My question is still about the response function programmed in TDDFT module of yambo.

I looked through two subroutines :O_driver.F and X_s.F, and have a confusion about quantities defined in X_s.F . Would you please do me a favor for this issue ?

I learned from X_s.F that it solves Dyson equation for $\chi$ from $\chi_0$ which is stored in X_mat. My confusion is about the last description for $\chi$:

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`X_mat(i1,i2,iw)=X_mat(i1,i2,iw)*4.*pi/bare_qpg(iq,i1)/bare_qpg(iq,i2)`

As far as i know, the solution for Dyson equation should be

$\chi=(1-\chi_0\upsilon-\chi_0 f_{xc})^{-1}\chi_0$.

My question is why we need multiply a quantity like Coulomb potential

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`4.*pi/bare_qpg(iq,i1)/bare_qpg(iq,i2)`

for X_mat ? In this situation, does X_mat store the exact information for the response function $\chi$ ? Or other attentions need pay to ?

In O_driver.F , I found the expression the $\epsilion_M$

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`X_epsilon(2,fr(1):fr(2))=1./(X_mat(1,1,:)*bare_qpg(iq,1)**2/Q_sq_modulus+1.)`

exactly follows the formula $\epilsion_M=1/(1+\upsilon\chi)$ . Therefore, in X_s.F why we perform a more calculation over X_mat as

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`X_mat(i1,i2,iw)=X_mat(i1,i2,iw)*4.*pi/bare_qpg(iq,i1)/bare_qpg(iq,i2)`

Thanks in advance!

Regards,

Hai-Ping