Kernel density estimation applied to bond length, bond angle, and torsion angle distributions.

ABSTRACT

We describe the method of kernel density estimation (KDE) and apply it to molecular structure data. KDE is a quite general nonparametric statistical method suitable even for multimodal data. The method generates smooth probability density function (PDF) representations and finds application in diverse fields such as signal processing and econometrics. KDE appears to have been under-utilized as a method in molecular geometry analysis, chemo-informatics, and molecular structure optimization. The resulting probability densities have advantages over histograms and, importantly, are also suitable for gradient-based optimization. To illustrate KDE, we describe its application to chemical bond length, bond valence angle, and torsion angle distributions and show the ability of the method to model arbitrary torsion angle distributions.