## Multiplicity Factor from KPOINTS

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Vasp1a
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Posts: 8
Joined: Tue Jan 28, 2020 3:08 pm

### Multiplicity Factor from KPOINTS

Dear Vasp Users,
I am trying to calculate the DOS effective mass from the effective mass tensor, which is defined as

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m*_DOS=M^(3/2) x (m_1 x m_2 x m_3)^(1/3)
with m_i being the eigenvalues of the effective mass tensor and M the multiplicity respectively.

While I manage to calculate the effective mass tensor, I am not quite sure how I can obtain the multiplicity factor M. For a given k-point, let's say L-point, it should state the number of equivalent k-points to that point of interest, or to rephrase it: How many L-points are there.

As vasp already provides the weights in the KPOINTS file, I thought I could maybe use that to avoid thinking too much about how one would get this number from the unit cell itself. However, I am not sure how to read/reformat the KPOINTs file:
This is a KPOINTS file for PbSe:

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Automatically generated mesh
826
Reciprocal lattice
0.00000000000000 0.00000000000000 0.00000000000000 1
0.04166666666667 0.00000000000000 -0.00000000000000 8
0.08333333333333 -0.00000000000000 0.00000000000000 8
0.12500000000000 -0.00000000000000 -0.00000000000000 8
0.16666666666667 -0.00000000000000 -0.00000000000000 8
0.20833333333333 -0.00000000000000 -0.00000000000000 8
0.25000000000000 -0.00000000000000 -0.00000000000000 8
0.29166666666667 0.00000000000000 -0.00000000000000 8
0.33333333333333 -0.00000000000000 0.00000000000000 8
0.37500000000000 -0.00000000000000 -0.00000000000000 8
0.41666666666667 -0.00000000000000 -0.00000000000000 8
0.45833333333333 -0.00000000000000 -0.00000000000000 8
0.50000000000000 -0.00000000000000 -0.00000000000000 4
0.04166666666667 0.04166666666667 -0.00000000000000 6
0.08333333333333 0.04166666666667 0.00000000000000 24
0.12500000000000 0.04166666666667 -0.00000000000000 24
...
-0.29166666666667 0.45833333333333 0.20833333333333 48
-0.25000000000000 0.45833333333333 0.20833333333333 24
-0.29166666666667 0.50000000000000 0.20833333333333 12
If I am interested at the L-point at 0.5/0.5/0.5,
how would I find the multipicity? This point is not in KPOINTS explicitly, so how do I find which point in the list is equivalent to 0.5/0.5/0.5? ( I removed most points in the list above to shorten the text).

Thanks a lot and all the best,

Carl-Friedrich

support_vasp
Global Moderator
Posts: 1817
Joined: Mon Nov 18, 2019 11:00 am

### Re: Multiplicity Factor from KPOINTS

Hi,

We're sorry that we didn’t answer your question. This does not live up to the quality of support that we aim to provide. The team has since expanded. If we can still help with your problem, please ask again in a new post, linking to this one, and we will answer as quickly as possible.

Best wishes,

VASP