<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"><HTML DIR=ltr><HEAD><META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1"></HEAD><BODY><DIV><FONT face='Arial' color=#000000 size=2>Dear Peter, Stefan, and WIEN users,</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>As far as WIEN is concerened, atoms are considered
equivalent if they have the </FONT></DIV>
<DIV><FONT face=Arial size=2>same atomic number, same number of </FONT><FONT
face=Arial size=2>nearest neighbors, and if there
exist symmetry </FONT></DIV>
<DIV><FONT face=Arial size=2>transformations </FONT><FONT face=Arial
size=2>(translations + rotations) </FONT><FONT face=Arial size=2>between the
atomic coordinates. </FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Before I ask my questions, let us consider a (2 x
2) surface unit cell with a </FONT></DIV>
<DIV><FONT face=Arial size=2>slab of 3 layers' thickness for </FONT><FONT
face=Arial size=2>(111) surface of an FCC lattice (4 atoms per layer, total
of 12)</FONT><FONT face=Arial><FONT size=2><FONT>.</FONT></FONT></FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Cell dimensions: a=b=12.27 Bohrs,
c=70.0184131 Bohrs (vacuum = 60 Bohr)</FONT></DIV>
<DIV><FONT face=Arial size=2>Angles: alpha = beta = 90, gamma =
120</FONT> </DIV>
<DIV>Lattice type: H</DIV>
<DIV> </DIV>
<DIV>(111) surface coordinates in (x, y, z) format:</DIV>
<DIV> </DIV>
<DIV> <U>Layer
1</U> <U>Layer
2 </U>
<U>Layer 3</U>
</DIV>
<DIV>(0.0, 0.0,
0.0) (0.33333,
0.166666,
d/c) (0.166666,
0.33333, 2*d/c)</DIV>
<DIV>(0.0, 0.5,
0.0) (0.33333,
0.666666,
d/c) (0.166666,
0.83333, 2*d/c)</DIV>
<DIV>(0.5, 0.0,
0.0) (0.83333,
0.166666,
d/c) (0.666666,
0.33333, 2*d/c) </DIV>
<DIV>(0.5, 0.5,
0.0) (0.83333,
0.666666,
d/c) (0.666666,
0.83333, 2*d/c)</DIV>
<DIV> </DIV>
<DIV>where d is the inter-layer separation = lattice const./sqrt(3.)</DIV>
<DIV> </DIV>
<DIV>It can clearly be seen that atoms on each layer are connected by simple
symmetry operations.</DIV>
<DIV>To create the case.struct file, I can EITHER enter all 12 atoms as
inequivalent (Space group # 1 P1) </DIV>
<DIV>OR I can enter 4 atoms on each layer as equivalent, i.e. total of 3
inequivalent atoms each with </DIV>
<DIV>4 atomic positions (Space group # 156 P3m1). Hence using the
latter for calculations is faster than </DIV>
<DIV>the former. </DIV>
<DIV> </DIV>
<DIV><U>My first question concerns the accuracy of the energies at the AFM
level with spin-orbit interactions:</U> </DIV>
<DIV>Why are the energies obtained in the case for 3 inequiv. atoms lower than
the energies obtained in </DIV>
<DIV>the case 12 inequiv. using the same set conditions (Rmt, Kmax, energy
convergence criterion, etc.)? </DIV>
<DIV>I must state, however, that I did not use the same number of
irreducible k-points because of the </DIV>
<DIV>different symmetries in the two cases;</DIV>
<DIV>12 inequivalent atoms --->16 irred. k-points, </DIV>
<DIV>3 inequivalent atoms ---> 19 irred. k-points.</DIV>
<DIV> </DIV>
<DIV><U>My second question:</U> In the case where I have 3 inequiv. atoms,
how do I obtain information </DIV>
<DIV>like magnetic moments in the sphere for each of the original
12 atoms? Should I assume that </DIV>
<DIV>MM for an inequivalent atom is the same for all four atoms? Also, for
the case of 3 inequiv. </DIV>
<DIV>atoms, I flipped the spins for the atom on layer 2 for
AFM calculations. Is this equivalent to </DIV>
<DIV>flipping the spins for the 4 individual atoms on layer 2 in the case
corresponding to 12 inequiv. atoms?</DIV>
<DIV> </DIV>
<DIV><U>Third question (unrelated):</U> In the user guide, it states that the
energy obtained using lstart (which is </DIV>
<DIV>fully relativistic) can be used as the energy of an isolated atom if
the element is light (section 6.4, pp. 67). </DIV>
<DIV>This therefore applies to elements such as C, N, O, Si, etcetera. Is this
always true? </DIV>
<DIV>The reason why I ask is that for O or C say, the gamma point, large FCC box
method outlined </DIV>
<DIV>in the FAQ section yield energies that are significantly higher than the
energies from lstart. </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV>Thanks</DIV>
<DIV> </DIV>
<DIV>Ray Atta-Fynn</DIV>
<DIV> </DIV>
<DIV> </DIV></BODY></HTML>