<html><head></head><body><div class="ydpcb773a14yahoo-style-wrap" style="font-family:Helvetica Neue, Helvetica, Arial, sans-serif;font-size:16px;"><div><div style="text-align: left; font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">Dear QE developers,</div><div style="text-align: left; font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><br></div><div style="text-align: left; font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">I am trying to understand the meaning of “orbital-resolved magnetic anisotropy” as demonstrated in: PP/examples/ForceTheorem_example.</div><div style="text-align: left; font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><br></div><div style="text-align: left; font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">From the documentation and the projwfc.x output, it appears that QE provides the contribution of each orbital character (e.g., dxy, dx2−y2, dz2, …) to the band-energy difference (MAE) obtained via the force theorem.</div><div style="text-align: left; font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><br></div><div style="text-align: left; font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">Question:</div><div style="text-align: left; font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">Is my understanding correct that QE reports the projected occupied-state contribution of a given orbital character (e.g., dxy = 0.9 meV), rather than an explicit second-order SOC coupling term between occupied and unoccupied orbitals (as typically reported in VASP, e.g., dxy|dz2 = 0.3 meV, dxy|dx2−y2 = 0.4 meV, …)?</div><div style="text-align: left; font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><br></div><div style="text-align: left; font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">In other words, if VASP reports:</div><div style="text-align: left; font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"> dxy|dz2 = 0.3 meV</div><div style="text-align: left; font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"> dxy|dx2−y2 = 0.4 meV</div><div style="text-align: left; font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"> dxy|dyz = 0.2 meV</div><div style="text-align: left; font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><br></div><div style="text-align: left; font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">then the QE-projected value will be: dxy = 0.9 meV ????</div><div style="text-align: left; font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><br></div><div style="text-align: left; font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">would correspond to the sum of all pairwise contributions involving dxy as the occupied partner. Could you please confirm whether projwfc.x computes this projection only from occupied states, and whether this interpretation is correct?</div><div style="text-align: left; font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><br></div><div style="text-align: left; font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;" dir="" data-setdir="true">Thank you very much.</div></div><br><br></div></body></html>