Atoms

About which files do you have to worry:

INCAR
POSCAR
POTCAR
KPOINTS

Before using a pseudopotential intensively, it is not only required to test it for various bulk phases, but the pseudopotential should also reproduce exactly the eigenvalues and the total energy of the free atom for which it was created. If the energy cutoff and the cell size are sufficient, the agreement between the atomic reference calculation (EATOM in the POTCAR file) and a calculation using VASP is normally better than 1 meV (but errors can be 10 meV for some transition metals). In most cases, calculations for an atom are relatively fast and unproblematic. For the calculation the $\Gamma$ should be used i.e. the KPOINTS file should have the following contents:

Monkhorst Pack
0
Monkhorst Pack
 1  1  1
 0  0  0

Table 3: Typical convenient settings for the cell size for the calculation of atoms and dimers are (reoughly 4-5 times the dimer length):

	cell size
Lithium	13 Å
Aluminium	12 Å
Potassium	14 Å
Copper, Rhodium, Palladium ...	10 Å
Nitrogen	7 Å
C	8 Å

A simple cubic cell is usually recommended; the size of the cell depends on the element in question. Some values for reliable results are compiled in Tab. 3. These cells are also large enough to perform calculations on dimers, explained in the next section. The POSCAR file is similar to:

atom
1
     10.00000    .00000    .00000
       .00000  10.00000    .00000
       .00000    .00000  10.00000
   1
cart
 0    0    0

The INCAR file can be very simple

SYSTEM = Pd: atom
 Electronic minimization
   ENCUT  = 200.00 eV  energy cut-off for the calculation (opt)
   NELMDL =  5         make five delays till charge mixing

   ISMEAR =    0; SIGMA=0.1    use smearing method

The only difference to the bulk calculation is that Gaussian smearing should be used. If the atomic orbitals are almost degenerated, you might have to set SIGMA to a smaller value (but be careful very small values might degrade convergence significantly). For initial tests, SIGMA=0.1 eV is usually a good starting point.

Mind: Extract the correct value for the energy, it is not $F=E+ \sigma S$ which contains a - meaningless - entropy term related to accidential orbital degeneracy, but the ``energy without entropy'' in the OUTCAR file.

In some rare cases, the real LDA/GGA groundstate might differ from the configuration for which the pseudopotential was generated (most transition metals, see Sec. 10), since the occupancies have been set manually during the pseudopotential generation. For Pd, for instance, a $s^1d^9$ configuration was chosen to be the reference configuration, which is not the LDA/GGA groundstate of the atom. In this case, it is necessary to set the occupancies for VASP manually in order to obtain the same energy as the one found in the POTCAR file. This can be done including the following lines in the INCAR file: This can be done including the following lines in the INCAR file:

  LDIAG = .FALSE.       ! keep ordering of eigenstates fixed
  ISMEAR = -2           ! keep occupancies fixed
  FERWE  =  5*0.9  0.5  ! set the occupancies manually

(5*0.9 is interpreted as 0.9 0.9 0.9 0.9 0.9). To determine the ordering of the eigenvalues it might be necessary to perform a calculation with ICHARG=12 (i.e. fixed atomic charge density). After a successful atomic calculation compare the differences between the eigenvalues with those obtained by the pseudopotential generation program. Also check the total energy, the differences should be smaller than $20$ meV.

Here another example: If the energy of an atom with a particular configuration has to be calculated, i.e. spin polarized Fe with a valence configuration of 3d6.2 4s1.8, the calculation has to be performed in two step. First a non selfconsistent calculation with the following INCAR must be performed:

 ISPIN = 2 
 ICHARG = 12
 MAGMOM = 4     ! magnetization in Fe is 4

This first step is required in order to determine a set of initial wavefunctions and the orbital ordering. In the OUTCAR file one finds the following level ordering:

 k-point   1 :       0.0000    0.0000    0.0000
  band No.  band energies    
      1         -5.0963      
      2         -5.0963      
      3         -5.0954      
      4         -5.0954      
      5         -5.0954      
      6         -4.6929      
      7         -0.7528      
      8         -0.7528      

 Spin component 2

 k-point   1 :       0.0000    0.0000    0.0000
  band No.  band energies     
      1         -3.6296       
      2         -2.2968       
      3         -2.2968       
      4         -2.2889       
      5         -2.2889       
      6         -2.2889       
      7         -0.1247       
      8         -0.1247

In the spin up component, the 5 d states have lower energy than the s state, whereas in the down component, the s state has lower energy than the d states. This ordering is important for supplying the occupancies in the lines FERWE and FERDO in the INCAR file in the second calculation. For a spherical atom, the final calculation is performed with the following INCAR file:

 ISTART = 1                 !  read in the WAVECAR file
 ISPIN = 2 
 MAGMOM = 4
 AMIX = 0.2 ; BMIX = 0.0001 !  recommended mixing for magnetic systems

 LDIAG = .FALSE.            !  keep ordering of eigenstates fixed
                            !  (Loewdin subspace rotation)
 ISMEAR = -2                !  keep occupancies fixed
 FERWE = 5*1  1*1     3*0   !  d5  s1, 3 other orbitals zero occ.
 FERDO = 0.8  5*0.24  3*0   !  s0.8 d1.2 other orbitals zero occ.

The determination of the spin-polarisation broken symmetry groundstate of atoms is discussed in the next section 9.5.

Mind: The size of the cell can be reduced if one special point is used instead of the $\Gamma$ point, i.e. if the KPOINTS file has the following contents:

Monkhorst Pack
0
Monkhorst Pack
 2  2  2
 0  0  0

The reasons for this behavior are: Due to the finite size of the cell a band dispersion exists i.e. the atomic eigenvalues split and form a band with finite width. To first order the center of the band lies exactly at the position of the atomic eigenvalues. At the $\Gamma$-point, however the eigenvalues at the bottom of the band are obtained. If the special point (0.25,0.25,0.25) 2$\pi/a$ is used instead of the $\Gamma$-point, the energy of the center of the band is obtained. Nevertheless we recommend this setting only for experts: in most cases the degeneracy of the p- and d-orbitals is removed and only the mean value of the eigenvalues remains physically significant. In this cases it is also necessary to increase $SIGMA$ or to set the partial occupancies by hand!