Dear Gavin, Thank you for your detailed and insightful response. The references you provided, particularly J. Luitz's dissertation, were very helpful.
Thanks again! FG On Sat, Apr 19, 2025 at 4:16 PM Francisco Garcia <[email protected]> wrote: > 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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