readme.tex

已经编译好的levoo程序

them, delete files with the extensions \texttt{.1} and \texttt{.2} and move
files \texttt{psi2.{[}option{]}} and \texttt{band.out} into \texttt{psi2.{[}option{]}.1}
and \texttt{band.out.1}, respectively. Then, you can run CASTEP for the 3rd
subset, rename the files produced by attaching the extension \texttt{.2} and
then run the \textbf{sum} again. This process must be repeated as many times
as necessary for each sequential pair of subsets.

The \textbf{summ}ing can be done automatically by constructing a shell-script.
Suppose, we have 5 subsets of the \textbf{k}-points and the corresponding \texttt{fort.15}
files for them are \texttt{fort.15.1}, \texttt{fort.15.2}, ..., \texttt{fort.15.5},
while the corresponding \textbf{CASTEP} codes are \textbf{castepx.1}, \textbf{castepx.2},
..., \textbf{castepx.5} (note that some of them may coincide but should have
different names anyway; use symbolic link in this case). Then, the following
script can be used: \begin{verbatim}
 #! /bin/csh -f
foreach num (1 2 3 4 5)
if( $num == '1' ) then
  set ext='1'
elseif
  set ext='2'
endif
 /bin/cp fort.15.$num fort.15
castepx.$num > problem.$num
if( -e band.out )  mv band.out band.out.$ext 
if ( -e psi2.DOS ) mv psi2.DOS psi2.DOS.$ext
if ( -e psi2.DOp ) mv psi2.DOp psi2.DOp.$ext
if ( -e psi2.SRF ) mv psi2.SRF psi2.SRF.$ext
if ( -e psi2.MAP ) mv psi2.MAP psi2.MAP.$ext
if( $ext == '2') then
  sum 2 > sum.$num
  mv band.out band.out.1
  if ( -e psi2.DOS ) mv psi2.DOS psi2.DOS.1
  if ( -e psi2.DOp ) mv psi2.DOp psi2.DOp.1
  if ( -e psi2.SRF ) mv psi2.SRF psi2.SRF.1
  if ( -e psi2.MAP ) mv psi2.MAP psi2.MAP.1
  if ( -e psi2.DOS.2 ) /bin/rm psi2.DOS.2
  if ( -e psi2.DOp.2 ) /bin/rm psi2.DOp.2
  if ( -e psi2.MAP.2 ) /bin/rm psi2.MAP.2
  if ( -e psi2.SRF.2 ) /bin/rm psi2.SRF.2
endif
end
#
mv band.out.1 band.out
if ( -e psi2.DOS.1 ) mv psi2.DOS.1 psi2.DOS
if ( -e psi2.DOp.1 ) mv psi2.DOp.1 psi2.DOp
if ( -e psi2.SRF.1 ) mv psi2.SRF.1 psi2.SRF
if ( -e psi2.MAP.1 ) mv psi2.MAP.1 psi2.MAP
\end{verbatim}


\section{Utility \texttt{\textit{lev00}}. Final stage: plotting}

Using files produced by the PW code, \textbf{tetr} and possibly \textbf{lev1}
or \textbf{lev2}, as well as some input files which are standard for the PW
code, the utility \textbf{lev00} performs a number of applications. All the
data calculated by the utility are represented in a graphical form using \texttt{GNUPLOT}
package. 

At present, the code has not been properly modified for the for-academia \textbf{CASTEP}.
The modifications required are minor and will be done when necessary. Therefore,
the discussion below refers only to old \textbf{CASTEP}.

To compile the utility you \textit{\emph{must}} use the \texttt{param.inc} file
of \textbf{CASTEP} or produced by \textbf{do\_param} after the \textbf{VASP}
run. {[}If you have split your CASTEP run as it was recommended in the previous
section, then the \textit{total} number of \textbf{k}-points should be indicated
in the \texttt{param.inc} file \textit{prior} to the compilation and the complete
\texttt{fort.15} file must be restored.{]} The shell-script to be executed is
called \textbf{lev00.comp}. You should run it from your working directory. The
detailed description of every option is not necessary since it is a menu-driven
thing and all you have to do is to try it out. Only some comments are needed
which are provided below.


\subsection{Calculation of the DOS}

The first five options of the main menu are devoted to the calculation of the
total/local/projected DOS of your system. The method of tetrahedra is used to
perform the BZ integration of the singular \( \delta  \)-function. You can
also do a \textit{smearing} (convolution) of your original (raw) DOS curves
for every band, \( N_{n}(\epsilon ) \), by carrying out the integral 
\begin{equation}
\label{13}
\bar{N}_{n}(\epsilon )=\int _{E_{bot}-\gamma \sigma }^{E_{top}+\gamma \sigma }g(\epsilon -\varepsilon )N_{n}(\varepsilon )d\varepsilon ,
\end{equation}
 where \( g(\epsilon -\varepsilon ) \) is a Gaussian function with some dispersion
\( \sigma  \), \( E_{bot} \) and \( E_{top} \) define the ``raw'' boundaries
of the band and the factor \( \gamma  \) allows you to broaden the band. Since
in the method of tetrahedra the raw DOS is always a set of continuous functions
of energy in finite intervals (within each tetrahedron), this integration can
be worked out analytically and the result is expressed through exponentials
and error functions. This method is slow but exact on many occasions. It is
therefore called \emph{slow}. Alternatively, the integral in Eq. (\ref{13})
can be calculated numerically in which case the method is called \emph{fast}. 

Generally, while running the DOS option, you will be given a table of ``physical
bands'' in your system extracted from the eigenvalues, i.e. energies and numbers
of states for the left and right boundaries of each band found by the code.
These could be core, valence and conduction bands. If states overlap (i.e. the
energy intervals spanned by the eigenvalues for all \( \mathbf{k} \)), then
they will appear as one physical band. In the following example there are 6
bands: \begin{verbatim}
 _______> Structure of ``physical'' bands <________
Band 1 spans energy interval: [-19.8216,-17.9913] and states { 1, 1}
Band 2 spans energy interval: [ -6.4785, -2.6852] and states { 2, 4}
Band 3 spans energy interval: [ -1.2610, -1.0436] and states { 5, 5}
Band 4 spans energy interval: [ -0.1859, 15.1450] and states { 6, 8}
Band 5 spans energy interval: [ 15.2456, 37.8405] and states { 9,18}
Band 6 spans energy interval: [ 37.9769, 41.0874] and states {19,20}
\end{verbatim} Amid them, bands 1,2 and 3 are core, valence and (presumably)
local bands while the remaining 3 bands are parts of one conduction band. The
latter can be judged from studying energy intervals they span (energies are
given in eV). You have also numbers of states (as they appear in the file \texttt{band.out})
in this table. This is important as you can immediately see, for example, that
only one state (5th) is responsible for the 3rd band and this particular state
could be a local state induced by a defect or irregularity. Then, you can go
and see the partial charge density associated with this state to find out where
it is localised in the cell, etc. 

The 0-th option of the main menu ``\texttt{Choose dispersion for the DOS smearing}''
of \textbf{lev00} allows you to choose a reasonable dispersion \( \sigma  \)
for your DOS smearing and the parameter \( \gamma  \) which controls the bands
broadening. A menu which opens here works in the same way as the DOS menu described
above. In this case, however, instead of ``groups'' of bands you are asked
to choose a set of dispersions. Then, after running the calculation (``Adopt
present setting and calculate DOS'') you can preview all curves simultaneously
together with the original one which allows you to choose the best possible
parameters which do not change significantly the structure of the raw DOS curve.

Once the dispersion is chosen, you should move on to do the actual total DOS
calculation (option 3). Fist of all, the distribution of ``physical'' states
is shown; then, a DOS/LDOS menu appears. You have the following options: 

\begin{itemize}
\item The current \emph{picture number} which would affect names of files produced
during the calculation. This tool allows you to produce many pictures in one
run of \textbf{lev00} and easily distinguish all the data files being produced.
Alternatively, you can leave the same number while playing with the DOS and
produce the same files all the time.
\item Maximum step on the energy scale for plotting (in eV). Normally, 0.1 eV is fine.
This step is needed only as a guidance as the actual step is chosen individually
for each ``physical'' band so that there will be at least 10 points even for
very narrow bands. 
\item If the smearing is enabled (the 3rd option), you will have dispersion \( \sigma  \)
and the parameter \( \gamma  \) to verify and change; use fast or slow method
and specify whether original (raw) or smeared DOS curves are to be shown on
the screen while previewing. Note that as the smearing is enables, the boundaries
of bands change which can be immediately realised in the table of ``physical''
bands.
\item The 7th option (``\texttt{Number of plots in the group}'') allows you to plot
simultaneously several DOS curves with different range of states; this is called
``group'' of DOS curves and is normally used to find out which states are
responsible for various particular features in the DOS; you have to choose at
least 1 curve in the group (mandatory); then you will be shown details of every
curve in the group and names of corresponding data and Postscript files which
will be produced during the run. 
\item Other options of the menu are self-explanatory and do not need special comments. 
\end{itemize}
There are two types of the output files. First of all, data files are produced
which contain energies \( \epsilon _{i} \) in the 1st column and then columns
with raw and smeared DOS follow. These files have the following names: \texttt{dos.datN\_M},
where \texttt{N} is the number of the current DOS in the group and \texttt{M}
is the picture number. You can also produce Postscript files for every plot
with names: \texttt{dos.datN\_M.ps}.

The calculation of the LDOS (either options DOS, PRO or DOp) are accomplished
by the options 1, 11 and 2 of the main menu of \textbf{lev00}. If everything
is fine, you will be prompted to the same sort of menu as described above for
the total DOS. Only one new mandatory item will appear (``\texttt{Current LDOS
task to be studied}''). This item needs some explanation. In either of your
LDOS calculations you can specify several spheres or layers. In the PRO case
there is also a possibility to calculate \( s \)-, \( p \)- and \( d \)-projected
LDOS for every sphere as well as the local DOS. For each such a case we have
a different factor \( A_{n\mathbf{k}} \) calculated either by \textbf{lev1}/\textbf{lev2}
or by \textbf{VASP}. Every such type of the LDOS is called a ``LDOS task''
and is to be considered separately. Tasks are numbered and you have to specify
a task number using a table which appears as you choose the menu item. In this
table, some useful additional information is shown. For example, in the case
of the DOS option there are: method of projection (conserving or non-conserving),
radius and position of the sphere and (in curly brackets) whether this is a
local DOS (\texttt{\{t\}}) or \( s \)-, \( p \)-, \( d \)-projections (\texttt{\{s\}},
\texttt{\{p\}}, \texttt{\{d\}}). This will help you to choose the task correctly.
The data files produced within this LDOS item of the main menu contain the total
DOS column as well. If smearing was enabled, then in the data file there are
smeared and raw total DOS and LDOS (i.e. 5 columns altogether including the
energy column). During the previewing, you will get on the screen both total
and local/projected DOS for every curve in the group (either smeared or not).
Use ``\texttt{Upper limit to the energy-range of the plot}'' to make the local/projected
DOS visible since the total DOS usually appears too high on the graph.


\subsection{Studying the partial or total charge/spin densities}

The items 5 and 55 of the main menu are responsible for plotting of your total
and spin charge densities. In fact, you can work with any file - if has the
right structure! Therefore, there is no special menu item for the CASTEP/CETEP
spin density, you have to produce the file and make a symbolical link to \texttt{fort.200}
and then it can be read in and studied using item 5. 

The 4th item of the main menu allows you to work with partial charge densities
\( \rho _{n}({\textbf {R}}) \). In the case of \textbf{lev1/lev2} it is the
MAP option and the corresponding data is contained in the file \texttt{psi2.MAP}.
You will have a possibility to choose the range of states \( [n_{1},n_{2}] \)
for which the partial density is to be presented. This is not possible for \textbf{VASP}
users as in this case the partial density in \texttt{PARCHG} is not split on
contributions. 

After the density is read in, the total charge is calculated (in the numbers
of electrons) and shown for your examination, for instance, \begin{verbatim}
 Reading in the density from fort.16 ...
 .....> Total charge = 7.9999961439984302  <.....
 Done!
\end{verbatim} This number should be very close to the correct number of electrons
in the system in the case of the total charge density or to the two times the
number of states, \( 2(n_{2}-n_{1}+1) \), in the case of the partial charge
density.

From this point on, all three options of the main menu (4, 5, 55) work similarly
and we only give here some brief comments. 

\begin{enumerate}
\item \texttt{Plot density along a line}. Produce a 1-dimensional plot along some
direction is space. In this case, a special ``LINE MENU'' opens. You will
have to specify the starting point, direction and the length along the line.
You can use either Cartesian, fractional coordinates or simply specify atomic
number (the 0-th item of the menu). Then, after performing the calculation in
which the density is interpolated for every point \textbf{R} along the line
(the nearest 8 grid points are used for that), you can preview it and produce
a Postscript file. There is also an additional menu item (``\texttt{Parameters
for the plotting}'') which allows you to choose resolution for the plot, low
or/and high chop and the multiplication factor. Parameters there have some preset
values which should be fine for the most applications. In the case of the partial
charge density, data and the Postscript files have the following names: \texttt{prt.chrN\_M}
and \texttt{prt.chrN\_M.ps}, respectively. In the case of the total density,
the names are: \texttt{out.dat\_M} and \texttt{out.dat\_M.ps}.
\item \texttt{Plot density in a plane}. Produce a 2-dimensional plot in some plane.
In this case a ``MENU for PLANE'' opens. You should specify: 

\begin{itemize}
\item normal vector to the plane or, alternatively, you can choose your plane by specifying
3 points in the cell; unite vecto