Keywords: pseudo-gen

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# 3 A worked example: Ti

Let us consider the Ti atom: Z = 22, electronic configuration: 1s22s22p63s23p63d24s2, with PBE XC functional. The input data for the AE calculation is simple:

     &input
       atom='Ti', dft='PBE', config='[Ar] 3d2 4s2 4p0'
     /

and yields the total energy and Kohn-Sham levels. Let us concentrate on the outermost states:

         3 0     3S 1( 2.00)        -4.6035        -2.3017       -62.6334
         3 1     3P 1( 6.00)        -2.8562        -1.4281       -38.8608
         3 2     3D 1( 2.00)        -0.3130        -0.1565        -4.2588
         4 0     4S 1( 2.00)        -0.3283        -0.1641        -4.4667
         4 1     4P 1( 0.00)        -0.1078        -0.0539        -1.4663

and on their spatial extension:

    s(3S/3S) =  1.000000  <r> =   1.0069  <r2> =    1.1699  r(max) =   0.8702
    s(3P/3P) =  1.000000  <r> =   1.0860  <r2> =    1.3907  r(max) =   0.8985
    s(3D/3D) =  1.000000  <r> =   1.6171  <r2> =    3.5729  r(max) =   0.9811
    s(4S/4S) =  1.000000  <r> =   3.5138  <r2> =   14.2491  r(max) =   2.9123
    s(4P/4P) =  1.000000  <r> =   4.8653  <r2> =   27.9369  r(max) =   3.8227

Note that the 3d state has a small spatial extension, comparable to that of 3s and 3p states and much smaller than for 4s and 4p states; the 3d energy is instead comparable to that of 4s and 4p states and much higher than the 3s and 3p energies.. Much of the chemistry of Ti is determined by its 3d states. What should we do? We have the choice among several possibilities:

1. single-projector NC-PP with 4 electrons in valence (3d24s2), with nonlinear core correction;
2. single-projector NC-PP with 12 electrons in valence ( 3s23p63d24s2);
3. multiple-projector US-PP with 12 electrons in valence;
4. multiple-projector US-PP with 4 electrons in valence and nonlinear core correction;
5. ...

The PP of case 1) will be hard due to the presence of 3d states, and its transferability may turn out not be sufficient for all purposes; PP's for 2) will be even harder due to the presence of 3d and semicore 3s and 3p states; PP 3) can be made soft, but generating one is not trivial; PP 4) may suffer from insufficient transferability.

Subsections

- 3.1 Single-projector, norm-conserving, no semicore
  - 3.1.1 Generation
  - 3.1.2 Testing
- 3.2 Single-projector, norm-conserving, with semicore states
- 3.3 Testing in molecules and solids

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