WIEN2k-FAQ: "open core" treatment of 4(5)f electrons

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"open core" treatment of 4(5)f electrons

The whole procedure is used to overcome the shortcommings of LDA, which will always put the 4f states at EF and yield a fractional occupation, but never an atomic like RE(3+) ion,.... A better approach would be to use LDA+U, which is available in WIEN2k.

lcore (as an atomic program) can only handle states with negative eigenvalues (positive eigenvalues with a potential V=0 at r=infinity ar not bound). Since we want to use it for a crystalline potential which does not go to zero at r=infinity, we must use a "trick":

When you shift a potential by a constant, your resulting eigenvalues also shift by exactly this constant. The wavefunctions (density) are not affected at all. Thus, for a 4f "open core" state, which has a positive energy in our crystal potential (usually at EF), we shift the potential by e.g. 1 Ry down, obtain a now a negative eigenvalue and shift this eigenvalue back to the original potential.

When you try this, you will see, that what I said above is true only, if the core state is a "good" core state, i.e. it is fully confined inside the atomic sphere. This is certainly not true for the 4f states, thus it's eigenvalue depends to some extend on the shift (in principle shift as little as possible). In addition you will have the core leakage problem,... (Use large spheres).

Example: fcc-Yb,

The aim of this example is to calculate fcc-Yb, forcing a trivalent ([Xe]4f^13) 5d^1 6s^2 configuration. The struct file is:

fcc-Yb 
F                            1
             RELA
 08.474900 08.474900 08.474900 90.000000 90.000000 90.000000
ATOM=  1: X=0.00000000 Y=0.00000000 Z=0.00000000
          MULT= 1          ISPLIT= 2
Yb               781     .000001000        2.50000       70.00000
LOCAL ROT MATRIX:    1.0000000 0.0000000 0.0000000
                     0.0000000 1.0000000 0.0000000
                     0.0000000 0.0000000 1.0000000
   0      NUMBER OF SYMMETRY OPERATIONS

Do a regular calculation first, to find out where the 4f-states are. From case.scf you find:

          ATOMIC SPHERE DEPENDENT PARAMETERS FOR ATOM  Yb

          OVERALL ENERGY PARAMETER IS    0.3000
          E( 0)=    0.3000
          E( 0)=   -3.1575   E(BOTTOM)=   -3.275   E(TOP)=   -3.040
          E( 1)=   -1.1250   E(BOTTOM)=   -1.460   E(TOP)=   -0.790
          E( 1)=    0.3000
          E( 3)=    0.5650   E(BOTTOM)=    0.520   E(TOP)=    0.610    <=======
          E( 2)=    0.4700   E(BOTTOM)=    0.470   E(TOP)= -200.000

Reducing the potential by 0.70 Ry will make all eigenvalues negative, as required when using an atomic program (lcore).

Change the following files: case.inc, case.in1 and case.in2:

1) case.inc: modify the Yb atoms: change the number of lines at the top, and add the downward shift of 0.70 Ry (due to modifications in the 4f occupancy, these 4f eigenvalues may change during the following scf, and you might need a larger shift later on (when lcore crashed)):

 
16 0.70     NUMBER OF ORBITALS (EXCLUDING SPIN), SHIFT
1,-1,2               ( N,KAPPA,OCCUP)
2,-1,2               ( N,KAPPA,OCCUP)
2, 1,2               ( N,KAPPA,OCCUP)
2,-2,4               ( N,KAPPA,OCCUP)
3,-1,2               ( N,KAPPA,OCCUP)
3, 1,2               ( N,KAPPA,OCCUP)
3,-2,4               ( N,KAPPA,OCCUP)
3, 2,4               ( N,KAPPA,OCCUP)
3,-3,6               ( N,KAPPA,OCCUP)
4,-1,2               ( N,KAPPA,OCCUP)
4, 1,2               ( N,KAPPA,OCCUP)
4,-2,4               ( N,KAPPA,OCCUP)
4, 2,4               ( N,KAPPA,OCCUP)
4,-3,6               ( N,KAPPA,OCCUP)
4, 3,6               ( N,KAPPA,OCCUP)
4,-4,7               ( N,KAPPA,OCCUP)
 0

2) case.in1: put the energy parameter for the f-electrons at a low (or high) value (e.g. -1.0 Ry, fixed, no search), such that the 4f states will not be found by lapw1:

WFFIL        (WFPRI, SUPWF)
  7.00       10    4 (R-MT*K-MAX; MAX L IN WF, V-NMT
  0.30    6  0    (GLOBAL E-PARAMETER WITH n OTHER CHOICES)
 0    0.30      0.000 CONT 1
 0   -4.06      0.005 STOP 1
 1   -1.85      0.010 CONT 1
 1    0.30      0.000 CONT 1
 3   -1.00      0.000 CONT 1
 2    0.30      0.010 CONT 1
K-VECTORS FROM UNIT:4    -7.0      1.5      emin/emax window

3) case.in2: remove 13 electrons (=reduce NE from 24 to 11):

TOT             (TOT,FOR,QTL,EFG,FERMI)
      -9.0      11.0                EMIN, NE
TETRA    0.000          (GAUSS,ROOT,TEMP,TETRA,ALL      eval)
 0 0 4 0 4 4 6 0 6 4
 16.          GMAX
FILE        FILE/NOFILE  write recprlist

Re-iterate now to convergency (running dstart first might be needed in order to avoid a very high :DIS in the first iterations).

You can compare the effect of the above procedure by comparing the electron occupations in the regular and the 'open core' calculations:

:PCS01: PARTIAL CHARGES SPHERE =  1 S,P,D,F, ...
Regular: 	:QTL01:  2.242   5.820   0.500   13.521
Open core: 	:QTL01:  2.250   5.887   0.856    0.009

In the regular calculation, there are two 5s electrons and 0.242 6s, almost six 5p electrons, 0.5 5d electrons and 13.5 4f electrons. The trivalent configuration with only 13 4f is clearly not fully realized. After applying the open core procedure, we know 13 4f electrons are in the core, and they do not show up any more in the valence region (only a negligible fraction of 0.009). The half extra electron went mostly to 5d, and a little bit to 5p and 6s. This configuration is a better approximation of the ([Xe]4f^13) 5d^1 6s^2 configuration.

Peter Blaha,