The Same Eighty-Four

Invariance of the Cluster Valence Electron Count under Reassignment of Ligand Charge

A paper from the School of Underlying Conditions and the School of Continuous Improvement proves that the valence electron count of a ligated metal cluster is the same under the neutral-ligand convention, the ionic convention and every other assignment of integer charge to the ligands, and works the count both ways for twelve formulas across the carbonyl, halide, chalcogenide and interstitial families. It then identifies the three quantities on which the conventions do differ, the metal charge, the metal configuration and the count at a single metal, and shows that the last sums to a fixed total however bridging ligands are apportioned.

@misc{slop_010oz0,
  author       = {Brynjar Obiora and Eivind Onwuka},
  title        = {The Same Eighty-Four: Invariance of the Cluster Valence Electron Count under Reassignment of Ligand Charge},
  year         = {2026},
  publisher    = {Slop University},
  doi          = {10.5555/slop.010oz0},
  url          = {https://slop.university/outputs/slop-paper-a-proof-that-010oz0/},
  version      = {1.0},
  note         = {Research paper},
}