Last updated -- 17 December 1999

The ``Static'' Tight-Binding Program: Example II

This page shows how to set up the input to run the static Tight-Binding program. Information about the interpretation of the output files is discussed on page 2. Further information is available in the other examples in this manual.

In this example we want get an idea of the equilibrium c/a ratio of titanium in the hexagonal close packed (hcp) phase at the equilibrium volume (238 Bohr³).

Detailed information about the construction of the input is in Example 1.

The tight-binding parameters for Titanium are available from http://web.archive.org/web/20111231202250/http://cst-www.nrl.navy.mil/bind/. Click on "Ti". Create a new working directory and save these parameters there under the name ti_par.

To find the space group information for the hcp lattice,

• go to the Crystal Lattice Structure (http://web.archive.org/web/20111231202250/http://cst-www.nrl.navy.mil/lattice/index.html) page,
• click on Hexagonal Close Packed and related structures, and then
• on A3 (hcp) Structure (http://web.archive.org/web/20111231202250/http://cst-www.nrl.navy.mil/lattice/struk/a3.html) .
• In this case we want the space group file in lattice coordinates (click on the Cartesian link to see why), so look for the lattice coordinate link.
• Save this file in the working directory under the name spcgp1.hcp.

Now get a copy of the SKIN (Slater-Koster INput) file, and save it in your working directory under the name SKIN. Let's examine this file.

The first few lines of the file are nearly the same as in Example 1:

Mode=3            (Calculate energy only -- no pressure)
0.005  0.500      (T_{Fermi}, Eigenvalue cutoff for P calculation)
ti_par

In this example we are interested in the energy as a function of c/a ratio, not volume. This means we do not need the pressure, so we set ``Mode=3''. Otherwise, except for the name of the parameter file, nothing is changed.

The lines describing the lattice have changed somewhat:

Titanium HCP (A3)
 hcp  1.30           (20 character label for SKENG)
 0.00                (Electrons in addition to nominal Ti charge (=4/atom))
-3                   (hexagonal lattice, read in V and c/a)
 238  1.30           (V in Bohr^3 and c/a)
 0                   (No additional strains applied)
 2                   (Atoms in the unit cell)
 4 4 4               (Neighbor search cutoff indices)
F                    (Logical variable -- no internal displacements)
1 0.33333333333333333 0.66666666666666667 0.25 0 0 0   (Atom 1 in lattice coord.)
1 0.66666666666666667 0.33333333333333333 0.75 0 0 0   (Atom 2 in lattice coord.)

• (line 2) Since the SKENG file will contain the volume of the unit cell, we use the label to specify the c/a ratio
• (line 4) We want to vary c/a at fixed volume for a hexagonal lattice. Looking at the available lattice types we see that -3 is the correct option here. (When the program is finished, you may want to check the SKOUT file to be sure that the lattice generated here is in agreement with the lattice used to generate the space group operations.
• (line 5) The specification of the hexagonal lattice requires two lattice parameters, here the volume (238) and c/a ratio (1.30).
• (lines 9 and 10) In the hcp structure the atoms are located at the points

  b₁ = 1/3 a₁ + 2/3 a₂ + 1/4 a₃   and

  b₂ = 2/3 a₁ + 1/3 a₂ + 3/4 a₃   ,

  so we have one line of input for each atom.

  Additionally, the first parameter, 1, is an indicator of the kind of element at each coordinate. If we were working with a diatomic compound, the first parameters would be 1 and 2. Meaning the first kind of element would be at one coordinate, and the second kind of element would be at a second coordinate.

  
  
  

In this example, we will let the program generate the k-points. The input looks like this:

NEWSYM=T             (Generate new set of k-points)
LATTIC=4             (Lattice type / Next is spacegroup file name:)
spcgp1.hcp
ILAT=T               (Space group file in lattice Coordinates)
    0                (Generate k-points)
lspec=f,linfok=f     (Regular points, no information points)
   12   12   12                  (Mesh:  must be (5I5) format)

• The first line is a flag indicating that a new k-point mesh will be generated
• The next line tells the program that this is an hexagonal lattice. This would help the program generate better "special" k-points, though we will use "regular" k-points here.
• The next line is the path to the space group file
• Since this is in lattice coordinates, we set "ILAT=T"
• We won't be generating any "information only" k-points,
• The flag "lspec=f" indicates that we'll generate "regular" k-points, i.e., the origin will be included in the set
• Finally, we choose the number of divisions along each reciprocal lattice vector. The larger the number, the more points in the mesh. This choice produces a set of 133 k-points, equivalent to the Order (6,6) mesh on the hexagonal k-point page.

Since we'll keep the same k-point mesh for further calculations, the remainder of the SKIN file is much simpler. For example, to find the energy at a c/a ration of 1.35, we enter

Titanium HCP
  8.0 0.0 2.0
18
-2
 238   1.35              # New c/a ratio
f hcp  1.35              # and corresponding label
 1.0 1.0 1.0
 4 4 4
 1 .3333333333333333  .6666666666666667  .25  0 0 0
 1 .6666666666666667  .3333333333333333  .75  0 0 0
16.5
NEWSYM=F

The "NEWSYM=F" line indicates that the previous k-point mesh will be used.

Now go to the output discussion to see what will happen.

Look at other examples.

Look for other available Tight-binding parameters in the periodic table.

Return to the static Reference Manual.