The distribution of distances from atoms of a particular element E to a probe atom X (oxygen in most cases), both bonded and intermolecular non-bonded contacts, has been analyzed. In general, the distribution is characterized by a maximum at short EX distances corresponding to chemical bonds, followed by a range of unpopulated distances the van der Waals gap and a second maximum at longer distances the van der Waals peak superimposed on a random distribution function that roughly follows a d3 dependence. The analysis of more than five million interatomic"non-bonded" distances has led to the proposal of a consistent set of van der Waals radii for most naturally occurring elements, and its applicability to other element pairs has been tested for a set of more than three million data, all of them compared to over one million bond distances.