readme.lyx

已经编译好的levoo程序

 file are sufficient for the present job, e.g.
 number of plane waves, etc.;
\layout Itemize

whether all input files are okay and consistent with each other and with
 the parameters in the 
\family typewriter 
param.inc
\family default 
 file.
\layout Itemize

allows you to choose the least necessary parameters to suppress as much
 as possible the size of the 
\series bold 
CASTEP
\end_deeper 
\layout Itemize


\series bold 
take
\series default 
 
\begin_inset Formula \( \rightarrow  \)
\end_inset 

 checks the convergence of eigenvalues calculated by the 
\series bold 
CASTEP
\series default 
 during the band-structure run as well as their correct order; also, it
 allows one to choose eigenvalues from any desired iteration;
\layout Itemize


\series bold 
sum
\series default 
 
\begin_inset Formula \( \rightarrow  \)
\end_inset 

 an utility which allows you to split one big 
\series bold 
CASTEP
\series default 
 job as a sequence of smaller jobs which less 
\begin_inset Formula \( \mathbf{k} \)
\end_inset 

-points.
 ; if files, produced at each run, are properly named, then the utility
 
\series bold 
sum
\series default 
 will 
\begin_inset Quotes eld
\end_inset 

gather
\begin_inset Quotes erd
\end_inset 

 the files and will produce the resulting file(s) 
\family typewriter 
psi2.[option]
\family default 
 and 
\family typewriter 
band.out
\family default 
 corresponding to just one (big) run of 
\series bold 
CASTEP
\series default 
.
 
\layout Section

Definitions
\layout Standard

Here we provide some basic definitions for a number of quantities which
 are calculated in the package.
 
\layout Itemize

Partial electronic density for the state 
\begin_inset Formula \( n \)
\end_inset 

 is defined as:
\begin_inset Formula 
\begin{equation}
\label{1}
\rho _{n}(\mathbf{R})=\frac{1}{N}\sum _{\mathbf{k}\in BZ}\left| \psi _{n\mathbf{k}}(\mathbf{R})\right| ^{2}=\sum _{\mathbf{k}\in SP}\omega _{\mathbf{k}}\left| \psi _{n\mathbf{k}}(\mathbf{R})\right| ^{2}
\end{equation}

\end_inset 

 where SP means a set of (special) 
\series bold 
k
\series default 
-points (i.e.
 the actual 
\series bold 
k
\series default 
-point sampling), 
\begin_inset Formula \( \psi _{n\mathbf{k}}(\mathbf{R}) \)
\end_inset 

 is the wave function and 
\begin_inset Formula \( \omega _{\mathbf{k}} \)
\end_inset 

 is the weighting factor.
\layout Itemize

Partial electronic density for an 
\emph on 
island
\emph default 
 of bands 
\begin_inset Formula \( n\in [n_{1},n_{2}] \)
\end_inset 

 is
\begin_inset Formula 
\begin{equation}
\label{2}
\rho _{[n_{1},n_{2}]}(\mathbf{R})=\sum ^{n_{2}}_{n=n_{1}}\rho _{n}(\mathbf{R})
\end{equation}

\end_inset 

 
\layout Itemize

Total Density of States (DOS): 
\begin_inset Formula 
\begin{equation}
\label{3}
N(\epsilon )=\frac{1}{N}\sum _{n}\sum _{\mathbf{k}\in BZ}\delta (\epsilon -\epsilon _{n\mathbf{k}})
\end{equation}

\end_inset 

where the sum over 
\begin_inset Formula \( n \)
\end_inset 

 is run over all states (both occupied and unoccupied) and 
\begin_inset Formula \( \epsilon _{n\mathbf{k}} \)
\end_inset 

 are Kohn-Sham eigenvalues.
\layout Itemize

Local DOS (projected on a sphere): 
\begin_inset Formula 
\begin{equation}
\label{4}
N_{\mathbf{P}_{R}}(\epsilon )=\frac{1}{N}\sum _{n}\sum _{\mathbf{k}\in BZ}A_{n\mathbf{k}}\delta (\epsilon -\epsilon _{n\mathbf{k}})
\end{equation}

\end_inset 

where 
\begin_inset Formula \( \mathbf{P}_{R} \)
\end_inset 

 is a sphere of radius 
\begin_inset Formula \( R \)
\end_inset 

 centered at point 
\begin_inset Formula \( \mathbf{P} \)
\end_inset 

, and the weighting factor is defined as:
\begin_inset Formula 
\begin{equation}
\label{5}
A_{n\mathbf{k}}=\int _{\mathbf{r}\in \mathbf{P}_{R}}|\Psi _{n\mathbf{k}}(\mathbf{r})|^{2}d\mathbf{r}
\end{equation}

\end_inset 

 where integration is performed over the sphere.
 
\layout Itemize


\shape italic 
\emph on 
Angular-momenta (
\begin_inset Formula \( s,p,d \)
\end_inset 

) projected DOS
\shape default 
 
\emph default 
is defined as above, but with the following factors: 
\begin_inset Formula 
\begin{equation}
\label{6}
A_{n\mathbf{k}}=\int _{\mathbf{r}\in \mathbf{P}_{R}}\, \sum _{m=-l}^{l}\left| \left\langle \psi _{n\mathbf{k}}(\mathbf{r})\right| \left. R_{nl}(r)S_{lm}(\widehat{\mathbf{r}})\right\rangle \right| ^{2}d\mathbf{r}
\end{equation}

\end_inset 

 where 
\begin_inset Formula \( S_{lm}(\widehat{\mathbf{r}}) \)
\end_inset 

 is a real spherical function for the momenta 
\begin_inset Formula \( l=0,1,2 \)
\end_inset 

.
 
\layout Itemize

DOS projected on a layer (slab calculation).
 The factors in this case are:
\begin_inset Formula 
\begin{equation}
\label{7}
A_{n\mathbf{k}}=\int _{\mathbf{r}\in (layer)}|\Psi _{n\mathbf{k}}(\mathbf{r})|^{2}d\mathbf{r}
\end{equation}

\end_inset 

where the layer is thought to be perpendicular to the 
\begin_inset Formula \( z \)
\end_inset 

-axis.
\layout Standard

In the case of the projected DOS (LDOS) and also while analysing the density,
 real space integrals are calculated numerically.
 Two methods are implemented which are referred to as 
\begin_inset Quotes eld
\end_inset 


\emph on 
conserving
\emph default 

\begin_inset Quotes erd
\end_inset 

 and 
\begin_inset Quotes eld
\end_inset 


\emph on 
non-conserving
\emph default 

\begin_inset Quotes erd
\end_inset 

 algorithms.
 
\layout Itemize


\shape italic 
\emph on 
The conserving
\shape default 
\emph default 
 method provides the correct charge inside a sphere or a layer, each grid
 point in the cell is scanned once and only those grid points contribute
 which are positioned inside the area of interest (subject to an arbitrary
 lattice translation).
 As the region of integration increases (e.g.
 the radius of the sphere) the integration volume approaches that of the
 cell since equivalent points separated by a translation are ignored.
 
\layout Itemize

In the 
\shape italic 
\emph on 
non-conserving
\shape default 
\emph default 
 method a finer grid is constructed in the region of interest (= a sphere
 or a layer) and the integrals are calculated by summing up contributions
 on this finer grid (interpolation is used).
 This method does not give the charge conservation for large regions going
 over to adjacent cells since equivalent points will all be included.
 
\layout Itemize

If the size of the cell is large enough with respect to the region of integratio
n, than both methods should give close results.
 
\layout Itemize

The conserving method is extremely demanding and scales linearly with the
 size of the system.
 The non-conserving method scales linearly with the size of its own grid.
 However, since this grid is limited to the size of the integration region,
 the time of the calculation does not depend on the size of the system at
 all, so that this method is extremely fast.
\layout Itemize

In the conserving method the original grid is used with the directions along
 the cell basic vectors 
\begin_inset Formula \( \mathbf{a}_{i} \)
\end_inset 

.
 That is why this method is inappropriate for calculations of the angular
 momenta projected DOS for non-simple-cubic cells or for the calculation
 of the dipole/quadrupole momenta of a molecule.
 On the contrary, the non-conserving method has its own grid which is always
 cubic (along the Cartesian axes) so that it has the atomic symmetry and
 is ideal for these calculations.
\layout Section

Program 
\shape italic 
tetr
\layout Subsection

Installation and general information
\layout Standard

The code 
\series bold 
tetr
\series default 
 must be compiled only once by performing the command 
\latex latex 

\backslash 
begin{verbatim}
\newline 
 make -f make.tetr
\newline 

\backslash 
end{verbatim}
\latex default 
 in your
\noun on 
 
\family typewriter 
\noun default 
~/TOOLS/TETR
\family default 
 directory
\noun on 
.

\noun default 
 
\layout Standard

The code is user-friendly and works interactively (menu-driven).
 After choosing the PW code you are working with from the very first menu,
 the main menu appears which essentially reflects all the features supported
 at present.
 If you use the first 3 options, it assumes that you are going to construct
 your geometry file from scratch, so that the existing file (if any) will
 not be read in; all other options, 
\emph on 
if invoked first
\emph default 
, require an existing geometry file.
 This file is either: 
\layout Itemize


\family typewriter 
\noun on 
fort.15
\family default 
\noun default 
 for 
\series bold 
CETEP
\family typewriter 
\series default 
 
\layout Itemize


\family typewriter 
\noun on 
[Seed].coord
\family default 
\noun default 
 for 
\series bold 
CASTEP
\family typewriter 
\series default 
 
\layout Itemize


\family typewriter 
CONTCAR 
\family default 
for 
\series bold 
VASP
\layout Standard

Just to make it clear: if you start with the first 3 options, you will be
 kicked back to the main menu with some geometry in the memory and you can
 continue working on it using other options; in this case if there is a
 geometry file, it will be ignored.
 Note that at present you 
\emph on 
have
\emph default 
 to go to option 5 to actually write the geometry and the 
\begin_inset Formula \( \mathbf{k} \)
\end_inset 

-point files.
 By using Quit (option 15) you will loose all the data.
\layout Standard

Note that in some rather complicated situations it is easier to fill in
 atomic 
\begin_inset Quotes eld
\end_inset 

flesh
\begin_inset Quotes erd
\end_inset 

 into your cell solely by a proper expansion (see section 
\begin_inset LatexCommand \ref{Sec::extention}

\end_inset 

) of the primitive unit cell (UC) of some reference system (e.g.
 the perfect crystal) with subsequent removal/addition of atoms in specific
 positions; the code allows you to do so and also it checks on the run whether
 any position is translationally equivalent to the already accepted ones.
 Mind, it is tricky to make a 3D step or kink system, believe it or not!
 
\layout Standard

The main menu options are:
\layout Enumerate

Generate geometry file from scratch: you can either key in all the lattice
 vectors or choose them from a set of options with subsequent extention
 (if needed).
 When you are back in the main menu, you can continue working on the geometry
 / 
\begin_inset Formula \( \mathbf{k} \)
\end_inset 

-point files.
\layout Enumerate

This is the same option as the previous one except that a self-explanatory
 file 
\family typewriter 
tetr.inp
\family default 
 with Cartesian coordinates of all atoms in the generated cell is printed
 out and the code stops.
 Then, you can edit/remove/add atoms in this file using a text editor, and
 then run 
\series bold 
tetr
\series default 
 again using the next option 3.
\layout Enumerate

The file 
\family typewriter 
tetr.inp
\family default 
 is read in and checked.
 You can continue working on the cell using other options of the main menu.
 
\layout Enumerate

An extremely powerful option! It allows you to modify your existing geometry
 in a number of ways and build up your final periodic cell.
 You will be given an extended menu with self-explanatory options.
 You should be able to change your lattice vectors; extend your cell; rotate,
 shift the system; add, remove, shift atoms; change their species; construct
 a slab for the surface calculation using e.g.
 Millers indices, etc.
 What is more, after every step a 
\family typewriter 
geom.xyz
\family default 
 (xyz-format) file with the system geometry is written so that you can preview
 your cell on the fly as you build it using some molecular viewer (e.g.
 
\family typewriter 
\series bold 
XMOL
\family default 
\series default 
)! In addition, you can preview it as an extended cell if you like.
 Every step can also be undone.
 
\layout Enumerate

For existing geometry, an appropriate 
\series bold 
k
\series default 
-point sampling for the DOS, ground state and band-structure calculations
 can be generated (the 
\series bold 
k
\series default 
-point generator).
 In the case of the DOS options, the point group symmetry is explored and
 symmetry nonequivalent 
\series bold 
k
\series default 
-points are produced; a file 
\family typewriter 
brill.dat
\family default 
 is written which contains an important data for the 
\series bold 
lev00
\series default 
 routine which calculates and previews the DOS/LDOS.
 At the same time, when you quit there, a geometry file will be produced:
\begin_deeper 
\layout Enumerate


\family typewriter 
\noun on 
fort.15_
\family default 
\noun default 
 for 
\series bold 
CETEP
\family typewriter 
\series default 
 
\layout Enumerate


\family typewriter 
\noun on 
[Seed].coord_
\family default 
\noun default 
 for 
\series bold 
CASTEP
\family typewriter 
\series default 
 
\layout Enumerate


\family typewriter 
CONTCAR_ 
\family default 
and
\family typewriter 
 KPOINTS_ 
\family default 
for 
\series bold 
VASP
\layout Standard

and the code stops.
\end_deeper 
\layout Enumerate

Coulomb potential at any desired point in the cell is calculated in the
 framework of the point-charge model; you will be asked to provide the charges
 on atoms either separately for every atom in the cell or only for different
 species; a file 
\family typewriter 
madel.dat
\family default 
 is produced with all your results within the option.
\layout Enumerate

For molecules only: the symmetry of vibrations is analysed and the distorted
 geometry corresponding to a chosen vibrational mode and the amplitude is
 generated in a new geometry file.
 Translational and rotational degrees of freedom (normally six; there will
 be five degrees of freedom for a linear molecule) are eliminated automatically
 by projecting them out from all the coordinates.
 The strength of distortion from equilibrium is also to be given.
 Using the geometry file corresponding to distorted geometry, you can run
 the PW code again saving energies in a file to be used in the next option.
\layout Enumerate

For molecules only (the follow-up option to the previous one): using the
 group-theoretical information about molecular vibrations, the energies
 both in equilibrium and distorted positions (see option 7) and atomic masses,
 vibrational frequency is calculated for the given active mode.
\layout Enumerate

A file 
\family typewriter