A hierarchical algorithm for calculating the isotopic fine structures of molecules

This article presents a memory efficient algorithm for accurately calculating the isotopic fine structures of molecules. Treating individual isotopic species of a molecule as different mass states, we introduce the concept of transitions between mass states and represent all mass states of the molecule in a hierarchical structure. We show that there exists a simple relationship between two different mass states at two different levels of the hierarchical structure. This allows us to efficiently and accurately compute both the mass and the abundance of every mass state of a small to medium-sized molecule, whose gross structures include small number of fine structures. A truncated calculation of this algorithm can be applied to calculate a majority of isotopic species (99.99% of cumulative abundance) of a large molecule.