Prediction of the reduction potential in transition‐metal containing complexes: How expensive? For what accuracy?

Accurate computationally derived reduction potentials are important for catalyst design. In this contribution, relatively inexpensive density functional theory methods are evaluated for computing reduction potentials of a wide variety of organic, inorganic, and organometallic complexes. Astonishingly, SCRF single points on B3LYP optimized geometries with a reasonably small basis set/ECP combination works quite well‐‐B3LYP with the BS1 [modified‐LANL2DZ basis set/ECP (effective core potential) for metals, LANL2DZ(d,p) basis set/LANL2DZ ECP for heavy nonmetals (Si, P, S, Cl, and Br), and 6‐31G(d') for other elements (H, C, N, O, and F)] and implicit PCM solvation models, SMD (solvation model based on density) or IEFPCM (integral equation formalism polarizable continuum model with Bondi atomic radii and α = 1.1 reaction field correction factor). The IEFPCM‐Bondi‐B3LYP/BS1 methodology was found to be one of the least expensive and most accurate protocols, among six different density functionals tested (BP86, PBEPBE, B3LYP, B3P86, PBE0, and M06) with thirteen different basis sets (Pople split‐valence basis sets, correlation consistent basis sets, or Los Alamos National Laboratory ECP/basis sets) and four solvation models (SMD, IEFPCM, IPCM, and CPCM). The MAD (mean absolute deviation) values of SCRF‐B3LYP/BS1 of 49 studied species were 0.263 V for SMD and 0.233 V for IEFPCM‐Bondi; and the linear correlations had respectable R2 values (R2 = 0.94 for SMD and R2 = 0.93 for IEFPCM‐Bondi). These methodologies demonstrate relatively reliable, convenient, and time‐saving functional/basis set/solvation model combinations in computing the reduction potentials of transition metal complexes with moderate accuracy. © 2017 Wiley Periodicals, Inc.

[1]  Abhigna Polavarapu,et al.  Understanding intrinsically irreversible, non-Nernstian, two-electron redox processes: a combined experimental and computational study of the electrochemical activation of platinum(IV) antitumor prodrugs. , 2014, Journal of the American Chemical Society.

[2]  Brett I. Dunlap,et al.  Fitting the Coulomb potential variationally in Xα molecular calculations , 1983 .

[3]  L. E. Roy,et al.  Calculation of one-electron redox potentials revisited. Is it possible to calculate accurate potentials with density functional methods? , 2009, The journal of physical chemistry. A.

[4]  Nathan J DeYonker,et al.  The correlation-consistent composite approach: application to the G3/99 test set. , 2006, The Journal of chemical physics.

[5]  Yi Lu,et al.  A density functional theory protocol for the calculation of redox potentials of copper complexes. , 2016, Physical chemistry chemical physics : PCCP.

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

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

[8]  W. R. Wadt,et al.  Ab initio effective core potentials for molecular calculations. Potentials for K to Au including the outermost core orbitals , 1985 .

[9]  P. Kebarle,et al.  Electron affinities and electron-transfer reactions , 1987 .

[10]  C. Cramer,et al.  Universal solvation model based on solute electron density and on a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions. , 2009, The journal of physical chemistry. B.

[11]  O. Hammerich,et al.  Techniques For Studies Of Electrochemical Reactions In Solution , 2015 .

[12]  Vincenzo Barone,et al.  Solvent effect on vertical electronic transitions by the polarizable continuum model , 2000 .

[13]  Brian J. Wright,et al.  Addition of Polarization and Diffuse Functions to the LANL2DZ Basis Set for P-Block Elements , 2001 .

[14]  M. Zeller,et al.  1,1′‐Di­bromo­ferrocene , 2004 .

[15]  Michael J. Frisch,et al.  Self‐consistent molecular orbital methods 25. Supplementary functions for Gaussian basis sets , 1984 .

[16]  Rudolph A. Marcus,et al.  Electron transfer reactions in chemistry. Theory and experiment , 1993 .

[17]  C. Koval,et al.  Ferrocene as an internal standard for electrochemical measurements , 1980 .

[18]  Neil G. Connelly,et al.  Chemical Redox Agents for Organometallic Chemistry. , 1996, Chemical reviews.

[19]  C. E. Webster,et al.  Electronic effects on a mononuclear Co complex with a pentadentate ligand for catalytic H₂ evolution. , 2014, Inorganic chemistry.

[20]  V. Barone,et al.  Quantum Calculation of Molecular Energies and Energy Gradients in Solution by a Conductor Solvent Model , 1998 .

[21]  M. Meot-ner Ion chemistry of ferrocene. Thermochemistry of ionization and protonation and solvent clustering. Slow and entropy-driven proton-transfer kinetics , 1989 .

[22]  Rudolph A. Marcus,et al.  On the Theory of Electron-Transfer Reactions. VI. Unified Treatment for Homogeneous and Electrode Reactions , 1965 .

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

[24]  Y. Kitagawa,et al.  A Density Functional Theory Based Protocol to Compute the Redox Potential of Transition Metal Complex with the Correction of Pseudo-Counterion: General Theory and Applications. , 2013, Journal of chemical theory and computation.

[25]  Thom H. Dunning,et al.  Gaussian basis sets for use in correlated molecular calculations. V. Core-valence basis sets for boron through neon , 1995 .

[26]  B. Sztáray,et al.  Binding energies and isomerization in metallocene ions from threshold photoelectron photoion coincidence spectroscopy. , 2010, Journal of the American Chemical Society.

[27]  Richard L Martin,et al.  Revised Basis Sets for the LANL Effective Core Potentials. , 2008, Journal of chemical theory and computation.

[28]  R. Friesner,et al.  Development of Accurate DFT Methods for Computing Redox Potentials of Transition Metal Complexes: Results for Model Complexes and Application to Cytochrome P450. , 2012, Journal of chemical theory and computation.

[29]  Timothy Clark,et al.  Efficient diffuse function‐augmented basis sets for anion calculations. III. The 3‐21+G basis set for first‐row elements, Li–F , 1983 .

[30]  V. V. Strelets,et al.  Electrochemical versus optical insight in frontier orbitals of Ti(IV), Zr(IV), and Hf(IV) bent metallocenes , 2000 .

[31]  Pedro Alexandrino Fernandes,et al.  General performance of density functionals. , 2007, The journal of physical chemistry. A.

[32]  Kirk A Peterson,et al.  Systematically convergent basis sets for transition metals. I. All-electron correlation consistent basis sets for the 3d elements Sc-Zn. , 2005, The Journal of chemical physics.

[33]  K. Wiberg,et al.  Solvent Effects. 5. Influence of Cavity Shape, Truncation of Electrostatics, and Electron Correlation on ab Initio Reaction Field Calculations , 1996 .

[34]  H. Gray,et al.  Rapid water reduction to H2 catalyzed by a cobalt bis(iminopyridine) complex. , 2011, Journal of the American Chemical Society.

[35]  W. Geiger Organometallic Electrochemistry: Origins, Development, and Future , 2007 .

[36]  A. Wachters,et al.  Gaussian Basis Set for Molecular Wavefunctions Containing Third‐Row Atoms , 1970 .

[37]  W. Kaim Chemical and electrochemical reduction of pentacarbonyl(4-cyanopyridine) complexes of chromium(0), molybdenum(0), and tungsten(0) , 1984 .

[38]  S. Trasatti The absolute electrode potential: an explanatory note (Recommendations 1986) , 1986 .

[39]  T. H. Dunning Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[40]  T. Dunning,et al.  Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions , 1992 .

[41]  D. Astruc,et al.  Metallocenes as references for the determination of redox potentials by cyclic voltammetry Permethylated iron and cobalt sandwich complexes, inhibition by polyamine dendrimers, and the role of hydroxy-containing ferrocenes , 2006 .

[42]  Krishnan Raghavachari,et al.  Highly correlated systems. Ionization energies of first row transition metals Sc–Zn , 1989 .

[43]  V. Barone,et al.  Toward reliable density functional methods without adjustable parameters: The PBE0 model , 1999 .

[44]  Giovanni Scalmani,et al.  Energies, structures, and electronic properties of molecules in solution with the C‐PCM solvation model , 2003, J. Comput. Chem..

[45]  Nathan J. DeYonker,et al.  Electrocatalytic and photocatalytic hydrogen production in aqueous solution by a molecular cobalt complex. , 2012, Angewandte Chemie.

[46]  Y. Tateyama,et al.  A method to calculate redox potentials relative to the normal hydrogen electrode in nonaqueous solution by using density functional theory-based molecular dynamics. , 2015, Physical chemistry chemical physics : PCCP.

[47]  W. R. Wadt,et al.  Ab initio effective core potentials for molecular calculations. Potentials for main group elements Na to Bi , 1985 .

[48]  Vincenzo Barone,et al.  Time-dependent density functional theory for molecules in liquid solutions , 2001 .

[49]  A. Das,et al.  Redox potential control by drug binding to cytochrome P450 3A4. , 2007, Journal of the American Chemical Society.

[50]  W. R. Wadt,et al.  Ab initio effective core potentials for molecular calculations , 1984 .

[51]  Nathan J DeYonker,et al.  The correlation consistent composite approach (ccCA): an alternative to the Gaussian-n methods. , 2006, The Journal of chemical physics.

[52]  J. Ludvík,et al.  Theoretical Predictions of Redox Potentials of Fischer-Type Chromium Aminocarbene Complexes , 2014 .

[53]  P. Jeffrey Hay,et al.  Gaussian basis sets for molecular calculations. The representation of 3d orbitals in transition‐metal atoms , 1977 .

[54]  T. Moore,et al.  Simple and accurate correlation of experimental redox potentials and DFT-calculated HOMO/LUMO energies of polycyclic aromatic hydrocarbons , 2013, Journal of Molecular Modeling.

[55]  J. Pople,et al.  Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules , 1972 .

[56]  Junming Ho Are thermodynamic cycles necessary for continuum solvent calculation of pKas and reduction potentials? , 2015, Physical chemistry chemical physics : PCCP.

[57]  S. Ketkov,et al.  Threshold ionization of cobaltocene: the metallocene molecule revealing zero kinetic energy States. , 2012, Angewandte Chemie.

[58]  Nathan J. DeYonker,et al.  Application of the Correlation Consistent Composite Approach (ccCA) to Third-Row (Ga-Kr) Molecules. , 2008, Journal of chemical theory and computation.

[59]  P. C. Hariharan,et al.  The influence of polarization functions on molecular orbital hydrogenation energies , 1973 .

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

[61]  J. Tomasi,et al.  Electrostatic interaction of a solute with a continuum. A direct utilizaion of AB initio molecular potentials for the prevision of solvent effects , 1981 .

[62]  C. Cramer,et al.  Computational electrochemistry: prediction of liquid-phase reduction potentials. , 2014, Physical chemistry chemical physics : PCCP.

[63]  K. Peterson,et al.  Basis set limit electronic excitation energies, ionization potentials, and electron affinities for the 3d transition metal atoms: Coupled cluster and multireference methods. , 2006, The Journal of chemical physics.

[64]  S. Papson “Model” , 1981 .

[65]  P. Winget,et al.  Computational electrochemistry: aqueous one-electron oxidation potentials for substituted anilines , 2000 .

[66]  T. Saji,et al.  Polarographic studies on bipyridines complexes , 1975 .

[67]  D. Lichtenberger,et al.  Gas-phase ionization energetics, electron-transfer kinetics, and ion solvation thermochemistry of decamethylmetallocenes, chromocene, and cobaltocene , 1994 .

[68]  Joel S. Miller,et al.  Decamethylosmocene and decamethylosmocenium: UV and x-ray photoelectron, magnetic, and electronic studies. Crystal and molecular structure of [Os(C5Me5)2].bul.+ [BF4]- , 1988 .

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

[70]  Rudolph A. Marcus,et al.  On the Theory of Oxidation‐Reduction Reactions Involving Electron Transfer. I , 1956 .

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

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

[73]  M. Hall,et al.  Basis sets for transition metals: Optimized outer p functions , 1996, Journal of computational chemistry.

[74]  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 .

[75]  R. Friesner,et al.  Computing Redox Potentials in Solution: Density Functional Theory as A Tool for Rational Design of Redox Agents , 2002 .

[76]  A. W. Addison,et al.  Conversion constants for redox potentials measured versus different reference electrodes in acetonitrile solutions at 25°C , 2000 .

[77]  T. Meyer,et al.  Proton-coupled electron transfer. , 2007, Chemical reviews.

[78]  M. Hill,et al.  Tetrabutylammonium tetrakis[3,5-bis(trifluoromethyl)phenyl]borate as a noncoordinating electrolyte : reversible 1e- oxidations of ruthenocene, osmocene, and Rh2(TM4)42+ (TM4 = 2,5-diisocyano-2,5-dimethylhexane) , 1991 .

[79]  W. Massa,et al.  1,1′-Bis(N,N-dimethylamino)ferrocene,1,1′-bis(N,N-dimethylamino) cobaltocenium hexafluorophosphate and 1,1′-bis(N,N-dimethylamino)titanocene dichloride. Crystal structure of 1,1′-bis(N,N-dimethylamino)titanocene dichloride , 1984 .

[80]  J. Dilworth,et al.  Probing the mechanism of hypoxia selectivity of copper bis(thiosemicarbazonato) complexes: DFT calculation of redox potentials and absolute acidities in solution. , 2006, Dalton transactions.

[81]  Andrew J. P. White,et al.  The Unusual Redox Properties of Fluoroferrocenes Revealed through a Comprehensive Study of the Haloferrocenes , 2015 .

[82]  Rudolph A. Marcus,et al.  Chemical and Electrochemical Electron-Transfer Theory , 1964 .