Molecular descriptors were identified by Shannon entropy analysis that correctly distinguished, in binary QSAR calculations, between naturally occurring molecules and synthetic compounds. The Shannon entropy concept was first used in digital communication theory and has only very recently been applied to descriptor analysis. Binary QSAR methodology was originally developed to correlate structural features and properties of compounds with a binary formulation of biological activity (i.e., active or inactive) and has here been adapted to correlate molecular features with chemical source (i.e., natural or synthetic). We have identified a number of molecular descriptors with significantly different Shannon entropy and/or "entropic separation" in natural and synthetic compound databases. Different combinations of such descriptors and variably distributed structural keys were applied to learning sets consisting of natural and synthetic molecules and used to derive predictive binary QSAR models. These models were then applied to predict the source of compounds in different test sets consisting of randomly collected natural and synthetic molecules, or, alternatively, sets of natural and synthetic molecules with specific biological activities. On average, greater than 80% prediction accuracy was achieved with our best models. For the test case consisting of molecules with specific activities, greater than 90% accuracy was achieved. From our analysis, some chemical features were identified that systematically differ in many naturally occurring versus synthetic molecules.