Diamond Version 5 User Manual: Polyhedra

Creating Coordination Polyhedra

In this article:
- Semi-automatic vs. manual creation
- Selecting Atom Types
- Using Fixed or Generic Spheres
- Define polyhedron's constituent atoms from atom site environment and define polyhedron prototypes for atom sites.
- Take the neighbouring atoms as is without complementing the missing neighbouring atoms inside the sphere boundaries.
- Getting Polygons Greater Than Triangles

Previous article: Overview
Next article: Polyhedra with no central atom

Semi-automatic vs. manual creation

In Diamond, every coordination polyhedron is addressed by its central atom. If there is no atom in the parameter list that can serve as central atom, you may define a dummy atom as central atom. One atom can only be center of one polyhedron; it cannot be center of multiple polyhedra.

There are in principle two different modes to create polyhedra:

a) The semi-automatic creation, where Diamond searches for the coordinating atoms within a given enclosure sphere and creates these atoms, if necessary.

b) The manual creation, where you select the atoms that will become corners of the polyhedron. In that case, Diamond searches for a suitable central atom or creates a dummy atom, when there is no suitable atom in the parameter list.

Manual creation is only possible if at least three atoms have been selected. With three or more selected atoms, you will be prompted for the polyhedron building mode, where you have the choice to create N polyhedra with the N selected atoms as centers or to create one single polyhedron with the N selected atoms as corners.

Semi-automatic creation

There are several ways to create coordination polyhedra using the semi-automatic method:

1. The easiest way is to construct polyhedra around selected (central) atoms, using default settings. For that, select one or more atoms, and then either push the (red marked) button in the Picture toolbar or use the "hotkey" Shift+Ctrl+H.

2. If you must change the default settings, especially the size of the polyhedron sphere, you select one or more (central) atoms, then click with the right mouse button into one of the selected atoms, and choose the Polyhedra command from the Add sub-menu of the context menu, or choose the Coordination Polyhedra command from the Polyhedra sub-menu of the Build main menu.

3. The third way works without selected central atoms. (No atom must be selected in this case!) You select the central atoms indirectly from an atom group list. (If you add polyhedra to selected atoms, this list is not available.)

All three ways open the Add Polyhedra dialog unless you have used the button in the Picture toolbar mentioned above. For informations about the selection of atom types, the sphere type and size, etc. read the following sections "Selecting Atom Types" and "Using Fixed or Generic Spheres".

Manual creation

This polyhedron building mode is only available if at least three atoms have been selected. In this mode of operation you choose the atoms to become corners of the coordination polyhedron and choose a central atom either from a list or create or use a dummy atom as center, if there is no suitable atom in the parameter list available.

Choose the command Construct Polyhedron from the Polyhedra sub-menu of the Build main menu, which will open the Construct Polyhedron dialog, where you choose if and how bonds can be involved in the creation of polyhedron/polygon edges and where you can select an atom from the parameter list or a new dummy atom to become the central atom of the polyhedron, the epsilon value as well as the design for the new polyhedron.

This polyhedron building mode is described in the article "Polyhedron construction from atoms and bonds".

Selecting Atom Types

As stated above, there are several ways to open the Add Coordination Polyhedra dialog.

This dialog offers two lists ("tree views"), both containing all atom groups of the current structure and in second order all sites of a group each.

The first list, named Central atom groups/sites, is to choose the atoms in the structure picture to be taken as central atoms of coordination polyhedra. The second list, Ligand atoms, is used to select the atom groups and/or atom sites that will become ligand atoms of the polyhedron spheres.

Add Coordination Polyhedra dialog for a structure with atom types (atom groups) Na+1, P+5, and S-2. The atom groups P+5 and Na+1 have been selected as central atoms, the coordination polyhedra shall be made up of sulphur atoms.

If you open this dialog when no atom is selected in the structure picture, the option Atoms of groups or sites selected below is the only available option in Apply to. If at least one atom is selected, the option Selected atoms in structure picture is preset and the Central atom groups/sites list is invisible. Nevertheless you can switch to the first mentioned option in this case to override the current selection of atoms for central atom candidates.

Using Fixed or Generic Spheres

The sphere of the coordination polyhedra can either have fixed dimensions, given by a minimum and maximum distance value, or can be variable ("generic"). This kind of distinguishing can be compared with that for fixed spheres and coordination spheres.

You can choose between fixed and generic sphere in the Add Polyhedra dialog in the Type of sphere group:

The generation of coordination polyhedra works with completed as well as incomplete coordination spheres. That means missing ligand atoms will be supplemented if necessary. Generic spheres are used to create ligand atoms which are bonded to the central atom. The dimensions of these spheres are defined in the connectivity list and vary thus from atom group (atom type) pair to atom group pair. The polyhedra procedure does not generate ligand atoms that are selected in the list Ligand atoms but are not selected as bonded in the connectivity list. If fixed spheres are used, even such ligand atoms will be created that are not defined as bonded in the connectivity list.

Define polyhedron's constituent atoms from atom site environment

Atom site environments can be used to define a coordination polyhedron (besides fixed-sized and generic spheres, i.e. basing upon connectivity bonding spheres) in the "Add polyhedra" function.

To change the definition of atomic environments, use the command Atomic Environments... from the Build menu. (Read this article for more informations: Atomic Environments.)

While up to Diamond version 3, only the sphere types "fixed size" and "generic" were available, the Type of sphere group of settings was extended for Atomic environments in version 4, which is at top and default setting.

Another extension as compared with Diamond version 3 was the ability to choose atom sites individually (and not only atom groups) as candidates for central atoms or neighbouring atoms, rsp., to be considered in the polyhedron building. (This atom-site-individual access is also available in several other functions for structure picture building, such as "Fill (coordination) spheres" or "Connect atoms".)

The option to use the atomic environment -- as defined under Build -> Atomic Environments... -- is also available to a lot of other building functions: The filling of (coordination) spheres, the connection of atoms, the creation of molecules or completion of fragments, rsp.

Define prototypes for atom sites' coordination polyhedra
With the individual assignment of atomic environments, it is easier to define coordination polyhedra with complex environments (many neighbouring atoms whose coordination spheres cannot be satisfyingly described by mean bond lengths or ionic/atomic radii sums, that means by bonding spheres dependent from atom types rather than individual sites).

Take the neighbouring atoms as is

Additionally to the three above mentioned sphere types (fixed, generic, or atomic environments) it is possible to take over the coordination sphere (the bonded neighbouring atoms) of a (central) atom as is, i.e. without filling/completing the coordination sphere.

Unlike the other options "Fixed size", "Generic", and "Atomic environments", this option does not complement the missing neighbouring atoms inside the sphere boundaries but constructs a coordination polyhedron from the neighbouring atoms currently connected to the central atom each.

This requires the neighbouring atoms to be bonded with the central atom. That means all atoms currently connected via a strong bond with the central atom will be considered as contributing atoms, individually from the actual distance from the central atom, whether the distance is chemically reasonable or not.

So you can build the polyhedron with Build -> Polyhedra -> Add Coordination Polyhedra... and use the fourth option in the Type of sphere settings group, named As is (use already connected atoms only).

The most probable usage of this scenario is that you want to build a polyhedron, although one or more atoms officially belong to the atomic environment or the "generic sphere" (made up from atom group pairs' bonding spheres) - and would be added to the polyhedron during polyhedron creation. (And to use a fixed sphere size from Rmin to Rmax is not possible to match the desired atoms.) With other words: You insert polygons (the polyhedron faces) into the building of surrounding atoms that is currently present.

The picture above shows in the left part the result of a conventional creation of a coordination polyhedra (one of the three options "atomic environment", "generic", or "fixed-size sphere") that automatically creates the missing atom(s) (here: one Cl atom outside the unit cell) with the expected NaCl6 octahedron, whereas the option "as is" creates a pyramid from the existing five Cl neighbours only.

Getting Polygons Greater Than Triangles

When Diamond builds a polyhedron, it collects all ligand atoms within the defined fixed or generic sphere, and constructs triangular polygons.

As far as these triangles build obtuse angles of intersection, they are united to polygons by removing the common intersection lines. Diamond uses an epsilon value for this angle to decide if four or more points define a larger polygon or if two or more triangles must not be united. The angle can be edited in the input field Angle epsilon in the Add Polyhedra dialog or in the Build Polyhedron dialog. The default value is one (degrees). You may enlarge it if the coordination differs significantly from ideal relations.

If you are not successful in finding an appropriate epsilon value, you can remove unwanted edges later, i.e. expand triangles to higher polygons. See the article "Modification and duplication of polyhedra".

Small polyhedra or just polygons

If a central atom lies outside the polyhedron or the polyhedron is actually not a 3D body but for instance just a triangle (coordination number 3) and the central atom is outside the triangle, there will be auxiliary bonds symbolizing the connection between "polyhedron's" center and the neighbouring atoms.

Previous article: Overview
Next article: Polyhedra with no central atom