Chiral volume

Okamoto, Y. Yashima, E. and Yamamoto, C. (2003) Optically active polymers with chiral recognition ability, in Green, M.M., Nolte, R.J.M., and Meijer, E.W. (eds.), Materials Chirality Volume 24 of Topics in Stereochemistry, John Wiley Sons Inc., New Jersey, pp. 157-208. 

Figure 14 The chiral volume defined as (vi-V4) [(V2-V4) x (V3-V4)] must be positive for this arrangement of atoms. The volume of the tetrahedron defined by the four atoms (1-4) is one-sixth the value of the chiral volume.

Chiral constraints are also used to maintain planarity by constraining four atoms to have zero volume. Because the chiral volume is more sensitive than the distance error term to minor variations from planarity, it is used to constrain planar groups more accurately. 

During the optimisation of the structure against the distance constraints it is usual to incorporate chiral consiraints. These are used to ensure that the final conformation is the desired stereoisomer. Chiral constraints are necessary because the interatomic distances in two enantiomeric conformations are identical and as a consequence the wrong isomer may quite legitimately be generated. Chiral constraints are usually incorporated into the error function as a chiral volume, calculated as a scalar triple product. For example, to maintain the correct stereochemistry about the tetrahedral atom number 4 in Figure 9,16, the following scalar triple product must be positive ... 

The other stereoisomer corresponds to a negative chiral volume. Chiral constraints are included in the penalty function by adding terms of the following form ... 

A special notice is given to the chiral and prochiral groups in molecules. Mathematically, chirality can be endowed with a potential by defining the so called chiral volume Vabcd that is the spade product defined as ... 

Actually, FLAT and CHIV both use the same algorithm. C HIV restrains the chiral volume of only one atom to any given value and FLAT restrains the (chiral) volume of a number of tetiahedia involving the atcms in questi[Pg.17]

The CHIV command is a restraint on the chiral volume of an atom. SHELXL defines the chiral volume as the volume of the tetrahedron formed by the three bonds to an atom, which must be bonded to three and only three non-hydrogen atoms in the... 

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 ). 

As their name suggests, free variables can be used to refine a multitude of different parameters and facilitate the formulation of constraints and restraints. The first free variable is always the overall scale factor (osf), which is used to bring the reflections in the dataset to an absolute scale. The example in Section 4.4.3 shows the effects of incorrect scaling on the refinement. Additional free variables can be linked to the site occupancy factors (sof) of groups of disordered atoms (for details see Chapter 5), but can also be related to other atomic parameters (x, y, z, sof, U, etc.) and even interatomic distances, chiral volumes, and other parameters. 

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