#LyX 2.1 created this file. For more info see http://www.lyx.org/
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\end_header

\begin_body

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
definecolor{olive}{rgb}{0,0.5,0}
\end_layout

\begin_layout Plain Layout


\backslash
newcommand{
\backslash
MI}[1]{
\backslash
texttt{
\backslash
textcolor{olive}{#1}}}
\end_layout

\end_inset


\end_layout

\begin_layout Title
Molecular band weight projectors
\end_layout

\begin_layout Author
Klaus Koepernik
\end_layout

\begin_layout Standard
This fatband task teaches you how to construct molecular band weight projectors.
 The solution will be found in the 
\family typewriter
solution
\family default
 directory.
 You will work in the 
\family typewriter
task
\family default
 directory.
 
\end_layout

\begin_layout Standard
We already setup and converged a simple SrRh
\begin_inset Formula $_{2}$
\end_inset

P
\begin_inset Formula $_{2}$
\end_inset

 calculation.
 The structure is shown in Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:SrRhP-unit-cell."

\end_inset

.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/str.jpg
	lyxscale 30
	width 60col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:SrRhP-unit-cell."

\end_inset

SrRh
\begin_inset Formula $_{2}$
\end_inset

P
\begin_inset Formula $_{2}$
\end_inset

 unit cell.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
We also already switched on the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{bandplot/weight}
\end_layout

\end_inset

 options and entered 
\family typewriter
=.bwdef
\family default
 into 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Weights def file}
\end_layout

\end_inset

 in the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{bandplot}
\end_layout

\end_inset

 submenu of 
\family typewriter
fedit
\family default
.
\end_layout

\begin_layout Standard
The objective is to find out how many electrons take part in the bonding
 between P
\begin_inset Formula $_{1}$
\end_inset

 and P
\begin_inset Formula $_{2}$
\end_inset

 (see Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:SrRhP-unit-cell."

\end_inset

).
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Standard
Please follow the instructions below:
\end_layout

\begin_layout Itemize
Please execute
\end_layout

\begin_deeper
\begin_layout LyX-Code
xfplo -bw &
\end_layout

\begin_layout Standard
You get the Band weight editor (BWE), Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:The-empty-band"

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status collapsed

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/xfplobw.png
	lyxscale 30
	width 80col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:The-empty-band"

\end_inset

The empty band weigth editor
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Itemize
From the menu select 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Activity $
\backslash
triangleright$ Structure =.in}
\end_layout

\end_inset

 to open the structure view (SV).
 
\end_layout

\begin_layout Itemize
Now, click on the SV to make it the current window and press 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{a a}
\end_layout

\end_inset

 (two times the a-key).
 This will show the cartesian coordinate frame in the lower right corner
 (Fig 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:SrRhP-unit-cell."

\end_inset

).
\end_layout

\begin_layout Itemize
In the BWE click the 
\family typewriter

\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{New molecular}
\end_layout

\end_inset


\family default
 button to open the molecular orbital dialog (MOD), Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Molecular-orbital-editor"

\end_inset


\end_layout

\begin_deeper
\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status collapsed

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/molorbdlg.png
	lyxscale 30
	width 40col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:Molecular-orbital-editor"

\end_inset

Molecular orbital dialog
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Itemize
Enter the name: 
\family typewriter
P p$_z$.
 $~s
\family default
 (The number of characters is limited.
 But the name can be changed later while plotting fatbands.)
\end_layout

\begin_deeper
\begin_layout Standard
Now, a new line appeared in the BWE and it should be selected (highlighted).
 Hit 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{space}
\end_layout

\end_inset

, 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{enter}
\end_layout

\end_inset

 or 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{double click}
\end_layout

\end_inset

 on it to edit it again.
 
\end_layout

\end_deeper
\begin_layout Itemize
Now, we add a contribution to the molecular projector: Hit the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{New Contrib}
\end_layout

\end_inset

 button, which brings up the molecular orbital contribution dialog MOCD
 Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:Molecular-orbital-contribution"

\end_inset

.
 It differs from the Atomic-Orbital-Dialog (AOD) by having an additional
 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{position}
\end_layout

\end_inset

 and a 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{factor}
\end_layout

\end_inset

.
 
\begin_inset Float figure
wide false
sideways false
status collapsed

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/molcontribdlg1.png
	lyxscale 30
	width 60col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:Molecular-orbital-contribution"

\end_inset

Molecular orbital contribution dialog
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_deeper
\begin_layout Standard
\begin_inset Box Frameless
position "t"
hor_pos "c"
has_inner_box 1
inner_pos "t"
use_parbox 0
use_makebox 0
width "100col%"
special "none"
height "1in"
height_special "totalheight"
status open

\begin_layout Plain Layout
\begin_inset Wrap figure
lines 0
placement r
overhang 0in
width "25col%"
status collapsed

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/scheme.pdf
	width 20col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:The-MO-projector."

\end_inset

The MO projector.
\end_layout

\end_inset


\end_layout

\end_inset

The reason for this is easy to understand.
 A molecular orbital projector consists of a linear combination of atomic
 orbitals at particular sites (position), each with a a certain coefficient
 (factor).
 A molecular projector for a (periodic) system can be defined in any unit
 cell.
 It's geometry is then translated into each unit cell to obtain corresponding
 Bloch sums.
 In order to define such a projector, we have to specify the positions of
 the individual orbital contributions in absolute coordinates in order to
 obtain their relative mutual positioning.
 (The site vector defined by the site number is not sufficient here.) This
 is what position is needed for.
 We will now setup a molecular orbital projector consisting of two 
\begin_inset Formula $p_{z}$
\end_inset

 orbitals at P
\begin_inset Formula $_{1}$
\end_inset

 and P
\begin_inset Formula $_{2}$
\end_inset

, such that they form a bonding (Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:The-MO-projector."

\end_inset

) and anti-bonding combination.
 The MOs are 
\begin_inset Formula 
\begin{eqnarray*}
\Phi_{\mathrm{bonding}} & = & \frac{1}{\sqrt{2}}\left(p_{z1}-p_{z2}\right)\\
\Phi_{\mathrm{anti-bonding}} & = & \frac{1}{\sqrt{2}}\left(p_{z1}+p_{z2}\right)
\end{eqnarray*}

\end_inset


\end_layout

\end_inset

 
\end_layout

\end_deeper
\begin_layout Itemize
Hit the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Get atom}
\end_layout

\end_inset

 button and click on the atom P
\begin_inset Formula $_{1}$
\end_inset

.
 Select 
\family typewriter
3p+0
\family default
 in the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{orbital}
\end_layout

\end_inset

 line edit.
 Set 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{factor}
\end_layout

\end_inset

 to 
\family typewriter
0.707
\family default
 (
\begin_inset Formula $\approx\frac{1}{\sqrt{2}}$
\end_inset

) and leave the axes unchanged.
 Hit 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{enter}
\end_layout

\end_inset

.
 
\begin_inset Newline newline
\end_inset


\series bold
Note, that the factors matter for the normalization of the resulting fatbands
 and DOS.
\end_layout

\begin_layout Itemize
Hit the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{New Contrib}
\end_layout

\end_inset

 button again followed by the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Get atom}
\end_layout

\end_inset

 button.
 Click on the P
\begin_inset Formula $_{2}$
\end_inset

 atom and chose 
\family typewriter
3p+0
\family default
 for 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{orbital}
\end_layout

\end_inset

 and 
\family typewriter
-0.707
\family default
 for 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{factor}
\end_layout

\end_inset

.
 Hit 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{enter}
\end_layout

\end_inset

.
 Please notice that you can use the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Get Position}
\end_layout

\end_inset

 button to only correct the position.
\end_layout

\begin_layout Itemize
Now, Select the first line by using cursor keys or single clicking on it.
\end_layout

\begin_layout Itemize
Hit the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{copy}
\end_layout

\end_inset

 button.
 Hit 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{enter}
\end_layout

\end_inset

 and change the end from 
\family typewriter
$~s
\family default
 to 
\family typewriter
$~s*
\family default
.
\end_layout

\begin_layout Itemize
In the BWE select the last line and hit 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{enter}
\end_layout

\end_inset

.
 Set the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{factor}
\end_layout

\end_inset

 to 
\family typewriter
0.707
\family default
 and hit 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{enter}
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
In general you can move stuff around with the 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{up/down arrow}
\end_layout

\end_inset

 buttons or by using 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Ctrl-Up/Ctrl-Down}
\end_layout

\end_inset

.
 If the current line is the title line of a molecular projector, the whole
 projector is moved.
 If is is a contribution only the contrib will be moved.
\end_layout

\begin_deeper
\begin_layout Standard
This is what you should have rigth now: 
\begin_inset Float figure
wide false
sideways false
status collapsed

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/molcontribdlgcontent.png
	lyxscale 30
	width 80col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:The-band-weigth"

\end_inset

The band weigth editor with content
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Itemize
In the BWE hit 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Ctrl-S}
\end_layout

\end_inset

 or use 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{File $
\backslash
triangleright$ Save}
\end_layout

\end_inset

.
\end_layout

\begin_layout Itemize
Leave the BWE (
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Ctrl-Q}
\end_layout

\end_inset

 or 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Activity $
\backslash
triangleright$ Quit all}
\end_layout

\end_inset

) and ignore warnings.
\end_layout

\begin_layout Itemize
Have a look at 
\family typewriter
=.bwdef
\family default
:
\end_layout

\begin_deeper
\begin_layout Standard
\begin_inset Box Shaded
position "t"
hor_pos "c"
has_inner_box 1
inner_pos "t"
use_parbox 0
use_makebox 0
width "100col%"
special "none"
height "1in"
height_special "totalheight"
status open

\begin_layout Plain Layout
\begin_inset CommandInset include
LatexCommand verbatiminput
filename "../solution/=.bwdef"

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Itemize
Now, open 
\family typewriter
fedit
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64
\family default
, and convince yourself that in 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{bandplot-submenu}
\end_layout

\end_inset

 both 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{bandstructure-plot}
\end_layout

\end_inset

 and 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{weights}
\end_layout

\end_inset

 are switched on as well as that 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{weights def file}
\end_layout

\end_inset

 contains 
\family typewriter
=.bwdef
\family default
.
 Check that in the 
\family typewriter
fedit
\family default
 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{main menu}
\end_layout

\end_inset

 the flag 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{use data directories}
\end_layout

\end_inset

 is switched on .
\end_layout

\begin_layout Itemize
Execute 
\family typewriter
fplo
\family default
:
\end_layout

\begin_deeper
\begin_layout LyX-Code
fplo
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
version{}
\end_layout

\end_inset

-x86_64 |tee out
\end_layout

\begin_layout Standard
You should now have the sub directories 
\family typewriter
+dos, +bdos
\family default
 and the files 
\family typewriter
+band
\family default
/
\family typewriter
+bweights_bwdef
\family default
.
\end_layout

\end_deeper
\begin_layout Itemize
Execute 
\end_layout

\begin_deeper
\begin_layout LyX-Code
xfbp bond.xpy
\end_layout

\begin_layout Standard
to obtain Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:The-bonding-analysis."

\end_inset

.
 Also, have a look at 
\family typewriter
bond.xpy
\family default
 by using 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{Edit $
\backslash
triangleright$ Script/transformations}
\end_layout

\end_inset

 to get a flavour of the possibilities.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status collapsed

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/bond.png
	lyxscale 30
	width 60col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:The-bonding-analysis."

\end_inset

The bonding analysis.
 The red curve is the spin sum of the bonding MO DOS and the blue the anti-bondi
ng MO DOS.
 The blue curve is the difference of the two corresonpding IDOS and shows
 how many more bonding electrons there are than anti-bonding electrons.
\begin_inset space ~
\end_inset

In our case the bond has a net 0.5 bonding electrons.
 If you use the wrong 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
MI{factor}
\end_layout

\end_inset

s this value changes!
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\begin_layout Itemize
Finally: 
\end_layout

\begin_deeper
\begin_layout LyX-Code
xfbp bwei.xpy
\end_layout

\begin_layout Standard
will show the fatbands (Fig.
 
\begin_inset CommandInset ref
LatexCommand ref
reference "fig:The-MO-fatbands."

\end_inset

), which are not of much use here.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\noindent
\align center
\begin_inset Graphics
	filename pics/bwei.png
	lyxscale 30
	width 60col%

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption Standard

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "fig:The-MO-fatbands."

\end_inset

The MO fatbands.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_deeper
\end_body
\end_document
