Basis set error estimation for DFT calculations of electronic g‐tensors for transition metal complexes

We present a detailed study of the basis set dependence of electronic g‐tensors for transition metal complexes calculated using Kohn–Sham density functional theory. Focus is on the use of locally dense basis set schemes where the metal is treated using either the same or a more flexible basis set than used for the ligand sphere. The performance of all basis set schemes is compared to the extrapolated complete basis set limit results. Furthermore, we test the performance of the aug‐cc‐pVTZ‐J basis set developed for calculations of NMR spin‐spin and electron paramagnetic resonance hyperfine coupling constants. Our results show that reasonable results can be obtain when using small basis sets for the ligand sphere, and very accurate results are obtained when an aug‐cc‐pVTZ basis set or similar is used for all atoms in the complex. © 2014 Wiley Periodicals, Inc.

[1]  F. Neese Analytic derivative calculation of electronic g-tensors based on multireference configuration interaction wavefunctions , 2007 .

[2]  G. Upreti Electron paramagnetic resonance of Mn2+ in ammonium and potassium-nickel tutton salt single crystals , 1974 .

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

[4]  E. Baerends,et al.  An evaluation of the density functional approach in the zero order regular approximation for relativistic effects: Magnetic interactions in small metal compounds , 2001 .

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

[6]  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.

[7]  N. Edelstein,et al.  Electron Paramagnetic Resonance Studies of the Electronic Structures of Bis(maleonitriledithiolato)copper(II), -nickel(III), -cobalt(II), and -rhodium(II) Complexes , 1964 .

[8]  H. Quiney,et al.  Relativistic calculation of hyperfine and electron spin resonance parameters in diatomic molecules , 2002 .

[9]  R. F. Campbell,et al.  Slow-motional ESR spectra for vanadyl complexes and their model dependence , 1980 .

[10]  David E. Woon,et al.  Gaussian basis sets for use in correlated molecular calculations. IV. Calculation of static electrical response properties , 1994 .

[11]  S. Sauer,et al.  On the Use of Locally Dense Basis Sets in the Calculation of EPR Hyperfine Couplings: A Study on Model Systems for Bio-Inorganic Fe and Co Complexes , 2014 .

[12]  H. Scholl,et al.  ESR and ENDOR of copper(II) complexes with nitrogen donors: probing parameters for prosthetic group modeling of superoxide dismutase , 1992 .

[13]  B. Weckhuysen,et al.  The siting of Cu(II) in mordenite: a theoretical spectroscopic study , 2002 .

[14]  W. Graham,et al.  ESR spectra of the MnO, MnO2, MnO3, and MnO4 molecules at 4 °K , 1977 .

[15]  P. Malmqvist,et al.  Calculation of EPR g tensors for transition-metal complexes based on multiconfigurational perturbation theory (CASPT2). , 2007, Chemphyschem : a European journal of chemical physics and physical chemistry.

[16]  Olav Vahtras,et al.  Ab initio calculations of electronic g-factors by means of multiconfiguration response theory , 1997 .

[17]  D. B. Chesnut,et al.  Locally dense basis sets for chemical shift calculations , 1989 .

[18]  S. Patchkovskii,et al.  Calculation of Hyperfine Tensors and Paramagnetic NMR Shifts Using the Relativistic Zeroth-Order Regular Approximation and Density Functional Theory. , 2011, Journal of chemical theory and computation.

[19]  H. Jensen,et al.  Correlated four-component EPR g-tensors for doublet molecules. , 2013, The Journal of chemical physics.

[20]  J. Morton,et al.  EPR spectrum of Cr(CO)4+ in krypton at 20 K , 1984 .

[21]  C. Lim,et al.  Polarization-consistent versus correlation-consistent basis sets in predicting molecular and spectroscopic properties. , 2007, The journal of physical chemistry. A.

[22]  O. Malkina,et al.  Relativistic four-component calculations of electronic g-tensors in the matrix Dirac–Kohn–Sham framework , 2010 .

[23]  K. Wieghardt,et al.  Nitridocyanometalates of CrV, MnV, and MnVI † , 1998 .

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

[25]  Jean-Philippe Blaudeau,et al.  Extension of Gaussian-2 (G2) theory to molecules containing third-row atoms K and Ca , 1995 .

[26]  P. Provasi,et al.  The effect of lone pairs and electronegativity on the indirect nuclear spin–spin coupling constants in CH2X (X=CH2, NH, O, S): Ab initio calculations using optimized contracted basis sets , 2001 .

[27]  G. Lushington Small Closed-Form CI Expansions for Electronic g-Tensor Calculations , 2000 .

[28]  J. Snyder,et al.  Substituent Effects on Scalar 2J(19F,19F) and 3J(19F,19F) NMR Couplings: A Comparison of SOPPA and DFT Methods , 2003 .

[29]  Frank Neese,et al.  Prediction of electron paramagnetic resonance g values using coupled perturbed Hartree–Fock and Kohn–Sham theory , 2001 .

[30]  M. Kaupp,et al.  Scalar relativistic calculations of hyperfine coupling tensors using the Douglas-Kroll-Hess method with a finite-size nucleus model. , 2004, Physical chemistry chemical physics : PCCP.

[31]  C. Marian,et al.  The g-tensor of AlO: Principal problems and first approaches , 2008 .

[32]  O. Kikuchi,et al.  Ab initio calculations of g values of free radicals by finite perturbation theory , 1991 .

[33]  J. Autschbach,et al.  Variational versus Perturbational Treatment of Spin-Orbit Coupling in Relativistic Density Functional Calculations of Electronic g Factors: Effects from Spin-Polarization and Exact Exchange. , 2013, Journal of chemical theory and computation.

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

[35]  T. Kupka Prediction of water's isotropic nuclear shieldings and indirect nuclear spin–spin coupling constants (SSCCs) using correlation‐consistent and polarization‐consistent basis sets in the Kohn–Sham basis set limit , 2009, Magnetic resonance in chemistry : MRC.

[36]  J. Morton,et al.  An ESR study at 4 K of the reaction between H and Ni(CO) 4 , 1984 .

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

[38]  B. Schimmelpfennig,et al.  Density Functional Calculations of Electronic g-Tensors Using Spin−Orbit Pseudopotentials and Mean-Field All-Electron Spin−Orbit Operators , 2000 .

[39]  Hans W. Horn,et al.  Fully optimized contracted Gaussian basis sets for atoms Li to Kr , 1992 .

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

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

[42]  R. Mcweeny,et al.  The calculation of spin-orbit splitting and g tensors for small molecules and radicals , 1973, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[43]  Mihály Kállay,et al.  Calculation of electronic g-tensors using coupled cluster theory. , 2009, The journal of physical chemistry. A.

[44]  Tom Ziegler,et al.  Calculation of the G-Tensor of Electron Paramagnetic Resonance Spectroscopy Using Gauge-Including Atomic Orbitals and Density Functional Theory , 1997 .

[45]  Frank Jensen,et al.  Basis Set Convergence of Nuclear Magnetic Shielding Constants Calculated by Density Functional Methods. , 2008, Journal of chemical theory and computation.

[46]  T. Kupka From correlation-consistent to polarization-consistent basis sets estimation of NMR spin–spin coupling constant in the B3LYP Kohn–Sham basis set limit , 2008 .

[47]  F. Jensen,et al.  Basis Set Recommendations for DFT Calculations of Gas-Phase Optical Rotation at Different Wavelengths. , 2012, Journal of chemical theory and computation.

[48]  A. Delabie,et al.  A reinterpretation of the EPR spectra of Cu(II) in zeolites A, Y and ZK4, based on ab initio cluster model calculations , 2001 .

[49]  F. Grein,et al.  Efficient calculation of electron paramagnetic resonance g-tensors by multireference configuration interaction sum-over-state expansions, using the atomic mean-field spin–orbit method , 2003 .

[50]  R. Nicholls,et al.  Nuclear spin-spin coupling in silane and its isotopomers: Ab initio calculation and experimental investigation , 2001 .

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

[52]  J. Kongsted,et al.  Improving the calculation of Electron Paramagnetic Resonance hyperfine coupling tensors for d-block metals. , 2012, Physical chemistry chemical physics : PCCP.

[53]  P. H. Kasai,et al.  COPPER CARBONYLS, CU(CO) AND CU(CO)3: MATRIX ISOLATION ESR STUDY , 1985 .

[54]  T. Enevoldsen,et al.  Correlated calculations of indirect nuclear spin-spin coupling constants using second-order polarization propagator approximations: SOPPA and SOPPA(CCSD) , 1998 .

[55]  A. van der Avoird,et al.  Density functional calculations of molecular g-tensors in the zero-order regular approximation for relativistic effects , 1997 .

[56]  S. Sauer,et al.  Structural trends of 77Se1H spin–spin coupling constants and conformational behavior of 2‐substituted selenophenes , 2010, Magnetic resonance in chemistry : MRC.

[57]  P. Provasi,et al.  Optimized basis sets for the calculation of indirect nuclear spin-spin coupling constants involving the atoms B, Al, Si, P, and Cl. , 2010, The Journal of chemical physics.

[58]  T. Kupka Complete basis set prediction of methanol isotropic nuclear magnetic shieldings and indirect nuclear spin–spin coupling constants (SSCC) using polarization‐consistent and XZP basis sets and B3LYP and BHandH density functionals , 2009, Magnetic resonance in chemistry : MRC.

[59]  T. DeVore,et al.  Titanium difluoride and titanium trifluoride molecules: electron spin resonance spectra in rare-gas matrices at 4 K , 1977 .

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

[61]  Suppression of quantum dot blinking in DTT-doped polymer films. , 2009, The journal of physical chemistry. C, Nanomaterials and interfaces.

[62]  J. Morton,et al.  The EPR spectrum of a single crystal of chromium hexacarbonyl doped with Fe(CO)5 , 1982 .

[63]  V Van Speybroeck,et al.  Accurate spin-orbit and spin-other-orbit contributions to the g-tensor for transition metal containing systems. , 2012, Physical chemistry chemical physics : PCCP.

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

[65]  W. H. Armstrong,et al.  Manganese clusters with relevance to photosystem II. , 2004, Chemical reviews.

[66]  S. Sauer,et al.  Erratum: “Unexpected differential sensitivity of nuclear spin–spin-coupling constants to bond stretching in BH4−, NH4+, and SiH4” [J. Chem. Phys. 113, 3121 (2000)] , 2001 .

[67]  A. Døssing,et al.  Optical and EPR spectra of the thionitrosyl complex [Cr(OH2)5(NS)]2+ , 2009 .

[68]  A. Barouch,et al.  Electron paramagnetic resonance in compounds of transition elements , 1974 .

[69]  A. Schäfer,et al.  Fully optimized contracted Gaussian basis sets of triple zeta valence quality for atoms Li to Kr , 1994 .

[70]  Konstantin M. Neyman,et al.  Calculation of Electronic g-Tensors Using a Relativistic Density Functional Douglas−Kroll Method , 2002 .

[71]  J. Kongsted,et al.  Optimized Basis Sets for Calculation of Electron Paramagnetic Resonance Hyperfine Coupling Constants: aug-cc-pVTZ-J for the 3d Atoms Sc-Zn. , 2011, Journal of chemical theory and computation.

[72]  S. Sauer,et al.  Unexpected differential sensitivity of nuclear spin–spin-coupling constants to bond stretching in BH4−, NH4+, and SiH4 , 2000 .

[73]  W. Lubitz,et al.  [NiFe] and [FeFe] hydrogenases studied by advanced magnetic resonance techniques. , 2007, Chemical reviews.

[74]  T. Kupka,et al.  Convergence of Nuclear Magnetic Shieldings in the Kohn-Sham Limit for Several Small Molecules. , 2010, Journal of chemical theory and computation.

[75]  D. Jayatilaka Electron spin resonance g tensors from general Hartree–Fock calculations , 1998 .

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

[77]  J. Kongsted,et al.  Validating and Analyzing EPR Hyperfine Coupling Constants with Density Functional Theory. , 2013, Journal of chemical theory and computation.