[QE-users] [QE users] pseudopotential hardness and transferability

[Aldo Ugolotti]

Dear QE users,

I am actually working on a system with C and N atoms. Checking the 
convergence of the total energy for finding the optimal values for the 
cutoffs (i.e. DE ~ 1mRy), I found that, despite in the atomic case the 
suggested values (for example the wfc cutoff are ~ 46 Ry for both) are 
good enough, in a sample of my system which is already relaxed (and 
whose geometry is in good agreement with reported results) the same 
convergence check determines a cutoff which is, again for example for 
the wavefunction, 2 to 3 times larger.

As I tried to modify the pseudo to make it softer, I have also run some 
transferability tests, which I am curious to hear your opinion about. In 
particular, the tests were running fine for the testing configurations 
with less electrons (e.g. 2s2 2p1 for C) but there were problems with 
tests with more electrons (e.g. 2s2 2p3 for C). In those cases the scf 
cycles did not converge at all, both at AE or PS level.

I found the same result with the pseudo US,PAW in the pslibrary of 
different versions, namely 1.0.0, 0.3.1 and 0.1. I also tried to change 
the radii, the local potential (adding a 3D empty orbital), the 
configuration (e.g, Ztot=5.5, Zval 1.5 for C) or the pseudization recipe 
(TM/RRKJUS).

Hence, I got few questions:

i) is it really a transferability issue, or do I need "only" to get 
those scf cycles to converge? how?

ii) if the pseudo is not good to represent electronic configurations 
with more electrons, that would be a viable explanation as to why the 
cutoffs for a sample systems are so much larger than the atomic cases?

Below I am reporting the output for the test of the configtf(2)='2s2 2p3'


      Message from routine scf:
      warning: convergence not achieved
      --------------------------- All-electron run 
----------------------------

C
      scalar relativistic calculation

      atomic number is  6.00
      dft =SLA PW PBX PBC   lsd =0 sic =0 latt =0  beta=0.20 tr2=1.0E-14
      Exchange-correlation      = SLA PW PBX PBC ( 1  4  3  4 0 0)
      mesh =1073 r(mesh) = 100.30751 a.u. xmin = -7.00 dx = 0.01250
      1 Ry =  13.60569193 eV, c = 137.03599966

      n l     nl                  e(Ry)          e(Ha) e(eV)
      1 0     1S 1( 2.00)       -19.6664        -9.8332 -267.5745
      2 0     2S 1( 2.00)        -0.6297        -0.3148 -8.5669
      2 1     2P 1( 3.00)        -0.0290        -0.0145 -0.3951

      final scf error:  2.4E-01 reached in 201 iterations

      Etot =     -78.638531 Ry,     -39.319266 Ha,   -1069.931632 eV

      Ekin =      73.218424 Ry,      36.609212 Ha,     996.187324 eV
      Encl =    -182.081805 Ry,     -91.040902 Ha,   -2477.348944 eV
      Eh   =      40.989732 Ry,      20.494866 Ha,     557.693668 eV
      Exc  =     -10.764883 Ry,      -5.382441 Ha,    -146.463680 eV


      normalization and overlap integrals

      s(1S/1S) =  1.000000  <r> =   0.2707  <r2> = 0.0993  r(max) =   0.1730
      s(1S/2S) = -0.000112
      s(2S/2S) =  1.000000  <r> =   1.6236  <r2> = 3.2283  r(max) =   1.2315
      s(2P/2P) =  1.000000  <r> =   2.1244  <r2> = 6.4268  r(max) =   1.2470

      ------------------------ End of All-electron run 
------------------------

      Message from routine run_pseudo:
      Warning: convergence not achieved

      ---------------------- Testing the pseudopotential 
----------------------

C
      scalar relativistic calculation

      atomic number is  6.00   valence charge is  4.00
      dft =SLA PW PBX PBC   lsd =0 sic =0 latt =0  beta=0.20 tr2=1.0E-14
      mesh =1073 r(mesh) = 100.30751 xmin = -7.00 dx = 0.01250

      n l     nl             e AE (Ry)        e PS (Ry)    De AE-PS (Ry)
      1 0     2S   1( 2.00)       -0.62966       -0.17919 -0.45046  !
      2 1     2P   1( 3.00)       -0.02904       -0.00000 -0.02904  !

      eps = 3.2E-04  iter =201

      Etot =     -78.638531 Ry,     -39.319266 Ha,   -1069.931632 eV
      Etotps =   -18.974270 Ry,      -9.487135 Ha,    -258.158068 eV
      dEtot_ae =      -3.108582 Ry
      dEtot_ps =      -1.208418 Ry,   Delta E=      -1.900164 Ry

      Ekin =      10.222924 Ry,       5.111462 Ha,     139.089950 eV
      Encl =     -31.022876 Ry,     -15.511438 Ha,    -422.087699 eV
      Ehrt =      12.620743 Ry,       6.310371 Ha,     171.713935 eV
      Ecxc =     -10.795060 Ry,      -5.397530 Ha,    -146.874254 eV
      (Ecc =      -0.958640 Ry,      -0.479320 Ha,     -13.042955 eV)

      ---------------------- End of pseudopotential test 
----------------------


      -------------- Test with a basis set of Bessel functions ----------

      Box size (a.u.) :   30.0

      Cutoff (Ry) :   30.0
                            N = 1       N = 2       N = 3
      E(L=0) =        -0.1788 Ry    0.1213 Ry    0.1854 Ry
      E(L=1) =         0.1263 Ry    0.1949 Ry    0.2715 Ry

      Cutoff (Ry) :   60.0
                            N = 1       N = 2       N = 3
      E(L=0) =        -0.1789 Ry    0.1213 Ry    0.1854 Ry
      E(L=1) =         0.1263 Ry    0.1949 Ry    0.2715 Ry

      Cutoff (Ry) :   90.0
                            N = 1       N = 2       N = 3
      E(L=0) =        -0.1789 Ry    0.1213 Ry    0.1854 Ry
      E(L=1) =         0.1263 Ry    0.1949 Ry    0.2715 Ry

      Cutoff (Ry) :  120.0
                            N = 1       N = 2       N = 3
      E(L=0) =        -0.1789 Ry    0.1213 Ry    0.1854 Ry
      E(L=1) =         0.1263 Ry    0.1948 Ry    0.2715 Ry

      -------------- End of Bessel function test ------------------------


Thank you in advance,

-- 
Aldo Ugolotti, Ph.D.

Post-doc fellow
Materials Science Dept. U5,
Università degli Studi di Milano-Bicocca
via Cozzi 55,
20125 Milano (MI)
Italy
e-mail: a.ugolotti at campus.unimib.it