9401774 Mislow Princeton A number of basic questions in stereochemistry will be studied by the use of non-numerical as well as computational methods. Geometric chirality measures will be correlated with similarity measures whose variable parameters are appropriate physical properties. An attempt will be made to prove the important conjecture that a molecular model and its enantiomorph form an achiral union under conditions of maximum overlap. A previously developed algorithm will be extended in order to unite topologically achiral molecular knots and links on the basis of graph commonality. An approach previously used to partition knots into heterochiral classes will be applied to the more complex problem of links and graphs. The hierarchical rankings of chiral molecules will be critically reexamined in light of a novel classification scheme that is capable of accommodating all such molecular structures. This grant from the Organic Dynamics Program supports the continuing work of Professor Kurt Mislow at Princeton University. This research addresses the classification and description of molecules and arrays of molecules in three-dimensional space. The arrays of molecules includes links of molecules similar to links in a chain and knots such as a figure-eight knot. Another type of molecule that will be classified are chiral molecules. These molecules are related as one's right hand to the left hand. The unique feature of this work is that the classification will be made in a quantitative manner so that there can be a hierarchical ranking of the "handedness" or chirality of a molecule. The work will then allow for a quantitative description of the three-dimensional nature of a molecule or array of molecules.
