QMCPACK / QMCPACK/qmcpack

How to Apply Holzmann et al.’s Finite-Size Correction?

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Description

I'm calculating TiS2 bulk structure for tracing this study.
https://dx.doi.org/10.1021/acs.jpca.0c05973

In this study, Holzmann et al.'s correction was employed as a potential energy correction.
To evaluate this correction, I performed DMC calculations
while recording the static structure factor using the following estimator:

` `

I then processed the results with the qmcfinitesize command and obtained the following output:
**%----------------------------------------**
**=========================================================
Finite Size Corrections:
=========================================================**
System summary:
Nelec = 192.00000000
Vol = 3094.43944186 [a0^3]
Ne/V = 0.06204678 [1/a0^3]
rs/a0 = 1.56698215


V_LO / electron = 0.00159580 +/- 0.00005100 [Ha/electron]
V_LO = 0.30639447 +/- 0.00979268 [Ha]
T_LO / electron = 0.00082837 +/- 0.00002648 [Ha/electron]
T_LO = 0.15904800 +/- 0.00508334 [Ha]
NB: This is a crude estimate of the kinetic energy correction!

Beyond Leading Order (Integrated corrections):
V_Int / electron = 0.00160340 +/- 0.00005687 [Ha/electron]
V_Int = 0.30785348 +/- 0.01091999 [Ha]
**%----------------------------------------**
I have attached the result for one of the twists.
[qmc.g000.s004.finitesize.txt](https://github.com/user-attachments/files/21852861/qmc.g000.s004.finitesize.txt)

However, I am unsure about the proper way to apply this finite-size correction to the raw DMC energy.

Specifically, when I averaged the V_Int values over each twist and simply added this average to the raw DMC energy (obtained using qmca -a -q e qmc.g*.s004.scalar.dat), the resulting size dependence of the energy differed significantly from that reported in the reference paper.

Image

Could you advise whether this procedure for applying the correction is appropriate,
or if there might be another underlying cause for the discrepancy?

I apologize if this is a very basic question, but I would greatly appreciate your guidance.

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