While ATOMS can deal equally as well with molecules as crystals, the input contains some options which are extraneous for molecules. The following sections give some guidelines for dealing with molecules and polymers. This is intended only for molecules which are input as single entities with absolute coordinates, not for molecules which are part of a crystal structure, which can be isolated with the Locate Groups command (Transform menu), the Find button in the Generated Atom Datadialog, or the special boundary options for molecules in crystals..
1. Coordinate Axes for Molecules.
The type of axial system specified in the Title/Axes dialog (Input1 menu) may depend on the symmetry of the molecule. Except for cases in which one 3-fold or 6-fold axis is present, i.e. trigonal or hexagonal symmetry, there is no reason not to use Cartesian reference axes. The symmetry may then be specified using the Point-groupsymmetry option if the molecule is in a standard orientation, or the Space-grouporCustom optionsif it is not. All these options use symmetry operations which are of the type used for crystals.
However, if a molecule has either a 3-fold or a 6-fold axis the full symmetry can be specified by means of crystallographic symmetry operations only if hexagonal structure axes are used. Both trigonal and hexagonal crystal systems by default use "hexagonal axes'', that is a1 and a2 axes at right angles to the c axis, and 120 degrees from one another. Trigonal crystals may also use rhombohedral axes, which are not applicable to molecules. Cartesian coordinates may be transformed to hexagonal coordinates, and vice-versa, with the following sets of equations (angles in degrees).
where a is the length of the hexagonal a axes (or ratio of lengths hexagonal over Cartesian if the Cartesian axes are not of length one). These equations assume that the two c or z axes are parallel and that the a2, b or y axes are parallel.
Trigonal and hexagonal point groups. If unit Cartesian axes are used and a trigonal or hexagonal point group is selected in the Point Group symmetry option, the standard matrices for this group (derived from the first space group in the point group in the International Tables) are converted from a basis of hexagonal axes to Cartesian axes. This implies a certain orientation of the symmetry elements. If a different orientation is desired, there are two options; you can use a space group with a different orientation, or you can select the Cartesiansymmetry option. The Cartesian option requires the preexistence of a file containing the symmetry matrices, which may be generated with the auxiliary program SYMGRP available from Shape software. With this option the symmetry elements may have any desired orientation with respect to the coordinate axes.
2. Boundary Options for Molecules and Polymers.
For an isolated molecule, the boundary option will normally be No boundaries this simply accepts all atoms in the original input and those generated by point-group symmetry no translations (lattice vectors) are applied. Again, if you want to locate a molecule in a crystal structure, see the Locate Groupscommand in the Transform menu, the Find button in the Generated Atom Datadialog, or the special boundary options for molecules in crystals.
For a polymer, there are two possible choices. The simplest is to use the Translation Limits option. This takes all the atoms in the central cell and those generated by translation within the given limits in the directions of the selected lattice vectors (axes). For a one-dimensional (chain) polymer, two of the translations should be disabled and for a two-dimensional (sheet) polymer, three should be disabled. This is certainly the best choice for a one-dimensional polymer.
The other choice is to use theEnter Formsoption, and manually disable one or two lattice translations. This allows for showing different parts of two-dimensional polymers. For example, consider a trigonal or hexagonal sheet; the Translation Limits option allows for showing only a rhombic slice of the sheet. Suppose that the polymer extends in the a and b (x and y) directions; then it can be limited by vertical faces such as (100), (010), etc. to give a slice with hexagonal or trigonal symmetry. Translation in the c (z) axis direction should be disabled.
The above choices again assume that the input is actually for a molecule, and not a crystal. For viewing molecules in crystals, the procedure is different. First, you can import several types of crystallographic files for structures containing molecules using the Isolate Molecules in Crystalboundary option (Input1 menu). The Free-Form (.inp) import option can be used to read in almost any type of atomic-coordinate information. You can also use the Locate Groups option in the Transform menu to isolate individual molecules or polymers.
3. Symmetry for Molecules and Polymers.
Symmetry of molecules is normally described in terms of point groups. The point group symmetry can be provided as crystallographic symmetry operations, or in the form of Cartesian symmetry matrices.
3.1. Crystallographic symmetry operations.
ATOMS can automatically provide the symmetry for the 32 point groups which are also crystal classes, i.e. contain no non-crystallographic symmetry elements such as 5-fold axes. Provided that the orientation of the symmetry elements with respect to the coordinate axes is standard, it is only necessary to give the Schoenflies or International (Hermann-Maughin) symbol for the point group in the Point-groupsymmetry option. Certain alternate orientations, related to the "standard'' ones by a rotation of 45 or 30 degrees on the c or z axis, can be attained by using the Space-group symmetry option. If the orientation is not attainable by either of these methods, appropriate symmetry operations can be entered with the Custom symmetry option.
There is no provision in ATOMS for strictly one-dimensional, two-dimensional or spiral symmetry elements, such as might occur in polymers. Nevertheless, most if not all of the symmetry in polymers may be included with judicious use of space groups, combined with disabling of repetition by translation in one or two dimensions. The space groups which are applicable are those which have no screw axes or glide planes with translation in a non-polymer direction. For example, an ideal silicate chain polymer is completely described by space group no. 28 Pma2-C2v4, with the chain running in the a (x) direction and the translations in the b and c directions disabled.
3.2 Cartesian Symmetry Matrices.
This symmetry option is necessary for non-crystallographic point symmetry, that is symmetry groups containing n-fold axes with n equal to 5 or higher than 6. It can also be used for trigonal and hexagonal symmetry if you want to use Cartesian atomic coordinates. Some symmetry files are provided, namely for the two icosahedral groups and the pentagonal groups; in other cases the Cartesian matrices must be generated before running ATOMS, by using the program SYMGRP, which generates self-consistent point symmetry groups in any orientation.