Energy of free atom

[satish2414]

There are several posts discussing this issue.

1)
What I am curious is about the energy level filling of d vs s orbitals. I tried several transition metal elements Ti, V, Pd etc. What I see is that first d orbitals are filled instead of s orbitals. See below for Pd atom. This configuration is d5 s1 (spin 1) and d4 (spin 2) = d9 s1. But, shouldn't the s orbitals be filled before d giving s1 d5 and d4 = s1d9?

PROCAR new format
# of k-points: 1 # of bands: 10 # of ions: 1

k-point 1 : 0.00000000 0.00000000 0.00000000 weight = 1.00000000

band 1 # energy -7.28949549 # occ. 1.00000000

ion s p d tot
1 0.000 0.000 0.895 0.895

band 2 # energy -7.12080615 # occ. 1.00000000

ion s p d tot
1 0.000 0.000 0.894 0.894

band 3 # energy -6.84744581 # occ. 1.00000000

ion s p d tot
1 0.000 0.000 0.890 0.890

band 4 # energy -6.75985025 # occ. 1.00000000

ion s p d tot
1 0.000 0.000 0.890 0.890

band 5 # energy -6.71846832 # occ. 1.00000000

ion s p d tot
1 0.000 0.000 0.889 0.889

band 6 # energy -4.66346711 # occ. 1.00000000

ion s p d tot
1 0.283 0.000 0.000 0.283
......zero occ. for others
k-point 1 : 0.00000000 0.00000000 0.00000000 weight = 1.00000000

band 1 # energy -6.20103008 # occ. 1.00000000

ion s p d tot
1 0.000 0.000 0.894 0.894

band 2 # energy -6.17344224 # occ. 1.00000000

ion s p d tot
1 0.000 0.000 0.894 0.894

band 3 # energy -6.16403739 # occ. 1.00000000

ion s p d tot
1 0.000 0.000 0.894 0.894

band 4 # energy -5.89965505 # occ. 1.00000000

ion s p d tot
1 0.000 0.000 0.892 0.892
...zero occ. for others

#INCAR for above:
ENCUT = 450.000000
BMIX = 0.000100
AMIX = 0.200000
SIGMA = 0.002000
EDIFF = 1.00e-05
PREC = Normal
ALGO = 38
ISYM = 0
ISPIN = 2
ISMEAR = 0
ISTART = 0
ICHARG = 1 #multiple runs were done
NELM = 100
NSW = 0
NPAR = 1
IVDW = 12
LCHARG = .TRUE.
LWAVE = .TRUE.
MAGMOM = 2
LORBIT=10
#POSCAR
12x13x14 Angstroms with atom at 0,0,0
#KPOINTS
Monkhorst pack, gamma point
#POTCAR
PAW_PBE

2) For Cr, setting nupdown=6 gives the correct orbital ordering where s is filled first followed by d giving s1d5 configuration.

3) I also tried the two step process of converging the atomic energies using icharg=11 and ismear=-2 (and other tags) as given in the manual. Again for several metals like Ti, V, etc, I see that d orbitals are filled first instead of s. Irrespective of the reference potentials (bulk or free atom) used to generate potcar, shouldn't the energy ordering be such that s is filled first and then d is filled?

For example, below is a case for Ti (with 10 electrons in POTCAR). In the first step, where icharg=11, s orbitals are filled first followed by d orbitals as they should be. However, when I set ISMEAR=-2 in the second step, the order reverses after the SCF step and d orbitals are filled first.

band 1 # energy -36.48590817 # occ. 1.00000000

ion s p d tot
1 0.000 0.991 0.000 0.991

band 2 # energy -36.48589961 # occ. 1.00000000

ion s p d tot
1 0.000 0.991 0.000 0.991

band 3 # energy -36.48587414 # occ. 1.00000000

ion s p d tot
1 0.000 0.991 0.000 0.991

band 4 # energy -3.82214452 # occ. 1.00000000

ion s p d tot
1 0.206 0.000 0.000 0.206

band 5 # energy -2.44033563 # occ. 0.49670291

ion s p d tot
1 0.000 0.000 0.791 0.791

band 6 # energy -2.44005237 # occ. 0.41739660

ion s p d tot
1 0.000 0.000 0.791 0.791

band 7 # energy -2.43990042 # occ. 0.37600046

ion s p d tot
1 0.000 0.000 0.791 0.791

band 8 # energy -2.43985117 # occ. 0.36285946

ion s p d tot
1 0.000 0.000 0.791 0.791

band 9 # energy -2.43979107 # occ. 0.34704057
ion s p d tot
1 0.000 0.000 0.791 0.791

band 10 # energy -1.12719640 # occ. 0.00000000

ion s p d tot
1 0.000 0.064 0.000 0.064
k-point 1 : 0.00000000 0.00000000 0.00000000 weight = 1.00000000

band 1 # energy -34.58759976 # occ. 1.00000000

ion s p d tot
1 0.000 0.991 0.000 0.991

band 2 # energy -34.58759079 # occ. 1.00000000

ion s p d tot
1 0.000 0.991 0.000 0.991

band 3 # energy -34.58756878 # occ. 1.00000000

ion s p d tot
1 0.000 0.991 0.000 0.991

band 4 # energy -3.37716078 # occ. 1.00000000

ion s p d tot
1 0.187 0.000 0.000 0.187
...rest zero occ.

4) Is there a way to make the calculation converge to sn dm configuration instead of dm sn (m,n are just number of electrons in d and s orbitals)? We can identify using icharg=11 calculation as to which orbital is filled first (as shown in (3)) but doing a following SCF step leads to dm sn instead of sn dm configuration.

5) How reliable are the energies I obtain for sn dm configuration vs dm sn?

6) On a different note, when reading PROCAR files, sometimes occupation within the same band for two orbitals (say s and d) are very close (say 0.1 and 0.2). I know that PROCAR makes an spherical shell approximation but how (if at all I should) do I interpret very close occupations between two orbitals?

[tfrankcombe]

Hi Satish

You do no specify whether you are talking about metals or atoms in boxes. If you are talking about isolated atoms, then it's well known that orbital energy ordering in transition metals does not follow the most obvious patterns. See e.g. https://chemistry.stackexchange.com/que ... ion-metals, or any one of many other similar pages. What you should be surprised at is that you get s orbital filling at all for Pd, as that's usually considered d10 in the neutral atom case.