Keywords: pseudo-gen

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## 3.2 Single-projector, norm-conserving, with semicore states

The results of transferability tests suggest that a Ti PP with only 3d , 4s , 4p states have limited transferability to cases with different 3d configurations. In order to improve it, a possible way is to put semicore 3s and 3p states in valence. The maximum for those states (0.87 a.u. and 0.90 a.u. respectively) is in the same range as for 3d (0.98 a.u.). Let us try thus the following:

     &input
       atom='Ti',  dft='PBE',  config='[Ar] 3d2 4s2 4p0',
       rlderiv=2.90, eminld=-4.0, emaxld=2.0, deld=0.01, nld=3,
       iswitch=3
     /
     &inputp
       pseudotype=1, rho0=0.001, ...
       file_pseudopw='Ti.pbe-sp-rrkj.UPF'
     /
    3
    3S 1 0 2.00  0.00 1.1 1.1
    3P 2 1 6.00  0.00 1.2 1.2
    3D 3 2 2.00  0.00 1.3 1.3
     &test
       configts(1)='3s2 3p6 3d2 4s2 4p0',
     /

Note the presence of the `&test` namelist: it is used in this context to supply the electronic valence configuration, to be used for unscreening. As a first step, we do not include the core correction. In place of the dots we should specify the local reference potential. If we use `lloc=-1` with large values of `rcloc`, (comparable to pseudization radii for the previous case) we get all kinds of mysterious errors:

         from compute_chi : error #         1
         n is too large

for `rcloc=2.5`, while `rcloc=2.7` produces an equally mysterious

         from run_pseudo : error #         1
         Errors in PS-KS equation

while smaller values (e.g. 1.5) lead to other errors:

         WARNING! Expected number of nodes: 0 = 2-1-1, number of nodes found: 1.

Even if the code doesn't stop, the presence of such messages is a signal of something going wrong in the generation algorithm. With some more experiments, though, one finds that `rcloc=1.3` yields a good potential. We still have other choices. In this case, d as reference potential: `lloc=2`, seems to work as well (and produces a PP with less projectors: only s and p ). The generation algorithm in the latter case yields these results for Kohn-Sham energies:

         n l     nl             e AE (Ry)        e PS (Ry)    De AE-PS (Ry)
         1 0     3S   1( 2.00)       -4.60347       -4.60348        0.00001
         2 1     3P   1( 6.00)       -2.85621       -2.85623        0.00002
         3 2     3D   1( 2.00)       -0.31302       -0.31301       -0.00001
         2 0     4S   1( 2.00)       -0.32830       -0.32892        0.00062
         3 1     4P   1( 0.00)       -0.10777       -0.10732       -0.00045

Note that the 3s , 3p , 3d levels should be the same by construction (the difference is numerical noise); the 4s and 4p levels are not guaranteed to be the same. The fact that they are, to a very good degree, is very reassuring. A look at the orbitals will reveal that 3s, 3p, 3d are nodeless, 4s and 4p have one node. The spherical wave basis set confirms the absence of ghosts:

        Cutoff (Ry) :   50.0
                               N = 1       N = 2       N = 3
         E(L=0) =        -4.5385 Ry   -0.3263 Ry   -0.0047 Ry
         E(L=1) =        -2.8427 Ry   -0.1071 Ry    0.0193 Ry
         E(L=2) =        -0.1511 Ry    0.0311 Ry    0.0685 Ry

         Cutoff (Ry) :  100.0
                               N = 1       N = 2       N = 3
         E(L=0) =        -4.5883 Ry   -0.3279 Ry   -0.0048 Ry
         E(L=1) =        -2.8547 Ry   -0.1073 Ry    0.0193 Ry
         E(L=2) =        -0.2918 Ry    0.0303 Ry    0.0649 Ry

         Cutoff (Ry) :  150.0
                               N = 1       N = 2       N = 3
         E(L=0) =        -4.5899 Ry   -0.3280 Ry   -0.0048 Ry
         E(L=1) =        -2.8549 Ry   -0.1073 Ry    0.0193 Ry
         E(L=2) =        -0.2936 Ry    0.0303 Ry    0.0649 Ry

Note that for l = 0 the first (N = 1 ) level is the 3s level, the second (N = 2 ) level is the 4s level, and the like for l = 1 . Let us now repeat the testing on the nine selected configurations as for the 4-electron PP. You will have to add `3s2 3p6` to all test configurations `configts`. Let us see check the errors on total energy differences:

    $ grep Delta ld1.test
         dEtot_ps =       0.227291 Ry,   Delta E=      -0.001230 Ry
         dEtot_ps =       0.540886 Ry,   Delta E=      -0.000918 Ry
         dEtot_ps =       1.540155 Ry,   Delta E=      -0.002640 Ry
         dEtot_ps =       0.343314 Ry,   Delta E=       0.000077 Ry
         dEtot_ps =       0.715061 Ry,   Delta E=       0.001142 Ry
         dEtot_ps =       1.849816 Ry,   Delta E=      -0.000820 Ry
         dEtot_ps =       3.522904 Ry,   Delta E=      -0.004735 Ry
         dEtot_ps =       6.702626 Ry,   Delta E=      -0.003032 Ry

Energy differences are reproduced with an error that does not exceed a few mRy (see column at the rhs). Eigenvalues are also well reproduced, e.g.:

         1 0     3S   1( 2.00)       -8.37382       -8.37230       -0.00152
         2 1     3P   1( 6.00)       -6.57173       -6.57195        0.00021
         3 2     3D   1( 0.00)       -3.84145       -3.83518       -0.00627
         2 0     4S   1( 0.00)       -2.73793       -2.74985        0.01192
         3 1     4P   1( 0.00)       -2.25938       -2.25525       -0.00412

although errors may reach 0.01 Ry (still one order of magnitude better than what we get with the previous 4-electron PP). The price to pay is the presence of more electrons in the valence.

Next: 3.3 Testing in molecules Up: 3 A worked example: Previous: 3.1 Single-projector, norm-conserving, no Contents