Hi all,<br>Recently a reviewer has warned me about a problem of the dielectric function calculation that I performed using the epsilon code, where I applied the scissor shift (option shift in the input) to correct the infamous gap problem. Following the referee's criticism I got to an article by Rodolfo del Sole and Rafaello Girlanda, PRB 48, 11780 (1993), when a scissor shift is applied to correct the LDA underestimation of the transition energies, the momentum matrix elements <c|e.p|v> must be multiplied by (Ec-Ev)/(Ec0-Ev0), (see unnumbered equation after Eq. (15) in the cited paper) , where Ec0-Ev0 is the LDA transition energy and Ec-Ev=Ec0-Ev0 +\Delta ( \Delta is the scissor shift). Equivalently, one can replace the \omega^2 in the denominator by (\omega-\Delta/\hbar)^2 (Eq. 17 and 19 of the above article) . As shown by del Sole and Girlanda (and repeated many times in the literature) this is a simple approximation for the fact that "exact" transition energies Ec-Ev arise from non-local self-energy (e.g. from GW) and for non-local one electron hamiltonians the interaction with an electromagnetivc wabe is not longer A.p. <br>
<br>It is very easy to set this correction in the code epsilon.x, for example , in subroutine eps_calc one can change <br><br> etrans = ( et(iband2,ik) -et(iband1,ik) ) * RYTOEV + shift<br>.......<br> epsi(:,iw) = epsi(:,iw) + dipole(:,iband1,iband2) * intersmear * w* &<br>
RYTOEV**3 * (focc(iband1,ik))/ &<br> (( (etrans**2 -w**2 )**2 + intersmear**2 * w**2 )* etrans )<br><br> epsr(:,iw) = epsr(:,iw) + dipole(:,iband1,iband2) * RYTOEV**3 * &<br>
(focc(iband1,ik)) * &<br> (etrans**2 - w**2 ) / &<br> (( (etrans**2 -w**2 )**2 + intersmear**2 * w**2 )* etrans )<br>
<br clear="all">by the following <br><br> etrans = ( et(iband2,ik) -et(iband1,ik) ) * RYTOEV + shift<br> <span style="color:rgb(0, 0, 153)"> shift_renorm = ( etrans/(etrans-shift) )**2</span><br style="color:rgb(0, 0, 153)">
<br> epsi(:,iw) = epsi(:,iw) + dipole(:,iband1,iband2) <span style="color:rgb(0, 0, 153)">*shift_renorm</span>* intersmear * w* &<br> RYTOEV**3 * (focc(iband1,ik))/ &<br>
(( (etrans**2 -w**2 )**2 + intersmear**2 * w**2 )* etrans )<span style="color:rgb(0, 0, 153)"></span><br><br> epsr(:,iw) = epsr(:,iw) + dipole(:,iband1,iband2) <span style="color:rgb(0, 0, 153)">*shift_renorm</span>* RYTOEV**3 * &<br>
(focc(iband1,ik)) * &<br> (etrans**2 - w**2 ) / &<br> (( (etrans**2 -w**2 )**2 + intersmear**2 * w**2 )* etrans )<span style="color:rgb(0, 0, 153)"></span><br style="color:rgb(0, 0, 153)">
<br>and similarly in a few other parts of the code. <br><br>This is equivalent to replace epsilon_2(omega) by epsilon2(omega- shift/hbar) , at least for small broadening parameter so that the "delta function" is sharp , and it corrects automatically the real part of the dielectric function. <br>
<br>This is valid for LDA, and in principle not valid for GGA, although I suspect that in practice gives the same results. In fact<br><br>I would appreciate a feedback to this comment. <br><br>Best regards<br><br>-- <br><div>
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<div><br></div>Eduardo Menendez Proupin<div>Departamento de Química Fisica Aplicada<br>Facultad de Ciencias<br>Universidad Autónoma de Madrid<br>28049 Madrid, Spain<br></div><div>Phone: <a href="tel:%2B34%2091%20497%206706" value="+34914976706" target="_blank">+34 91 497 6706</a></div>
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<div>On leave from: Departamento de Fisica, Facultad de Ciencias, Universidad de Chile URL: <a href="http://fisica.ciencias.uchile.cl/%7Eemenendez" target="_blank">http://fisica.ciencias.uchile.cl/~emenendez</a><div><br>
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