Molecule Types Vibrational Structure Force Field Analysis | <Prev Next> |

Symmetry coordinates, **S**, are specified by giving the
transformation matrix, **U**, between **S** and the
internal coordinates, **R**:

S=U R=U BΔx

The symmetry coordinates window, shown below for
C_{2}H_{4}, allows the display and editing of the
**U** matrix and (optionally) the force field in terms of
symmetry coordinates, **F**. To create a symmetry coordinates
object, right click on the `Electronic
State` object object and select "`Add New...,
Symmetry Coords`". To bring up the window right click on the
symmetry coordinates object and select "View...". If a symmetry
coordinates object is not present, or the **U** matrix is left
blank, an identity matrix is assumed for the **U** matrix.
Note that the current version of the program ignores the point
group set for the molecule as a whole, and the symmetry set for
the individual vibrational modes when doing the force field
calculation. This may be changed in future versions of the
program.

With the current version the choice of symmetry
co-ordinates for degenerate modes may require some care; the
values calculated for the Coriolis coupling constants and some
other vibration-rotation constants can be sensitive to the choice
made. This is partly mitigated by forcing the largest coefficient
for each mode in the **L** matrix to be positive by
multiplying the vibrational mode by -1 as required. The `PreserveS` flag (see below) can
also be helpful in keeping modes consistent. The simplest results
are obtained if the co-ordinates chosen for different degenerate
modes have the same transformation properties under the operations
of the point group.

The plot at the bottom shows the current symmetry coordinate,
i.e. the selected row in the top left grid. The arrows indicate
how far each atom moves. The plot updates semi-automatically; use
"`Operate, Check`" to force an update.

+

The "Plot Plane" control allows the selection of the plane in which to plot the molecule.

The magnification selects the scale factor to use for the arrows.

The status bar shows the latest mouse position; draw a box with the mouse to measure distance and angles.

The operate button brings up a menu of possible operations:

Check |
Check the contents of the top grids, and
update the plot to match |

Apply |
Check the contents of the top grids, and
display the details of the vibrational mode calculation in
the Log Window. This also forces
other objects to update. |

Make
Extra Operators |
Create vibrational perturbations - see Other Potential Terms. |

Show F Matrix |
Print the F matrix in the Log
Window calculated from the matrix
elements and frequencies given in the vibrational mode objects.
The transformation is done by calculating the matrix lL,
which relates the symmetry coordinates, S, and
normal coordinates, Q:The L matrix is available from:providing the internal coordinates are fully specified and the F matrix can then be calculated from: Note that the U matrix is not necessarily required,
but if there are redundant internal coordinates L^{-1}
can't be calculated. In this case an alternative
relationship can be used:provided that L L^{T}= 1. |

Set F Matrix |
Clear the f matrix grid (top right) and set it
from the matrix elements and frequencies
given in the vibrational mode
objects. See the entry above for details of the calculation.l |

Sort F Matrix by Value |
Sort the F matrix grid (top right) in descending
order of the first column. |

Sort F Matrix by Mode |
Sort the F matrix grid (top right) by mode
numbers, with diagonal elements first. |

The grid at the top right allows the force field to be given in terms of valence coordinates:

V= ½S^{T}FS =½ Σ_{ij}F_{ij}S_{i}S_{j}

The non zero elements of the **F** matrix,
*F*_{ij} are specified in the grid, with the
force constant in the first column, and *i* and *j* in
the next two columns. (The fourth column is to allow future
expansion to cubic and higher terms.) The force constants can be
given as simple numerical values, but can also be given as general
expressions involving symbolic values. This is typically more
useful as it allows, for example, relationships between
isotopologues to be added naturally. For the example shown here
the constants are expressed as the product of two factors, such as
`k2*F2`. The intent is that `k2` is a scaling
factor, as commonly used in interpreting * ab initio*
calculations; here a different scaling factor is used for each
mode, but an obvious change would allow the same scaling factor to
be used for each mode. When reading the force constant matrix,
unknown variables are automatically created as parameters to the
current internal coordinates object, and they can then be edited
in the Constants Window. If
dealing with more than one isotopologue, these variables are
better placed in a variables object,
(with `Global` set to
true) so the same value can be used in all species.

Note that the force constant grid will expand automatically as atoms
are added. The grid can be left blank if the potential energy is to
be expressed in terms of internal coordinates. Other types of
potential terms can also be added, typically where (different)
electronic states are specified. See the Other Potential
Terms section under internal coordinates.
The grid at the top right allows the