[CP2K-user] [CP2K:17935] Possibly incorrect GTH-PBE pseudopotential for Tl

[Nicholas Winner]

I was optimizing Tl lattice parameter, and found a large discrepancy with 
published PBE results.  On a hunch, I decided to re-optimize the 
pseudopotential, and based on what I tried, it seems the GTH 
pseudopotential for Tl that ships with CP2K is not correct. The published 
potential is:

```
Tl GTH-PBE-q13 GTH-PBE
    2    1   10
     0.55000000    1    12.29058515
    3
     0.51280306    2     7.19017017    -2.86301073
                                        3.69613096
     0.57711505    2     4.76094580    -3.67332496
                                        4.34633671
     0.39323001    2   -11.01268700     6.42159202
                                       -7.28140093
```

But, if you run pseudopotential optimization, then you get the following. 
Note only 1 number changes: `0.39323001  -> 0.32379979 `

```
Tl GTH-PBE-q13
    2    1   10    0
    0.55000000       1   12.29058515
       3
    0.51280306       2    7.19017017   -2.86301073
                                        3.69613096
    0.57711505        2    4.76094580  -3.67332496
                                        4.34633671
    0.32379979       2  -11.01268700    6.42159202
                                       -7.28140093
```

The input file I used to generate this is is listed at the end of this 
message. 

Can the devs, especially Prof. Hutter, comment on whether this is a real 
issue? If it is, then I hope it can be updated in the repo.


&GLOBAL

        PROGRAM_NAME ATOM

&END GLOBAL

&ATOM

        ELEMENT Tl

        RUN_TYPE PSEUDOPOTENTIAL_OPTIMIZATION

        ELECTRON_CONFIGURATION [Xe] 6s2 5d10 6p1

        CORE [Xe]

        ! MAX_ANGULAR_MOMENTUM 2

        COULOMB_INTEGRALS ANALYTIC

        EXCHANGE_INTEGRALS ANALYTIC

        &METHOD

                METHOD_TYPE KOHN-SHAM

                RELATIVISTIC DKH(3)

                &XC

                        &XC_FUNCTIONAL PBE

                        &END XC_FUNCTIONAL

                &END XC

        &END METHOD

        &OPTIMIZATION

                EPS_SCF 5e-9

                max_iter 1000

                damping .2

                n_diis 15

        &END OPTIMIZATION

        &PRINT

                &BASIS_SET

                &END

        &END

        &AE_BASIS

                BASIS_TYPE GEOMETRICAL_GTO

        &END AE_BASIS

        &PP_BASIS

                BASIS_TYPE GEOMETRICAL_GTO

        &END PP_BASIS

        &POTENTIAL

                PSEUDO_TYPE GTH

                POTENTIAL_FILE_NAME POTENTIAL

                POTENTIAL_NAME GTH-PBE-q13

        &END POTENTIAL

        &POWELL

                ACCURACY 1.e-10

                STEP_SIZE 0.5

                WEIGHT_PSIR0 0.1

        &END POWELL

&END ATOM

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