More specifically, Burden suggested putting the atomic numbers on the diagonal of the matrix. In suggesting that a set of compounds could be ordered by eigenvalue he was actually proposing a 1- dimensional chemistry space. Registry File of approximately 12 million structures. Using a test database of 60,000 compounds, they were delighted to find that Burden's suggestion compared surprisingly well with the results of an accepted similarity searching procedure. Second, we are interested in diversity with respect to the way in which compounds might interact with a bioreceptor.
Atomic number has almost no bearing on the strength of intermolecular interactions.
Fourth, we demonstrated that both the lowest and highest eigenvalues of Burden-like matrices should reflect aspects of the molecular structure. Since both the highest and lowest eigenvalues should be relevant and since they are relatively uncorrelated, this would result in a 6-dimensional BCUT space. The choice of exactly which six BCUT values are best for a given population can be made using a chi-squared approach based on the principle that the best choice will be that which results in the most uniform distribution of compounds in chemistry space. However, it should be emphasized that BCUT values based solely on 2D connection tables have proven quite satisfactory for diversity purposes. Note that the chi-squared approach yields the set of BCUT values best for a particular population of compounds.