`<text> and <>`

Geometry references are defined by the symbols <text> and <>, and by the Z-matrix or geometry file. <text> defines a geometric variable, and the spacer <> defines a variable that is not a geometry reference. The geometry references are best described by examples.

Consider ethylene. There are three quantities of interest, the C-C distance, the C-H distance and the C-C-H angle. The following MOPAC data set shows ethylene, defined using SYMMETRY. In this case, the first three geometry data are marked for optimization. These data also correspond to the quantities of interest. If there is text between the "<" and the ">" symbols, the corresponding adjustable geometric parameter is defined as a geometric reference. So in this case, the first symbol is "<C-C>" and this corresponds to the geometric quantity 1.328 Ångstroms, this being the C-C distance. The second reference, "<C-H>" corresponds to the distance 1.0809 Ångstroms, and the third "<C-C-H>" can be identified with the C-C-H angle of 123.509 degrees.

Each geometric symbol corresponds to a geometric variable, in order.

SYMMETRY
Ethylene
 GR=HERZ1966 <C-C> <C-H> <C-C-H>
  C         0.00000000  0    0.0000000  0    0.0000000  0                     -0.2864
  C         1.32800000  1    0.0000000  0    0.0000000  0    1    0    0      -0.2864
  H         1.08090000  1  123.5090000  1    0.0000000  0    2    1    0       0.1432
  H         1.08182856  0  123.4931754  0    0.0000000  0    1    2    3       0.1432
  H         1.08182856  0  123.4931754  0  180.0000000  0    1    2    3       0.1432
  H         1.08182856  0  123.4931754  0    0.0000000  0    2    1    5       0.1432
 
   3  1    4    5    6
   3  2    4    5    6

A more complicated example - Benzene, without symmetry

In this somewhat artificial example, there are exactly two geometric references, a C-C distance and a C-H distance. The angles are defined by symmetry and are not marked for geometry optimization. Only one C-C distance is important, the first C-C. This is indicated on the third line by "<C-C>". (Line 1, with the MOPAC keyword DEBUG, would normally not have any keywords. DEBUG is here to show where Line 1 is.) The next four C-C distances, although marked for optimization, are not to be used as reference data in the parameterization To indicate that they are not to be used, four spacers, "<>", are present. The next datum, a C-H bond-length is to be used as a reference datum, so it is indicated by "<C-H>". The rest of the geometry is not interesting, and can be ignored.

What is written in the text block is up to the user - it is not used by PARAM, except that it must be at least one and less than 11 characters if it is to be used as a geometry reference. Don't use "cute" symbols in the text, such as "<" or ">" - these will only confuse the program.

DEBUG
Benzene
  <C-C> <> <> <> <> <C-H> GR=TIK1976 
  C         0.00000000  0    0.0000000  0    0.0000000  0                     -0.1436
  C         1.39900000  1    0.0000000  0    0.0000000  0    1    0    0      -0.1436
  C         1.39864939  1  120.0000000  0    0.0000000  0    2    1    0      -0.1436
  C         1.39864939  1  120.0000000  0    0.0000000  0    3    2    1      -0.1436
  C         1.39864939  1  120.0000000  0    0.0000000  0    4    3    2      -0.1436
  C         1.39864939  1  120.0000000  0    0.0000000  0    5    4    3      -0.1436
  H         1.08400000  1  120.0000000  0  180.0000000  0    1    6    5       0.1436
  H         1.08820182  1  120.0000000  0  180.0000000  0    5    6    1       0.1436
  H         1.08820182  1  120.0000000  0  180.0000000  0    2    1    6       0.1436
  H         1.08820182  1  120.0000000  0  180.0000000  0    6    1    2       0.1436
  H         1.08820182  1  120.0000000  0  180.0000000  0    3    2    1       0.1436
  H         1.08820182  1  120.0000000  0  180.0000000  0    4    3    2       0.1436

How geometric data are used in a parameterization run

At the start of a parameterization run, all reference data geometric quantities are re-defined as "fixed" - as if the optimization flag had been set to zero. The geometry is then optimized. In the case of ethylene (above), there would be no geometric variables, because all three geometric variables are also reference data, and would thus be "fixed." In the case of benzene (above), there would be 9 geometric variables that would be optimized: 4 C-C distances and 5 C-H distances. When the geometry optimization is complete, the reference geometric data are re-defined as "optimize" - that is, the optimization flag are re-set to "1". The gradient for each geometric datum is then calculated. If this is zero (never happens) then the method would, by definition, predict that geometric quantity with zero error. In practice, the gradient is non-zero, and is used as a measure of error for optimizing the parameters, in exactly the same way as the errors in the calculated heats of formation, dipole, and I.P. are used.

How geometric data are used in a survey run

In a survey, the reference geometric data are stored, and the geometry is then optimized. After the optimization is complete, the stored geometric data are compared with the calculated geometric data. The difference between the two (reference - calculated geometric quantity) is then a measure of the error in the calculated quantity. Note that in a survey, the reference data geometric parameters are not fixed, that is a parameterization run and a survey run are very different.