[QE-users] Extra states in conduction band and PDOS/Total DOS mismatch in strained hBN unit cell

[Ms. Chandrika K.]

Thank you Prof. Giovanni Cantele,for your insightful response.
Here is a brief update on the tests I performed.
Tested denser k-meshes for the NSCF calculation as suggested, 48x48x1 and 72x72x1, and also performed a vacuum convergence test with several vacuum thicknesses, but in the strained (compressive strain of 3%) unit cell (Figure 2), additional states at the edge of the conduction band are still visible, and also the total DOS is not accounted  by either the B or N projected DOS individually or collectively.
Further, I have started the |psi|^2 visualization using pp.x as advised and will update this thread with the results once the analysis is finished.

Below I have shared  nscf input file  for reference.

# denser  k mesh
&CONTROL
  calculation  = 'nscf'
  prefix           = '  --------'
  outdir           = '---------  '
  pseudo_dir   = '-------- '
 /

&SYSTEM
 ibrav         = 4               ! Hexagonal lattice
  celldm(1)    = 4.592          ! a in Bohr ::2.43Å
  celldm(3)    = 8.23           !20 A vaccum
  nat          = 2
  ntyp         = 2
  ecutwfc      = 60
  ecutrho      = 480
  nbnd          =8
  occupations  = 'smearing'
  smearing     = 'gaussian'
  degauss      = 0.01
/

&ELECTRONS
  conv_thr     = 1.0d-8
  mixing_beta  = 0.4
/

ATOMIC_SPECIES
  B   10.811  B.pbe-n-rrkjus_psl.1.0.0.UPF
  N   14.007  N.pbe-n-rrkjus_psl.1.0.0.UPF

ATOMIC_POSITIONS (crystal)
B             0.6667000000        0.3333000000        0.0000000000
N             0.3333000000        0.6667000000        0.0000000000

K_POINTS {automatic}
  48 48 1 0 0 0



Chandrika Yadav K

Research Scholar

NanoElectronics Laboratory

Amrita Viswa Vidyapeetham

Bangalore


________________________________
From: Giovanni Cantele <giovanni.cantele at spin.cnr.it>
Sent: Thursday, March 26, 2026 3:31 PM
To: Ms. Chandrika K. <BL.EN.R4ECE21001 at bl.students.amrita.edu>; Quantum ESPRESSO users Forum <users at lists.quantum-espresso.org>
Subject: Re: [QE-users] Extra states in conduction band and PDOS/Total DOS mismatch in strained hBN unit cell

Hi,

generally speaking, it is expected that, as one moves to higher energies (in the unoccupied manifold), the sum of the projected DOS over all atoms/species becomes smaller than the total DOS.
This is because projwfc.x projects Kohn–Sham states onto atomic wavefunctions defined in the pseudopotential files. These atomic functions are constructed to describe well the valence states and,
to some extent, low-lying unoccupied states. However, higher-energy states may contain components that are not well represented within this atomic-like basis, and therefore are only partially captured
 by the projections. You can directly observe this behavior in the projwfc.x output: the quantity reported after each eigenvalue (the sum of projections, i.e. |psi|^2 onto the atomic basis) is typically very close to
1 for occupied states, while it starts to decrease for unoccupied states and continues to do so with increasing energy.

That said, it is important to understand whether your specific observation has a physical origin or is instead a numerical artifact. A few points you may want to check:
- while a 36×36×1 grid for NSCF should already give a reasonable DOS, I would still test denser meshes. The presence of many peaks in your DOS
could indicate insufficient Brillouin zone sampling rather than a physical effect;

- identify the k-points and energies corresponding to the states at the conduction band edge in the strained system, and visualize the corresponding |psi|^2 (e.g. with pp.x).
If these states are more delocalized in the interstitial or vacuum region, rather than localized on B/N atoms or bonds, then it is expected that atomic projections do not fully capture them;

- is this bulk or monolayer hBN? In the monolayer case, vacuum regions can play an important role, and low-lying conduction states may have significant weight outside the atomic regions.
Did you check, if it applies, convergence with respect to the vacuum?

- make sure the strain has been applied consistently and that atomic positions have been properly relaxed. Geometrical inconsistencies can lead to spurious states near the band edges;

- sharing input files and band structure plots would help to better assess whether the observed features are physical.

Giovanni

--

Prof. Giovanni Cantele
Dipartimento di Fisica "Ettore Pancini"
Universita' degli Studi di Napoli "Federico II"
Complesso Universitario M. S. Angelo - Ed. 6
Via Cintia, I-80126, Napoli, Italy
e-mail: giovanni.cantele at unina.it<mailto:giovanni.cantele at unina.it>
Phone: +39 081 676910

Web page: https://sites.google.com/view/giovanni-cantele/home


Il giorno gio 26 mar 2026 alle ore 09:35 Ms. Chandrika K. via users <users at lists.quantum-espresso.org<mailto:users at lists.quantum-espresso.org>> ha scritto:
Hello everyone,
I am performing DFT calculations on a pristine and uniaxially strained hexagonal boron nitride (hBN) unit cell using Quantum ESPRESSO with the following computational parameters:

  *   Pseudopotentials: B.pbe-n-rrkjus_psl.1.0.0.UPF and N.pbe-n-rrkjus_psl.1.0.0.UPF (USPP, PBE, scalar relativistic)
  *   ecutwfc: 60 Ry | ecutrho: 480 Ry
  *
K-mesh: 12×12×1 (SCF), 36×36×1 (NSCF)
  *   Broadening: ngauss = 0, degauss = 0.004 Ry, DeltaE = 0.004 eV
  *
DOS tool: projwfc.x only (both total DOS and PDOS from same run)
  *
Basis: Only s and p orbitals present for both B and N

  *
In the pristine unit cell DOS (Figure 1), the total DOS and the sum of B and N projected DOS match upto certain point in the conduction band.

  *
However, in the strained unit cell (Figure 2), additional states at the edge of conduction band are visible  and also the total DOS is not accounted  by either the B or N projected DOS individually or collectively.
Any insights on the origin of the extra conduction band states and the enhanced PDOS mismatch in the strained system would be greatly appreciated.

Chandrika Yadav K


Research Scholar

NanoElectronics Laboratory

Amrita Viswa Vidyapeetham

Bangalore


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