[CP2K-user] [CP2K:19430] Re: units of psi^2

[Lukas C]

Hi again,

Let me please answer at least party to myself as I just figured out how to 
get the dimensionless wavefunction and someone might need this at some 
point.

Considering:
1. the volume V of a voxel
2. the DFT wavefunction Psi
2. that the sum of the "actual" or dimensionless wavefunction Psi_A squared 
over the normalization volume V equals 1
we can say: 
V * sum( Psi_A² ) = 1, where the sum goes over all voxels.
as well as:
sum( Psi² ) = F    ....   F is just some factor that appears due to the 
normalization

we can then get the dimensionless probability density by
Psi_A²=Psi²/(V*F).

So far so good. Now I am not sure how to proceed when calcuating the 
hyperfine Hamiltonian S A I, with S is the spin (here 1/2) and I is the 
nuclear spin.
A is given in MHz but do i multiply this with hbar or h to get the energy?

Lukas

Lukas C schrieb am Donnerstag, 26. Oktober 2023 um 13:10:21 UTC+9:

> hi everyone!
>
> I am using the cp2k implementation to calculate hyperfine tensors. no 
> problems here so far, i got some results using an all-electron basis set.
>
> now, unfortunately, i cannot find any information on how this is done 
> internally and also i cannot assign the units. e.g. in which units is 
> |Psi(x,y,z)|^2 ? I know that it has to be normalized, but to which volume?
>
> one starting point was the vasp manual, in which they clearly say how the 
> calculations works. https://www.vasp.at/wiki/index.php/LHYPERFINE
>
> does cp2k work similarly?
>
> Thank you!
>
> Best,
> Lukas
>

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