Ordering molecular energies by moving boxes

Structures such as isoprotonic–isoelectronic molecules can be mathematically represented by Young diagrams (or integer partitions), whose columns correspond to the different nuclear charges in a molecule. We found that these Young diagrams, when ordered by majorization, produce a partially ordered set, which is equivalent to the ordering of ground-state energies of the represented molecules. This result shows that the ordering of such energies can be derived by moving boxes in Young diagrams. The correspondence between majorization order and energy ordering opens the door for obtaining new general expressions for molecular properties.