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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