Generalized gradient approximation

[Quantamania]

Hello, friends.

I have been continuing with my dissertation work-up and have come across some questions that I may wish to ask here.

When I was comparing local density approximation (LDA) with generalized gradient approximation (GGA), I noted that the difference between these Kohn-Sham methods is the way GGA takes in account the gradient of the density at a coordinate being computed.  LDA does not include this feature in its calculations of the same electron density, focusing only on the local electron density at the particular coordinate.  While I use both of these methods in my dissertation data, I want to know the benefits that inclusion of a gradient would have on the properties obtained from the electron density in a system (such as a unit cell and its contents).

Basically, how would gradient change the results of a calculation for the coordinate point?  How does it relate to the difference between LDA and GGA methods?

[Anders Blom]

There is no simple answer to this question.

In theory GGA should be better, because it's a higher-level correction to LDA, but the correction involves a parameter which needs to be determined. This has been done for a test set of small molecules, resulting in the most commonly used PBE parameterization (there are many versions of that, like revPBE etc, but the idea and test set is roughly the same). For those molecules in the test set - and many other ones - GGA does indeed give better HOMO-LUMO gap etc.

However, the parameters are not universal, and so for other cases, LDA fares better.

Many texts have been written on the respective benefits and shortcoming of various exchange-correlation potentials. A Google search on "lda gga" brings up a lot of useful references among the first 5-10 hits.