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Kernel density estimation of CSD distributions - an application to knowledge based molecular optimisation

Journal of Cheminformatics20146 (Suppl 1) :P10

  • Published:


  • Kernel Function
  • Kernel Density Estimation
  • Cambridge Structural Database
  • Kernel Density Estimator
  • Smooth Kernel

The Cambridge Structural Database ( CSD ) contains a large amount of molecular structure data ( bond length, bong angle and torsion angle data.) Much of this data has previously been extracted in histogram form and provided in the Mogul program. Histograms however have several disadvantages e.g. they are not smooth, they depend on bin widths and bin end points.

Kernel density estimators do not bin data and have no end points but centre a kernel function at each data point and smooth kernel functions will generate smooth density estimates [1]. A difficulty of the approach though is how wide to make the kernel functions.

In this work kernel density estimation is used to generate probability density functions ( pdfs ) for bond length, bond angle and torsion angle histograms derived from the CSD. Gaussian kernels are used for bond length and bond angle data and a von Mises kernel is used for the torsion angle data [2]. The resulting pdfs are smooth and are suitable for application to molecular geometry optimisation.

Authors’ Affiliations

CCDC, 12 Union Road, Cambridge, CB2 1EZ, UK
Taylor Cheminformatics Software, 54 Sherfield Avenue, Rickmansworth, Herts., WD3 1NL, UK


  1. Silverman BW: Density Estimation for Statistics and Data Analysis. Chapman & Hall/CRC Monographs on Statistics & Applied Probability. 1986, Chapman and Hall/CRCGoogle Scholar
  2. Evans M, Hastings NAJ & Peacock: Statistical distributions. 2000, WileyGoogle Scholar


© McCabe et al; licensee Chemistry Central Ltd. 2014

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver ( applies to the data made available in this article, unless otherwise stated.