New Benchmark Set of Transition-Metal Coordination Reactions for the Assessment of Density Functionals.

We present the WCCR10 data set of 10 ligand dissociation energies of large cationic transition metal complexes for the assessment of approximate exchange-correlation functionals. We analyze nine popular functionals, namely BP86, BP86-D3, B3LYP, B3LYP-D3, B97-D-D2, PBE, TPSS, PBE0, and TPSSh by mutual comparison and by comparison to experimental gas-phase data measured with well-known precision. The comparison of all calculated data reveals a large, system-dependent scattering of results with nonnegligible consequences for computational chemistry studies on transition metal compounds. Considering further the comparison with experimental results, the nonempirical functionals PBE and TPSS turn out to be among the best functionals for our reference data set. The deviation can be lowered further by including Hartree-Fock exchange. Accordingly, PBE0 and TPSSh are the two most accurate functionals for our test set, but also these functionals exhibit deviations from experimental results by up to 50 kJ mol(-1) for individual reactions. As an important result, we found no functional to be reliable for all reactions. Furthermore, for some of the ligand dissociation energies studied in this work, invoking semiempirical dispersion corrections yields results which increase the deviation from experimental results. This deviation increases further if structure optimization including such dispersion corrections is performed, although the contrary should be the case, pointing to the need to develop the currently available dispersion corrections further. Finally, we compare our results to other benchmark studies and highlight that the performance assessed for different density functionals depends significantly on the reference molecule set chosen.

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

[2]  Donald G. Truhlar,et al.  Effectiveness of Diffuse Basis Functions for Calculating Relative Energies by Density Functional Theory , 2003 .

[3]  Swee-Ping Chia,et al.  AIP Conference Proceedings , 2008 .

[4]  Nathan J. DeYonker,et al.  Quantitative computational thermochemistry of transition metal species. , 2007, The journal of physical chemistry. A.

[5]  K. Burke,et al.  Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)] , 1997 .

[6]  David A Dixon,et al.  Accurate thermochemistry for transition metal oxide clusters. , 2009, The journal of physical chemistry. A.

[7]  M. Ratner Molecular electronic-structure theory , 2000 .

[8]  Trygve Helgaker,et al.  Molecular Electronic-Structure Theory: Helgaker/Molecular Electronic-Structure Theory , 2000 .

[9]  L. Curtiss,et al.  Gaussian‐1 theory: A general procedure for prediction of molecular energies , 1989 .

[10]  Stefan Grimme,et al.  Semiempirical GGA‐type density functional constructed with a long‐range dispersion correction , 2006, J. Comput. Chem..

[11]  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.

[12]  Stefan Grimme,et al.  A General Database for Main Group Thermochemistry, Kinetics, and Noncovalent Interactions - Assessment of Common and Reparameterized (meta-)GGA Density Functionals. , 2010, Journal of chemical theory and computation.

[13]  Markus Reiher,et al.  MOVIPAC: Vibrational spectroscopy with a robust meta‐program for massively parallel standard and inverse calculations , 2012, J. Comput. Chem..

[14]  Stefan Grimme,et al.  Benchmarking of London Dispersion-Accounting Density Functional Theory Methods on Very Large Molecular Complexes. , 2013, Journal of chemical theory and computation.

[15]  Filipp Furche,et al.  The performance of semilocal and hybrid density functionals in 3d transition-metal chemistry. , 2006, The Journal of chemical physics.

[16]  H. Stoll,et al.  Energy-adjustedab initio pseudopotentials for the second and third row transition elements , 1990 .

[17]  Gheorghe Duca,et al.  Homogeneous Catalysis with Metal Complexes: Fundamentals and Applications , 2012 .

[18]  S. Grimme Comment on: "On the accuracy of DFT methods in reproducing ligand substitution energies for transition metal complexes in solution: the role of dispersive interactions" by H. Jacobsen and L. Cavallo. , 2012, Chemphyschem : a European journal of chemical physics and physical chemistry.

[19]  Donald G Truhlar,et al.  Density functionals for inorganometallic and organometallic chemistry. , 2005, The journal of physical chemistry. A.

[20]  J. Schwartz,et al.  Organometallics , 1987, Science.

[21]  Markus Reiher,et al.  Theoretical study of the Fe(phen)(2)(NCS)(2) spin-crossover complex with reparametrized density functionals. , 2002, Inorganic chemistry.

[22]  Donald G. Truhlar,et al.  Development and Assessment of a New Hybrid Density Functional Model for Thermochemical Kinetics , 2004 .

[23]  Peter Chen,et al.  Gas-phase thermochemistry of ruthenium carbene metathesis catalysts. , 2008, Journal of the American Chemical Society.

[24]  Donald G Truhlar,et al.  Benchmark Databases for Nonbonded Interactions and Their Use To Test Density Functional Theory. , 2005, Journal of chemical theory and computation.

[25]  Peter Chen,et al.  Experimental and theoretical study of a gold(I) aminonitrene complex in the gas phase. , 2010, Chemphyschem : a European journal of chemical physics and physical chemistry.

[26]  Wolfram Koch,et al.  A Chemist's Guide to Density Functional Theory , 2000 .

[27]  Krishnan Raghavachari,et al.  Investigation of Gaussian4 theory for transition metal thermochemistry. , 2009, The journal of physical chemistry. A.

[28]  S. Grimme,et al.  "Mindless" DFT Benchmarking. , 2009, Journal of chemical theory and computation.

[29]  P. Wormer,et al.  Theory and Applications of Computational Chemistry The First Forty Years , 2005 .

[30]  Luigi Cavallo,et al.  On the accuracy of DFT methods in reproducing ligand substitution energies for transition metal complexes in solution: the role of dispersive interactions. , 2012, Chemphyschem : a European journal of chemical physics and physical chemistry.

[31]  Luigi Cavallo,et al.  Reply to the Comment by Grimme on: "On the Accuracy of DFT Methods in Reproducing Ligand Substitution Energies for Transition Metal Complexes in Solution: The Role of Dispersive Interactions" , 2012 .

[32]  Evert Jan Baerends,et al.  Assessment of density functional methods for reaction energetics: Iridium‐catalyzed water oxidation as case study , 2013, J. Comput. Chem..

[33]  Manoj K. Kesharwani,et al.  Explicitly correlated coupled cluster benchmarks with realistic-sized ligands for some late-transition metal reactions: basis sets convergence and performance of more approximate methods , 2014, Theoretical Chemistry Accounts.

[34]  G. Scuseria,et al.  Assessment of the Perdew–Burke–Ernzerhof exchange-correlation functional , 1999 .

[35]  Peter Chen,et al.  Co-C bond energies in adenosylcobinamide and methylcobinamide in the gas phase and in silico. , 2013, Journal of the American Chemical Society.

[36]  Donald G Truhlar,et al.  Databases for transition element bonding: metal-metal bond energies and bond lengths and their use to test hybrid, hybrid meta, and meta density functionals and generalized gradient approximations. , 2005, The journal of physical chemistry. A.

[37]  Donald G. Truhlar,et al.  Robust and Affordable Multicoefficient Methods for Thermochemistry and Thermochemical Kinetics: The MCCM/3 Suite and SAC/3 , 2003 .

[38]  Kirk A. Peterson,et al.  Explicitly correlated composite thermochemistry of transition metal species. , 2013, The Journal of chemical physics.

[39]  Alexandre Tkatchenko,et al.  Two- and three-body interatomic dispersion energy contributions to binding in molecules and solids. , 2010, The Journal of chemical physics.

[40]  Walter Kohn,et al.  Nobel Lecture: Electronic structure of matter-wave functions and density functionals , 1999 .

[41]  Donald G Truhlar,et al.  Tests of Exchange-Correlation Functional Approximations Against Reliable Experimental Data for Average Bond Energies of 3d Transition Metal Compounds. , 2013, Journal of chemical theory and computation.

[42]  Markus Reiher,et al.  Optimized unrestricted Kohn-Sham potentials from ab initio spin densities. , 2012, The Journal of chemical physics.

[43]  Donald G. Truhlar,et al.  Benchmark Data for Interactions in Zeolite Model Complexes and Their Use for Assessment and Validation of Electronic Structure Methods , 2008 .

[44]  Christoph R Jacob,et al.  Unambiguous optimization of effective potentials in finite basis sets. , 2011, The Journal of chemical physics.

[45]  Peter Chen,et al.  Threshold CID investigation of isomeric Cu(I) azabox complexes. , 2007, Inorganic chemistry.

[46]  Peter Chen,et al.  Gas-phase energetics of reductive elimination from a palladium(II) N-heterocyclic carbene complex. , 2010, Chemistry.

[47]  Nathan J DeYonker,et al.  Toward accurate theoretical thermochemistry of first row transition metal complexes. , 2012, The journal of physical chemistry. A.

[48]  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.

[49]  Donald G Truhlar,et al.  Benchmark database of barrier heights for heavy atom transfer, nucleophilic substitution, association, and unimolecular reactions and its use to test theoretical methods. , 2005, The journal of physical chemistry. A.

[50]  Gheorghe Duca,et al.  Homogeneous Catalysis with Metal Complexes , 2012 .

[51]  L. Curtiss,et al.  Assessment of Gaussian-3 and density functional theories for a larger experimental test set , 2000 .

[52]  M. Frisch,et al.  Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields , 1994 .

[53]  Peter Chen,et al.  Experimental Gas-Phase Thermochemistry for Alkane Reductive Elimination from Pt(IV) , 2014 .

[54]  G. Scuseria,et al.  Comparative assessment of a new nonempirical density functional: Molecules and hydrogen-bonded complexes , 2003 .

[55]  Stefan Grimme,et al.  Does DFT-D estimate accurate energies for the binding of ligands to metal complexes? , 2011, Dalton transactions.

[56]  A. Bach,et al.  Simple fitting of energy-resolved reactive cross sections in threshold collision-induced dissociation (T-CID) experiments. , 2007, The journal of physical chemistry. A.

[57]  Johannes Neugebauer,et al.  Fundamental vibrational frequencies of small polyatomic molecules from density-functional calculations and vibrational perturbation theory , 2003 .

[58]  D. Dixon,et al.  Chemical accuracy in ab initio thermochemistry and spectroscopy: current strategies and future challenges , 2012, Theoretical Chemistry Accounts.

[59]  Jianmin Tao,et al.  Erratum: “Comparative assessment of a new nonempirical density functional: Molecules and hydrogen-bonded complexes” [J. Chem. Phys. 119, 12129 (2003)] , 2004 .

[60]  Giovanni Occhipinti,et al.  Metal-phosphine bond strengths of the transition metals: a challenge for DFT. , 2009, The journal of physical chemistry. A.

[61]  Peter Hofmann,et al.  Inter- and Intramolecular Interactions in Triptycene-Derived Bisphosphite Hydroformylation Catalysts: Structures, Energies, and Caveats for DFT-Assisted Ligand Design , 2013 .

[62]  J. Perdew,et al.  Density-functional approximation for the correlation energy of the inhomogeneous electron gas. , 1986, Physical review. B, Condensed matter.

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

[64]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[65]  Hans W. Horn,et al.  ELECTRONIC STRUCTURE CALCULATIONS ON WORKSTATION COMPUTERS: THE PROGRAM SYSTEM TURBOMOLE , 1989 .

[66]  Donald G Truhlar,et al.  Benchmark Energetic Data in a Model System for Grubbs II Metathesis Catalysis and Their Use for the Development, Assessment, and Validation of Electronic Structure Methods. , 2009, Journal of chemical theory and computation.

[67]  Kwang S. Kim,et al.  Theory and applications of computational chemistry : the first forty years , 2005 .

[68]  L. Curtiss,et al.  Assessment of Gaussian-3 and density-functional theories on the G3/05 test set of experimental energies. , 2005, The Journal of chemical physics.

[69]  Per-Ola Norrby,et al.  Dispersion and back-donation gives tetracoordinate [Pd(PPh3)4]. , 2011, Angewandte Chemie.

[70]  Markus Reiher,et al.  Quantum chemical calculation of vibrational spectra of large molecules—Raman and IR spectra for Buckminsterfullerene , 2002, J. Comput. Chem..

[71]  Peter Chen,et al.  Structure and bonding of isoleptic coinage metal (Cu, Ag, Au) dimethylaminonitrenes in the gas phase. , 2010, Journal of the American Chemical Society.

[72]  Angela K. Wilson,et al.  Comparative Study of Single and Double Hybrid Density Functionals for the Prediction of 3d Transition Metal Thermochemistry. , 2012, Journal of chemical theory and computation.

[73]  F. Weigend Accurate Coulomb-fitting basis sets for H to Rn. , 2006, Physical chemistry chemical physics : PCCP.

[74]  S. Grimme,et al.  Efficient and Accurate Double-Hybrid-Meta-GGA Density Functionals-Evaluation with the Extended GMTKN30 Database for General Main Group Thermochemistry, Kinetics, and Noncovalent Interactions. , 2011, Journal of chemical theory and computation.

[75]  Stefan Grimme,et al.  Effect of the damping function in dispersion corrected density functional theory , 2011, J. Comput. Chem..

[76]  Peter Chen,et al.  Electrospray Ionization Tandem Mass Spectrometric Determination of Ligand Binding Energies in Platinum(II) Complexes , 2005 .

[77]  Krishnan Raghavachari,et al.  Gaussian-2 theory for molecular energies of first- and second-row compounds , 1991 .

[78]  P. B. Armentrout,et al.  Statistical modeling of collision-induced dissociation thresholds , 1997 .

[79]  L. Curtiss,et al.  Assessment of Gaussian-2 and density functional theories for the computation of enthalpies of formation , 1997 .

[80]  G. Scuseria,et al.  Climbing the density functional ladder: nonempirical meta-generalized gradient approximation designed for molecules and solids. , 2003, Physical review letters.

[81]  Alexandre Tkatchenko,et al.  Popular Kohn-Sham density functionals strongly overestimate many-body interactions in van der Waals systems , 2008 .

[82]  Peter Chen,et al.  Transmetalation of methyl groups supported by Pt(II)-Au(I) bonds in the gas phase, in silico, and in solution. , 2011, Journal of the American Chemical Society.

[83]  Richard A Friesner,et al.  Correcting Systematic Errors in DFT Spin-Splitting Energetics for Transition Metal Complexes. , 2011, Journal of chemical theory and computation.

[84]  D. Truhlar,et al.  The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals , 2008 .

[85]  John P. Perdew,et al.  Jacob’s ladder of density functional approximations for the exchange-correlation energy , 2001 .

[86]  Donald G. Truhlar,et al.  Small Representative Benchmarks for Thermochemical Calculations , 2003 .

[87]  Richard A Friesner,et al.  A B3LYP-DBLOC empirical correction scheme for ligand removal enthalpies of transition metal complexes: parameterization against experimental and CCSD(T)-F12 heats of formation. , 2012, Physical chemistry chemical physics : PCCP.