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: [email protected] 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. < [email protected]> 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 <[email protected]> > *Sent:* Thursday, March 26, 2026 3:31 PM > *To:* Ms. Chandrika K. <[email protected]>; Quantum > ESPRESSO users Forum <[email protected]> > *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: [email protected] > 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 < > [email protected]> 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 > > > > > _______________________________________________________________________________ > The Quantum ESPRESSO Foundation stands in solidarity with all civilians > worldwide who are victims of terrorism, military aggression, and > indiscriminate warfare. > > -------------------------------------------------------------------------------- > Quantum ESPRESSO is supported by MaX (www.max-centre.eu) > users mailing list [email protected] > https://lists.quantum-espresso.org/mailman/listinfo/users > >
_______________________________________________________________________________ The Quantum ESPRESSO Foundation stands in solidarity with all civilians worldwide who are victims of terrorism, military aggression, and indiscriminate warfare. -------------------------------------------------------------------------------- Quantum ESPRESSO is supported by MaX (www.max-centre.eu) users mailing list [email protected] https://lists.quantum-espresso.org/mailman/listinfo/users
