[QE-users] Projection over atomic states are not normalized.

[Seyed Mohammad Farzaneh]

Hi All,

I am studying monolayer black phosphorus using version 6.0. The primitive
unit cell of the crystal contains four atoms each with four valence
orbitals (s, px, py, pz). So, in total there are 16 orbitals in the unit
cell.
I run scf and nscf calculations by setting nbnd=16. Then using projwfc
module I get the projection of the wavefunctions over atomic orbitals at
k=0 by setting kresolved=.true..
Also, I am using a norm-conserving scalar relativistic pseudopotential.
Here are the results for the 16 energy bands at the Gamma point (k=0).

==== e(   1) =   -19.25235 eV ==== |psi|^2 = 0.997
==== e(   2) =   -16.76376 eV ==== |psi|^2 = 0.994
==== e(   3) =   -13.46989 eV ==== |psi|^2 = 0.996
==== e(   4) =    -9.99107 eV ==== |psi|^2 = 0.977
==== e(   5) =    -8.95201 eV ==== |psi|^2 = 0.996
==== e(   6) =    -8.74968 eV ==== |psi|^2 = 0.983
==== e(   7) =    -7.87978 eV ==== |psi|^2 = 0.987
==== e(   8) =    -6.19935 eV ==== |psi|^2 = 0.977
==== e(   9) =    -5.92184 eV ==== |psi|^2 = 0.981
==== e(  10) =    -4.28819 eV ==== |psi|^2 = 0.979
==== e(  11) =    -3.24853 eV ==== |psi|^2 = 0.945
==== e(  12) =    -2.54804 eV ==== |psi|^2 = 0.735
==== e(  13) =    -1.77330 eV ==== |psi|^2 = 0.905
==== e(  14) =    -1.10489 eV ==== |psi|^2 = 0.978
==== e(  15) =     0.18973 eV ==== |psi|^2 = 0.008
==== e(  16) =     0.25455 eV ==== |psi|^2 = 0.009
As you can see not all the bands are normalized, especially the last two
ones (|psi|^2 << 1).
I should mention that scf is converging and there are no diagonalization
issues.

My question is that why are these wavefunctions not normalized?
Do we expect them to be normalized at all? Why not?

Thanks in advance,
Seyed
-- 
*S. M. Farzaneh*
Graduate Student
ECE Department
New York University
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