# Into which spin channel do excess electrons go?

If you do unrestricted DFT calculations with CP2K for charged systems, you may wonder which spin channel the electron is taken from or added to. Moreover, the sign convention for any output (Hirshfeld or Mulliken spin charge, cube files) may be of interest to you.

The answer can be derived using these rules:

#### Alpha ≥ Beta

The number of electrons in the alpha channel is greater or equal the number of electrons in the beta channel. It does not matter whether you charge your system by adding an electron (then you have n+1 electrons in channel alpha and n electrons in channel beta) or whether you charge it by taking out one electron (then you have n electrons in channel alpha and n-1 electrons in channel beta).

#### Sign Convention

In the output log file, the sign convention is such that alpha channel population is positive and beta channel population is negative. So if you have an atom with four spins up (+4, because up=alpha) and one spin down (-1, because down=beta), then your spin charge is +3.

#### Cube Files

In the cube files for the spin density, you get the difference between alpha and beta channel, but the voxel data is signed. Following the point above on the sign convention, the value in the cube file is alpha+beta (spin up plus spin down) which is identical to the absolute value of the beta channel subtracted from the absolute value of the alpha channel.