Symmetry Definition Format

Standard Symmetry File Format

The format of a symmetry definition has three parts:

• Name: Line 1 has the name, the structure used to recognize the symmetry and the type of symmetry
• Correspondence: The next set of lines mark a correspondence between atoms in the structure and the type of symmetry that atom can take
• Symmetry: The last line gives the numeric symmetry number

A typical input block looks like this:

ExternalSymmetry-C(B1)(B2)(B2)(B2)-L  CarbonAtom ExternalSymmetry

0: a2 : L

1: a3 a4 a5 : N

Symmetry: 3

Name Line:

The first line

ExternalSymmetry-C(B1)(B2)(B2)(B2)-L  CarbonAtom ExternalSymmetry

defines a Optical isomer symmetry with the name of ExternalSymmetry-C(B1)(B2)(B2)(B2)-L. The structure associated with the symmetry is CarbonAtom, which is a structure from CMLStructures:

<molecule id="CarbonAtom" xmlns="http://www.xml-cml.org/schema">

  <atomArray>

    <atom id="a1" elementType="C" x2="16.88" y2="41.187200000000004" formalCharge="0" hydrogenCount="0"/>

    <atom id="a2" title="*" elementType="Du" x2="16.5002" y2="42.622" formalCharge="0" hydrogenCount="3"/>

    <atom id="a3" title="*" elementType="Du" x2="18.3148" y2="41.567" formalCharge="0" hydrogenCount="3"/>

    <atom id="a4" title="*" elementType="Du" x2="16.88" y2="39.668" formalCharge="0" hydrogenCount="3"/>

    <atom id="a5" title="*" elementType="Du" x2="15.4452" y2="40.8074" formalCharge="0" hydrogenCount="3"/>

  </atomArray>

  <bondArray>

    <bond id="b1" atomRefs2="a1 a2" order="S"/>

    <bond id="b2" atomRefs2="a1 a3" order="S"/>

    <bond id="b3" atomRefs2="a1 a4" order="S"/>

    <bond id="b4" atomRefs2="a1 a5" order="S"/>

  </bondArray>

</molecule>

This basically defines a general carbon bonded with 4 R groups (The R groups have the name "Du" in the structure).

The definition of the symmetry is dependent on the type of groups these R groups represent. In this case the R groups are atoms a2, a3, a4 and a5.

Correspondences:

The specification of characteristics of the R groups is done in the next block. The form of each line is an index, the set of atom labels from the structure and the characterization of the labels. In the example:

0: a2 : L

1: a3 a4 a5 : N

Each line defines a correspondence to the CMLStructure. In the example, there are two lines. If the atom labels on one line means they are exactly the same group. Thus a3, a4 and a5 have to be the same group. For those listed on another line means they should be different. For example, a3, a4 and a5 could all be methyl groups. The R group with the label a2 has to be different from a3, a4 and a5. In addition, the L specification means that a2 must be a linear structure. Further specification are explained below.

Symmetry:

The last line of the definition defines the symmetry associated with this definition:

Symmetry: 2

This says that when a structure is found that satisfies the structure definition's criteria, namely that GeneralPeroxyGroup matches somewhere in the molecule and the R groups satisfy the desired criteria, then a symmetry of 2 can be applied.

File format:

This is a summary of the three blocks of the file format.

First Line: Name, Structure and Symmetry Type

• Symmetry Name:The name of the symmetry table being specified. This corresponds to the SymmetryName in the SymmetryPairAssignments table
• Structure: The name of the structure to be matched. This structure must exist within CMLElements.
• Type:: The type of symmetry element being specified, for example ExternalSymmetry, InternalSymmetry or OpticalSymmetry.

Group Specifications (Multiple lines)

The next set of lines specifies the groups of unspecified atoms within the named structure that have to be the same and have the specified symmetry constraint. There are three parts to this line and they are delimited by semi-colons (:):

• Group Index: This is a number specifying the group
• List of labels: This is a list of labels (unspecified atoms) within the named structure (from line 1) that have to be the same. This list is space or tab delimited.
• Symmetry specification: This is an extra specification of the structural groups corresponding to the unspecified atoms. Not only do the groups starting from the unspecified atoms have to be the same, but they must also match the symmetry condition. There are basically three types of symmetry conditions, X, which means that the symmetry of the substructures doesn't matter, L, which means that the isolated structure has to be linear and the third type gives a symmetry number (typically 2 or 3).

Symmetry Specification

The end of the group specification is the keyword *Symmetry* (at the beginning of the line) followed by a colon and the symmetry number corresponding to the specification.

Database Modifications

Reading in this format modifies two tables in the database:

• SymmetryDefinition: This holds the basic information about the defined symmetry, the name, structure, type and symmetry number.
• SymmetryPairAssignments: This holds the atom label correspondences. There is one entry in this table for each line of the Correspondences.

Symmetries

Three type of symmetries are defined with this format:

• Internal Symmetry
• External Symmetry
• Optical Symmetry

Correspondences

The format of the correspondences are as follows (separated with ": ":

• Index count (starting with zero)
• The set of R group labels within the given structure
• The characterization of the given R group

The R group specification of the structural groups corresponding to the unspecified atoms. Not only do the groups starting from the unspecified atoms have to be the same, but they must also match the symmetry condition. There are basically three types of symmetry conditions:

• X or N: The R group can be any structure, the symmetry of the substructures doesn't matter,
• L: The R group has to be a linear structure
• Number: The R group itself has to have this symmetry number (typically 2 or 3).

Standard Symmetry Definitions

The following is the set of the standard symmetry definition in JThermodynamics: