Note that when we discuss rigid bodies, we have two independent coordinate systems. One for the rigid body, which does not have any translational symmetry and where the coordinate system is Cartesian; the axes are orthogonal and the coordinate units are in Å. The crystal system, where translational symmetry is present, uses fractional coordinates and the angles between axes are dictated by the crystal system as we have seen throughout the book. There are two steps in using rigid bodies in GSAS-II. In the first step, the body is defined. For this the source information may be in Cartesian or fractional coordinates, but the rigid body information will be stored as Cartesian. In the second step, the atoms in the phase are related to the atoms in the rigid body. I usually refer to that process as inserting the rigid body into the phase. In that second step, we will determine how the rigid body coordinate system is transformed to produce atom positions in fractional coordinates via position and orientation parameters for the rigid body. Also note that if a rigid body appears in multiple places in a phase (or even several phases in a project), it only needs to be defined once and can be inserted as many times as is needed. Each insertion will have separate position and orientation parameters.
In many cases, it does not matter how the Cartesian axes for the rigid body are oriented with respect to the atoms. However, as will be discussed in detail in §26.7, if the rigid body will lie on a symmetry axis, plane or point in the unit cell, that axis or plane must be aligned with the Cartesian axes, so that that it can be oriented with respect to the crystal axes. The best location for the origin of the rigid body is at the center of mass for a body, particularly if TLS refinement will be used (discussed in §26.9), but if the rigid body will be located on a special position point (most commonly this will be a \(\overline {1}\) operator), the origin of the rigid body must preserve that symmetry. Even when a rigid body will be placed in a location of the unit cell without any special symmetry, it is still a good idea to define the rigid body axes and origin in a way that represents any symmetry of the fragment. For example, if many of the atoms in the rigid body lie on a plane, I will try to align the axes so that those atoms have one coordinate as approximately zero; usually, I will put those atoms into the x-y plane.
If the coordinates are imported from a file, the axes and origin can be determined from computations in the window created in the second step after use of the “Extract from file” menu command (seen in Fig. 26.4). There are three actions that can be performed here:
My experience is that these options work best if used in the sequence listed above, meaning that the top button in the set is used first, then the middle and then the lower button in that order. Note that the atom selection must be repeated yet again, after use of these buttons, to select the atoms in this window that will be included in the vector or residue rigid body.
For vector rigid bodies, when the coordinates are generated with paper, pencil and calculator, the axes and origin choice are part of the design. If the coordinates are imported from a file, the axes and origin can be determined from settings the window generated by the “Extract from file” menu command, as described above in §26.3.1.0.
If the “Import XYZ” menu command is used to read the coordinates for a residue rigid body, the origin and axes that were defined by the program that created those coordinates will be retained, when the coordinates are read. Likewise, the window created in the second step after use of the “Extract from file” menu command (seen in Fig. 26.4) can also be used to set the axes and origin for a residue body as part of the process of converting the coordinates to Cartesian space.
However, as was presented in the discussion of the residue rigid body data window (seen in Fig. 26.5), the axes orientation and origin values can optionally be overridden by controls there. The orientation of the axes and the origin can be changed here by specifying three atoms for the “Orientation reference” settings, which I will label as A, B and C. The first atom (A) will be set as the origin and the vector from the A atom to the second atom (B) will define the x-axis. The third atom (C) will define the y-axis so that the A, B and C atoms all lie in the x-y plane.
While you can create a rigid body from fractional coordinates found in a crystal structure, for example from a database, be careful doing this. An individual crystal structure may not have a very accurate representation of the expected interatomic distances and angles and any errors in your rigid body input will be replicated in your results. For this reason, with organic molecular fragments, it is often a good idea to use a molecular forcefield program (unless you have access/ability to use higher-level theory) to obtain an optimized model for the molecule or molecular fragment you wish to use for your rigid body. There are many commercial molecular modeling programs, but if you need something free, the open source Avogadro program is a good choice (https://sourceforge.net/projects/avogadro). This is available for Windows, Linux or MacOS, or as source code. Note that the XYZ files produced by Avogadro can be read by GSAS-II. A free account on the MolDraw website (https://www.moldraw.com) may also work for you. The MOGUL program from the Cambridge Crystallographic Database can be used to find the average geometry of a molecular fragment across many crystal structures.
It should be noted that the molecular modeling, as well as first-principles codes, will compute the “in vacuum” structures for the input atoms, corresponding to an isolated object. However, in a crystal structure, molecules and ions will often change configuration to minimize the energetics of packing interactions. In almost all cases, the changes to these moieties will be due to torsion angle changes. It is well worthwhile to review crystallographic results with the moiety to be used for a rigid body to ensure that the common structural configurations can be achieved once torsional modes are included.