Size-intensive descriptors.

Non-linear effects in multi-linear structure-property (QSPR) models are sometimes included by using descriptors transformed by mathematical functions such as the square root or logarithm. Less commonly, products of two descriptors are used to account for cross dependencies. As described here, simple division of descriptors by chemical sample size (e.g. molecular weight, length, area or volume) creates size-intensive descriptors (alternatively, intrinsic descriptors) that are independent of the size of the chemical sample described, weakly correlated with the original descriptor, and important contributors to the best QSPR models. In our automated QSPRs, size-intensive descriptors in competition with their extensive descriptors are frequently selected as the best descriptors in the models with the highest r (2). Examples of QSPR models that use size-intensive descriptors are given, the lack of correlation of descriptors with their size-intensive version is demonstrated, and their physical significance is discussed.