Coordination Bonding in Dicopper and Dichromium Tetrakis (μ-acetato)-diaqua Complexes: Nature, Strength, Length, and Topology Michal Malc ˇ ek ,* [a] Barbora Vénosová, [a] Ingrid Puškárová, [a] Jozef Kožíšek, [a] Marián Gall, [b] and Lukáš Buc ˇ inský * [a] Geometry optimization, energetics, electronic structure, and topology of electron density of dicopper (I) and dichromium (II) tetrakis(μ-acetato)-diaqua complexes are studied focusing on the metal–metal interactions. The performance of broken sym- metry (BS) single-determinant ab initio (Hartree–Fock, Møller– Plesset perturbation theory to the second and third orders, coupled clusters singles and doubles) and density functional theory (BLYP, B3LYP, B3LYP-D3, B2PLYP, MPW2PLYP) methods is compared to multideterminant ab initio (CASSCF, NEVPT2) methods as well as to the multipole model of charge density from a single-crystal X-ray diffraction experiment (Herich et al., Acta Cryst. 2018, B74, 681–692). In vacuo DFT geometry optimi- zations (improper axial water ligand orientation) are compared against the periodic ones. The singlet state is found to be energetically preferred. J coupling of (I) becomes under- estimated for all ab initio methods used, when compared to experiment. It is concluded that the strength of the direct M─M interactions correlates closely with the J coupling magnitude at a given level of theory. The double potential well character of (II) and of the dehydrated form of (II) are considered with respect to the Cr─Cr distance. The physical effective bond order of the metal–metal interaction is small (below 0.1 e) in (I) and moderate (0.4 e) in (II). The CASSCF results overestimate the electron density of the metal–metal bond critical point by 20% and 50% in (I) and (II), respectively, when compared to the mul- tipole model. © 2019 Wiley Periodicals, Inc. DOI: 10.1002/jcc.26121 Introduction Metal–metal (M─M) interactions have raised a considerable attention since the discovery of M 2 (CO) 10 complexes (where M = Mn and Re). [1] The carbonyls have been quickly extended by additional classes of complexes with direct M─M interac- tions such as halogenide ions like [Re 2 Cl 8 ] 2- for instance and double dentate ligands interconnecting the metal centers [M 2 L 4 ] or [M 2 L 2 ] such as carboxylate anions (although the group of bidentate ligands is considerably large and the coordination number depends on the ligand charge and the oxidation state of the central metal atom). [2] Currently, the number of com- plexes that exhibit M─M interactions and/or bondings is huge, in the case of 3d homodimers (with M─M distance limited to 2.8 Å), the Cambridge Structural Database (version 5.40 2018) search yields 50, 101, 353, 149, 3231, 1342, 359, 1957, and 47 hits for Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn, respectively, when no other metal is bonded to one of the metal atoms.* This is reflected in the revision of 3d homometalic M─M com- plexes of Lyngdoh et al., [2] summarizing the current state and general trends about the bond lengths and bond orders in the particular systems from an experimental and theoretical view- point. In addition, M─M interactions have been further reviewed from the stand point of the topology of electron den- sity by Lepetit et al. [3] As highlighted already in the second edition of Cotton and Wilkinson’s Inorganic Chemistry Textbook, [4] the M─M distance (with respect to the covalent radius) can be regarded as a good measure of M─M bond strengths. In the presence of carboxylate anions, this range starts at weak interactions (formally a single bond) in Cu─Cu and reaches a multiple bond mode in Mo─Mo systems. Hence, the bond order within the M─M moiety ranges from a multiple bond mode in, for example, [Re 2 Cl 8 ] 2- or [Mo 2 (OOCR) 4 ] to only weak rather ligand bridge stabilized interactions in, for exam- ple, [Cu 2 (OOCR) 4 ]. Other M─M moieties, such as Cr─Cr for instance, can be formally considered bonded in a multiple nature, albeit the physical criteria showed on a weak single bond. [4] A further important point to mention (aside of a [a] M. Malc ˇek, B. Vénosová, I. Puškárová, J. Kožíšek, L. Buc ˇinský Faculty of Chemical and Food Technology, Institute of Physical Chemistry and Chemical Physics, Slovak University of Technology in Bratislava, Radlinského 9, SK-812 37 Bratislava, Slovak Republic E-mail: michal.malcek@stuba.sk or lukas.bucinsky@stuba.sk [b] M. Gall Faculty of Chemical and Food Technology, Institute of Information Engineering, Automation, and Mathematics, Slovak University of Technology in Bratislava, Radlinského 9, SK-812 37 Bratislava, Slovak Republic Contract Grant sponsor: Agentúra na Podporu Výskumu a Vývoja; Contract Grant numbers: APVV-15-0053, APVV-15-0079; Contract Grant sponsor: Vedecká Grantová Agentúra MŠVVaŠ SR a SAV; Contract Grant numbers: 1/0466/18, 1/0598/16, 1/0718/19; Contract Grant sponsor: European Region Development Funds; Contract Grant number: 26230120002 © 2019 Wiley Periodicals, Inc. *A simple structure search of any bond type between two metals lead to 48206 hits in the CSD database (version 5.40 2018) or 35724 when the bond distance is limited to 2.8 Å. WWW.C-CHEM.ORG FULL PAPER Wiley Online Library Journal of Computational Chemistry 2019 1