# Is LDA better than GGA for elastic constants?

I have calculated elastic constants for Si, GaAs, and GaN using LDA and GGA in VASP.

LDA is giving better results than GGA for elastic constants.

Is there is a reason behind the good results by LDA in this case. Is there any reference I can read to understand why this is so?

I also found some reviews on this but I am not able to understand the explanation.

Reviews:

1. Råsander, M., and M. A. Moram. "On the accuracy of commonly used density functional approximations in determining the elastic constants of insulators and semiconductors." The Journal of chemical physics 143.14 (2015): 144104.

2. Van de Walle, A., and G. Ceder. "Correcting overbinding in local-density-approximation calculations." Physical Review B 59.23 (1999): 14992.

• Could you clarify what sort of reference you are looking for? While GGAs are in principle better than LDAs, that is no guarantee they will better for all systems and all properties.
– Tyberius
May 18, 2020 at 22:40
• I just want to know the reason behind why does LDA performs better in this case? May 19, 2020 at 5:47
• How much "better" are the LDA results? Do they compare to the results in Phys Rev B 69,075102 (2004)? You might find that even with a single XC functional, things like pseudopotential and calculation parameters can affect lattice constants by a few %. May 21, 2020 at 16:06
• While you appear to be dealing in periodic crystals and not, say, absorption on a surface, it may be worthwhile to check for the influence of dispersion/van-der-Waals forces. Sometimes, a LDA gives better results than PBE due to its overbinding when vdW is involved. Grimme's DFT-D3 was also implemented for periodic systems and should work for VASP input. Jun 17, 2020 at 15:09

I don't think you will find a reference showing that LDAs are better than GGAs for computing elastic constants. More specifically, I don't think a paper could reasonably offer an explanation of why LDA does better than GGA for any specific case.

In principle, a GGA is more physically consistent than an LDA, as we know that the true exchange-correlation functional of DFT should depend on the gradient of the density. In practice, DFT functionals are typically parameterized to minimize errors in the energy for test set of molecules/compounds. Due to the approximate nature of the functional used in practice, there will always be cases where the "inferior" functional does better simply due to coincidental cancellation of error. There might be classes of compounds/problems where the source of this cancellation can be determined and a rigorous explanation of the good performance of the "inferior" functional can be formulated, but this is rare and generally very challenging.

You are looking at a small selection of materials with fairly different properties (e.g. different crystal structure), so its unlikely that there is some clear, common factor that is making LDA better for these cases. A paper in the Journal of Computational Material Science[1] found that for cubic crystal, there were cases where LDA produced better elastic constants and there were cases where it was much worse than GGA.

### References:

1. Jamal, M.; Jalali Asadabadi, S.; Ahmad, I.; Rahnamaye Aliabad, H. Elastic constants of cubic crystals. Computational Materials Science 2014, 95, 592–599. DOI: 10.1016/j.commatsci.2014.08.027.
• Sorry about going off topic, but when you say coincidental cancellation of error, does this mean that the error cancels off for a specific single calculation (for a given material and given system size etc), or does this occur consistently between similar types of system regardless of the system size and so on?
– PBH
Feb 1 at 10:46
• @PBH you might happen to find a small collection of systems where the error cancellation for LDA could be rationalized, but generally I would expect it's mostly random, with fairly similar compounds potentially having very different errors.
– Tyberius
Feb 1 at 14:19
• Understood. Thanks
– PBH
Feb 1 at 14:59