The Nature of the Transition Metal-Carbonyl Bond and the Question about the Valence Orbitals of Transition Metals. A Bond-Energy Decomposition Analysis of TM(CO) 6 q (TM q ) Hf 2- , Ta - , W, Re + , Os 2+ , Ir 3+ ) † Axel Diefenbach, ‡ F. Matthias Bickelhaupt, §, * and Gernot Frenking ‡, * Contribution from the Fachbereich Chemie, Philipps-UniVersita ¨ t Marburg, Hans-Meerwein-Strasse, D-35032 Marburg, Germany and the Scheikundig Laboratorium der Vrije UniVersiteit, De Boelelaan 1083, NL-1081 HV Amsterdam, The Netherlands ReceiVed February 23, 2000. ReVised Manuscript ReceiVed May 9, 2000 Abstract: The equilibrium geometries and bond-dissociation energies for loss of one CO and loss of six CO from TM(CO) 6 q (TM q ) Hf 2- , Ta - , W, Re + , Os 2+ , Ir 3+ ) have been calculated at the BP86 level using Slater type basis sets. The bonding interactions between TM(CO) 5 and one CO and between TM q in the t 2g 6 valence state and the ligand cage (CO) 6 were analyzed in the framework of Kohn-Sham MO theory with the use of the quantitative ETS energy-partitioning scheme. The BDEs exhibit a U-shaped curve from Hf(CO) 6 2- to Ir- (CO) 6 3+ , with W(CO) 6 having the lowest BDE for loss of one CO while Re(CO) 6 + has the lowest BDE for loss of 6 CO. The stabilizing orbital interaction term, ΔE orb , and the electrostatic attraction term, ΔE elstat , have comparable contributions to the (CO) 5 TM q sCO bond strength. The largest orbital contributions relative to the electrostatic attraction are found for the highest charged complexes, Hf(CO) 6 2- and Ir(CO) 6 3+ . The contribution of the (CO) 5 TM q rCO σ donation continuously increases from Hf(CO) 6 2- to Ir(CO) 6 3+ and eventually becomes the dominant orbital interaction term in the carbonyl cations, while the (CO) 5 TM q fCO π-back-donation decreases in the same direction. The breakdown of the contributions of the d, s, and p valence orbitals of the metals to the energy and charge terms of the TM q r(CO) 6 donation shows for a single AO the order d . s > p, but the contributions of the three p orbitals of TM q are larger than the contribution of the s orbital. Introduction The nature of the chemical bond is at the very heart of chemical research. The lack of true insight into the interatomic interactions in molecules in the prequantum chemical period prior to 1925 1 forced chemists to use heuristic models that were developed by correlating experimental observations with plau- sible ad-hoc assumptions. Whereas these models proved to be very helpful as an ordering scheme for experimental observa- tions and as a tool for the design of new experiments, they do not provide any information about the nature of the chemical bond. Only after sophisticated quantum chemical methods were developed and powerful computers were available did it become possible to accurately analyze the interatomic interactions of molecules and to understand the physical nature of the chemical bond. The progress in quantum chemistry also contributed to the development of bonding models, with molecular orbital (MO) theory being the most prominent example. MO theoretical models belong now to the standard curriculum of modern chemical textbooks. The enormous success of MO theory, particularly in form of the frontier molecular orbital model, 2 led to its widespread use in organic and inorganic chemistry for explaining the structure and reactivity of molecules. There is a danger, however, in the uncritical use of the frontier orbital model for explaining chemical bonding, because other factors such as electrostatic interactions and Pauli repulsion may also play a significant role. A thorough analysis of the different factors which contribute to the strength of the interatomic interactions is seldom done, and the results of such studies often reveal that the nature of the chemical bond is more complicated than the simple bonding models which are commonly used. Nevertheless, it is fair to say that much progress has been made in the understanding of the chemical bond in the past decades. Most quantum chemical analyses of the chemical bond focused, in the beginning, on the elements of the first row of the periodic system. The extension of the bonding concepts which were developed for the first octal row to the heavier main- group elements already has proven to be more complicated than most chemists would have expected. 3 Nevertheless, quantum chemical calculations gave insight into the bonding situation of the main-group elements beyond neon. A detailed analysis of the multiple bonds of light and heavy main-group elements, which led to some surprising results, gave an understanding for the different geometries and significantly lower stabilities of molecules with multiple bonds between heavier elements. 3,4 The † Theoretical Studies of Organometallic Compounds. Part 42. Party 41: Deubel, D.; Sundermeyer, J.; Frenking, G. J. Am. Chem. Soc., submitted for publication. ‡ Philipps-Universita ¨t Marburg. § Vrije Universiteit Amsterdam. (1) Heitler, W.; London, F. Z. Physik, 1927, 44, 455. (2) (a) Fukui, K. Acc. Chem. Res. 1971, 4, 57. (b) Fleming, I. Frontier Orbitals and Organic Chemical Reactions; Wiley: New York, 1976. (3) Kutzelnigg, W. Angew. Chem. 1984, 96, 262; Angew. Chem., Int. Ed. Engl. 1984, 23, 272. (4) (a) Schmidt, M. W.; Truong, P. N.; Gordon, M. S. J. Am. Chem. Soc. 1987, 109, 5217. (b) Jacobsen, H.; Ziegler, T. J. Am. Chem. Soc. 1994, 116, 3667. 6449 J. Am. Chem. Soc. 2000, 122, 6449-6458 10.1021/ja000663g CCC: $19.00 © 2000 American Chemical Society Published on Web 06/23/2000