I generated Wannier centers but am having trouble understanding how they relate to the atoms in my system: there are more Wannier centers than atoms?

I'm trying to calculate dipole moments from Wannier centers for the first time and there are basics I don't understand and can't figure out from online resources.

The software I'm using has a simple "output Wannier centers" option. So I now have output, which is a file with Wannier centers and atomic positions. My system contains many water molecules but here's a simple example for a system that has only one H2O. The "X" are Wannier centers:

X          6.50000026       6.18706578       6.50000000
X          6.50000000       6.71337672       6.50000002
X          6.50000008       6.95339960       6.49999998
X          6.49999971       6.54636884       6.50000000
H          6.50000000       7.09480000       7.26880000
H          6.50000000       7.09480000       5.73120000
O          6.50000000       6.50000000       6.50000000

• Why are there four X for one H2O? I vaguely assumed that there would be one X, corresponding to one H2O. Do the four X correspond somehow to different molecular configuration possibilities? I have tried to look this up but probably don't even know the right search terms.

I included "Wannier90" as a tag because it seems relevant and generates output formatted like my example but I am not using Wannier90.

H2O has 10 electrons, two of which are oxygen 1s. This leaves you eight electrons. These eight electrons fit onto 4 spatial orbitals in a spin-restricted calculation for the singlet.

Determining localized orbitals [1] (for periodic boundary conditions these are called Wannier functions), the 4 orbitals localize into two covalent OH bonds, and two lone pairs on the oxygen atom. You have obtained the centroids of these orbitals, which are determined by the expectation value $$\langle {\bf r} \rangle$$.

[1]: Note that there is more than one way to determine localized orbitals; for instance, we have proposed Pipek-Mezey Wannier functions in J. Chem. Theory Comput. 2017, 13, 2, 460–474

• +1 for another very quick answer, backed with a good reference, as always! I'm sure the OP appreciates your efficiency! Jun 17, 2021 at 23:42
• Yes, I certainly do appreciate it! Thank you for the comment about periodic BC too. That clears up some confusion. May I please make sure I'm clear about something? Does it matter if the H2O is H2O or if it dissociates? I am dealing with high-ish temperature and this may have happened.
– NTS
Jun 18, 2021 at 5:20
• @NTS no; what matters is only the number of electrons. Of course, the dissociation is not captured by the calculation if you use spin-restricted orbitals; you need a broken-symmetry unrestricted calculation to be able to dissociate H2O Jun 18, 2021 at 23:19