I am trying to calculate the quasiparticle corrections for a 1d system (periodic along x) using a coulomb cutoff "box yz" and the random integration method for the Coulomb potential.

Using the standard parameters RandQpts = 1000000 and RandGvec = 1, I obtain the following report

- Code: Select all
`[04] Coloumb potential Random Integration (RIM)`

===============================================

[RD./SAVE//ndb.RIM]-----------------------------------------

Brillouin Zone Q/K grids (IBZ/BZ): 33 64 33 64

Coulombian RL components : 1

Coulombian diagonal components :yes

RIM random points : 1000000

RIM RL volume [a.u.]: 0.02669

Real RL volume [a.u.]: 0.02660

Eps^-1 reference component :0

Eps^-1 components : 0.00 0.00 0.00

RIM anysotropy factor : 0.000000

- S/N 002743 --------------------------- v.03.04.01 r.3187 -

Summary of Coulomb integrals for non-metallic bands |Q|[au] RIM/Bare:

Q [1]:0.1000E-40.8187 * Q [2]: 0.02132 0.19701

Q [3]: 0.04264 0.42336 * Q [4]: 0.06395 0.59031

Q [5]: 0.08527 0.70378 * Q [6]: 0.106590 0.780348

Q [7]: 0.127908 0.832871 * Q [8]: 0.149226 0.869775

Q [9]: 0.170544 0.896378 * Q [10]: 0.191862 0.916030

Q [11]: 0.213180 0.930879 * Q [12]: 0.234497 0.942328

Q [13]: 0.255815 0.951317 * Q [14]: 0.277133 0.958490

Q [15]: 0.298451 0.964296 * Q [16]: 0.319769 0.969056

Q [17]: 0.341087 0.973005 * Q [18]: 0.362405 0.976313

Q [19]: 0.383723 0.979111 * Q [20]: 0.405041 0.981498

Q [21]: 0.426359 0.983550 * Q [22]: 0.447677 0.985326

Q [23]: 0.468995 0.986873 * Q [24]: 0.490313 0.988228

Q [25]: 0.511631 0.989423 * Q [26]: 0.532949 0.990480

Q [27]: 0.554267 0.991421 * Q [28]: 0.575585 0.992261

Q [29]: 0.596903 0.993015 * Q [30]: 0.618221 0.993693

Q [31]: 0.639539 0.994306 * Q [32]: 0.660857 0.994862

Q [33]: 0.682175 0.995382

i.e. the ratio RIM/bare differs quite significantly from 1 for low q. In the forum Daniele suggested that for convergence it only matters that the ratio approaches 1 at the Brillouin zone boundary(?). Can this value of 0.995382 then be considered converged?

As far as the understanding of the method is concerned, I am still struggling a lot and I would be very grateful for a few hints.

I have read through the formulae in http://www.yambo-code.org/theory/docs/doc_RIM.php . At the end there is a comparison between "RIM" and "without RIM" for a chain of H2 molecules.

What does "without RIM" mean? Does it mean that the integral over dq has been replaced by a sum over q_i for *both* F(q+G) and the potential (as in the formula after "The integral over the BZ is usually numerically evaluated as ...")?

Wouldn't this mean that the potential is evaluated at q+G=0, leading immediately to a divergence?

And in connection to this: what is the difference between the "Bare" and "RIM" Coulomb integrals?

Best,

Leopold