PROCAR: Sum of orbital projections not equal to 1

[paromita_dutta]

Dear All,

I have a question regarding the interpretation of the TOT values in the PROCAR file. For each (k-point, band), I expected that the sum of projections over all atoms and orbitals would be close to 1, corresponding to a normalized wavefunction. As stated in the VASP Wiki: “Each (k-point, band) pair contains the projections for every ion |⟨Yₗₘ|Φₗₘ⟩|², where Yₗₘ is the spherical harmonic centered at ion index, with angular momentum (l) and magnetic quantum number (m), and Φ is the wavefunction. The line and column with ‘tot’ represent the corresponding sums.” However, I observe the following:

1. For collinear calculations, the sum over all atomic and orbital projections in the charge channel does not approach 1. While I understand it may not be exactly unity, I expected values close to it (e.g., ~0.9–1.0), but instead I obtain significantly lower values such as ~0.86 or ~0.75.
2. For non-collinear calculations, a similar deviation is observed, not only for the charge channel but also for the spin components (Sx, Sy, Sz).

I would appreciate any clarification on whether this behavior is expected and what factors might lead to such deviations.

Best

Paromita

[henrique_miranda]

Dear Paromita,

What you are describing is known and due to the fact that the radial part of the orbitals onto which we project the KS states for plotting the projected density of states don't extend over the full space.
As such it is somehow expected that the sum of the projections don't sum to 1.
While it is in principle possible to force it to be one using a singluar value decomposition of the projections matrix (https://www.vasp.at/wiki/Category:Wanni ... tion_(SVD)), that might not be meaningful either.
There we would just be assigning the missing weight to the projection with largest overlap with that particular region of space.
There are quite a few schemes such as Bader analysis that make particular choices about how to assign the space to each projection such that all the space in the unit cell is assigned to at least one.

For LORBIT=1 you can tune the https://vasp.at/wiki/RWIGS variable for the different species and try to cover as much of the space as possible.
That should give you the sum of the total projections closer to 1 but it might not be entirely physical either.

In short: there is no unique way to decide how to assign the missing weight to the default PAW projectors (LORBIT=11) that is unless the orbitals onto which you project already cover the full space which is what you try to do with LORBIT=1 and RWIGS.
Because there are many choices that one can make, the one that is made in VASP is to just use the PAW projectors.

[paromita_dutta]

Thank you for the clearing my doubts regarding this.