DOI: 10.1002/chem.200900239 A Bonding Quandary—or—A Demonstration of the Fact That Scientists Are Not Born With Logic Santiago Alvarez, [a] Roald Hoffmann, [b] and Carlo Mealli [c] Dedicated to Professor Yitzhak Apeloig on the occasion of his 65th birthday Introduction The chemical bond is at the heart of our enterprise, yet its nature continues to be debated. Into the idea of a chemical bond enter experimental measures—distances, energies, force constants, spectroscopic and magnetic criteria—and theoretical ones: bond orders, overlap populations, quantum theory of atoms in molecules (QTAIM) bond paths, electron localization function (ELF) plots, and energy decomposi- tions. If one allows oneself to use a multiplicity of criteria, bonds may exist by one measure, not by another. This is not a reason to wring our hands, nor complain how unscientific chemistry is (or how obstinate chemists are). Chemistry has done more than well in creating a universe of structure and function on the molecular level with just this “imperfectly defined” concept of a chemical bond. Or maybe it has done so well precisely because the concept is flexible and fuzzy. We want to share with the community how a discussion on bonding played out around a specific group of com- pounds: small, sulfur-containing clusters of copper with asso- ciated ligands. Its a real story, with some fierce debate among friends, who questioned each others bonding assign- ment both in print and in private conversations. We believe our discussion has something of value to other chemists, for several reasons: 1) There is in our exchange an underlying question of the existence or absence of a chemical bond (in this case, an S  S bond), a matter, as we have said, debated across the community and not just for these compounds. 2) The reaction in question—making or breaking a bond— is formally an oxidative addition or reductive elimina- tion, a fundamental and widely useful organometallic re- action. So are redox reactions in general. 3) Polynuclear metal complexes of oxygen and sulfur are used by nature in a wide variety of biological redox reac- tions. Abstract: We document here a spirited debate among three colleagues and friends who have strong opinions on a specific bonding problem, the presence or absence of a cross-ring sulfur–sulfur bond in a trinuclear Cu 3 S 2 cluster. The example may seem esoteric, but through their struggles with this specific bond (and with each other) the authors approach the more general problem- atic of chemistry, the chemical bond. The discussion fo- cuses on bond lengths and the population of bonding and antibonding orbitals, and on oxidation states, elec- tron counting, and associated geometries. It expands to encompass other bonding criteria, and introduces exam- ples ranging far across organic and inorganic chemistry. The authors suggest molecules that might test their ideas. An Appendix to the paper discusses a matter rarely broached in the chemical literature—should one review for publication a paper which criticizes one of your own contributions. Keywords: bond lengths · chemical bonding · cluster compounds · S  S bonding · sulfides [a] Prof. S. Alvarez Departament de Química Inorgànica and Institut de Química Teòrica i Computacional (IQTC-UB) Universitat de Barcelona Martí i Franqus 1-11, 08028 Barcelona (Spain) Fax: (+ 34) 93-4907725 [b] Prof. R. Hoffmann Department of Chemistry and Chemical Biology Cornell University Ithaca, NY 14853-1301 (USA) Fax: (+ 1) 6072555707 [c] Dr. C. Mealli Istituto di Chimica dei Composti Organometallici ICCOM-CNR Via Madonna del Piano 10, 50019 Sesto Fiorentino, Firenze (Italy) Fax: (+ 39) 055225203  2009 Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim Chem. Eur. J. 2009, 15, 8358 – 8373 8358