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fix real-space Wannier function normalization #2

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eassmann opened this issue Dec 22, 2015 · 2 comments
Open
2 of 4 tasks

fix real-space Wannier function normalization #2

eassmann opened this issue Dec 22, 2015 · 2 comments
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bug enhancement testing wplot
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2.1

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eassmann commented Dec 22, 2015 •
edited

In wplot, the Wannier functions are currently not normalized. Rather, ⟨w|w⟩ = Nk X where Nk is the number of k-points and X an unknown factor.

Additionally, in tests with SOC, there is a factor (~2.16) between a setup with and one without RLOs.

  • Take number of k-points into account.
  • Figure out what X is and take it into account as well.
  • Figure out RLO-induced factor.
  • Document in user's guide.
@eassmann eassmann self-assigned this Dec 22, 2015
@eassmann eassmann added this to the 1.1.0 milestone Dec 22, 2015
@eassmann eassmann added the wplot label Dec 30, 2015
@eassmann eassmann changed the title Fix real-space Wannier function normalization fix real-space Wannier function normalization Dec 30, 2015
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eassmann commented Feb 3, 2016 •
edited

Normalization by #k now fixed (f14e29c).

eassmann referenced this issue Dec 3, 2016
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SRC_wplot/main.F: fix normalization by number of k-points
f14e29c 
Previously, `w(r)` as printed in `case.psink` was normalized as
`|w²(r)|/#k` leading to a factor `#k`.  Fix this to `|w(r)/#k|²`.

Thanks to Ulrich Wedig.
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The remaining factor is simply due to the units. If AU units are requested in case.inwplot, then sum(case.psink) * dV ≈ 1 holds, where in the simplest case dV = (L / [Np - 1])³ with axis length L as given in the header of case.psink and Np points in each direction.

If ANG units are selected, L must also be in Å, of course. Otherwise, an extra factor of (Å/Bohr)³ ≈ 6.75 appears.

The RLO-related factor remains to be tested in 2.0.

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