[CP2K-user] [CP2K:21447] Questions regarding pseudopotential and basis set generation.

[Michael LaCount]

I have been working on generating a 3 valence electron Gallium 
pseudopotential and basis (for r2SCAN). Acknowledging that pseudizing the 
d-electrons is questionable, it may become necessary for what I am trying 
to do.

I was tempted to email Jürg Hutter directly, but am posting it here in case 
it is of use to future users.

With regards to the ATOM code, I tried a few variations in optimizing the 
pseudopotential based on the PBE pseudopotential, SCAN pseudopotential and 
SCAN but with an additional local contraction term. I understand that the 
optimization is 90% trial and error with the POWELL settings (STEP_SIZE, 
STEP_SIZE_SCALING, MAX_INIT, and MAX_FUN). What is not clear to me though 
is how to evaluate whether I have made a good or bad pseudopotential. From 
my runs I have 3 candidates:

PBE:
Final value of function                                    0.1530340305
 Reference configuration          1               Method number             
   1
    L    N    Occupation      Eigenvalue [eV]           dE [eV]         
 dCharge 
    0    1          2.00        -9.2192459546 VA   0.000325[ 0]     
0.008127[26]
    0    2          0.00         0.8396512255 U1  -0.007898[ 8]     
0.001720[ X]
    0    3          0.00         6.5350291666 U2  -0.076920[ 0]     
0.008006[ 0]
    1    1          1.00        -2.5060816724 VA   0.000353[ 0]     
0.006282[15]
    1    2          0.00         2.3918661427 U1  -0.001140[ X]     
0.001833[ X]
    1    3          0.00         9.2353950765 U2  -0.055747[ 0]     
0.006591[ 0]
    2    1          0.00         2.2546328512 U1   0.003031[ 0]     
0.004738[ 0]
    2    2          0.00         6.4400471697 U2  -0.069520[ 0]     
0.011434[ 0]
    3    1          0.00         4.2413610819 U1   0.014969[50]   
 -0.000072[ X]
    s-states N=    1                   Wavefunction at r=0:         
0.005050[ 0]
    s-states N=    2                   Wavefunction at r=0:         
0.016265[ 0]
    s-states N=    3                   Wavefunction at r=0:         
0.032084[ 0]

 Number of target values reached:                                       4 
of  15

SCAN:
Final value of function                                  587.1874144433
 Reference configuration          1               Method number             
   1
    L    N    Occupation      Eigenvalue [eV]           dE [eV]         
 dCharge 
    0    1          2.00        -9.2169294346 VA   0.002641[ 2]     
0.006948[ 0]
    0    2          0.00         0.8283557076 U1  -0.019194[ 0]     
0.002138[ X]
    0    3          0.00         6.5240034385 U2  -0.087945[ 0]     
0.008142[ 0]
    1    1          1.00        -2.4873044888 VA   0.019130[98]     
0.000623[ 0]
    1    2          0.00         2.3990344827 U1   0.006028[ 0]     
0.001717[ X]
    1    3          0.00         9.2663576926 U2  -0.024784[ X]     
0.006565[ 0]
    2    1          0.00         2.2541499839 U1   0.002548[ X]     
0.001125[ X]
    2    2          0.00         6.4898896260 U2  -0.019678[ X]     
0.004534[ 0]
    3    1          0.00         4.2330247834 U1   0.006633[ 0]   
 -0.000068[ X]
    s-states N=    1                   Wavefunction at r=0:         
0.010116[ 0]
    s-states N=    2                   Wavefunction at r=0:         
0.018885[ 0]
    s-states N=    3                   Wavefunction at r=0:         
0.036626[ 0]

 Number of target values reached:                                       7 
of  15

and SCAN (2nd local contraction):
Final value of function                                    2.2705690182
 Reference configuration          1               Method number             
   1
    L    N    Occupation      Eigenvalue [eV]           dE [eV]         
 dCharge 
    0    1          2.00        -9.2192585449 VA   0.000312[ 0]     
0.007863[49]
    0    2          0.00         0.8401648110 U1  -0.007385[ 3]     
0.001685[ X]
    0    3          0.00         6.5372420030 U2  -0.074707[ 0]     
0.007822[ 0]
    1    1          1.00        -2.5061070718 VA   0.000328[ 0]     
0.006045[28]
    1    2          0.00         2.3923327908 U1  -0.000674[ X]     
0.001777[ X]
    1    3          0.00         9.2375753924 U2  -0.053566[ 0]     
0.006499[ 0]
    2    1          0.00         2.2546302822 U1   0.003028[ 0]     
0.004673[ 0]
    2    2          0.00         6.4410410581 U2  -0.068526[ 0]     
0.011278[ 0]
    3    1          0.00         4.2412241163 U1   0.014832[20]   
 -0.000072[ X]
    s-states N=    1                   Wavefunction at r=0:         
0.003682[ 0]
    s-states N=    2                   Wavefunction at r=0:         
0.015481[ 0]
    s-states N=    3                   Wavefunction at r=0:         
0.030640[ 0]

 Number of target values reached:                                       4 
of  15

Some of these might be improved with more iterations, but I am unsure how I 
should evaluate each of the pseudopotentials against the others. Is it 
better to have a lower "Final value of function", or to have a greater 
number of target values reached. Is there a rule of thumb for knowing when 
I have reached a reasonable PP?

Next, I have a small question about the generation of MOLOPT style basis 
sets. I have gone through Jürg Hutter's github and get 90% of the workflow 
for that. I just don't quite understand the uncontracted basis set 
generation. I can use the ATOM code to generate an uncontracted 'complete' 
basis set, but the results seem very dependent on the initial guess. Is 
there a general rule for how many basis functions I should use and/or the 
range of the exponential terms? Other than taking more time, can I just 
make an overkill basis (something like 12 functions per orbital type with 
value ranging from 100 to .01) set for the purposes of making the final 
basis?

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