[Wien] [Q] Counting the numer of electrons / slight metallic states

[Son Won-joon]

Dear WIEN2k Gurus.

I am a novice with WIEN2k calculations, and now doing some
spin polarized GGA(+U) caculations of Gd-Halide systems.

And I have some trivial (but annoying to me) questions:

1.
When I check TOTAL CORE-CHARGE of Gd after lstart (and scf file),

 TOTAL CORE-CHARGE:                   46.000000
 TOTAL CORE-CHARGE INSIDE SPHERE:     45.999929
 TOTAL CORE-CHARGE OUTSIDE SPHERE:     0.000071

MAGNETIC MOMENT IN SPHERE seems quite reasonable,
but I would like to make sure whether this order of charge leakage
can be negligible in total energy calculations (with different spin
configurations).

I am using the default RMT and R0 values in my struct file.
Gd        NPT=  781  R0=.000010000 RMT=   2.50000   Z:  64.00000

2.
Also, in the end of outputst, OCCUPANCY and ENERGY(RYD) of Gd looks like
...
  4D*     2.000    -1.1219532E+01
  4D*     2.000    -1.0774702E+01
  4D      3.000    -1.0797164E+01
  4D      3.000    -1.0354003E+01
  5S      1.000    -3.7282009E+00
  5S      1.000    -3.4775735E+00
  5P*     1.000    -2.2946120E+00
  5P*     1.000    -2.0836248E+00
  5P      2.000    -1.9680388E+00
  5P      2.000    -1.7786762E+00
  4F*     3.000    -7.9075700E-01
  4F*     0.000    -3.9080067E-01
  4F      4.000    -7.3468784E-01
  4F      0.000    -3.3752094E-01
...

Since I assigned the default -6.0 Ry for separating core and valence states,
5S and 5P come into my band states. so, I have 5S, 5P and 4F, 5D, 6S
in my valence states.

When I check NUMBER OF ELECTRONS(:NOE) in scf file
as well as the TOTAL CORE-CHARGE of Gd, I can confirm that each
Gd has total 18 e-'s in its band states, and QTL values also suggest
Gd has 5s and 5p states occupied.
And, estimation of the number of electrons from the sum of QTL values
is ~ 85 % of :NOE, which I think reasonable.

But when I run x tetra to draw the DOS plot, and check outputtdn/up files,
the up+dn sum of the NUMBER OF ELECTRONS UP TO EF
is about 61 % of the number from :NOE.

Even though I exclude the 5S and 5P electrons (10 e-) from counting in :NOE,
the number from NUMBER OF ELECTRONS UP TO EF is still smaller.
Is it normal to have much smaller (like 2/3) values in outputtdn/up
than that of :NOE? Or those two numbers are of different meaning?

3.
When I plot the DOS, with settings in int file as
 -0.500   0.00001   0.8  0.0005     #Emin, DE, Emax, Gauss-Broad
this results in slight VBM tail crossing the EF.

I expect from the simple electron countings,
this system should shows the gap between VBM and CBM,
suspecting this is solely due to the Gaussian broadening.
(Even though I use the GGA+U scheme, this tail is still there.)

So, I checked outputtup/dn file, and I find
I have non-integer occupation number in up spin, like 195.9998, at EF
and it sustains the decimal value upto the conduction band minimum.
The down spin shows exact interger number of electrons up to EF.

I would like to know whether the 0.0002 e- deficiency
is due to the numerical error (thus can be neglected),
or I should check with the band structure to determine the metallicity
of the system.

When the number from the outputtup/dn file suggests sort of band gap,
then could I consider this system as a semi-conductor regardless of the
metallic states tail in dos1up/dn files?

And, if 0.0002 e- is due to the numerics,
is there any way to remove this annoying number?
(I am using RKMAX=8, GMAX=14, and quite large number of kpoints.)

I am terribly sorry for bothering you,
but I still hope you will give me a kind consideration.

Many thanks in advance.

Sincerely,
Won-joon Son