[QE-users] Extra states in conduction band and PDOS/Total DOS mismatch in strained hBN unit cell
Giovanni Cantele
giovanni.cantele at spin.cnr.it
Fri Mar 27 14:18:37 CET 2026
I believe I may have identified the issue. I performed a quick test and, by
visualizing the square modulus of the wavefunction for the first conduction
band at Gamma,
I found that this state is localized a few angstroms away from the
monolayer.
This reminded me of the so-called nearly free electron (NFE) states, which
I encountered some years ago. I recall a paper on MXenes discussing this
phenomenon, which I was able to locate:
Physical Review B 93, 205125 (2016).
In addition, I found another relevant reference:
Physical Review B 86, 245406 (2012)
which appears to discuss similar states in BN systems.
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
Phone: +39 081 676910
Web page: https://sites.google.com/view/giovanni-cantele/home
Il giorno ven 27 mar 2026 alle ore 12:01 Ms. Chandrika K. <
BL.EN.R4ECE21001 at bl.students.amrita.edu> ha scritto:
> 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
> 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> 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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