Diamond Version 5 User Manual: Building up structural parts

About Atoms, Atom Groups, Bonds, and Bond Groups

This article in brief:
Definitions: Created atoms, atom codes, atom groups, bond groups, created bonds, connectivity.
About Mixed Sites
About Atom Groups
Assigning a New Atom Group at Runtime
About Atom Codes
About Bond Groups
About Created Atoms
About Created Bonds
Tables and Atom List

Previous article: Using Exploration view with an individidually designed structure picture
Next article: Filter

In the usual case, where the compound is a crystal structure with translational symmetry, each atom of the structure picture (e.g. the molecule or the contents of the unit cell) bases upon an atom in the parameter list. The atom in the picture, here called the "created atom", is constructured by applying suitable symmetry operations and (integer) cell translations. Both index of the atom in the parameter list and symmetry operations are coded in the atom code.

Additionally, the atoms of the parameter list are grouped together in a list of so-called "atom groups". By default, atom groups differ by ordinal number and oxidation number. Diamond groups all atoms having the same ordinal number and oxidation number into one atom group. These atom groups have a lot of properties (radii, design etc.) which serve as basis for the corresponding properties of the created atoms.

Definitions

The following definitions about the different kinds of atoms and bonds used in Diamond refer to the usual case that the compound is a crystal structure with translational symmetry. That means the compound is built up by a three-dimensional lattice with an infinitesimal number of equal copies of the unit cell.

Created atoms

In Diamond, the atoms in a structure picture are called "created atoms", since Diamond does not automatically create atoms from the atoms in the parameter list. (The following articles will tell you a lot of functions to create atoms, such as filling a cell range or creating molecules. Besides this, there are functions that let Diamond create a proposed picture for you.) Each of these created atoms has been produced from an atom of the parameter list by applying suitable symmetry operations and - as far as necessary - cell translations.

Atom codes

The atom code is the identifier for both the index of the atom in the parameter list and the symmetry operations and cell translations to be applied to produce the "created atom". See Atom Codes for a detailed definition and examples.

Atom groups

The list of atom groups is a collection of atoms from the parameter list, which differ only in ordinal number and oxidation number. Mixed sites are treated in a rather complicated way. For details and examples, see Mixed Sites and Atom Groups. Atom groups are used to group atoms with common chemical properties together and to define the basic design for the created atoms.

Bond groups

Bond groups are created from the atom group list. Each bond group represents one atom group combination. That means, for N atom groups, we get N * (N + 1) / 2 bond groups. Like atom groups, bond groups define the basic design for "created bonds".

Created bonds

Whereas each created atom can be reduced to a definite atom of the parameter list, bonds cannot. (Diamond supports connection parameter lists but these are optional.) A bond is created by one of the bond creating functions of Diamond, but only if the atom group combination (the bond group) is (a) enabled for bonding and (b) if the interatomic distance is within the bonding sphere.

Connectivity

The connectivity list is derived from the bond group list. Thus it contains all N(N+1)/2 combinations of N atom groups of a structure (picture). For each atom group pair a bonding sphere is defined and a flag if this bonding sphere is active or not, i.e. whether bonds are allowed for that atom group pair or not. Diamond offers a sophisticated method to edit and check the connectivity. For details, see Connectivity.

Mixed Sites

Whenever atoms are created from atoms of the parameter list, Diamond does not access the parameter list directly, but makes use of a separate list, which contains all sites of the unit cell. If the structure does not have any mixed sites, that means two or more atoms do not share the same position, the list of sites has as many entries as the sum of the multiplicities of all atoms of the parameter list with valid coordinates.

This has the advantage that Diamond needs not apply symmetry operations and Bravais translations for each atom to be created but only the integer cell translations as far as necessary.

Another important reason for Diamond to work with the site list is to prevent the creation of multiple atoms on one and the same position. This would happen, if all symmetry operations would be applied to an atom on a special site.

If the structure has mixed sites, Diamond processes only one representative for all atoms sharing the same site. The representative of a site is the atom with the highest site occupation factor. If some or all atoms on the site have the same site occupation factor, the first one of these atoms in the parameter list will be taken. The non-representative atoms on this site will become "buddies" of the representative. These buddies are often trace elements.

The site list is invisible for you, but you have several functions to get informations about the number of sites as well as mixed sites:

(1) The total number of sites (the sum of multiplicities) is part of the Pearson symbolref_pearsonsymbol in the data sheet and additionally given on the Contents page of the Properties view, which you can open with the Properties command in the View menu.

(2) The composition of mixed sites can be visualized using alternative color differentiations, which you will find in the Color differentiation dialog, which is opened with the Color differentiation command in the Display menu.

Atom Groups

The list of atom groups is a collection of atoms from the parameter list, which differ only in ordinal number and oxidation number. The usage of a list of atom groups separate from the list of atomic parameters has two main reasons:

(1) In most crystal structures, especially in "organic" molecular structures, atoms of the same species disperse on different sites. These atoms usually have the same or similar chemical properties and often similar coordination. Therefore, Diamond has many functions for building up or designing structural parts, which access the list of atom groups instead of the list of atomic parameters.

(2) Each atom type defines the basic design for all created atoms basing upon an atom of the parameter list, that belongs to this atom group. Example: The atomic parameter list has three atoms of the species C (carbon) ("C 1", "C 2", and "C 3"). If the color for the atom group "C" is grey, all atoms which have been created from one of the atoms "C 1", "C 2", and "C 3" have also the color grey. (Colors of created atoms may be changed individually thereafter.)

Furthermore, an effective radius is defined for each atom group. This effective radius is the effective ionic or atomic radius used to define the bonding sphere, if no mean bond length value is available for a given atom group combination. See the article about connectivity to get more informations how bonding spheres are calculated.

Different atoms sharing the same site (mixed sites) are grouped together in separate atom types. If e.g. a structure has both Si and Al on single sites and additionally one site with 50 percent Si and 50 percent Al, this will result in at least three atom types: 1. Si; 2. Al; 3. SiAl. If there are more mixed sites with Si and Al, this will result in the same atom type "SiAl", even if the composition varies (e.g. 25 percent Si and 75 percent Al instead of 50 : 50).

Ordinal number, oxidation number - as far as defined -, and eventually mixed sites are the criteria for Diamond to differentiate the atoms in the parameter list, when the list of atom groups is initialized. This happens whenever a structure has been imported or the atomic parameter list has been edited. Beyond that, you can change the default assignment of atom groups to atoms of the parameter list. The article "Assigning a New Atom Group at Runtime" explains how this is done.

Assigning a New Atom Group at Runtime

Whenever a structure has been imported or the atomic parameter list has been edited, Diamond initializes the atom group list automatically. All atoms with the same ordinal number (or ordinal numbers if it is a mixed site) and - as far as defined - the same oxidation number, are grouped together to one atom group.

If one ore more atoms belonging to the same atom group, but have different chemical properties or different coordinations, you can assign it or them a new atom group, using the following steps:

1. From the Build menu, choose the Atom Groups command.

2. In the Atom Groups dialog, select the atom group, where the new atom group is to be derived from.

3. Push the New button. (This inserts a copy of the original atom group into the atom group list; the symbol of the copy has an "A" attached to the original symbol; you may edit the symbol if needed.)

4. In the atom site list, select the atom(s), you want the new atom group to be assigned to, and then push the Assign button.

5. Close the Atom Groups dialog with "OK", when you have finished editing atom groups and atom group assignments.

The new atom group will thereafter appear in the atom group lists used by several building and designing functions. So you can define coordination spheres for the new atom group, which are different from the "original" atom group, different designs, different coordination polyhedra etc.

Atom Codes

In the usual case, that means the crystal structure has translational symmetry, all atoms of the structure picture, here called the "created atoms", base upon atoms of the parameter list. A special code is stored with each created atom, which encodes the symmetry operations, Bravais translations and integer cell translations, which have been applied to produce this atom from the corresponding "asymmetric" atom in the parameter list.

The atom code consists of:

(1) the sequence number of the atom in the parameter list;

(2) the sequence number of the symmetry operation;

(3) the sequence number of the Bravais translation;

(4) three integer cell translations along the base vectors a, b, c of the unit cell.

The sequence number of the atom in the parameter list has a maximum value of 2^31 - 1. The sequence number of the symmetry operation has a maximum value of 48, that for the Bravais translation a maximum value of 4. Each integer cell translation has an internal range capacity from ‑128 through +127.

The sequential number of the symmetry operation refers to the sequential order of the symmetry matrices for the current space group, which are defined in the Diamond space group file. See the article "Editing of Structural Data: Symmetry and cell parameters" how to get informations about the current space group. The symmetry operation with the number 1 is "x,y,z" in any case.

To get informations about the Bravais translations, choose the Filter dialog from the Edit menu. In the Filter dialog, view the list Bravais translations. The Bravais translation with the number 1 is "+(0,0,0)" in any case.

On input or output, the atom code has the form

            AXYZSSB

with:

Since only one digit is reserved for each integer cell translation, "only" a range of -5 ("0") through +4 ("9") can be used for the integer cell translations on input. On output, an asterisk (*) marks an overflow.

Most of the building operations of Diamond do not face you with atom codes. But if you want to define atoms by code, see the article "Generating atoms directly" how to do this.

Bond Groups

A bond group is defined by a definite pair of atom groups. The list of bond groups is directly created from the list of atom groups. For N atom groups, we get N * (N + 1) / 2 bond groups.

The usage of bond groups has two main reasons:

(1) Each bond group defines the basic design for all bonds of the structure picture, here called "created bonds". Example: If the color for the bond group "P+5 - O-2" is yellow, all bonds between atoms belonging to atom groups "P+5" and "O-2" have the same color yellow. (Colors of created bonds may be changed individually thereafter.)

(2) Each bond group has a definition, whether bonding is enabled for this atom group combination, and the dimension of the bonding sphere.

Since the discussion of bonding spheres is essential for the building functions of Diamond that create bonds, especially the generation of molecules, this is handled separately with the connectivity list.

Created Atoms

In Diamond, the atoms in a structure picture are called "created atoms". Each of these created atoms has been produced from an atom of the parameter list by applying suitable symmetry operations and - as far as necessary - cell translations.

In principal, Diamond offers two adverse strategies how to generate atoms:

1. Selecting one, more, or all atoms from the parameter list, and applying symmetry operations and cell translations as far as needed.

2. Defining a range of the lattice, where atoms are to be generated and molecules are to be built, rsp.

Created Bonds

A bond is created by one of the bond creating functions of Diamond, but only if the atom group combination (the bond group) is (a) enabled for bonding and (b) if the interatomic distance is within the bonding sphere. Bonds will be created automatically when

(1) the surrounding atoms in the coordination spheres of selected (central) atoms are generated; (There is a similar function that fills spheres with fixed dimensions and that does not connect the surrounding atoms with the central atom.)

(2) molecules are built or molecular fragments are completed.

Furthermore, bonds can be generated at any time after atoms have been generated, e.g. after the generation of all atoms of the unit cell (a procedure which does not automatically create bonds).
Bonds between two atoms, which do not belong to an atom group combination (that means to a bond group) that is enabled to be connected, or which are "too short" or "too long", can be created manually.
For details, see the article "Generating bonds directly".

Tables and Atom List

The Diamond user interface offers tables in the data pane where the atomic parameters as well as the atom groups, created atoms, bond groups, and created bonds are listed, for example to select atoms in the structure picture in order to edit their display settings or to use them as starting points for building operations. These can be viewed with corresponding commands in the Table sub-menu of the View menu. See the article "Tables of objects like atoms, bonds, molecules etc." for details.

The "Atom list" can be used to access the atom groups, their associated atom sites and the created atoms currently present in the structure picture in a hierarchical view. See the article "Atom list: Hierarchical list of atom groups, atom sites, and created atoms of a structure picture" for details.

Previous article: Using Exploration view with an individidually designed structure picture
Next article: Filter