readme.lyx

已经编译好的levoo程序

coord.dat
\family default 
 containing Cartesian coordinates of all atoms is generated.
 
\layout Enumerate

XYZ-type 
\family typewriter 
geom.xyz
\family default 
 file with Cartesian coordinates is generated; more than a single cell can
 be produced and then previewed with any molecular viewer program: you will
 be prompted to breed your primitive cell before writing the file.
\layout Enumerate

Distances between atoms in the cell are studied taking into account images
 in the adjacent cells; you can explore either the shortest distances for
 
\shape italic 
all
\shape default 
 atomic pairs or a set of distances for a 
\shape italic 
given pair
\shape default 
 of atoms; in the latter case distances up to a desired order of neighbours
 are provided in the ascending order; a file 
\family typewriter 
distance.dat
\family default 
 is produced tracing all your actions within the option.
\layout Enumerate

This option allows you to check any points in space if they are equivalent
 to any atoms in the system.
\layout Enumerate

Only for
\series bold 
 CASTEP
\series default 
: an XYZ-type file 
\family typewriter 
geom_film.xyz
\family default 
 is produced from the 
\family typewriter 
SEED.coord
\family default 
 file.
\layout Enumerate

An atom can be displaced from its positions, and all other atoms which are
 equivalent to it due to the 
\emph on 
point-group 
\emph default 
symmetry of the cell (detected automatically) will be moved appropriately
 to keep the symmetry.
 This is useful if one wants to calculate the potential energy surface (PES)
 with respect to full-symmetry displacements of atoms in the system.
\layout Enumerate

Quit the program
\layout Subsection

k-point generator
\layout Subsubsection

Symmetry operations
\layout Standard

If the 
\series bold 
k
\series default 
-point sampling is generated for the DOS case, the point-group symmetry
 of the cell is automatically determined and only non-equivalent 
\series bold 
k
\series default 
-points with appropriate weighting factors are finally written into the
 file containing 
\begin_inset Formula \( \mathbf{k} \)
\end_inset 

-points.
 Symmetry is also used in some other options of 
\series bold 
tetr 
\series default 
as stated above.
\layout Standard

The complete list of the symmetry operations is shown in Fig.1 and Fig.2
\begin_float fig 
\layout Standard
\align center 

\begin_inset Figure size 425 362
file Oh.xfig.ps
width 1 15
flags 9

\end_inset 


\layout Caption

Symmetry operations of the 
\begin_inset Formula \( O_{h} \)
\end_inset 

 group.
\end_float 
\layout Standard

\begin_float fig 
\layout Standard
\align center 

\begin_inset Figure size 425 328
file D6h.xfig.ps
width 1 15
flags 9

\end_inset 


\layout Caption

Additional symmetry operations due to the D
\begin_inset Formula \( _{6h} \)
\end_inset 

 group.
\end_float 
\layout Subsubsection

Additional information about the k-point generator (DOS)
\layout Standard

If the symmetry and/or special constraints imposed on atomic coordinates
 have not been used at the stage of atomic relaxation while running the
 PW code, the symmetry generator may fail to determine the correct symmetry
 group due to numerical errors caused.
 Therefore, to make your symmetry group as rich as possible, you may sometimes
 need to generate 
\series bold 
k
\series default 
-points for the symmetry you expect to be the right one and which will be
 higher than the one determined automatically.
 One method is to use the geometry of the 
\shape italic 
unrelaxed
\shape default 
 system (if it should have the same symmetry) to generate 
\begin_inset Formula \( \mathbf{k} \)
\end_inset 

-points.
 Other (brr!!!) would be to edit your geometry file to make sure that there
 is no any numerical noise in the atomic coordinates (in some cases this
 is a real challenge!).
 Alternatively, use the 
\begin_inset Formula \( \mathbf{k} \)
\end_inset 

-point generator which is built up into the code: it allows you to play
 with the symmetry operations by adding/removing them, each time the whole
 group is generated and shown.
 It is nice in its own right and can be used to teach symmetry to students,
 especially, for trying out group generators (i.e.
 by specifying only a limited number of group elements (usually 2 or 3)
 sufficient to generate the whole group).
\layout Standard

At the moment, all symmetry operations are fixed to the axes of the Cartesian
 coordinate system, so that in practice you may need to shift/rotate your
 system in order to improve the symmetry 
\shape italic 
prior
\shape default 
 to the calculation of the DOS with the PW code.
 Note that the ground state density matrix can be left unchanged if you
 just 
\shape italic 
rotate
\shape default 
 your coordinate system (we assume that it is written with respect to the
 fractional coordinates of the grid points in your cell).
 However, if you have to 
\shape italic 
shift
\shape default 
 your system by some vector, then the density matrix should be recalculated
 and a new file must be produced.
 This option is provided by the utility 
\series bold 
lev00
\series default 
 (see below).
 Therefore, it is always wise to think about it 
\emph on 
before
\emph default 
 running the ground state calculation: choose the most symmetrical orientation
 of the system with respect to the Cartesian axes, use 
\series bold 
tetr
\series default 
 to show the group every time!
\layout Standard

The 
\series bold 
k
\series default 
-point generator allows you to build a point group of your Bravais lattice.
 In fact, it disregards possible fractional translations of the system and
 therefore generates only the largest possible group corresponding to a
 symmorphic lattice.
 Therefore, the actual point group of the BZ might be richer if your lattice
 corresponds to some nonsymmorphic space group.
 At the moment, this is not checked automatically but you can add group
 elements yourself interactively.
\layout Standard

How does the generator work? The generator first checks the point symmetry
 of the Bravais lattice (
\begin_inset Quotes eld
\end_inset 


\emph on 
\noun on 
Your crystal class group is
\emph default 
 
\noun default 
...
\begin_inset Quotes erd
\end_inset 

) and then each operation of this group is applied to every atom in the
 cell.
 In this way, an actual point group is built (
\begin_inset Quotes eld
\end_inset 


\noun on 
Your largest symmorphic group is 
\noun default 
...
\begin_inset Quotes erd
\end_inset 

) and shown (the name of the group and all the elements as shown in Figs.
 1 and 2).
 A menu which opens up here allows you to either adopt this group (
\begin_inset Quotes eld
\end_inset 


\noun on 
Adopt the largest symmorphic group
\noun default 

\begin_inset Quotes erd
\end_inset 

), continue generation of the group by adding new elements from the crystal
 class group (
\begin_inset Quotes eld
\end_inset 


\noun on 
Proceed generation from
\noun default 

\begin_inset Quotes erd
\end_inset 

) or start generation from scratch.
 In the last two cases you can add/remove elements, the generator multiplies
 all the elements with each other, adds new elements (if necessary) and
 then shows you the current group generated so far.
 
\layout Standard

At last, when the group is built, you will be asked about the number of
 
\begin_inset Quotes eld
\end_inset 


\shape italic 
divisions
\shape default 

\begin_inset Quotes erd
\end_inset 

.
 The larger this number is, the larger is the number of tetrahedra generated
 and, likely the larger is the number of nonequivalent 
\series bold 
k
\series default 
-points.
 All this vital information is shown on the screen as you can play with
 the generator and try different number of divisions.
 It is worth mentioning that sometimes with the larger number of divisions
 (and the larger number of tetrahedra) you can get 
\shape italic 
the same
\shape default 
 or only slightly larger number of 
\series bold 
k
\series default 
-points.
 Of course, the larger number of tetrahedra, the better.
\layout Subsubsection

Slab calculations
\layout Standard

If you are asked whether to suppress the 
\begin_inset Formula \( z \)
\end_inset 

-direction or not, think twice! This is a very important option, particularly
 for calculations in the slab model when the vector 
\begin_inset Formula \( \mathbf{a}_{3} \)
\end_inset 

 connecting parallel slabs is usually chosen large enough (in comparison
 with the slab width) in order to reduce interaction between slabs across
 the vacuum gap.
 Consequently, the basic vector 
\begin_inset Formula \( \mathbf{b}_{3} \)
\end_inset 

 of the reciprocal lattice will be small enough and the BZ is strongly squeezed
 in its direction.
 If you choose this option, the corresponding planar (2-dimensional) reciprocal
 lattice will be used and all the 
\series bold 
k
\series default 
-vectors generated by the generator will be assigned zero component along
 
\begin_inset Formula \( \mathbf{b}_{3} \)
\end_inset 

 corresponding to the planar (2D) BZ.
\layout Subsection

Additional information about the geometry generator
\begin_inset LatexCommand \label{Sec::extention}

\end_inset 


\layout Standard

Some additional comments are necessary about the cell generators.
 It is called by options 1 and 2 before filling in atoms occupying the cell.
 You will be first asked to specify your 
\emph on 
primitive unit cell 
\emph default 
using a menu with various Bravais lattices; a manual option is included
 as well.
 Your actual cell can be a some extension of the primitive one.
 To built it, you have three options: (i) keep the primitive vectors; (ii)
 specify an integer extension matrix 
\begin_inset Formula \( \mathbf{l}=\parallel l_{ij}\parallel  \)
\end_inset 

 which carry out the transformation 
\begin_inset Formula 
\begin{equation}
\label{8}
\mathbf{a}_{i}=\sum _{j=1}^{3}l_{ij}\mathbf{A}_{j}
\end{equation}

\end_inset 

 from the primitive basic vectors, 
\begin_inset Formula \( \mathbf{A}_{i} \)
\end_inset 

, to the cell vectors, 
\begin_inset Formula \( \mathbf{a}_{i} \)
\end_inset 

; (iii) specify the lattice vectors 
\begin_inset Formula \( \mathbf{a}_{i} \)
\end_inset 

 directly in which case you will be given the menu with the Bravais vectors
 and the generator will check whether your choice corresponds to some integer
 extension matrix
\series bold 
 
\begin_inset Formula \( \mathbf{l} \)
\end_inset 


\series default 
 or not.
 Then, all atoms in the cell are specified by species in Cartesian coordinates.
 Translationally equivalent atoms are ignored.
\layout Subsection

The structure of 
\family typewriter 
tetr.inp
\family default 
 file
\layout Standard

Finally, for the reference purposes, we consider the structure of the 
\family typewriter 
tetr.inp
\family default 
 file: at the beginning, basic lattice vectors follow (in columns), then
 the number of atoms in the cell, and then all atoms follow with their Cartesian
 coordinates and the species number; one line per atom, all atoms of the
 1st species, then all atoms of the 2nd species, etc.
 Three comment lines (before, after lattice vectors and before the coordinates
 of atoms) should be also provided (mandatory).
 An example of the 
\family typewriter 
tetr.inp
\family default 
 file for a cell consisting of 17 atoms (a two layer slab of MgO with one
 oxygen atom put above a Mg atom, Mg is the 1st and O is the 2nd species)
 is given below: 
\latex latex 

\backslash 
begin{verbatim}
\newline 
 # lattice vectors of the supercell
\newline 
   4.24400   -4.24400    0.00000
\newline 
   4.24400    4.24400    0.00000
\newline 
   0.00000    0.00000   10.61000
\newline 
 # number of atoms (sublattices) in it
\newline 
17
\newline 
 # sublattices (Cartesian coordinates) and species
\newline 
   -1.06100   -1.06100   -0.02716  1
\newline 
    1.06100    1.06100   -0.02716  1
\newline 
   -3.18300    1.06100   -0.02716  1
\newline 
   -1.06100    3.18300   -0.02716  1
\newline 
   -1.06100   -3.18300   -2.09484  1
\newline 
    1.06100   -1.06100   -2.09484  1
\newline 
   -3.18300   -1.06100   -2.09484  1
\newline 
   -1.06100    1.06100   -2.09484  1
\newline 
    0.43900   -0.43900    1.21495  2
\newline 
   -1.06096   -3.18296    0.03289  2
\newline 
    1.06100   -1.06100    0.03289  2
\newline 
   -3.18300   -1.06100    0.03289  2
\newline 
   -1.06100    1.06100    0.03289  2
\newline 
   -1.06100   -1.06100   -2.15489  2
\newline 
    1.06100    1.06100   -2.15489  2
\newline 
   -3.18300    1.06100   -2.15489  2
\newline 
   -1.06100    3.18300   -2.15489  2
\newline 

\backslash 
end{verbatim}
\layout Section

Working with VASP
\layout Standard

In this section we consider several issues not yet covered above which are
 concerned with running 
\series bold 
lev00 
\series default 
with 
\series bold 
VASP
\series default 
.
 The auxiliary utility 
\series bold 
do_param
\series default 
 will be needed (supplied) to work out some necessary information from the
 
\series bold 
VASP
\series default 
 output file
\family typewriter 
 OUTCAR
\family default 
.
 This additional utility is described below in section 
\begin_inset LatexCommand \ref{Sec::do_param}

\end_inset 

.
\layout Standard

Basically, the following options are supported at the moment:
\layout Itemize

Total DOS
\layout Itemize

Projected DOS and 
\begin_inset Formula \( s,p,d \)
\end_inset 

-projected DOS (only on atoms of the system)
\layout Itemize

Total electronic density
\layout Itemize

Spin density
\layout Itemize

Partial density
\layout Standard

The utility 
\series bold 
tetr
\series default 
 can be used to produce the input files 
\family typewriter 
CONTCAR
\family default 
 and 
\family typewriter 
KPOINTS
\family default 
.
 If the DOS option is used while generating 
\begin_inset Formula \( \mathbf{k} \)
\end_inset 

-points, the file 
\family typewriter 
brill.dat
\family default 
 is also written.
 This last step is necessary if 
\series bold 
lev00 
\series default 
is to be used for the DOS calculation (otherwise, one can simply use 
\family typewriter 
DOSCAR
\family default 
 file with no additional niceties of 
\series bold 
lev00
\series default 
).
 
\layout Standard

Note that in all cases considered below 
\series bold 
VASP
\series default 
 input files 
\family typewriter 
KPOINTS 
\family default 
and 
\family typewriter 
CONTCAR
\family default 
 are needed.
 You may also need 
\family typewriter 
OUTCAR
\family default 
 file as well in most cases.
\layout Subsection

Utility 
\family typewriter 
do_param
\family default 

\begin_inset LatexCommand \label{Sec::do_param}