possible to define a proper derivative of the TB09 potential, and hence the total energy and the forces is not well correlated any more.
In the worst case, it can end up with having non-zero forces in the minimum or having zero forces in a non-extreme.

thank you, I've got it. It's very kind of you.

[Yue-Wen Fang]

The TB09 was constructed by the authors for giving accurate bandstructure (i.e. band gaps) of insulators and semi-conductors, it was never intended for giving good total energies and forces.

in conclusion, because we cannot get accurate information about bandstructure, it is not possible for ATK to define a proper derivative of the TB09 potential, and hence we also cannot get good total energies and forces, is it right?

thank you very much

[Nordland]

Yes and no.

It is not ATK - it is the functional itself.

The way they use in the paper originally, is that the optimize the structure using LDA and once they have optimized the structure they use their functional TB09
to recalculate the bandstructure etc.

[Yue-Wen Fang]

Yes and no.

It is not ATK - it is the functional itself.

The way they use in the paper originally, is that the optimize the structure using LDA and once they have optimized the structure they use their functional TB09
to recalculate the bandstructure etc.

Yeah, I see! Thank you, captain!

[Anders Blom]

Also note that LDA and GGA usually give excellent geometries for semiconductors, so there isn't really any need to use MGGA for this. The ability of a functional to properly predict geometries and band structures are thus not immediately correlated. This is of course is a pity and takes some of the "first-principleness" out of DFT, but there isn't today any universal way to get around this problem, and we need to be happy for what we have, which isn't all that bad after all.