All-electron wave functions

[deyan_mihaylov2]

Hi,

As far as I understand, the contents of WAVECAR are the pseudo wave functions - only the first term in the right-hand side of Eq. 2 in "From ultrasoft pseudopotentials to the projector augmented-wave method", Phys. Rev. B 59, 1758 (1999). The contents of CHGCAR is the density as defined in Eq. 3 (the AE charge density). Therefore, when I try constructing the density, exactly as it appears in CHGCAR from the wave functions as they are output in WAVECAR using the standard definition of Fourier transforming the orbitals into real space and constructing the density, I am able to construct the density as it is CHGCAR, but only away from the nuclei, which is what one should expect. To further verify, when I run a calculation for hydrogen using a 1/r potential, I am able to reconstruct the exact density from CHGCAR, even near the nuclei. In general, the softer the PP, the bigger the difference between CHGCAR density and density constructed from WAVECAR near the nuclei. So, I was wondering, is there a way to obtain the AE wave functions (as defined in Eq. 2) when using PPs? I am using 5.4.4.
Thank you!

Deyan

[martin.schlipf]

Could you clarify what exactly you want to do, e.g., do you want to plot the wave functions or calculate an expectation value with them?

Of course it is possible to recover the all-electron wave functions, that is the point of the PAW method. However it is typically not a good idea to represent them on the plane-wave grid. You would need a much denser grid to get a meaningful representation of the AE wave function, so whenever we want to calculate something with the wave functions, we use the actual AE wave functions expanded in radial functions times spherical harmonics.

[deyan_mihaylov2]

I am trying to calculate expectation values in post-DFT calculations (MBPT, Monte Carlo), but using just the plane wave coefficients as they are output in WAVECAR I lose some accuracy. Could you point me to a good source that describes how this AE wave function construction can be done with standard VASP output?

Thank you!

Deyan

[martin.schlipf]

Typically you wouldn't do that externally in Vasp because you would need to reimplement lots of things that are already done and optimized in Vasp. I can point you to a few things that may be helpful:
There is a flag 2E4W that calculates 2 electron 4 orbital integrals in the basis of Wannier functions. Otherwise you can try to look at routines for RPA or MP2 to see how these things are done inside Vasp. Note that a lot of this functionality has improved considerably since Vasp 5.4.4 though, so depending on what you want to do specifically, upgrading to Vasp 6 may be worth considering.