<html><head></head><body><div class="yahoo-style-wrap" style="font-family:Helvetica Neue, Helvetica, Arial, sans-serif;font-size:16px;"><div dir="ltr" data-setdir="false"><div><p class="ydp37f8b6d3my-2" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial; margin-right: 0px; margin-left: 0px; font-family: fkGroteskNeue, ui-sans-serif, system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, "Helvetica Neue", Arial, "Noto Sans", sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji", "Hiragino Sans", "PingFang SC", "Apple SD Gothic Neo", "Yu Gothic", "Microsoft YaHei", "Microsoft JhengHei", Meiryo; font-size: 16px; letter-spacing: 0.08px;">Dear Quantum ESPRESSO Developers / User Community,</p><div style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial; margin-right: 0px; margin-left: 0px; font-family: fkGroteskNeue, ui-sans-serif, system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, "Helvetica Neue", Arial, "Noto Sans", sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji", "Hiragino Sans", "PingFang SC", "Apple SD Gothic Neo", "Yu Gothic", "Microsoft YaHei", "Microsoft JhengHei", Meiryo; font-size: 16px; letter-spacing: 0.08px;">I am currently working on magnetic anisotropy energy (MAE) calculations using Quantum ESPRESSO and reviewing the force-theorem approach for orbital-resolved MAE decomposition, specifically as implemented via projwfc.x. (<a href="https://gitlab.com/QEF/q-e/-/tree/f184591e9f34cfcc7767505a23977a92286e8ba6/PP/examples/ForceTheorem_example" rel="nofollow" target="_blank" style="font-family: "Helvetica Neue", Helvetica, Arial, sans-serif;" class="">https://gitlab.com/QEF/q-e/-/tree/f184591e9f34cfcc7767505a23977a92286e8ba6/PP/examples/ForceTheorem_example</a><span style="font-family: "Helvetica Neue", Helvetica, Arial, sans-serif;">)</span></div><div><br></div><p class="ydp37f8b6d3my-2" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial; margin-right: 0px; margin-left: 0px; font-family: fkGroteskNeue, ui-sans-serif, system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, "Helvetica Neue", Arial, "Noto Sans", sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji", "Hiragino Sans", "PingFang SC", "Apple SD Gothic Neo", "Yu Gothic", "Microsoft YaHei", "Microsoft JhengHei", Meiryo; font-size: 16px; letter-spacing: 0.08px;">From my understanding, the method attributes MAE contributions based on the projection of wavefunctions of occupied states onto atomic orbitals (e.g., <span class="ydp37f8b6d3katex" style="border-width: 0px; border-style: solid; scrollbar-color: initial; max-width: 100%;"><span class="ydp37f8b6d3katex-mathml" style="scrollbar-color: initial; scrollbar-width: initial;">dxy</span><span class="ydp37f8b6d3katex-html" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"><span class="ydp37f8b6d3base" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"><span class="ydp37f8b6d3strut" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial; vertical-align: -0.2861em; min-height: 0.9805em;"></span><span class="ydp37f8b6d3mord" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"><span class="ydp37f8b6d3mord ydp37f8b6d3mathnormal" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;">d</span><span class="ydp37f8b6d3msupsub" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"><span class="ydp37f8b6d3vlist-t ydp37f8b6d3vlist-t2" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"><span class="ydp37f8b6d3vlist-r" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"><span class="ydp37f8b6d3vlist" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial; min-height: 0.1514em;"><span style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial; margin-left: 0em; margin-right: 0.05em;"><span class="ydp37f8b6d3pstrut" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial; min-height: 2.7em;"></span><span class="ydp37f8b6d3sizing ydp37f8b6d3reset-size6 ydp37f8b6d3size3 ydp37f8b6d3mtight" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"><span class="ydp37f8b6d3mord ydp37f8b6d3mtight" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"><span class="ydp37f8b6d3mord ydp37f8b6d3mathnormal ydp37f8b6d3mtight" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;">x</span><span class="ydp37f8b6d3mord ydp37f8b6d3mathnormal ydp37f8b6d3mtight" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial; margin-right: 0.03588em;">y</span></span></span></span></span><span class="ydp37f8b6d3vlist-s" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"></span></span><span class="ydp37f8b6d3vlist-r" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"><span class="ydp37f8b6d3vlist" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial; min-height: 0.2861em;"><span style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"></span></span></span></span></span></span></span></span></span>, <span class="ydp37f8b6d3katex" style="border-width: 0px; border-style: solid; scrollbar-color: initial; max-width: 100%;"><span class="ydp37f8b6d3katex-mathml" style="scrollbar-color: initial; scrollbar-width: initial;">dz2</span><span class="ydp37f8b6d3katex-html" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"><span class="ydp37f8b6d3base" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"><span class="ydp37f8b6d3strut" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial; vertical-align: -0.1776em; min-height: 0.8721em;"></span><span class="ydp37f8b6d3mord" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"><span class="ydp37f8b6d3mord ydp37f8b6d3mathnormal" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;">d</span><span class="ydp37f8b6d3msupsub" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"><span class="ydp37f8b6d3vlist-t ydp37f8b6d3vlist-t2" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"><span class="ydp37f8b6d3vlist-r" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"><span class="ydp37f8b6d3vlist" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial; min-height: 0.3448em;"><span style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial; margin-left: 0em; margin-right: 0.05em;"><span class="ydp37f8b6d3pstrut" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial; min-height: 2.7em;"></span><span class="ydp37f8b6d3sizing ydp37f8b6d3reset-size6 ydp37f8b6d3size3 ydp37f8b6d3mtight" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"><span class="ydp37f8b6d3mord ydp37f8b6d3mtight" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"><span class="ydp37f8b6d3mord ydp37f8b6d3mtight" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"><span class="ydp37f8b6d3mord ydp37f8b6d3mathnormal ydp37f8b6d3mtight" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial; margin-right: 0.04398em;">z</span><span class="ydp37f8b6d3msupsub" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"><span class="ydp37f8b6d3vlist-t" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"><span class="ydp37f8b6d3vlist-r" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"><span class="ydp37f8b6d3vlist" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial; min-height: 0.7463em;"><span style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial; margin-right: 0.0714em;"><span class="ydp37f8b6d3pstrut" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial; min-height: 2.5em;"></span><span class="ydp37f8b6d3sizing ydp37f8b6d3reset-size3 ydp37f8b6d3size1 ydp37f8b6d3mtight" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial; font-size: 0.714286em;"><span class="ydp37f8b6d3mord ydp37f8b6d3mtight" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;">2</span></span></span></span></span></span></span></span></span></span></span></span><span class="ydp37f8b6d3vlist-s" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"></span></span><span class="ydp37f8b6d3vlist-r" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"><span class="ydp37f8b6d3vlist" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial; min-height: 0.1776em;"><span style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial;"></span></span></span></span></span></span></span></span></span>, etc.), without explicitly resolving the spin–orbit coupling between occupied and unoccupied orbitals.</p><p class="ydp37f8b6d3my-2" style="border-width: 0px; border-style: solid; scrollbar-color: initial; scrollbar-width: initial; margin-right: 0px; margin-left: 0px; font-family: fkGroteskNeue, ui-sans-serif, system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, "Helvetica Neue", Arial, "Noto Sans", sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji", "Hiragino Sans", "PingFang SC", "Apple SD Gothic Neo", "Yu Gothic", "Microsoft YaHei", "Microsoft JhengHei", Meiryo; font-size: 16px; letter-spacing: 0.08px;">Could you please confirm if this interpretation is correct? Additionally, is there any recommended procedure or add-on tool within Quantum ESPRESSO for analyzing MAE in terms of pairwise orbital coupling mediated by SOC, similar to the perturbative approaches used in other codes like VASP?<br><br></p><div>Thanks and Regards</div><div dir="ltr" data-setdir="false">Yashika</div><p></p></div><br></div></div></body></html>