The Hausdorff chirality measure and a proposed Hausdorff structure measure

Authors: Yewande, Emmanuel¹; Neal, Maureen¹; Low, Robert²

Source: Molecular Physics, Volume 107, Number 3, October 2009 , pp. 281-291(11)

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Abstract:

The Hausdorff chirality measure quantifies the chirality of a geometric representation of an object by measuring the degree of coincidence of the object with its mirror image. It can also allow comparison between a chiral dopant and host molecules which may illuminate mechanisms for chirality transfer. It has been applied to real molecules very infrequently in comparison to application of chiral indices as it is complex and time consuming to calculate. In this paper we introduce and verify a simulated annealing algorithm for the Hausdorff chirality measure that has proven rapid, robust and relatively simple to apply. We verify the method, finding good agreement between its results and those of Mislow and co-workers. We introduce a Hausdorff structure measure that does not permit overlap and allows a structure to be built one molecule at a time. We present results for a simple model and real biphenyl molecules and discuss promising building blocks of crystal and incommensurate structures formed in relation to experimental results.

Keywords: Hausdorff; chirality; structure

Document Type: Research article

DOI: http://dx.doi.org/10.1080/00268970902835611

Affiliations: 1: Department of Computing & Mathematics, Manchester Metropolitan University, Manchester, M1 5GD, UK 2: Department of Mathematical Sciences, Coventry University, Coventry, UK

Publication date: 2009-10-01

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