About XC functionals available

[ivansc...@gmail.com]

Dear CP2K community,

I attach the test.png file where I have tested different XC functionals of my interest in a table format. I have tried CP2K versions from 6.1 to 8.1. Questions:

1) Functional with directives LDA_C_HL, LDA_C_PZ, LDA_C_WIGNER, GGA_C_AM05, GGA_X_AM05 and GGA_X_RPBE do not seem to be recognised for version 7.1 and 6.1, but they work well for 8.1. Is this correct? If not, what I am doing wrong? The only two XC subroutines I have found in the src folder for version 8.1 related to the above functionals is wigner_slater_functional (for WIGNER defined in src/atom_utils.F, created in 2008) and (for PZ, in src/xc/xc_perdew_zunger.F, created in 2004). So I wonder why LDA_C_WIGNER nor LDA_C_PZ are recognised for versions 6.1 and 7.1.

2) This is related to 1), somehow. Apart from WIGNER, PZ, PBE, REVPBE and PBESOL, I cannot find the subroutines that correspond to the other functionals using grep. Could you please instruct me how/where to find the relevant subroutines?

3) Shall one use PADE potentials for HL, PZ and Wigner? 

4) Shall one use PBE potentials for AM05, RPEB, PBESOL?

5) Regarding AM05: if I want to use this functional, shall I specify both GGA_C_AM05 and GGA_X_AM05 together as follows?

&XC

  &XC_FUNCTIONAL

     &GGA_X_AM05

     &END GGA_X_AM05

     &GGA_C_AM05

     &END GGA_C_AM05

  &END XC_FUNCTIONAL

&END XC

6) For LDA_C_HL, “_C_” refers that the HL only proposed a correlation term, and used the Slater functional for the exchange part (from the paper Hedin and Lundquist wrote). Does LDA_C_HL (and the rest LDA_C_ of the table) include the exchange part already? Or one also need to include directive LDA_X (Slater exchange) in the input file? I mean, shall LDA_X block below be defined or not?

&XC

  &XC_FUNCTIONAL

     &LDA_X 

     &END LDA_X

     &LDA_C_HL

     &END LDA_C_HL

  &END XC_FUNCTIONAL

&END XC

Thanks a lot in advance for your help with these questions

[Frederick Stein]

Dear Ivan,

Short answer:

All section names you are referring to are actually functionals from LibXC. That is why you do not find the respective code in CP2K.

A pseudo potential optimized for a functional of a given class usually provides reasonable results for other functionals of the same class. For metals, you should check that separately.

Long answer:

To 1+2) Do you mean by accident the master branch instead of 8.1 ? Your given functional names are functional names from LibXC. In the recent trunk, we have added separate sections for the functionals from LibXC. That is why you will not find the code in CP2K but in LibXC and why these sections do not work with older versions of CP2K. Some more information about the the naming scheme of LibXC (also consult the manual of LibXC):

- Names starting with "HYB_" refer to hybrid functionals for which you have to set up a separate Hartree-Fock section on your own.

- Then, you will find the class of the underlying DFT functional ("LDA", "GGA", "MGGA").

- Then, the type of functional ("K" for kinetic energy, "X" for exchange-only, "C" for correlation-only, "XC" for exchange-correlation functional).

- Finally, the functional name (have a look at the manual of LibXC for you LibXC distribution in-use).

There is one functional which sticks to the above convention but is not provided by LibXC but by CP2K (LDA_HOLE_T_C_LR).

Some functionals from LibXC are natively supported by CP2K like LYP (in LibXC: GGA_C_LYP) or PZ81 (in LibXC: LDA_C_PZ).

To 3+4)

Basically yes, but you should always check the suitability of the pseudopotentials, especially for metals.

To 5)

Probably yes. In case of doubt, check the references in the LibXC manual (I do not know these functionals)

To 6)

As stated above, "_C_" tells you that the corresponding functional is just a correlation functional and you have to add a suitable exchange functional (or Hartree-Fock). For LDA-based functionals, it is LDA_X (from LibXC) or XALPHA (from CP2K).

I hope it helps you. If you have more questions, just ask.

Best,

Frederick

[Ivan Scivetti]

Dear Frederick, 

Thanks a lot for your clear answers. Indeed, they help a lot!

Regarding question 1 above, now it makes sense. However, my confusion originated after looking at the PURE SUBROUTINE wigner_slater_functional in src/atoms_util.F:

   PURE SUBROUTINE wigner_slater_functional(rho, vxc)
      REAL(KIND=dp), DIMENSION(:), INTENT(IN)            :: rho
      REAL(KIND=dp), DIMENSION(:), INTENT(OUT)           :: vxc

      INTEGER                                            :: i
      REAL(KIND=dp)                                      :: ec, ex, rs, vc, vx

      vxc = 0._dp
      DO i = 1, SIZE(rho)
         IF (rho(i) > 1.e-20_dp) THEN
            ! 3/4 * (3/pi)^{1/3} == 0.7385588
            ex = -0.7385588_dp*rho(i)**0.333333333_dp
            vx = 1.333333333_dp*ex
            rs = (3._dp/fourpi/rho(i))**0.333333333_dp
            ec = -0.88_dp/(rs + 7.8_dp)
            vc = ec*(1._dp + rs/(3._dp*(rs + 7.8_dp)))
            vxc(i) = vx + vc
         END IF
      END DO

   END SUBROUTINE wigner_slater_functional

You can see this subroutine computes both the correlation energy (ec, vc) as well as the exchange energy (ex,vx), which contradicted the flag LDA_C_WIGNER to compute only the correlation bit. Now your explanation helps to unpuzzle my concern. Since there was no date recorded in the description of each sections in the online manual, I could not even guess when these flags were introduced.

I shall continue investigating further. Thanks a lot for your help.

Best wishes

Ivan

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