## Quantities defined in X_s.F

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### Quantities defined in X_s.F

Dear Developers:
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 $\chi$:
Code: Select all
 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
Code: Select all
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 $\epsilion_M$
Code: Select all
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
Code: Select all
 X_mat(i1,i2,iw)=X_mat(i1,i2,iw)*4.*pi/bare_qpg(iq,i1)/bare_qpg(iq,i2)

Regards,
Hai-Ping
Hai-Ping LAN,
Department Of Electronics,
Peking University, 100871,Beijing, CHINA
hplan

Posts: 58
Joined: Thu Mar 26, 2009 2:26 pm

### Re: Quantities defined in X_s.F

Dear Hai-Ping,

The output of X_s, X_mat, is Chi(q,G,G') (from the solution of the Dyson equation) multiplied by 4\pi/[(q+G)(q+G')].

This quantity corresponds to a "symmetrized" inverse microscopic dielectric function \epsilon^{-1}.
I am not sure (Andrea can confirm/correct this), but I think the reason is that this quantity can be directly/conveniently used in several expressions involving the microscopic dielectric function (e.g. for the evaluation of the mass operator).

Regards,

Myrta
Dr Myrta Grüning
Atomistic Simulation Centre
Queen's University Belfast - Northern Ireland

http://www.researcherid.com/rid/B-1515-2009

myrta gruning

Posts: 303
Joined: Tue Mar 17, 2009 11:38 am

### Re: Quantities defined in X_s.F

myrta gruning wrote: I think the reason is that this quantity can be directly/conveniently used in several expressions involving the microscopic dielectric function (e.g. for the evaluation of the mass operator).

You're right. The symmetrized expression is used in the evaluation of the mass operator and of the Bethe-Salpeter kernel.
Andrea MARINI
Istituto di Struttura della Materia, CNR, (Italy)

andrea marini

Posts: 447
Joined: Mon Mar 16, 2009 4:27 pm

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