Automatic Generation of Auxiliary Basis Sets.

A procedure was developed to automatically generate auxiliary basis sets (ABSs) for use with the resolution of the identity (RI) approximation, starting from a given orbital basis set (OBS). The goal is to provide an accurate and universal solution for cases where no optimized ABSs are available. In this context, "universal" is understood as the ability of the ABS to be used for Coulomb, exchange, and correlation energy fitting. The generation scheme (denoted AutoAux) works by spanning the product space of the OBS using an even-tempered expansion for each atom in the system. The performance of AutoAux in conjunction with different OBSs [def2-SVP, def2-TZVP, def2-QZVPP, and cc-pwCVnZ (n = D, T, Q, 5)] has been evaluated for elements from H to Rn and compared to existing predefined ABSs. Due to the requirements of simplicity and universality, the generated ABSs are larger than the optimized ones but lead to similar errors in MP2 total energies (on the order of 10-5 to 10-4 Eh/atom).

[1]  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.

[2]  Frank Neese,et al.  Periodic Trends in Lanthanide Compounds through the Eyes of Multireference ab Initio Theory. , 2016, Inorganic chemistry.

[3]  Florian Weigend,et al.  Approximated electron repulsion integrals: Cholesky decomposition versus resolution of the identity methods. , 2009, The Journal of chemical physics.

[4]  Roland Lindh,et al.  Unbiased auxiliary basis sets for accurate two-electron integral approximations. , 2007, The Journal of chemical physics.

[5]  Evgeny Epifanovsky,et al.  General implementation of the resolution-of-the-identity and Cholesky representations of electron repulsion integrals within coupled-cluster and equation-of-motion methods: theory and benchmarks. , 2013, The Journal of chemical physics.

[6]  Dmitrij Rappoport,et al.  Property-optimized gaussian basis sets for molecular response calculations. , 2010, The Journal of chemical physics.

[7]  Kirk A. Peterson,et al.  Accurate correlation consistent basis sets for molecular core–valence correlation effects: The second row atoms Al–Ar, and the first row atoms B–Ne revisited , 2002 .

[8]  Michael Dolg,et al.  Energy-consistent relativistic pseudopotentials and correlation consistent basis sets for the 4d elements Y-Pd. , 2007, The Journal of chemical physics.

[9]  Frank Neese,et al.  SparseMaps--A systematic infrastructure for reduced-scaling electronic structure methods. III. Linear-scaling multireference domain-based pair natural orbital N-electron valence perturbation theory. , 2016, The Journal of chemical physics.

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

[11]  Mihály Kállay,et al.  A systematic way for the cost reduction of density fitting methods. , 2014, The Journal of chemical physics.

[12]  K. Ruedenberg,et al.  Even‐tempered atomic orbitals. VI. Optimal orbital exponents and optimal contractions of Gaussian primitives for hydrogen, carbon, and oxygen in molecules , 1974 .

[13]  Michael Dolg,et al.  Energy-consistent pseudopotentials and correlation consistent basis sets for the 5d elements Hf-Pt. , 2009, The Journal of chemical physics.

[14]  Wei An,et al.  Ab initio calculation of bowl, cage, and ring isomers of C20 and C20-. , 2005, The Journal of chemical physics.

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

[16]  Wenjian Liu,et al.  A small-core multiconfiguration Dirac–Hartree–Fock-adjusted pseudopotential for Tl – application to TlX (X = F, Cl, Br, I) , 2000 .

[17]  Kirk A Peterson,et al.  Molecular core-valence correlation effects involving the post-d elements Ga-Rn: benchmarks and new pseudopotential-based correlation consistent basis sets. , 2010, The Journal of chemical physics.

[18]  P. Schwerdtfeger,et al.  Relativistic small-core energy-consistent pseudopotentials for the alkaline-earth elements from Ca to Ra. , 2006, The Journal of chemical physics.

[19]  T. Noro,et al.  Segmented contracted basis sets for atoms H through Xe: Sapporo-(DK)-nZP sets (n = D, T, Q) , 2012, Theoretical Chemistry Accounts.

[20]  Enrico Clementi,et al.  Geometrical basis set for molecular computations , 1982 .

[21]  P. Schwerdtfeger,et al.  All-electron and relativistic pseudopotential studies for the group 1 element polarizabilities from K to element 119. , 2005, The Journal of chemical physics.

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

[23]  Paul von Ragué Schleyer,et al.  Pseudopotential approaches to Ca, Sr, and Ba hydrides. Why are some alkaline earth MX2 compounds bent? , 1991 .

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

[25]  H. Schaefer,et al.  The alkaline earth dimer cations (Be2 +, Mg2 +, Ca2 +, Sr2 +, and Ba2 +). Coupled cluster and full configuration interaction studies† , 2013 .

[26]  J. Almlöf,et al.  Integral approximations for LCAO-SCF calculations , 1993 .

[27]  Michael Dolg,et al.  Small-core multiconfiguration-Dirac–Hartree–Fock-adjusted pseudopotentials for post-d main group elements: Application to PbH and PbO , 2000 .

[28]  F. Neese,et al.  Efficient, approximate and parallel Hartree–Fock and hybrid DFT calculations. A ‘chain-of-spheres’ algorithm for the Hartree–Fock exchange , 2009 .

[29]  Nathan J. DeYonker,et al.  Systematically convergent correlation consistent basis sets for molecular core-valence correlation effects: the third-row atoms gallium through krypton. , 2007, The journal of physical chemistry. A.

[30]  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.

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

[32]  Florian Weigend,et al.  A fully direct RI-HF algorithm: Implementation, optimised auxiliary basis sets, demonstration of accuracy and efficiency , 2002 .

[33]  Christof Hättig,et al.  Optimization of auxiliary basis sets for RI-MP2 and RI-CC2 calculations: Core–valence and quintuple-ζ basis sets for H to Ar and QZVPP basis sets for Li to Kr , 2005 .

[34]  B. Shepler,et al.  On the spectroscopic and thermochemical properties of ClO, BrO, IO, and their anions. , 2006, The journal of physical chemistry. A.

[35]  Guntram Rauhut,et al.  Energy-consistent pseudopotentials for group 11 and 12 atoms: adjustment to multi-configuration Dirac–Hartree–Fock data , 2005 .

[36]  F. Weigend,et al.  Gaussian basis sets of quadruple zeta valence quality for atoms H–Kr , 2003 .

[37]  Angela K. Wilson,et al.  Gaussian basis sets for use in correlated molecular calculations. VII. Valence, core-valence, and scalar relativistic basis sets for Li, Be, Na, and Mg , 2011 .

[38]  Arnim Hellweg,et al.  Optimized accurate auxiliary basis sets for RI-MP2 and RI-CC2 calculations for the atoms Rb to Rn , 2007 .

[39]  Michael Dolg,et al.  The accuracy of the pseudopotential approximation: non-frozen-core effects for spectroscopic constants of alkali fluorides XF (X = K, Rb, Cs) , 1996 .

[40]  Roland Lindh,et al.  New relativistic ANO basis sets for transition metal atoms. , 2005, The journal of physical chemistry. A.

[41]  Rui Yang,et al.  Automatically generated Coulomb fitting basis sets: design and accuracy for systems containing H to Kr. , 2007, The Journal of chemical physics.

[42]  Roland Lindh,et al.  Main group atoms and dimers studied with a new relativistic ANO basis set , 2004 .

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

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

[45]  J. Almlöf,et al.  Principles for a direct SCF approach to LICAO–MOab‐initio calculations , 1982 .

[46]  Hans Horn,et al.  Prescreening of two‐electron integral derivatives in SCF gradient and Hessian calculations , 1991 .

[47]  S. Ten-no,et al.  On approximating electron repulsion integrals with linear combination of atomic‐electron distributions , 1996 .

[48]  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.

[49]  Frank Neese,et al.  Improved Segmented All-Electron Relativistically Contracted Basis Sets for the Lanthanides. , 2016, Journal of chemical theory and computation.

[50]  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 .

[51]  Peter R. Taylor Eric Bylaska,et al.  C20: Fullerene, Bowl or Ring? New Results from Coupled-Cluster Calculations , 1995 .

[52]  Florian Weigend,et al.  Hartree–Fock exchange fitting basis sets for H to Rn † , 2008, J. Comput. Chem..

[53]  F. Weigend,et al.  Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations , 2002 .

[54]  Alistair P. Rendell,et al.  COUPLED-CLUSTER THEORY EMPLOYING APPROXIMATE INTEGRALS : AN APPROACH TO AVOID THE INPUT/OUTPUT AND STORAGE BOTTLENECKS , 1994 .

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

[56]  Holger Patzelt,et al.  RI-MP2: optimized auxiliary basis sets and demonstration of efficiency , 1998 .

[57]  B. Roos,et al.  New relativistic ANO basis sets for actinide atoms , 2005 .

[58]  Robert J. Harrison,et al.  An implementation of RI–SCF on parallel computers , 1997 .

[59]  F. Neese,et al.  Comparison of two efficient approximate Hartee–Fock approaches , 2009 .

[60]  T. Noro,et al.  Relativistic segmented contraction basis sets with core-valence correlation effects for atoms 57La through 71Lu: Sapporo-DK-nZP sets (n = D, T, Q) , 2012, Theoretical Chemistry Accounts.

[61]  Marco Häser,et al.  Improvements on the direct SCF method , 1989 .

[62]  H. Stoll,et al.  Systematically convergent basis sets with relativistic pseudopotentials. II. Small-core pseudopotentials and correlation consistent basis sets for the post-d group 16–18 elements , 2003 .

[63]  Jacek Koput,et al.  Ab initio potential energy surface and vibrational-rotational energy levels of X2Σ+ CaOH , 2002 .

[64]  Mariusz Klobukowski,et al.  Well-tempered Gaussian basis sets for the calculation of matrix Hartree-Fock wavefunctions , 1993 .

[65]  S. Ten-no,et al.  Three-center expansion of electron repulsion integrals with linear combination of atomic electron distributions , 1995 .

[66]  T. Noro,et al.  Sapporo-(DKH3)-nZP (n = D, T, Q) sets for the sixth period s-, d-, and p-block atoms , 2013, Theoretical Chemistry Accounts.

[67]  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.

[68]  N. H. Beebe,et al.  Simplifications in the generation and transformation of two‐electron integrals in molecular calculations , 1977 .

[69]  B. Miguel,et al.  A comparison of the geometrical sequence formula and the well-tempered formulas for generating GTO basis orbital exponents , 1990 .