Information and Organic Molecules:  Structure Considerations via Integer Statistics

Information in relation to organic molecules was investigated in a previous work (Graham and Schacht, J. Chem. Inf. Comput. Sci. 2000, 40, 187). The topic is given further consideration here with the help of integer statistics. Discussed are the ramifications of an integer variable Ω_t which quantifies the total number of binding complexions for an organic molecule. Offered is a statistical view of the maximum allowed number of independent regions D expressed by the molecule, dependent on Ω_t. We illustrate the distribution properties of D along with upper limit estimates of the regioinformation μ, also dependent on Ω_t. Integer statistics based on elementary number theory establish the key distribution properties of D and μ. In so doing, the traits distinguishing high regioinformation molecules are enumerated. The statistical approach encompasses all possible molecules and conditions, not just those reported to date in chemical databases. The aim is to view the regioinformation expressed by molecules in an alternative and general way.