LFXC = .TRUE. and TDDFT or mBSE

[hong_tang1]

Dear VASP team,

I have a more fundamental question about TDDFT or mBSE calculations with " LFXC = .TRUE." . My question is especially when metaGGA is used in the calculations.

For LFXC, the vasp wiki https://www.vasp.at/wiki/index.php/LFXC shows a formula for fxc_loc. It seems that fxc_loc is calculated as the 2nd functional derivative by density rho there. It is straight-forward for LDA, which only depends on rho.

My question is how about for GGA and MetaGGA?
For GGA, it depends also on the gradient of rho. Does VASP code (say Version 6.5.0) include the derivative by the gradient of rho in calculation of fxc_loc?

For metaGGA, it also depends on the gradient of rho and tau (the kinetical energy density). If I use a metaGGA, like SCAN, how does VASP get the fxc_loc? Are those effects of the gradient of rho and tau included? or ignored?

I appreciate your help very much!

Best,

Hong

[hong_tang1]

Dear VASP experts,

Could you please help my question and reply it?

Thanks very much!

Best,
Hong

[alexey.tal]

Dear Hong,

Sorry for the late response.
It is important to distinguish here between two TDDFT implementations in VASP: ALGO=TDHF and ALGO=TIMEEV.
The ALGO=TDHF algorithm solves the Casida equation and we need to calculate the exchange-correlation kernel as explained on the wiki.
Here, the support of the xc-kernels is quite limited and only the derivative with respect to the density is calculated. However, I would point out that the results in Singh et al., Phys. Rev. B, 035151 (2019)
indicate that the difference between adiabatic LDA and GGA kernels for the dielectric function is quite small in semiconductors. The metaGGA functionals are not supported in the TDHF algorithm.

The ALGO=TIMEEV algorithm can in principle be used to calculate any supported xc functional in VASP including metaGGAs. However, as discussed in Sander et al., J. Chem. Phys., 064110 (2017), metaGGA
functionals should incorporate the 1/q2 divergence in the long-range limit. As of now, there is no implementation for this diverging contribution for metaGGAs in TIMEEV.

Best,
Alexey