Planarity restraints

Generally, twinned crystals tend to have a poor effective data to parameter ratio, so they often require restraints in order to obtain a satisfactory refinement (Watkin, 1994). The following restraints can be useful distance restraints for chemically equivalent 1,2- and 1,3-distances, planarity restraints for groups such as phenyl rings, rigid bond ADP restraints (Hirshfeld, 1976 Rollett, 1970 Traeblood and Dunitz, 1983) and similar ADP restraints (Sheldrick, 1997b). Even when restraints are employed, the distribution of the displacement parameters (ORTEPplot) and residual features in a difference electron density map can be less satisfactory than for a normal structure determination. 

It was necessary to introduce some restraints there are nine chemically equivalent phenyl rings, so all chemically equivalent 1,2- and 1,3-distances in the nine rings are restrained to be the same. For every phenyl ring a planarity restraint is employed. For the anisotropic displacement parameters of the carbon atoms it was necessary to use the rigid bond and similarity restraints. There is also one disordered ethanol molecule in the cell distance and ADP restraints are employed to refine it. 

Scuseria and Schaefer [202a] followed up some earlier work by attempting to determine whether the open trimer of HF represents a true minimum in the potential energy surface. Within the context of their double-C basis set, it was found that the cis open trimer is indeed a minimum (Hessian matrix has all positive eigenvalues), whereas the trans structure is a transition state. However, the situation is decidedly different when polarization functions are added to the basis set wherein the trans geometry becomes a transition state and the cis type does not correspond to a stationary point of any order. Nor does relaxing the fully planar restraint lead to a cis stationary point. Vibrational frequencies and intensities were reported for the stationary points. 

A molecular dynamics force field is a convenient compilation of these data (see Chapter 2). The data may be used in a much simplified fonn (e.g., in the case of metric matrix distance geometry, all data are converted into lower and upper bounds on interatomic distances, which all have the same weight). Similar to the use of energy parameters in X-ray crystallography, the parameters need not reflect the dynamic behavior of the molecule. The force constants are chosen to avoid distortions of the molecule when experimental restraints are applied. Thus, the force constants on bond angle and planarity are a factor of 10-100 higher than in standard molecular dynamics force fields. Likewise, a detailed description of electrostatic and van der Waals interactions is not necessary and may not even be beneficial in calculating NMR strucmres. 

Another algorithm attributed to Crippen, linearized embedding, does actually involve the creation of a trial metric matrix, but is otherwise very different from the standard embed algorithm.29 Its main virtue is the incorporation of covalent restraints, chirality, and ring planarity at a more fundamental level than the original embed algorithm. Unfortunately, there does not yet seem to be much experience with the method. 

These restrictions severely limit the spectrum of configurational patterns available to a polymer of proline and, coupled with the fact that two distinct structures are found in solution, indicated that these restraints play an important stabilizing role. However, it must not be assumed, given the planarity of the peptide grouping, that steric restrictions alone are sufficient for stabilization. Solvation phenomena appear to play a key role, as will be demonstrated below. 

The default target value of the chiral volume V is 0 (restraining an atom s environment to be planar), and the default value of the standard uncertainty s is 0.1 A. This restraint is especially useful for the refinement of biological macromolecules (the chiral volume of the alpha carbon atom in an amino acid residue is about 2.5 A ). 

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