Quantifying the effect of high-spin/low-spin crossover on electron delocalization in d 5 d 5 M 2 Cl 9 3 (M /Fe, Ru, Os) dimers Robert Stranger a, *, Timothy Lovell a,1 , John E. McGrady b a Department of Chemistry, The Faculties, The Australian National University, Canberra, ACT 0200, Australia b Department of Chemistry, The University of York, Heslington, York YO10 5DD, UK Received 6 November 2001; accepted 13 May 2002 Abstract Density functional theory has been used to investigate the effect of high-spin/low-spin crossover on the delocalization of metal- based electrons in homo- and hetero-bimetallic d 5 d 5 face-shared M 2 Cl 9 3 (M/Fe, Ru, Os) dimers. The energetic contributions of the ligand-field, DE LF , spin-polarization, DE spe , and orbital overlap, DE ovlp , terms to the high-spin/low-spin and localized/ delocalized equilibria in these dimer systems have been quantified. The two equilibria are found to exhibit a strong linear dependence, which can be attributed to their connection with the single-ion spin-polarization energy. It can be concluded that metal /metal bond formation necessitates a crossover from a high-spin to low-spin configuration in these dimer systems, and, therefore, neither delocalized high-spin or localized low-spin d 5 d 5 structures are likely to occur. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: Density functional theory; Face-shared dimers; Metal /metal bonding; High-spin/low-spin crossover; Electron delocalization; Broken- symmetry; Antiferromagnetic coupling 1. Introduction In previous work we have made extensive use of density functional theory, in conjunction with the broken-symmetry (BS) methodology, to examine peri- odic trends in metal  /metal bonding for bioctahedral face-shared M 2 Cl 9 n and edge-shared M 2 Cl 10 n dimers containing Group IV to VII transition metals [1]. In symmetric dimer systems such as these, the presence of symmetry elements connecting the two metal centers forces complete delocalization of the metal-based elec- trons leading to a poor description of metal  /metal bonding in the weakly-coupled limit and, ultimately, to an underestimation of metal  /metal separations by as much as 1.0 A ˚ . In the BS approach developed by Noodleman and co-workers, [2] these symmetry con- straints are removed so that the two metal centers behave independently thus allowing (but not forcing) the magnetic electrons in the antiferromagnetic state to localize on one or the other center if such a situation is energetically favorable. We have demonstrated that this approach not only leads to calculated structures in better agreement with experiment (metal /metal separa- tions generally within 0.1 A ˚ ), but is also capable of representing the entire range of metal /metal interac- tions from weak antiferromagnetic coupling through to multiple metal  /metal bonding. Recently, we examined the potential energy curves for the d 5 d 5 dimers M 2 Cl 9 3 (M /Fe, Ru, Os) in order to understand how the high-spin (HS) or low-spin (LS) configuration on the metal affected the metal  /metal bonding in this series [3]. In earlier studies of d 1 d 1 ,d 2 d 2 and d 3 d 3 dimers, we were able to quantify the metal / metal bonding in terms of the competition between two energetic parameters, namely the single-ion exchange (spin-polarization) energy which favors unpaired spins and thus localized, weakly-coupled metal centers, and metal  /metal orbital overlap which favors delocalized, metal  /metal bonded structures [1b,1d,1e,1f]. In the present paper, we extend our earlier studies on the * Corresponding author. Tel.:  /61-2-625-2934; fax:  /61-2-6249- 0760 E-mail address: rob.stranger@anu.edu.au (R. Stranger). 1 Present address: Department of Molecular Biology, The Scripps Research Institute, La Jolla, CA 92037, USA. Polyhedron 21 (2002) 1969  /1977 www.elsevier.com/locate/poly 0277-5387/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII:S0277-5387(02)01105-1