Program MAKPOL

(This program is NOT a function within MOPAC, instead it is a utility program for building data sets for infinite systems. A copy of the MAKPOL executable for use on WINDOWS systems is available.)

Construction of data sets for multiple unit cells is tedious. By automating this process, only the fundamental unit cell need be specified, the other unit cells being generated by translation. In addition, since the geometry of all fundamental unit cells in a polymer are identical, symmetry conditions can be imposed on each unit cell. This has two advantages: first, the calculation runs significantly faster, and second, periodic boundary conditions are imposed not only on the whole cluster, but also on each fundamental unit cell.

A data set for MAKPOL is similar to a data set for MOPAC. It consists of one or more lines of keywords, followed by comments (if needed), then a geometry in Cartesian or internal coordinates. The name of the input data set should be of form 'make_filename.dat', in which case the resulting data set will be 'filename.dat'.

MAKPOL uses the unit cell supplied by the user to generate all the unit cells used in the cluster unit cells. The number of unit cells in the cluster is determined by the keyword MERS(n3,n2,n1). If the system is a layer structure then "n3," is omitted. If the system is a polymer, then "n3,n2," is omitted. The order in which cells are generated is as follows: Cell(0,0,0), Cell(0,0,1), Cell(0,0,2), ...Cell(0,0,N1-1), Cell(0,1,0), Cell(0,1,1), ...Cell(0,N2-1,N1-1), Cell(1,0,0), ...Cell(N3-1,N2-1,N1-1).

See Description of BZ for more information on the values of n₁, n₂, and n₃. and MERS for how to construct a data set for use by BZ

The geometry of the extended system is first calculated in Cartesian coordinates. There are two ways the atoms can be arranged. The default order is as follows: all atoms in the first unit cell, all atoms in the second unit cell, etc. An alternative is to have atom one in all the unit cells then atom two in all unit cells, then atom three, etc. The choice of which order to use depends on the purpose for which the cluster data set will be used.

The whole system is then converted into internal coordinates if INT is present, and the translation vectors added. If wanted, symmetry conditions can be imposed - this is useful when the geometry is to be optimized.

How to use MAKPOL

Make up a data set for the solid. The name of the data set must be in the form "Make_<data-set name>.dat" An example of the data set for rutile, would be as follows:

 MERS=(3,2,3) 
Rutile

 Ti    0.000000000  1   0.000000000  1   0.000000000  1  
  O   -0.896000000  1  -0.896000000  1  -1.479000000  1  
  O    0.896000000  1   0.896000000  1  -1.479000000  1  
  O    1.401000000  1  -1.401000000  1   0.001000000  1  
  O   -1.401000000  1   1.401000000  1   0.001000000  1  
 Ti   -2.297000000  1  -2.297000000  1  -1.479000000  1  
 Tv    0.000000000  1   0.000000000  1  -2.959000000  1  
 Tv    0.000000000  1   4.594000000  1   0.000000000  1  
 Tv    4.594000000  1   0.000000000  1   0.000000000  1  
 

To use this data set, put it into a file called "make_Rutile.dat"

Edit the command file "makpol.cmd" to replace the path in "s:\utility\makpol-F90" with the path to the folder where Makpol-F90.exe is stored.

Replace the "vi" editor with your preferred editor. If you don't have one, remove this line, and edit the data set after makpol.cmd has finished.

To run MAKPOL, use the command "Makpol <file>", e.g. "Makpol Rutile" Note that although the data set has the name "Make_Rutile.dat", the command argument does not include the "Make_" or the ".dat"
After Makpol is run, a new file called "<file>.dat", e.g., "Rutile.dat", will be created. This is a data file for use with MOPAC. Before running it, however, edit the file to check that it is big enough, that the three translation vectors are large enough, and that the data set is not too big - data sets with more than ~300 atoms might take a long time to run. A simple check on the Tv would be to verify that the largest difference in the "X" values of the three Tv is greater than about 6 Ångstroms for an insulator and greater than about 8 Ångstroms for a narrow band gap solid, then do the same for "Y" and "Z".

Keywords used by MAKPOL

Any of the keywords used by MOPAC can be used in a MAKPOL data set, but, only a few keywords will be used by MAKPOL: the rest will be ignored. Keywords that are used in MAKPOL are given below.

BCC: When BCC is added (Body Centered Cubic), all odd unit cells are omitted. An odd unit cell is one for which the addition of the cell indices results in an odd number, thus (0,0,0) and (1,1,0) would be allowed, but (1,1,1) and (2,1,0) would not. Diamond is an example of a BCC solid.

DEBUG: Print diagnostic data on how MAKPOL is working. This is not a particularly useful keyword--do not use it for routine work.

LET: Use this keyword when the resulting data set is to be used for band structure, i.e., Brillouin zone work. The default, when LET is not present, is to re-arrange the atoms so as to make entire molecules, if possible. This step is not done when LET is present. In addition, when LET is present, the MOPAC keyword BZ is added to the data set. Do NOT attempt to make a data set for solid state work by adding keyword BZ to a data set - if you do, you'll almost certainly make a mistake.

When "LET" is present, only the atoms that make up the unit cell should be present. The unit cell must also be stoichiometric, that is, there must be an exact integer multiple of the formula present. For example, TiO₂ in the rutile structure has a unit cell with one titanium atom at a vertex and one at the center of the tetragonal unit cell. There must also be four oxygen atoms, two inside the unit cell and two on the surface of the unit cell.

MERS=(n3,n2,n1): The number of unit cells in each direction is defined by n₃, n₂, and n₁. The total number of unit cells generated will be n₃.n₂.n₁, or, if BCC is used, (n₃.n₂.n₁)/2.
SORT: The default order of atoms in a cluster is as follows: all atoms in the first unit cell, all atoms in the second unit cell, etc. An alternative order can be requested by adding SORT. In this case, the order of occurrence is: atom one in all the unit cells, atom two in all unit cells, atom three, etc. The choice of which order to use depends on the purpose for which the cluster data set will be used.; For geometry optimizations, SORT is useful, particularly when used with SYMMETRY.; For band structure calculations, SORT should not be used--these calculations require the default order of atoms. To emphasize this point, if SORT is specified, then the keyword MERS will be deleted from the resulting data set.

SYMMETRY: This keyword has two distinct functions. When SYMMETRY is specified, then any symmetry data present in the input data set will be used. This is useful for reducing the number of variables that need to be changed on going from one system to another (for example, on going from diamond to cubic boron nitride). If no symmetry data are present, then this function will not be used.; The second function of SYMMETRY is to impose symmetry conditions on the resulting cluster data set. Only four symmetry conditions are recognized: bond-lengths that are equal, bond angles that are equal, equal dihedral angles, and dihedral angles that are the negative of reference dihedrals.; For high symmetry systems, the cluster data set should be edited to increase the symmetry. For example, in diamond, all angles and dihedrals are symmetry defined, so all the optimization flags for these variables should be set to zero, and all symmetry functions involving angles and dihedrals should be deleted. In addition, all "bond lengths" in diamond are simple multiples of the fundamental C-C distance, so extra symmetry functions (involving function 19) should be added. If this is done correctly, then only one geometric variable will be left.