I am using VASP to calculate the projected DOS, but I am not sure why we aren't using the principal quantum number when doing the projection.
According to the VASP wiki, LORBIT would control VASP to generate PROCAR file, which contains the spd- and site projected wave function character of each orbital. It is called
lm-decomposed, where l,m are the angular moment and magnetic quantum numbers.
Since the electronic band structure is composed of atom orbitals, shouldn't we use the principal quantum number for projection as well? Taking Titanium as an example, its electron configuration is 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d². If we only do lm-decomposition, how should we distinguish the contribution from 3s and 4s?
There are three types of pseudopotentials in VASP for Titanium:
Ti_sv: VRHFIN =Ti: 3s3p4s3d ZVAL = 12.000
Ti_pv: VRHFIN =Ti: d3 s1 ZVAL = 10.000
Ti: VRHFIN =Ti: d3 s1 ZVAL = 4.000