Rigid-body least-squares refinement

Figure 4. The molecular framework of atactic poly(vinyl alcohol) on the b-projection used in the rigid-body least -squares refinements. (Reproduced with permission from reference 7. Copyright 1997, Wiley-InterScience)...

Scheringer, C. Least-squares refinement with the minimum number of parameters for structures containing rigid-body groups of atoms. Acta Cryst. 16, 546-550 (1963). 

The chitobiose unit has been treated as a rigid body, and by using the full-matrix, least-squares, rigid-body, refinement procedure, the structure was refined to an R factor of 40.7%. Visually estimated intensities were used. The structure was found to be free from short contacts, and to be stabilized by an intrachain OH-3—0-5 hydrogen-bond and one interchain N-H—O hydrogen-bond. 

Next, the side chains of P2 were replaced with the side chains of ALBP at corresponding positions in the amino-acid sequence to produce the first ALBP model. The position and orientation of this model were refined by least squares, treating the model as a rigid body. Subsequent refinement was by simulated annealing. At first, all temperature factors were constrained at 15.0 A2. After the first round of simulated annealing, temperature factors were allowed to refine for atoms in groups, one value of B for all backbone atoms within a residue and another for side-chain atoms in the residue. 

Once least-squares methods came into general use it became standard practice to refine not only atomic positional parameters but also the anisotropic thermal parameters or displacement parameters (ADPs), as they are now called [22]. These quantities are calculated routinely for thousands of crystal structures each year, but they do not always get the attention they merit. It is true that much of the ADP information is of poor quality, but it is also true that ADPs from reasonably careful routine analyses based on modem point-by-point or area diffractometer measurements can yield physically significant information about atomic motions in solids. We may tend to think of crystal structures as static, but in reality the molecules undergo translational and rotational vibrations about their equilibrium positions and orientations, as well as internal motions. Cruickshank taught us in 1956 how analysis of ADPs can yield information about the molecular rigid-body motion [23], and many improvements and modifications have been introduced since then. In particular, various computer programs are available to estimate the amplitudes of simple postulated types of internal molecular motion e.g., torsion-... 

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