[Wien] sum rules-TiC

[Pavel Ondračka]

Brik Hamida píše v Út 27. 05. 2014 v 17:46 +0200:
> I have calculated the optical properties of TiC. I have just followed
> all the steps given in UG. The only difference , I haven't found the
> TiC.in2c in order to change TOT to FERMI  but I do it in TiC.in2..I
> think that is ok ?? no ?

> 
> My question is about its sum rules. I found : 
>  sum rule 1: Int(sigma)dw 4.6253 
> sum rule 2: Int(eloss.w)dw     0.1719
> sum rule 3: Int(eloss/w)dw    0.2839

Dear Brik,

don't know if this will actually help you, but I've spend a lot of time
trying to compute the precise sumrule with Wien2k so just few notes.
Also hopefully someone familiar with the optic code can shed more light.

The sum rule integrates eps_i over whole energy range it is hugely
dependent on the EMAX value. If you use the default value of 1.5 in
case.in1 this is way to low, when you increase it sufficiently, you
should get far better results. Also don't forget to increase EMAX also
in case.inop and case.injoint.

Also for optics you need in general more k-points that for other
calculations so also check how your sum rule converges with number of
k-points.

Main problem is, even with all those numerical parameters tweaked and
with absorption beyond the EMAX extrapolated it is still not high
enough. This is to my knowledge a limitation of the method, I've asked
for help with this some time ago, but got no response
( http://zeus.theochem.tuwien.ac.at/pipermail/wien/2013-December/020342.html ).

So in theory if you increased EMAX high enough you should get slightly
less that 16 electrons for TiC (C - 2s2 2p2, Ti - 3s2 3p6 4s2 3d2, but
depends on core and valence states separation energy).

Also its probably a good idea to check the sumrule before the kram, or
at least set broadening to 0 in case.inkram as I don't think it
preserves the sum rule. 
> 
> But When I read  Claudia Ambrosch-Drax's paper (Linear optical
> properties of solids within the full-potential linearized augmented
> planewave method)I found That The first two give an effective number of
> electrons contributing to the absorption process as a function of
> energy.!!!
Its worth noting that the sum rule doesn't for example guarantee that
when you calculate it for all valence electron transitions, you will get
a number of valence electrons. The "effective electron number"
contributing to valence or core electron excitation may differ from the
actual number of electrons present, but is guaranteed to sum up to a
total number of electrons in compound. 

> So, my calculations are wrong ?? But When I work on another compound I
> found That sum rule (1-2) are different . Sum rule 3 is different to =
> π/2 !!
Well this is expected as different compounds have different number of
electrons contributing. But still, the sum rule is IMHO not a good test
of validity of your calculations
> Can some one help me Please ? What Can I do
> Best Regards

Best regards
Pavel Ondračka