Last updated -- 17 December 1999

The ``Static'' Tight-Binding Program: Example I -- Setup Part I

This page shows how to obtain files necessary to run the static Tight-Binding total energy/band structure evaluation program. Information on setting up the input file is on page 2, and the interpretation of the output files is discussed on page 3.

First we must decide which element to choose. For this example, we will use palladium.
1. We then must get the tight-binding parameters for palladium. To do this, we go to http://web.archive.org/web/20111231202250/http://cst-www.nrl.navy.mil/bind/ and click on "Pd" in the periodic table.
  You have two choices. For this example click on the one that says "R_cut = 10.5 a.u." (You might want to try the other parameter file to see the differences between the parametrizations.)
2. Create a working directory and write this page into it under the name pd_par. If you used an earlier version of this program, note that we have added some parametrization-specific information to the top file. Previously much of this information had to be entered into the SKIN (Slater-Koster INput) file. Let's look at the header of the file:
```
NN00000                 (Old style Overlap Parameters)
Palladium -- Shortened interaction distance
1                       (One atom type in this file)
10.5   0.5              (RCUT and SCREENL for 1-1 interactions)
9                       (Orbitals for atom 1)
106.4                   (Atomic Weight of Atom 1)
 0.0  0.0 10.0          (formal spd valence occupancy for atom 1)
```
  - The first line tells the program what kind of parameters to expect. The first N means that the parameters are non-orthogonal, i.e., that we have included a parametrization of the overlap matrix elements. The second N indicates that the parameters are non-magnetic. There will be no spin polarization. The "00000" following gives the version number of the parameterization. At present there are only two. "00000" is the "old-fashioned" parametrization technique, better known as the "Vanadium-style" parametrization from the NRL Tight-Binding Method.
  - The second line is a descriptive title.
  - The third line shows the number of atoms described in this file. Since this is just Palladium, it is set to 1.
  - The next line shows the cutoff distance and screening parameter for this input file. The Slater-Koster parameters in this file are smoothed by a function f(R) = 1/[1 + exp(R - RCUT + 5/SCREENL)] . This ensures that the parameters are effectively zero at distances R > RCUT. Thus atoms separated by more than RCUT will not interact directly.
  - The next line says that there are 9 basis functions for each atom. This means that s, p, and d Palladium orbitals were included in the fit.
  - 106.4 is the atomic weight of Palladium in standard units. This is for use by molecular dynamics programs.
  - Finally, the last line of the header indicates the formal valence of the atom, giving the s, p, and d decomposed electron count. static only uses the total valence charge of Palladium, 10 electrons.
Now we must choose the problem we wish to solve. For this example, we want to look at the energy of Pd in the fcc and bcc phases.
1. For each lattice we require a space group file, which reveals the symmetry of the lattice, and a k-point file, which gives us an integration mesh so that we can evaluate the total energy of the crystal by summing over the eigenvalues in the first Brillouin zone.
2. We have stored some pre-generated k-point meshes at http://web.archive.org/web/20111231202250/http://cst-www.nrl.navy.mil/bind/kpts/. Space group files for the lattices associated with each mesh are also available from this site.
3. To find an appropriate "k-point" mesh for the fcc crystal, click on the face-centered cubic lattices about half-way down the page. A wide variety of k-point meshes are available here. K-point meshes with higher orders are denser, and so more accurate, than those of lower order. For this example we'll use the mesh labeled "Order 8" under the "REGULAR" heading. This file has 85 k-points, and includes the origin, Gamma. Save this file in the same directory as the tight-binding parameters, using the name "fcc.08".
4. We can also retrieve the space group file from here. Use the "back" button on the browser to return to the face-centered cubic lattices k-point page, and look down at the bottom of the page, where there is a link to the space group Fm(-3)m (#225). Clicking on this link takes you into our Crystal Lattice Structures database. Click on the icon of the fcc lattice to find out more about this structure.
5. We want a Cartesian representation of the space group. Search for the link labeled Cartesian on the line that begins "Space Group". Clicking on this will reveal a representation of all 48 operations in the full cubic space group. Save this file in the working directory under the name "spcgrp.fcc".
6. Repeat the above process for the bcc lattice. That is
  1. Return to the k-point page, http://web.archive.org/web/20111231202250/http://cst-www.nrl.navy.mil/bind/kpts/
  2. Find the link to body-centered cubic lattices.
  3. From this link, get the Regular Order 8 mesh, which contains 55 k-points. Save this file as "bcc.08".
  4. Returning to the body-centered cubic lattices page, find the link to the Im(-3)m (#229) space group. Click on the icon for the bcc structure, and look for the link to the Cartesian representation of the space group file. Save this file under the name "spcgrp.bcc". (You may notice a slight relationship between the fcc and bcc space group files.)

Your working directory should now look something like this:

$ls -l
total 80
-rw-r-----   1 mehl usr  2410 Aug 13 14:10 bcc.08
-rw-r-----   1 mehl usr  3468 Aug 13 14:08 fcc.08
-rw-r-----   1 mehl usr  7162 May 25 11:00 pd_par
-rw-r-----   1 mehl usr 10003 Aug 13 14:11 spcgrp.bcc
-rw-r-----   1 mehl usr 10003 Aug 13 14:10 spcgrp.fcc

We're now ready to construct the input file.

Go on to page 2 to learn how to construct an input file.

Skip to the output discussion to see what will happen.

Look at other examples.

Get other parameters from the Tight-binding periodic table.

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