Coordination bonding in dicopper and dichromium tetrakis(μ‐acetato)‐diaqua complexes: Nature, strength, length, and topology

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 symmetry (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 optimizations (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 underestimated 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 multipole model. © 2019 Wiley Periodicals, Inc.

[1]  R. Bader Atoms in molecules : a quantum theory , 1990 .

[2]  Tian Lu,et al.  Multiwfn: A multifunctional wavefunction analyzer , 2012, J. Comput. Chem..

[3]  R. E. Rundle,et al.  Polynuclear Metal Carbonyls. I. Structures of Mn2(CO)10 and Re2(CO)10 , 1957 .

[4]  A. Genoni,et al.  Libraries of Extremely Localized Molecular Orbitals. 3. Construction and Preliminary Assessment of the New Databanks. , 2018, The journal of physical chemistry. A.

[5]  Y. Kitagawa,et al.  Approximately spin-projected geometry optimization method and its application to di-chromium systems , 2007 .

[6]  M. Fink,et al.  Structure of dichromium tetraacetate by gas-phase electron diffraction , 1985 .

[7]  P. Jerabek,et al.  Influence of Relativistic Effects on Bonding Modes in M(II) Dinuclear Complexes (M = Au, Ag, and Cu). , 2017, Inorganic chemistry.

[8]  Celestino Angeli,et al.  A novel perturbation-based complete active space-self-consistent-field algorithm: Application to the direct calculation of localized orbitals , 2002 .

[9]  Devesh Kumar,et al.  On copper–copper bond in hydrated cupric acetate , 2015 .

[10]  K. Andersson,et al.  The structure of dichromium tetraformate , 1996 .

[11]  Björn O. Roos,et al.  Multiconfigurational perturbation theory with level shift — the Cr2 potential revisited , 1995 .

[12]  Xavier Fradera,et al.  The Lewis Model and Beyond , 1999 .

[13]  F. Neese,et al.  Electronic structures of five-coordinate complexes of iron containing zero, one, or two pi-radical ligands: a broken-symmetry density functional theoretical study. , 2007, Chemistry.

[14]  B. Silvi,et al.  Topological analysis of the metal-metal bond: A tutorial review , 2017 .

[15]  R. Boča Theoretical foundations of molecular magnetism , 1999 .

[16]  A. Tsipis DFT challenge of intermetallic interactions: From metallophilicity and metallaromaticity to sextuple bonding , 2017 .

[17]  F. Neese,et al.  Square planar vs tetrahedral coordination in diamagnetic complexes of nickel(II) containing two bidentate pi-radical monoanions. , 2005, Inorganic chemistry.

[18]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[19]  S. Grimme,et al.  A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. , 2010, The Journal of chemical physics.

[20]  E. Francisco,et al.  Electron number probability distributions for correlated wave functions. , 2007, The Journal of chemical physics.

[21]  Thomas Bredow,et al.  Consistent Gaussian basis sets of triple‐zeta valence with polarization quality for solid‐state calculations , 2013, J. Comput. Chem..

[22]  F. Neese,et al.  Ab initio and coupled-perturbed density functional theory estimation of zero-field splittings in MnII transition metal complexes. , 2008, The journal of physical chemistry. A.

[23]  J. Tanaka,et al.  Electronic structure and spectra of cupric acetate mono-hydrate revisited , 2010 .

[24]  Bartolomeo Civalleri,et al.  Quantum‐mechanical condensed matter simulations with CRYSTAL , 2018 .

[25]  J. M. Ugalde,et al.  Complete vs Restricted Active Space Perturbation Theory Calculation of the Cr2 Potential Energy Surface. , 2011, Journal of chemical theory and computation.

[26]  J. Pople,et al.  Self‐consistent molecular orbital methods. XX. A basis set for correlated wave functions , 1980 .

[27]  S. H. Vosko,et al.  Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis , 1980 .

[28]  V. Petříček,et al.  Electronic structure of two isostructural ‘paddle-wheel’ complexes: a comparative study , 2018, Acta Crystallographica Section B, Structural Science, Crystal Engineering and Materials.

[29]  Celestino Angeli,et al.  Multireference Perturbation Theory with Cholesky Decomposition for the Density Matrix Renormalization Group , 2016, Journal of chemical theory and computation.

[30]  F. Cotton,et al.  Partial paramagnetism of the chromium-chromium quadruple bond , 1992 .

[31]  A. Becke Density-functional thermochemistry. III. The role of exact exchange , 1993 .

[32]  P. Macchi,et al.  Electron Density and Dielectric Properties of Highly Porous MOFs: Binding and Mobility of Guest Molecules in Cu3(BTC)2 and Zn3(BTC)2. , 2019, Journal of the American Chemical Society.

[33]  F. Neese,et al.  Systematic theoretical study of the zero-field splitting in coordination complexes of Mn(III). Density functional theory versus multireference wave function approaches. , 2010, The journal of physical chemistry. A.

[34]  H. Schaefer,et al.  Metal-Metal (MM) Bond Distances and Bond Orders in Binuclear Metal Complexes of the First Row Transition Metals Titanium Through Zinc. , 2018, Chemical reviews.

[35]  Nucleophilic addition reaction in coordinated non-linear pseudohalides: experimental charge density analysis in trans-bis(cyanamidonitrato-N:O)bis-(imidazole-N(3))copper(II) complex. , 2002, Acta crystallographica. Section B, Structural science.

[36]  P. Malmqvist,et al.  Potential Energy Surface of the Chromium Dimer Re-re-revisited with Multiconfigurational Perturbation Theory. , 2016, Journal of chemical theory and computation.

[37]  Philip Coppens,et al.  Aspherical-atom scattering factors from molecular wave functions. 1. Transferability and conformation dependence of atomic electron densities of peptides within the multipole formalism. , 2002, Acta crystallographica. Section A, Foundations of crystallography.

[38]  C. Jelsch,et al.  Optimal local axes and symmetry assignment for charge-density refinement , 2008 .

[39]  R. Cimiraglia,et al.  Calibration of the n-electron valence state perturbation theory approach. , 2004, The Journal of chemical physics.

[40]  A. Becke,et al.  Density-functional exchange-energy approximation with correct asymptotic behavior. , 1988, Physical review. A, General physics.

[41]  F. Neese,et al.  Molecular and electronic structures of tetrahedral complexes of nickel and cobalt containing N,N'-disubstituted, bulky o-diiminobenzosemiquinonate(1-) π-radical ligands , 2006 .

[42]  Viktor Bezugly,et al.  Electron localizability indicators ELI–D and ELIA for highly correlated wavefunctions of homonuclear dimers. II. N2, O2, F2, and Ne2 , 2009, J. Comput. Chem..

[43]  Qiming Sun,et al.  N-Electron Valence State Perturbation Theory Based on a Density Matrix Renormalization Group Reference Function, with Applications to the Chromium Dimer and a Trimer Model of Poly(p-Phenylenevinylene). , 2015, Journal of chemical theory and computation.

[44]  P. Schwerdtfeger,et al.  Accurate potential energy curves for the group 12 dimers Zn2, Cd2, and Hg2 , 2011 .

[45]  Celestino Angeli,et al.  Introduction of n-electron valence states for multireference perturbation theory , 2001 .

[46]  R. Bader,et al.  Spatial localization of the electronic pair and number distributions in molecules , 1975 .

[47]  F. Neese Importance of direct spin-spin coupling and spin-flip excitations for the zero-field splittings of transition metal complexes: a case study. , 2006, Journal of the American Chemical Society.

[48]  F. Schoening,et al.  A new type of copper complex as found in the crystal structure of cupric acetate, Cu2(CH3COO)4.2H2O , 1953 .

[49]  A. D. McLean,et al.  Contracted Gaussian basis sets for molecular calculations. I. Second row atoms, Z=11–18 , 1980 .

[50]  A Kokalj,et al.  XCrySDen--a new program for displaying crystalline structures and electron densities. , 1999, Journal of molecular graphics & modelling.

[51]  Thomas Müller,et al.  Large-scale parallel uncontracted multireference-averaged quadratic coupled cluster: the ground state of the chromium dimer revisited. , 2009, The journal of physical chemistry. A.

[52]  F. Weigend,et al.  Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. , 2005, Physical chemistry chemical physics : PCCP.

[53]  Claude Lecomte,et al.  On Building a Data Bank of Transferable Experimental Electron Density Parameters Applicable to Polypeptides , 1995 .

[54]  Frank Neese,et al.  An improvement of the resolution of the identity approximation for the formation of the Coulomb matrix , 2003, J. Comput. Chem..

[55]  N. Hill,et al.  The insignificance of metal–metal bonding in the antiferromagnetism of copper(II) carboxylate dimers , 1969 .

[56]  J. Malrieu,et al.  Remarks on the Proper Use of the Broken Symmetry Approach to Magnetic Coupling , 1997 .

[57]  Celestino Angeli,et al.  N-electron valence state perturbation theory: a fast implementation of the strongly contracted variant , 2001 .

[58]  Haibo Ma,et al.  Externally-Contracted Multireference Configuration Interaction Method Using a DMRG Reference Wave Function. , 2018, Journal of chemical theory and computation.

[59]  Cristina Puzzarini,et al.  Systematically convergent basis sets for transition metals. II. Pseudopotential-based correlation consistent basis sets for the group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) elements , 2005 .

[60]  F. Cotton,et al.  The crystal and molecular structures of dichromium tetraacetate dihydrate and dirhodium tetraacetate dihydrate , 1971 .

[61]  Anton Kokalj,et al.  Computer graphics and graphical user interfaces as tools in simulations of matter at the atomic scale , 2003 .

[62]  V. Tsirelson,et al.  On the transferability of QTAIMC descriptors derived from X-ray diffraction data and DFT calculations: substituted hydropyrimidine derivatives. , 2011, Acta crystallographica. Section B, Structural science.

[63]  S. Grimme,et al.  Towards chemical accuracy for the thermodynamics of large molecules: new hybrid density functionals including non-local correlation effects. , 2006, Physical chemistry chemical physics : PCCP.

[64]  A.M.K. Müller,et al.  Explicit approximate relation between reduced two- and one-particle density matrices , 1984 .

[65]  Louis Noodleman,et al.  The Xα valence bond theory of weak electronic coupling. Application to the low‐lying states of Mo2Cl84− , 1979 .

[66]  F. Neese,et al.  Theoretical evidence for the singlet diradical character of square planar nickel complexes containing two o-semiquinonato type ligands. , 2002, Inorganic chemistry.

[67]  F. Cotton,et al.  After 155 Years, A Crystalline Chromium Carboxylate with a Supershort Cr−Cr Bond , 2000 .

[68]  A. H. Pakiari,et al.  Geometry and electronic structure of ultrafine/nanoparticle chromium clusters (Crn, n = 2–5) and their interaction with oxygen (triplet) and ethylene molecules: A DFT–NBO study , 2016 .

[69]  Gold-standard coupled-cluster study of the ground-state chromium dimer cation , 2013 .

[70]  Axel D. Becke,et al.  A Simple Measure of Electron Localization in Atomic and Molecular-Systems , 1990 .

[71]  Frank Neese,et al.  Coupled Cluster Method with Single and Double Excitations Tailored by Matrix Product State Wave Functions. , 2016, The journal of physical chemistry letters.

[72]  Laura Gagliardi,et al.  Reaching the maximum multiplicity of the covalent chemical bond. , 2007, Angewandte Chemie.

[73]  F. Schoening,et al.  The structure of crystalline chromous acetate revealing paired chromium atoms , 1953 .

[74]  Takeshi Yanai,et al.  Second-order perturbation theory with a density matrix renormalization group self-consistent field reference function: theory and application to the study of chromium dimer. , 2011, The Journal of chemical physics.

[75]  R. Wiest,et al.  The CrCr quadruple bond length: Ab initio study of ligand effects , 1983 .

[76]  A. Forni,et al.  Experimental and theoretical charge density of hydrated cupric acetate , 2012 .

[77]  I. Hamilton,et al.  Chemical bonding in groups 10, 11, and 12 transition metal homodimers — An electron density study , 2013 .

[78]  F. Neese,et al.  Analysis and interpretation of metal-radical coupling in a series of square planar nickel complexes: correlated Ab initio and density functional investigation of [Ni(L(ISQ))(2)] (L(ISQ)=3,5-di-tert-butyl-o-diiminobenzosemiquinonate(1-)). , 2003, Journal of the American Chemical Society.

[79]  Andreas Savin,et al.  Atomic Shell Structure and Electron Numbers , 1996 .

[80]  E. Stevens,et al.  Experimental and theoretical electron density analysis of metal-metal bonding in dichromium tetraacetate , 1980 .

[81]  Tetsuya Tsunekawa,et al.  Ab initio molecular orbital calculations of effective exchange integrals between transition metal ions , 1988 .

[82]  Frank Neese,et al.  Software update: the ORCA program system, version 4.0 , 2018 .

[83]  S. Grimme Semiempirical hybrid density functional with perturbative second-order correlation. , 2006, The Journal of chemical physics.

[84]  B. Dittrich,et al.  A simple approach to nonspherical electron densities by using invarioms. , 2004, Angewandte Chemie.