screened Coulomb matrix elements in Yambo

[damao4361556]

Dear Daniele,

I am sorry I have troubled you so much, your replies help me a lot.
Now I have a new question about the Columb matrix, <cvk|W|c'v'k'>.

I add the following lines into the K.F file,

Code: Select all

if (i_k_bz==1.and.i_p_bz==1) then 
write(unit,*)  i_v_k , i_c_k,  i_v_p , i_c_p, real(H_c),aimag(H_c)
endif

and get the following elements:

Code: Select all

           6           9           6           9  2.1154428E-02 -2.0464450E-04
           6           9           6          10      -5.0695528E-09  6.0955498E-09
           6           9           7           9      -1.6944994E-05 -1.3251445E-04
           6           9           7          10      5.9321499E-11  3.4019274E-11
           6           9           8           9     -1.4239850E-05 -3.2842021E-05
           6           9           8          10    -3.4264525E-11  2.6545804E-10
           6          10           6          10    2.1554479E-02 -2.0579009E-04
           6          10           7           9    4.7524276E-11 -4.9220631E-11
           6          10           7          10   -1.6944987E-05 -1.3251445E-04
           6          10           8           9     2.6813624E-10  2.4152331E-11
           6          10           8          10    -1.4232191E-05 -3.2845310E-05
           7           9           7           9     2.1156007E-02 -2.0464837E-04
           7           9           7          10    -5.0859521E-09  6.0975420E-09
           7           9           8           9    -6.2035298E-07 -2.1643978E-06
           7           9           8          10   2.5001262E-12 -4.3753104E-12
           7          10           7          10   2.1552280E-02 -2.0578071E-04
           7          10           8           9   -9.3766292E-13 -1.3393811E-12
           7          10           8          10   -6.2033115E-07 -2.1644059E-06
           8           9           8           9    2.1156013E-02 -2.0585512E-04
           8           9           8          10   -5.0718660E-09  6.1032805E-09
           8          10           8          10    2.1552283E-02 -2.0698753E-04

here, 6,7,8 is the occupied orbitals, 9,10 is the unoccupied orbitals.

I was thought that the Columb matrix elements should be for two KS orbitals, like VB-CB, 9-6
but now the Columb matrix elements shown above is for two excitons, e.g., 6->9 and 6->9, according to <cvk|W|c'v'k'>

My question is it possible to extract the Columb matrix elements for two KS orbitals?

Or there is something wrong with what I understood?
For example, Columb matrix elements for 6->9 and 6->9 is exactly the Screened Columb element for KS orbitals 6-9. But how about Columb matrix elements for 6->9 and 6->10

thanks and best wishes.

Wei

[Daniele Varsano]

Dear Wei,
The BSE equation has 4-point kernel, once diagonalized the exciton wave function will be a linear combination of single particle-hole transitions:
\psi(re,rh)=\sum_cv A_cv \phi_c(r_e)\phi_v(r_h)
where A_cv is the eigenvector of the BSE matrix.
The screened Columb matrix element is between two eh transitions (which is your basis set).
You can have a look at the paper by Rohlfing and Luoie PRB 62, 4927
Part.2 Section C for a complete treatment of the electron-hole interaction, in particular, Eq. 24.

Best,

Daniele