<html xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta name="Generator" content="Microsoft Word 15 (filtered medium)">
<style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
{font-family:"Malgun Gothic";
panose-1:2 11 5 3 2 0 0 2 0 4;}
@font-face
{font-family:Aptos;
panose-1:2 11 0 4 2 2 2 2 2 4;}
@font-face
{font-family:"\@Malgun Gothic";}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
font-size:12.0pt;
font-family:"Aptos",sans-serif;
mso-ligatures:standardcontextual;}
span.EmailStyle17
{mso-style-type:personal-compose;
font-family:"Aptos",sans-serif;
color:windowtext;}
span.fadeinm1hgl8
{mso-style-name:_fadein_m1hgl_8;}
.MsoChpDefault
{mso-style-type:export-only;}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
{page:WordSection1;}
/* List Definitions */
@list l0
{mso-list-id:107480258;
mso-list-type:hybrid;
mso-list-template-ids:-1859492720 67698703 67698713 67698715 67698703 67698713 67698715 67698703 67698713 67698715;}
@list l0:level1
{mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;}
@list l0:level2
{mso-level-number-format:alpha-lower;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;}
@list l0:level3
{mso-level-number-format:roman-lower;
mso-level-tab-stop:none;
mso-level-number-position:right;
text-indent:-9.0pt;}
@list l0:level4
{mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;}
@list l0:level5
{mso-level-number-format:alpha-lower;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;}
@list l0:level6
{mso-level-number-format:roman-lower;
mso-level-tab-stop:none;
mso-level-number-position:right;
text-indent:-9.0pt;}
@list l0:level7
{mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;}
@list l0:level8
{mso-level-number-format:alpha-lower;
mso-level-tab-stop:none;
mso-level-number-position:left;
text-indent:-.25in;}
@list l0:level9
{mso-level-number-format:roman-lower;
mso-level-tab-stop:none;
mso-level-number-position:right;
text-indent:-9.0pt;}
@list l1
{mso-list-id:1097871371;
mso-list-template-ids:-949607728;}
ol
{margin-bottom:0in;}
ul
{margin-bottom:0in;}
--></style>
</head>
<body lang="EN-US" link="#467886" vlink="#96607D" style="word-wrap:break-word">
<div class="WordSection1">
<p class="MsoNormal"><span style="font-size:11.0pt">Hello all,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p><span class="fadeinm1hgl8">I am computing the tight-binding (TB) Hamiltonian of a monolayer MoS₂ (1×1 unit cell with three atoms) using Quantum ESPRESSO + Wannier90. I'm using d orbitals for Mo and p orbitals for S atoms.<o:p></o:p></span></p>
<p><o:p> </o:p></p>
<p><span class="fadeinm1hgl8">Here is a snippet of my wannier90 settings:</span><o:p></o:p></p>
<p class="MsoNormal"><span style="font-size:11.0pt">```<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">num_iter = 0<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">dis_num_iter = 0<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">…<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">wannier_plot = True<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">…<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">begin projections<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> Mo:d:z=0,0,1:x=1,0,0<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> S:l=1,mr=2:z=0,0,1:x=1,0,0<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> S:l=1,mr=3:z=0,0,1:x=1,0,0<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"> S:l=1,mr=1:z=0,0,1:x=1,0,0 <o:p>
</o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">end projections<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">```<o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;mso-ligatures:none">Please note that I have set num_iter =0 because I want to preserve wannier function shape as typical orbital (px py pz dxy …) This
configuration enforces the order of the p</span><span style="font-size:11.0pt;font-family:"Cambria Math",serif;mso-ligatures:none">_x</span><span style="font-size:11.0pt;mso-ligatures:none">, p_y, p_z orbitals (Actually its p_x, p_x, p_y, p_y, p_z, p_z for
two S atoms) . I expected this setup to generate the y-axis as (0,1,0). <o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;mso-ligatures:none"><o:p> </o:p></span></p>
<p><span style="font-size:11.0pt">Using wannier90 result, </span><span style="font-size:11.0pt">I’m analyzing the p–p Hamiltonian matrix (3×3) for two S atoms aligned along the x-axis (let’s call this
</span><span style="font-size:11.0pt">H_deg0</span><span style="font-size:11.0pt">) and after a 60° rotation about the z-axis (</span><span style="font-size:11.0pt">H_deg60</span><span style="font-size:11.0pt">).</span><span style="font-size:11.0pt">
</span><span class="fadeinm1hgl8">I applied the rotation using the operator D(R), where R is the 60° rotation matrix around the z-axis.<o:p></o:p></span></p>
<p><o:p> </o:p></p>
<p><span class="fadeinm1hgl8">Although the absolute values of the rotated Hamiltonian match those of H_deg60, some components (off diagonal terms) show opposite signs, which was unexpected. This discrepancy suggests that the directions of the p_x, p_y, and
p_z orbitals used in Wannier90 may not align with the conventional (x, y, z) coordinate system.<o:p></o:p></span></p>
<p><o:p> </o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;mso-ligatures:none">I also have visualized the Wannier functions via
</span><span style="font-size:11.0pt;mso-ligatures:none">.xsf</span><span style="font-size:11.0pt;mso-ligatures:none"> files, it seems that the p_y orbital has an opposite sign: the yellow lobes for -y direction and blue lobes for +y direction. This probably
suggests that p_y orbital used in Wannier90 has an opposite sign, generating left-handed coordinate.<o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;mso-ligatures:none"><o:p> </o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;mso-ligatures:none">In summary, my main questions are:<o:p></o:p></span></p>
<ol start="1" type="1">
<li class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l1 level1 lfo2">
<span style="font-size:11.0pt;mso-ligatures:none">Could someone explain how Wannier90 determines the sign and orientation of wannier function?
<o:p></o:p></span></li><li class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l1 level1 lfo2">
<span class="fadeinm1hgl8"><span style="font-size:11.0pt">Is there a way to constrain the positions of Wannier functions at the center of each atom and enforce their shapes to resemble standard atomic orbitals (e.g., p</span></span><span class="fadeinm1hgl8"><span style="font-size:11.0pt;font-family:"Cambria Math",serif">_x</span></span><span class="fadeinm1hgl8"><span style="font-size:11.0pt">,
p_y, p_z, d_z^2, etc.)— to use Wannier90 like LCAO. </span></span><span style="font-size:11.0pt;mso-ligatures:none"><o:p></o:p></span></li></ol>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;mso-ligatures:none">Best regards,<o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-family:"Calibri",sans-serif;color:black;mso-ligatures:none">------------------</span><span style="font-size:11.0pt;mso-ligatures:none"><o:p></o:p></span></p>
<div>
<div>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-family:"Calibri",sans-serif;color:black;mso-ligatures:none">Moon-ki Choi, Ph.D.<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-family:"Calibri",sans-serif;color:black;mso-ligatures:none">Postdoctoral researcher<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-family:"Calibri",sans-serif;color:black;mso-ligatures:none">Material Research Laboratory, University of Illinois Urbana-Champaign<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-family:"Calibri",sans-serif;color:black;mso-ligatures:none">612-229-9732<o:p></o:p></span></p>
<p class="MsoNormal" style="vertical-align:baseline"><span style="font-family:"Calibri",sans-serif;color:black;mso-ligatures:none">Personal website: <a href="https://sites.google.com/view/moonkichoi/"><span style="color:#0563C1;border:none windowtext 1.0pt;padding:0in">https://sites.google.com/view/moonkichoi/</span></a><o:p></o:p></span></p>
</div>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
</body>
</html>