[Wien] Valence Broadening of Emission Spectrum

[Francisco Garcia]

Dear Prof. Blaha,


I have two questions about the valence band emission spectra calculation in
the subroutine valencebroadening.f: one question is about the usage of the
parameter W and the other question is on how the Lorenztian convolution is
done.


(i) I thought W was a flag which determines which flavour of the broadening
parameter gamma will be used (see the initial comments in the subroutine
valencebroadening.f below). However, gamma appears to be a multiple of W in
the emission calculation (please see below), which I find very confusing.
Any reason(s) why?


      subroutine
ValenceBroadening(X,Y,yend,w,absorb,istep,wshift,E0,E1,E2,EF,delta,nimax)
!     VALENCE BROADENING : the array y is broadened by convolution with a
Lorentz-function.
!     The result is in array yend.  Three different broadening schemes are
available :
!     - w=0 : the width of the Lorentz does not depend on energy
!     - w=1 : the width of the Lorentz varies linearly with energy
!     - w=2 : the width of the Lorentz varies quadratically with energy
!     - w=3 : the width of the Lorentz is given by the scheme of Moreau et
al.

.

.

.

!     EMISSION PART:
               if(E0.NE.E2) then
                  if (X(i1).gt.E0) then
                     gamma=W*(1-((X(i1)-E0)/(EF-E0)))**2
                  elseif (X(i1).gt.E1) then
                     gamma=W
                  else
                     gamma=W+W*(1-((X(i1)-E2)/(E1-E2)))**2
                  endif
               else
                  gamma=W*(1-((X(i1)-E0)/(EF-E0)))**2
               endif
            endif



(ii) My second question is how the convolution of the Gaussian-broadened
DOS with the Lorentzian was performed. In the subroutine
valencebroadening.f, the Lorenztian convolution was computed as follows
after setting gamma:

            do i2=1,nimax

               yend(i2)=yend(i2)+y(i1)/pi* &
              (atan((X(i1)-X(i2)+delta)/gamma) &
              -(atan((X(i1)-X(i2)-delta)/gamma)))

            enddo


It appears that an integral in the closed form was used to evaluate the
convolution. I know that the integral of the Lorenztian can be obtained in
a closed form: $$\int \frac{\gamma^2}{\pi(x^2+\gamma^2)} dx =
\frac{\gamma}{\pi}} arctan(x / \gamma)$$. So that seems to be part of the
explanation. But I am highly interested in how the above discretization was
obtained from the convolution.


Thank you Sir.


FG
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