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<p>Dear Michal,</p>
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> Now, how do I convert the complex susceptibility chi (from the output of turbo_lanczos) to epsilon? I know that in principle epsilon = 1 + chi, but then the results don’t make sense. Am I missing some unit conversion or something else?</div>
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> Moreover, turbo_lanczos is complaining it hasn’t got enough information to compute S - what could be the cause of this?</div>
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<p>S is the oscillator strength. Some useful information is written in the output file of the turbo_spectrum calculation (for finite systems):</p>
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<span style="font-variant-ligatures: no-common-ligatures">chi_i_j: dipole polarizability tensor in units of e^2*a_0^2/energy</span></p>
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<span style="font-variant-ligatures: no-common-ligatures">S: oscillator strength in units of 1/energy</span></p>
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S(\hbar \omega) = 2m/( 3 \pi e^2 \hbar) \omega sum_j chi_j_j<br>
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S(\hbar \omega) satisfies the f-sum rule: \int_0^\infty dE S(E) = N_el<br>
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<p>In your case you are interested in epsilon for periodic systems, so you may look in the code <span style="font-family: Menlo; font-size: 15px;">TDDFPT/tools/</span><span style="font-family: Menlo; font-size: 15px;">tddfpt_calculate_spectrum.f90. E.g. on
lines 463-475 it is written:</span></p>
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<span style="font-variant-ligatures: no-common-ligatures; color: #d17125">DO</span><span style="font-variant-ligatures: no-common-ligatures"> ip</span><span style="font-variant-ligatures: no-common-ligatures; color: #d17125">=</span><span style="font-variant-ligatures: no-common-ligatures; color: #ca3323">1</span><span style="font-variant-ligatures: no-common-ligatures">,n_ipol</span></p>
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<span style="font-variant-ligatures: no-common-ligatures"> </span><span style="font-variant-ligatures: no-common-ligatures; color: #d17125">DO</span><span style="font-variant-ligatures: no-common-ligatures"> ip2</span><span style="font-variant-ligatures: no-common-ligatures; color: #d17125">=</span><span style="font-variant-ligatures: no-common-ligatures; color: #ca3323">1</span><span style="font-variant-ligatures: no-common-ligatures">,n_ipol</span></p>
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<span style="font-variant-ligatures: no-common-ligatures"> </span><span style="font-variant-ligatures: no-common-ligatures; color: #5620f4">!</span></p>
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<span style="font-variant-ligatures: no-common-ligatures; color: #000000"> </span><span style="font-variant-ligatures: no-common-ligatures">!eps(ip,ip2) = (1.d0,0.d0)-(32.d0*pi/omega)*green(ip,ip2)</span></p>
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<span style="font-variant-ligatures: no-common-ligatures"> </span><span style="font-variant-ligatures: no-common-ligatures; color: #5620f4">!</span></p>
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<span style="font-variant-ligatures: no-common-ligatures; color: #000000"> </span><span style="font-variant-ligatures: no-common-ligatures; color: #d17125">WRITE</span><span style="font-variant-ligatures: no-common-ligatures; color: #000000">(</span><span style="font-variant-ligatures: no-common-ligatures">17</span><span style="font-variant-ligatures: no-common-ligatures; color: #000000">,</span><span style="font-variant-ligatures: no-common-ligatures">'(5x,"chi_",i1,"_",i1,"=",2x,3(e21.15,2x))'</span><span style="font-variant-ligatures: no-common-ligatures; color: #000000">)
</span><span style="font-variant-ligatures: no-common-ligatures; color: #db27da">&</span></p>
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<span style="font-variant-ligatures: no-common-ligatures"> ip2, ip, start,
</span><span style="font-variant-ligatures: no-common-ligatures; color: #38b9c7">dble</span><span style="font-variant-ligatures: no-common-ligatures">(green(ip,ip2)),
</span><span style="font-variant-ligatures: no-common-ligatures; color: #38b9c7">aimag</span><span style="font-variant-ligatures: no-common-ligatures">(green(ip,ip2))</span></p>
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<span style="font-variant-ligatures: no-common-ligatures; color: #000000"> </span><span style="font-variant-ligatures: no-common-ligatures">! write(*,'(5x,"eps_",i1,"_",i1,"=",2x,3(e21.15,2x))') &</span></p>
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<span style="font-variant-ligatures: no-common-ligatures; color: #000000"> </span><span style="font-variant-ligatures: no-common-ligatures">! ip2, ip, ry*omeg, dble(eps), aimag(eps)</span></p>
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<span style="font-variant-ligatures: no-common-ligatures"> </span><span style="font-variant-ligatures: no-common-ligatures; color: #5620f4">!</span></p>
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<span style="font-variant-ligatures: no-common-ligatures"> </span><span style="font-variant-ligatures: no-common-ligatures; color: #d17125">ENDDO</span></p>
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<span style="font-variant-ligatures: no-common-ligatures; color: #d17125">ENDDO</span></p>
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<span style="font-variant-ligatures: no-common-ligatures; color: #d17125"><br>
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<span style="font-variant-ligatures: no-common-ligatures;"><span style="color: rgb(0, 0, 0); font-family: Arial, Helvetica, sans-serif; font-size: 12pt;">What you need is "eps", but it is commented out. So just uncomment it here and check in other places in
this program and see what you obtain. Since this is commented out, one has to be careful and check if the result is correct. I do not know where the factor 32 comes from (one has to think</span><font face="Arial, Helvetica, sans-serif" size="3">). It was not
me who coded this. You may also check the </font><font face="Arial, Helvetica, sans-serif">literature</font><font face="Arial, Helvetica, sans-serif" size="3"> how the dielectric matrix is obtained from the susceptibility matrix (i.e. what are the prefactors).</font></span></p>
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<span style="font-variant-ligatures: no-common-ligatures; color: rgb(0, 0, 0); font-family: Arial, Helvetica, sans-serif; font-size: 12pt;">HTH</span></p>
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<span style="font-variant-ligatures: no-common-ligatures; color: #d17125"><br>
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<span style="font-variant-ligatures: no-common-ligatures; color: rgb(0, 0, 0); font-family: Arial, Helvetica, sans-serif; font-size: 12pt;">Iurii</span></p>
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<font size="3" face="'Times New Roman', Times, serif" color="808080">--<br>
Dr. Iurii Timrov<br>
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<font size="3" face="'Times New Roman', Times, serif" color="808080"><font size="3" face="'Times New Roman', Times, serif" color="808080">Swiss Federal Institute of Technology Lausanne (EPFL<font color="808080"><font face="'Times New Roman', Times, serif">)</font></font></font><br>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> users <users-bounces@lists.quantum-espresso.org> on behalf of Michal Krompiec <michal.krompiec@gmail.com><br>
<b>Sent:</b> Monday, April 20, 2020 10:27:29 PM<br>
<b>To:</b> Quantum Espresso users Forum<br>
<b>Subject:</b> [QE-users] dielectric function from turbo_lanczos</font>
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<div>Hello,<br>
I'm trying to compare refractive index spectra calculated with epsilon.x and TDDFpT with the turbo_lanczos code. My system is a periodic supercell, I am using PBEsol functional, Gamma-only sampling and norm-conserving PPs.</div>
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<div dir="auto">From the output of epsilon.x, I calculate refractive index n as follows:</div>
n = np.sqrt(np.sqrt(np.square(eps_real_iso)+np.square(eps_imag_iso)+eps_real_iso)) </div>
<div dir="auto"># eps_real_iso and eps_imag_iso are averages of the spatial components of real and imaginary epsilon<br>
<br>
<div dir="auto">Now, how do I convert the complex susceptibility chi (from the output of turbo_lanczos) to epsilon? I know that in principle epsilon = 1 + chi, but then the results don’t make sense. Am I missing some unit conversion or something else?</div>
<div dir="auto">Moreover, turbo_lanczos is complaining it hasn’t got enough information to compute S - what could be the cause of this?</div>
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<div dir="auto">Thanks,</div>
<div dir="auto">Michal Krompiec </div>
<div dir="auto">Merck KGaA</div>
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