<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Dear Wien Users, <div><br></div><div>This is an earlier communication I made with Peter.</div><div>It might be useful to be documented in the archive.</div><div><br></div><div>Regards, </div><div><br></div><div>Jianxin<br><div><br><div>Begin forwarded message:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;"><span style="font-family:'Helvetica'; font-size:medium; color:rgba(0, 0, 0, 1);"><b>From: </b></span><span style="font-family:'Helvetica'; font-size:medium;">Peter Blaha <<a href="mailto:pblaha@theochem.tuwien.ac.at">pblaha@theochem.tuwien.ac.at</a>><br></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;"><span style="font-family:'Helvetica'; font-size:medium; color:rgba(0, 0, 0, 1);"><b>Date: </b></span><span style="font-family:'Helvetica'; font-size:medium;">September 18, 2010 1:31:45 AM MDT<br></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;"><span style="font-family:'Helvetica'; font-size:medium; color:rgba(0, 0, 0, 1);"><b>To: </b></span><span style="font-family:'Helvetica'; font-size:medium;">Jian-Xin Zhu <<a href="mailto:jxzhu@lanl.gov">jxzhu@lanl.gov</a>><br></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;"><span style="font-family:'Helvetica'; font-size:medium; color:rgba(0, 0, 0, 1);"><b>Subject: </b></span><span style="font-family:'Helvetica'; font-size:medium;"><b>Re: Wien2k: Rhombohedral lattice</b><br></span></div><br><div>Yes, everithing is as statet in the UG (even if it is very unlogical<br>to specify hexagonal lattice parameters and rhombohedral coordinates).<br><br>PS: This is an IDEAL question for the mailing list. Others could learn<br>from the answer too and I do not have to answer this 15 times/year.<br><br>Jian-Xin Zhu schrieb:<br><blockquote type="cite">Dear Peter, I am trying to calculate a system of rhombohedral lattice. From the UG, I am advised that special care should be taken for preparing the structure file, e.g., rhomb.struct. ---<br></blockquote><blockquote type="cite">1/ On page 39, for the input of unit cell parameters (a,b,c), it reads "...<br></blockquote><blockquote type="cite">for rhombohedral (R) lattices the hexagonal lattice constants must be specified. (The following may help you to convert between hexagonal and rhombohedral specifications:<br></blockquote><blockquote type="cite"> <span class="Apple-tab-span" style="white-space:pre"> </span> <span class="Apple-tab-span" style="white-space:pre"> </span>$a_{hex} = 2 cos (\frac{\pi- \alpha_{rhomb}}{2} ) a_{rhomb}$<br></blockquote><blockquote type="cite"> <span class="Apple-tab-span" style="white-space:pre"> </span> <span class="Apple-tab-span" style="white-space:pre"> </span>$c_{hex} = 3 \sqrt{a_{rhomb}^2 - \frac{1}{3} a_{hex}^2 } $<br></blockquote><blockquote type="cite"> <span class="Apple-tab-span" style="white-space:pre"> </span> <span class="Apple-tab-span" style="white-space:pre"> </span>and (for fcc-like lattices) $a_{rhomb}=a_{cubic}/\sqrt{2} $<br></blockquote><blockquote type="cite">"<br></blockquote><blockquote type="cite">It means I should put in the lattice parameter of the corresponding hexagonal lattice. So in the above formula, alpha_rhomb is the angle between any of two rhombohedral primitive unit vectors, for example, alpha_homb=60 degree. Is it correct?<br></blockquote><blockquote type="cite">2/ Then for the position of atom in internal units (x,y,z), it reads "...<br></blockquote><blockquote type="cite">For R lattice use rhombohedral coordinates. (To convert from hexagonal into rhombohedral coordinates use the auxiliary program *hex2rhomb*, which can be called at a command-line:<br></blockquote><blockquote type="cite"> <span class="Apple-tab-span" style="white-space:pre"> </span> <span class="Apple-tab-span" style="white-space:pre"> </span>$ \vec X_{ortho} = \vec X_{hex} \left ( \begin{array}{ccc} 0 & 1 & 0 \\ \frac{\sqrt{3}}{2} & \frac{-1}{2} & 0 \\ 0 & 0 & 1 \end{array} \right ) $<br></blockquote><blockquote type="cite"> <span class="Apple-tab-span" style="white-space:pre"> </span> <span class="Apple-tab-span" style="white-space:pre"> </span>$ \vec X_{rhomb} = \vec X_{ortho} \left ( \begin{array}{ccc} \frac{1}{\sqrt{3}}... ...rt{3}} & \frac{-2}{\sqrt{3}}\\ -1 &1 & 0 \\ 1 & 1 & 1 \end{array} \right ) $<br></blockquote><blockquote type="cite">"<br></blockquote><blockquote type="cite">Here when you say "For R lattice use rhombohedral coordinates". Does it means I should use the following x,y,z values in<br></blockquote><blockquote type="cite">vecr = x veca_rhombohedral + y vecb_rhombohedral + z vecc_rhombohedal<br></blockquote><blockquote type="cite">rather than in<br></blockquote><blockquote type="cite">vecr = x veca_hexagonal + y vecb_hexagonal + z vecc_hexagonal<br></blockquote><blockquote type="cite">although we use the hexagonal lattice constants for the unit cell parameters of the rhombohedral lattice? Here veca_rhombohedral, vecb_rhombohedral, vecc_rhombohedral, are three primitive translation vectors for the rhombohedral lattice I am going to study while veca_hexagonal, vecb_hexagonal, vecc_hexagonal, are those for the hexagonal lattice mentioned in the above point 1.<br></blockquote><blockquote type="cite">I want to make sure I really understand these points of care correctly.<br></blockquote><blockquote type="cite">Best regards, Jian-Xin<br></blockquote><blockquote type="cite">P.S.: Since it is not about the code itself and also might be too trivial for other users, I don't post it to the mailing list. --<br></blockquote><blockquote type="cite">###############################<br></blockquote><blockquote type="cite">Jian-Xin Zhu, Ph.D<br></blockquote><blockquote type="cite">Theorertical Division, MS B262<br></blockquote><blockquote type="cite">Los Alamos National Laboratory<br></blockquote><blockquote type="cite">Los Alamos, NM 87545<br></blockquote><blockquote type="cite">Phone: (505) 667 2363<br></blockquote><blockquote type="cite">Fax: (505) 665 4063<br></blockquote><blockquote type="cite">Emai: <a href="mailto:jxzhu@lanl.gov">jxzhu@lanl.gov</a> <<a href="mailto:jxzhu@lanl.gov">mailto:jxzhu@lanl.gov</a>><br></blockquote><blockquote type="cite">Email (backup): <a href="mailto:physjxzhu@gmail.com">physjxzhu@gmail.com</a> <<a href="mailto:physjxzhu@gmail.com">mailto:physjxzhu@gmail.com</a>><br></blockquote><blockquote type="cite">URL: <a href="http://theory.lanl.gov">http://theory.lanl.gov</a><br></blockquote><blockquote type="cite">###############################<br></blockquote><br>-- <br>-----------------------------------------<br>Peter Blaha<br>Inst. Materials Chemistry, TU Vienna<br>Getreidemarkt 9, A-1060 Vienna, Austria<br>Tel: +43-1-5880115671<br>Fax: +43-1-5880115698<br>email: <a href="mailto:pblaha@theochem.tuwien.ac.at">pblaha@theochem.tuwien.ac.at</a><br>-----------------------------------------<br></div></blockquote></div><br><div>
<span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; font-size: medium; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; font-size: medium; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; font-size: medium; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; font-size: medium; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><div>-- </div><div>###############################</div><div>Jian-Xin Zhu, Ph.D</div><div>Theoretical Division, MS B262</div><div>Los Alamos National Laboratory</div><div>Los Alamos, New Mexico 87545</div><div>Phone: (505) 667 2363</div><div>Fax: (505) 665 4063</div><div>Email (main): <a href="mailto:jxzhu@lanl.gov">jxzhu@lanl.gov</a></div><div>Email (backup): <a href="mailto:physjxzhu@gmail.com">physjxzhu@gmail.com</a></div><div>URL: <a href="http://theory.lanl.gov">http://theory.lanl.gov</a></div><div>###############################</div></div><div><br></div></div></span><br class="Apple-interchange-newline"></div></span><br class="Apple-interchange-newline"></div></span><br class="Apple-interchange-newline"></span><br class="Apple-interchange-newline">
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