The whole business of the constraints is rather complex, I'm afraid. We're trying to clean it up to have only one in the future (one that works in all cases and is always correct!).
About centering the coordinates, this is crucially important for the "RealSpaceDensity" constraint, but doesn't seem to matter for the other ones. Actually, if you center the coordinates, the "RealSpaceDensity" constraint is quite a good choice often.
To use "DensityMatrix", you need to edit the script by hand, and enter it into the segment which normally looks like
two_probe_algorithm_parameters = twoProbeAlgorithmParameters(
electrode_constraint = ElectrodeConstraints.Off,
initial_density_type = InitialDensityType.NeutralAtom
)
Here, set
electrode_constraint = ElectrodeConstraints.DensityMatrix,
The Off constraint does not produce a physically correct effective potential (even if you are not going to take the difference).