Improved Segmented All-Electron Relativistically Contracted Basis Sets for the Lanthanides.

Improved versions of the segmented all-electron relativistically contracted (SARC) basis sets for the lanthanides are presented. The second-generation SARC2 basis sets maintain efficient construction of their predecessors and their individual adaptation to the DKH2 and ZORA Hamiltonians, but feature exponents optimized with a completely new orbital shape fitting procedure and a slightly expanded f space that results in sizable improvement in CASSCF energies and in significantly more accurate prediction of spin-orbit coupling parameters. Additionally, an extended set of polarization/correlation functions is constructed that is appropriate for multireference correlated calculations and new auxiliary basis sets for use in resolution-of-identity (density-fitting) approximations in combination with both DFT and wave function based treatments. Thus, the SARC2 basis sets extend the applicability of the first-generation DFT-oriented basis sets to routine all-electron wave function-based treatments of lanthanide complexes. The new basis sets are benchmarked with respect to excitation energies, radial distribution functions, optimized geometries, orbital eigenvalues, ionization potentials, and spin-orbit coupling parameters of lanthanide systems and are shown to be suitable for the description of magnetic and spectroscopic properties using both DFT and multireference wave function-based methods.

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

[2]  Björn O. Roos,et al.  Second-order perturbation theory with a complete active space self-consistent field reference function , 1992 .

[3]  C. Van Alsenoy,et al.  Ab initio calculations on large molecules: The multiplicative integral approximation , 1988 .

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

[5]  F. Cimpoesu,et al.  The theoretical account of the ligand field bonding regime and magnetic anisotropy in the DySc2N@C80 Single Ion Magnet endohedral fullerene. , 2014, Physical chemistry chemical physics : PCCP.

[6]  A. Popov,et al.  Prato and Bingel-Hirsch cycloaddition to heptagon-containing LaSc2N@C(s)(hept)-C80: importance of pentalene units. , 2015, Chemical communications.

[7]  Florian Weigend,et al.  Auxiliary basis sets for main row atoms and transition metals and their use to approximate Coulomb potentials , 1997 .

[8]  J. P. Dahl,et al.  Molecular Electronic Structures of Transition Metal Complexes II , 2012 .

[9]  Markus Reiher,et al.  Douglas–Kroll–Hess Theory: a relativistic electrons-only theory for chemistry , 2006 .

[10]  Jorge M. Seminario,et al.  Recent developments and applications of modern density functional theory , 1996 .

[11]  J. L. Whitten,et al.  Coulombic potential energy integrals and approximations , 1973 .

[12]  Evert Jan Baerends,et al.  Relativistic total energy using regular approximations , 1994 .

[13]  D. N. Laikov.  Fast evaluation of density functional exchange-correlation terms using the expansion of the electron density in auxiliary basis sets , 1997 .

[14]  B. Roos,et al.  A modified definition of the zeroth-order Hamiltonian in multiconfigurational perturbation theory (CASPT2) , 2004 .

[15]  B. Scott,et al.  Uncovering f-element bonding differences and electronic structure in a series of 1 : 3 and 1 : 4 complexes with a diselenophosphinate ligand , 2013 .

[16]  F. E. Jorge,et al.  Accurate universal Gaussian basis set for all atoms of the Periodic Table , 1998 .

[17]  B. Roos,et al.  Relativistic quantum chemistry: the multiconfigurational approach , 2004 .

[18]  Roland Lindh,et al.  New relativistic atomic natural orbital basis sets for lanthanide atoms with applications to the Ce diatom and LuF3. , 2008, The journal of physical chemistry. A.

[19]  Frank Neese,et al.  Efficient and accurate approximations to the molecular spin-orbit coupling operator and their use in molecular g-tensor calculations. , 2005, The Journal of chemical physics.

[20]  Björn O. Roos,et al.  The CASSCF state interaction method , 1989 .

[21]  C. Barnes,et al.  Systematic investigation of thorium(IV)- and uranium(IV)-ligand bonding in dithiophosphonate, thioselenophosphinate, and diselenophosphonate complexes. , 2013, Inorganic chemistry.

[22]  Attila Kovács,et al.  Structure and Vibrations of Lanthanide Trihalides. An Assessment of Experimental and Theoretical Data. , 2004 .

[23]  Evert Jan Baerends,et al.  Relativistic regular two‐component Hamiltonians , 1993 .

[24]  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.

[25]  Frank Neese,et al.  Calibration of scalar relativistic density functional theory for the calculation of sulfur K-edge X-ray absorption spectra. , 2010, Inorganic chemistry.

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

[27]  Marco Häser,et al.  Auxiliary basis sets to approximate Coulomb potentials , 1995 .

[28]  M. Dolg.  Computational Methods in Lanthanide and Actinide Chemistry: Dolg/Computational Methods in Lanthanide and Actinide Chemistry , 2015 .

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

[30]  M. Hargittai.  The molecular geometry of gas-phase metal halides , 1988 .

[31]  M. Reiher.  Relativistic Douglas–Kroll–Hess theory , 2012 .

[32]  Trond Saue,et al.  Relativistic Hamiltonians for chemistry: a primer. , 2011, Chemphyschem : a European journal of chemical physics and physical chemistry.

[33]  A. Popov,et al.  Magnetic anisotropy of endohedral lanthanide ions: paramagnetic NMR study of MSc2N@C80-I h with M running through the whole 4f row , 2015, Chemical science.

[34]  Frank Neese,et al.  All-Electron Scalar Relativistic Basis Sets for the Lanthanides. , 2009, Journal of chemical theory and computation.

[35]  Rick A. Kendall,et al.  The impact of the resolution of the identity approximate integral method on modern ab initio algorithm development , 1997 .

[36]  Frank Neese,et al.  First principles approach to the electronic structure, magnetic anisotropy and spin relaxation in mononuclear 3d-transition metal single molecule magnets , 2015 .

[37]  Hong Jiang,et al.  3d-4f magnetic interaction with density functional theory plus u approach: local Coulomb correlation and exchange pathways. , 2013, The journal of physical chemistry. A.

[38]  Frank Neese,et al.  All‐electron basis sets for heavy elements , 2014 .

[39]  Stephen R. Langhoff,et al.  Quantum mechanical electronic structure calculations with chemical accuracy , 1995 .

[40]  C. Platas‐Iglesias,et al.  Toward the Prediction of Water Exchange Rates in Magnetic Resonance Imaging Contrast Agents: A Density Functional Theory Study. , 2015, The journal of physical chemistry. A.

[41]  Evert Jan Baerends,et al.  Self-consistent molecular Hartree—Fock—Slater calculations I. The computational procedure , 1973 .

[42]  Frank Jensen,et al.  Atomic orbital basis sets , 2013 .

[43]  Florian Weigend,et al.  Error-Balanced Segmented Contracted Basis Sets of Double-ζ to Quadruple-ζ Valence Quality for the Lanthanides. , 2012, Journal of chemical theory and computation.

[44]  K. Hirao,et al.  The Douglas-Kroll-Hess approach. , 2012, Chemical reviews.

[45]  F. Neese,et al.  A fully variational spin-orbit coupled complete active space self-consistent field approach: application to electron paramagnetic resonance g-tensors. , 2013, The Journal of chemical physics.

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

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

[48]  John R. Sabin,et al.  On some approximations in applications of Xα theory , 1979 .

[49]  Frank Neese,et al.  The ORCA program system , 2012 .

[50]  R. Cimiraglia,et al.  n-electron valence state perturbation theory: A spinless formulation and an efficient implementation of the strongly contracted and of the partially contracted variants , 2002 .

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

[52]  R. Salcedo,et al.  Computational study of μ–η6η6-phenyl, η5-cyclopentadienyllanthanum(II) complexes and their relative stability , 2013 .

[53]  Ph. Durand,et al.  Regular Two-Component Pauli-Like Effective Hamiltonians in Dirac Theory , 1986 .

[54]  S. Nakashima,et al.  Bonding Study on the Chemical Separation of Am(III) from Eu(III) by S-, N-, and O-Donor Ligands by Means of All-Electron ZORA-DFT Calculation. , 2015, Inorganic chemistry.

[55]  Luis Serrano-Andrés,et al.  The multi-state CASPT2 method , 1998 .

[56]  M. Botta,et al.  Solution structure of Ln(III) complexes with macrocyclic ligands through theoretical evaluation of 1H NMR contact shifts. , 2012, Inorganic chemistry.

[57]  Michael Dolg,et al.  Segmented Contracted Douglas-Kroll-Hess Adapted Basis Sets for Lanthanides. , 2011, Journal of chemical theory and computation.

[58]  G. Rajaraman,et al.  Decisive interactions that determine ferro/antiferromagnetic coupling in {3d-4f} pairs: a case study on dinuclear {V(IV)-Gd(III)} complexes. , 2013, Dalton transactions.

[59]  Celestino Angeli,et al.  Third-order multireference perturbation theory: the n-electron valence state perturbation-theory approach. , 2006, The Journal of chemical physics.

[60]  S. Nakashima,et al.  Benchmark study of the Mössbauer isomer shifts of Eu and Np complexes by relativistic DFT calculations for understanding the bonding nature of f-block compounds. , 2015, Dalton transactions.