<div dir="ltr"><div>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, </div><div>I found that this state is localized a few angstroms away from the monolayer.<br>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:<br>Physical Review B 93, 205125 (2016).<br>In addition, I found another relevant reference:<br>Physical Review B 86, 245406 (2012)<br>which appears to discuss similar states in BN systems.</div><div></div><div>Giovanni</div><div><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><span style="color:rgb(0,0,0)">-- <br><br>Prof. Giovanni Cantele<br>Dipartimento di Fisica "Ettore Pancini"<br>Universita' degli Studi di Napoli "Federico II"<br>Complesso Universitario M. S. Angelo - Ed. 6<br>Via Cintia, I-80126, Napoli, Italy<br>e-mail: <a href="mailto:giovanni.cantele@unina.it" target="_blank">giovanni.cantele@unina.it</a><br>Phone: +39 081 676910<br><br>Web page: </span><a href="https://sites.google.com/view/giovanni-cantele/home" style="color:rgb(17,85,204)" target="_blank">https://sites.google.com/view/giovanni-cantele/home</a><br></div></div></div><br></div><br><div class="gmail_quote gmail_quote_container"><div dir="ltr" class="gmail_attr">Il giorno ven 27 mar 2026 alle ore 12:01 Ms. Chandrika K. <<a href="mailto:BL.EN.R4ECE21001@bl.students.amrita.edu">BL.EN.R4ECE21001@bl.students.amrita.edu</a>> ha scritto:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div class="msg1461033738020347091">
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Thank you Prof. Giovanni Cantele,for your insightful response. </div>
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Here is a brief update on the tests I performed.</div>
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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.</div>
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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.</div>
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Below I have shared nscf input file for reference.</div>
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# denser k mesh</div>
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&CONTROL</div>
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calculation = 'nscf'</div>
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prefix = ' --------'</div>
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outdir = '--------- '</div>
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pseudo_dir = '-------- '</div>
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&SYSTEM</div>
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ibrav = 4 ! Hexagonal lattice</div>
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celldm(1) = 4.592 ! a in Bohr ::2.43Å</div>
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celldm(3) = 8.23 !20 A vaccum </div>
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nat = 2</div>
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ntyp = 2</div>
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ecutwfc = 60</div>
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ecutrho = 480</div>
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nbnd =8</div>
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occupations = 'smearing'</div>
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smearing = 'gaussian'</div>
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degauss = 0.01</div>
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&ELECTRONS</div>
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conv_thr = 1.0d-8</div>
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mixing_beta = 0.4</div>
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ATOMIC_SPECIES</div>
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B 10.811 B.pbe-n-rrkjus_psl.1.0.0.UPF</div>
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N 14.007 N.pbe-n-rrkjus_psl.1.0.0.UPF</div>
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ATOMIC_POSITIONS (crystal)</div>
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B 0.6667000000 0.3333000000 0.0000000000</div>
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N 0.3333000000 0.6667000000 0.0000000000</div>
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K_POINTS {automatic}</div>
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48 48 1 0 0 0</div>
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Chandrika Yadav K</div>
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<span style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">Research Scholar</span></p>
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<span style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">NanoElectronics Laboratory </span></p>
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<span style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">Amrita Viswa Vidyapeetham </span></p>
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<span style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">Bangalore</span></p>
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<b>From:</b> Giovanni Cantele <<a href="mailto:giovanni.cantele@spin.cnr.it" target="_blank">giovanni.cantele@spin.cnr.it</a>><br>
<b>Sent:</b> Thursday, March 26, 2026 3:31 PM<br>
<b>To:</b> Ms. Chandrika K. <<a href="mailto:BL.EN.R4ECE21001@bl.students.amrita.edu" target="_blank">BL.EN.R4ECE21001@bl.students.amrita.edu</a>>; Quantum ESPRESSO users Forum <<a href="mailto:users@lists.quantum-espresso.org" target="_blank">users@lists.quantum-espresso.org</a>><br>
<b>Subject:</b> Re: [QE-users] Extra states in conduction band and PDOS/Total DOS mismatch in strained hBN unit cell</div>
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<div style="direction:ltr">Hi,</div>
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</div>
<div style="direction:ltr">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.<br>
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, </div>
<div style="direction:ltr">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</div>
<div style="direction:ltr"> 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 </div>
<div style="direction:ltr">1 for occupied states, while it starts to decrease for unoccupied states and continues to do so with increasing energy.</div>
<div style="direction:ltr"><br>
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:<br>
- 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 </div>
<div style="direction:ltr">could indicate insufficient Brillouin zone sampling rather than a physical effect;</div>
<div style="direction:ltr"><br>
- 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). </div>
<div style="direction:ltr">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;</div>
<div style="direction:ltr"><br>
- 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.</div>
<div style="direction:ltr">Did you check, if it applies, convergence with respect to the vacuum?</div>
<div style="direction:ltr"><br>
- 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;</div>
<div style="direction:ltr"><br>
- sharing input files and band structure plots would help to better assess whether the observed features are physical.</div>
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</div>
<div style="direction:ltr">Giovanni</div>
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<div style="direction:ltr"><span style="color:rgb(0,0,0)">-- <br>
<br>
Prof. Giovanni Cantele<br>
Dipartimento di Fisica "Ettore Pancini"<br>
Universita' degli Studi di Napoli "Federico II"<br>
Complesso Universitario M. S. Angelo - Ed. 6<br>
Via Cintia, I-80126, Napoli, Italy<br>
e-mail: <a id="m_8514051425887437966OWA4ecbb6b7-3174-a0ff-b28f-939a69030632" href="mailto:giovanni.cantele@unina.it" target="_blank">
giovanni.cantele@unina.it</a><br>
Phone: +39 081 676910<br>
<br>
Web page: </span><span style="color:rgb(17,85,204)"><a style="color:rgb(17,85,204)" id="m_8514051425887437966OWAec0b89f6-3784-0b21-232f-31357c890315" href="https://sites.google.com/view/giovanni-cantele/home" target="_blank">https://sites.google.com/view/giovanni-cantele/home</a></span></div>
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<div style="direction:ltr">Il giorno gio 26 mar 2026 alle ore 09:35 Ms. Chandrika K. via users <<a id="m_8514051425887437966OWAdc38f57b-3df9-87b0-6815-11f5a0fd235b" href="mailto:users@lists.quantum-espresso.org" target="_blank">users@lists.quantum-espresso.org</a>> ha scritto:</div>
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Hello everyone,</div>
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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:</div>
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<b>Pseudopotentials:</b> B.pbe-n-rrkjus_psl.1.0.0.UPF and N.pbe-n-rrkjus_psl.1.0.0.UPF (USPP, PBE, scalar relativistic)</li><li style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0);direction:ltr">
<b>ecutwfc:</b> 60 Ry | <b>ecutrho:</b> 480 Ry</li><li style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
<div style="direction:ltr" role="presentation"><b>K-mesh:</b> 12×12×1 (SCF), 36×36×1 (NSCF)</div>
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<b>Broadening:</b> ngauss = 0, degauss = 0.004 Ry, DeltaE = 0.004 eV</li><li style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)">
<div style="direction:ltr" role="presentation"><b>DOS tool:</b> projwfc.x only (both total DOS and PDOS from same run)</div>
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<div style="direction:ltr" role="presentation"><b>Basis:</b> Only s and p orbitals present for both B and N</div>
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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.</div>
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However, in the strained unit cell (Figure 2), additional states at the edge of conduction band are visible and also the total DOS is
<b>not accounted </b> by either the B or N projected DOS individually or collectively.</div>
<div style="direction:ltr" role="presentation">Any insights on the origin of the extra conduction band states and the enhanced PDOS mismatch in the strained system would be greatly appreciated.</div>
<p role="presentation" style="direction:ltr;text-align:left;text-indent:0px;background-color:rgb(255,255,255);margin:0px">
Chandrika Yadav K</p>
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Research Scholar</div>
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NanoElectronics Laboratory </p>
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Amrita Viswa Vidyapeetham </p>
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Bangalore</p>
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