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Symmetry and Molecular Images

The Images commands allows symmetric images of the primary molecule(s) to participate in the energy and structure of a system.

The syntax of image input and output commands is given in section Input-Output Commands.

By reading an image file (`.IMG'), the images of the primary atoms are included in any energy and force determinations for the remainder of the calculation (unless another image file is read). The main use for this facility is to simulate crystal environments or to obtain periodic boundary conditions. It is also acceptable to use this facility in finite systems such as dimers and tetramers.

• Files for Images: Description of the Image data file.
• Operation of Images: Some details and requirements for operation

Image Files

An Image file contains all of the information needed to define the position and orientation of all symmetric images of the primary atoms. The file is a card image file and a sample file is given:

*  IMAGE FILE FOR BETA SHEET TEST CASE
*  ONLY ONE TRANSFORMATION (Z AXIS ROTATION)
*
    1
  1.0       1.0       1.0
ZROT
 -1.0       0.0       0.0
  0.0      -1.0       0.0
  0.0       0.0       1.0
  0.0       0.0       0.0

The title is in standard CONGEN format, see section Glossary of Syntactic Terms. The next contains the number of transformations (I5). The following line contains the unit cell dimensions (multiplying factors) (3F10.5).

The remaining lines are in groups of five, one group for each transformation . For each group, the first line contains the name of the transformation (A8). The next three lines contains the rotation matrix, and the last line contains the translation vector (all 3F10.5).

The rotation matrix must be unitary, however, a non-unitary rotation matrix will only result in a warning. The use of an anti-unitary matrix can be used to include the mirror image of any system into the calculation. The values of the translation vector are multiplied by the cell dimensions listed at the beginning of the file to generate the actual translation steps. For the use in this program the translation is done after the rotation has been made.

One other restriction on the transformations is that every transformation must have an inverse. Again, there is only a warning if this restriction is violated as there may be examples where this is desired. In the example above, this transformation is its own inverse. Non-physical results will be obtained if this restriction is violated.

The maximum number of allowed transformations is 26 (the number needed for simple 3-dimensional periodic boundaries). This limit can easily be increased by modifying INIMAG.

For other examples of image files see the test cases.

Image Operation

The routines in IMAGES.FLX can be classified into three sections. These categories are:

1. Set up images -- IMIGIO, IMREAD, IMWRIT, REIMAG, INIMAG.
2. Set up energy terms -- IMHBON, NEWHBL, IMHBFX, NBONDM.
3. Compute energy -- EIMAGE, TRANSO, TRANSI, SFLSET.

The first category involves reading the image file (IMREAD) and setting up the data structure (REIMAG, INIMAG) see the CONGEN source file `IMAG.FCM'.

The second category in addition to finding the energy terms, also selects which image residues are to be kept. This selection process is repeated each time the nonbonded list is updated. Since the list of atoms can change its not possible to maintain a fixed list of hydrogen bonds explicitly for image interactions. It is also the case that the image Hbond list must be recomputed each time a new nonbond list is generated. This is done automatically, but it is highly recommended to keep INBFRQ and IBHFRQ (see section Options Common to Minimization and Dynamics) the same to avoid confusion. The ST2 interactions are also computed when the nonbonded list is updated (NBONDM).

The third category is concerned with the computation of energy terms. For the actual computation of energy, standard routines are used (ENBOND, EHBOND, ENST2) with a modified calling sequence. The procedure used is:

1. Compute coordinates for all image atoms.
2. Set up arrays for self energy terms (atom with its own image).
3. Compute self terms, divide energy by 2, zero out image forces.
4. Compute remaining terms including forces on image atoms.
5. Transform forces on image atoms back into the primary space.

Since there is no treatment of the second derivative of the energy for image atoms, the procedures involving Newton-Raphson minimizations (see section Minimization Options) and vibrational analysis (see section Vibrational Analysis) will not function properly.

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