Atomic orbital basis sets

Electronic structure methods for molecular systems rely heavily on using basis sets composed of Gaussian functions for representing the molecular orbitals. A number of hierarchical basis sets have been proposed over the last two decades, and they have enabled systematic approaches to assessing and controlling the errors due to incomplete basis sets. We outline some of the principles for constructing basis sets, and compare the compositions of eight families of basis sets that are available in several different qualities and for a reasonable number of elements in the periodic table. © 2012 John Wiley & Sons, Ltd.

[1]  M. D. O'Connell,et al.  Correction , 2013, Nature.

[2]  P. Gill,et al.  Gaussian Expansions of Orbitals. , 2012, Journal of chemical theory and computation.

[3]  F. Jensen Polarization consistent basis sets. VII. The elements K, Ca, Ga, Ge, As, Se, Br, and Kr. , 2012, The Journal of chemical physics.

[4]  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.

[5]  Michael Dolg,et al.  Relativistic pseudopotentials: their development and scope of applications. , 2012, Chemical reviews.

[6]  David Feller,et al.  On the effectiveness of CCSD(T) complete basis set extrapolations for atomization energies. , 2011, The Journal of chemical physics.

[7]  Edward F. Valeev,et al.  Low-order tensor approximations for electronic wave functions: Hartree-Fock method with guaranteed precision. , 2011, The Journal of chemical physics.

[8]  Michael Dolg,et al.  Pseudopotentials and modelpotentials , 2011 .

[9]  Alexander B. Pacheco Introduction to Computational Chemistry , 2011 .

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

[11]  F. Jensen Describing Anions by Density Functional Theory: Fractional Electron Affinity. , 2010, Journal of chemical theory and computation.

[12]  J Grant Hill,et al.  Correlation consistent basis sets for explicitly correlated wavefunctions: valence and core-valence basis sets for Li, Be, Na, and Mg. , 2010, Physical chemistry chemical physics : PCCP.

[13]  G. A. Petersson,et al.  MP2/CBS atomic and molecular benchmarks for H through Ar. , 2010, The Journal of chemical physics.

[14]  F. E. Jorge,et al.  Augmented Gaussian basis sets of double and triple zeta valence qualities for the atoms K and Sc–Kr: Applications in HF, MP2, and DFT calculations of molecular electric properties , 2009 .

[15]  F. E. Jorge,et al.  Gaussian basis set of triple zeta valence quality for the atoms from K to Kr: Application in DFT and CCSD(T) calculations of molecular properties , 2009 .

[16]  David Feller,et al.  A survey of factors contributing to accurate theoretical predictions of atomization energies and molecular structures. , 2008, The Journal of chemical physics.

[17]  G. A. Petersson,et al.  The CCSD(T) complete basis set limit for Ne revisited. , 2008, The Journal of chemical physics.

[18]  F. E. Jorge,et al.  Gaussian basis set of double zeta quality for atoms K through Kr: Application in DFT calculations of molecular properties , 2008, J. Comput. Chem..

[19]  G. A. Petersson,et al.  Uniformly convergent n-tuple-zeta augmented polarized (nZaP) basis sets for complete basis set extrapolations. I. Self-consistent field energies. , 2008, The Journal of chemical physics.

[20]  Hideo Sekino,et al.  Basis set limit Hartree-Fock and density functional theory response property evaluation by multiresolution multiwavelet basis. , 2008, The Journal of chemical physics.

[21]  Hans-Joachim Werner,et al.  Systematically convergent basis sets for explicitly correlated wavefunctions: the atoms H, He, B-Ne, and Al-Ar. , 2008, The Journal of chemical physics.

[22]  Frank Jensen,et al.  Polarization consistent basis sets. 4: the elements He, Li, Be, B, Ne, Na, Mg, Al, and Ar. , 2007, The journal of physical chemistry. A.

[23]  F. E. Jorge,et al.  Gaussian basis sets of 5 zeta valence quality for correlated wave functions , 2006 .

[24]  F. E. Jorge,et al.  Gaussian basis sets of triple and quadruple zeta valence quality for correlated wave functions , 2006 .

[25]  B. Ruscic,et al.  W4 theory for computational thermochemistry: In pursuit of confident sub-kJ/mol predictions. , 2006, The Journal of chemical physics.

[26]  Frederick R. Manby,et al.  R12 methods in explicitly correlated molecular electronic structure theory , 2006 .

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

[28]  Christian Ochsenfeld,et al.  Multipole-based integral estimates for the rigorous description of distance dependence in two-electron integrals. , 2005, The Journal of chemical physics.

[29]  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.

[30]  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.

[31]  F. E. Jorge,et al.  Gaussian basis sets for correlated wave functions. Hydrogen, helium, first- and second-row atoms , 2005 .

[32]  F. Jensen Contracted basis sets for density functional calculations: segmented versus general contraction. , 2005, The Journal of chemical physics.

[33]  Sandro Chiodo,et al.  Newly developed basis sets for density functional calculations , 2005, J. Comput. Chem..

[34]  T. Helgaker,et al.  Polarization consistent basis sets. V. The elements Si-Cl. , 2004, The Journal of chemical physics.

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

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

[37]  Erik Van Lenthe,et al.  Optimized Slater‐type basis sets for the elements 1–118 , 2003, J. Comput. Chem..

[38]  G. A. Petersson,et al.  On the optimization of Gaussian basis sets , 2003 .

[39]  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 .

[40]  Frank Jensen,et al.  Polarization consistent basis sets. III. The importance of diffuse functions , 2002 .

[41]  N. Handy,et al.  Density functional generalized gradient calculations using Slater basis sets , 2002 .

[42]  Reinhold Schneider,et al.  Wavelet approximation of correlated wave functions. I. Basics , 2002 .

[43]  J. Pople,et al.  Self-consistent molecular orbital methods. 21. Small split-valence basis sets for first-row elements , 2002 .

[44]  F. Jensen Erratum: “Polarization consistent basis sets: Principles” [J. Chem. Phys. 115, 9113 (2001)] , 2002 .

[45]  Frank Jensen,et al.  Polarization consistent basis sets: Principles , 2001 .

[46]  Mark A. Ratner,et al.  6‐31G* basis set for third‐row atoms , 2001, J. Comput. Chem..

[47]  Angela K. Wilson,et al.  Gaussian basis sets for use in correlated molecular calculations. X. The atoms aluminum through argon revisited , 2001 .

[48]  Frank Jensen,et al.  The basis set convergence of the Hartree–Fock energy for H3+, Li2 and N2 , 2000 .

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

[50]  T. Noro,et al.  Valence and correlated basis sets for the first-row transition atoms from Sc to Zn , 2000 .

[51]  Frank Jensen,et al.  The basis set convergence of the density functional energy for H2 , 2000 .

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

[53]  Mark R. Pederson,et al.  Optimization of Gaussian basis sets for density-functional calculations , 1999 .

[54]  F. E. Jorge,et al.  Improved generator coordinate Hartree–Fock method: application to first-row atoms , 1999 .

[55]  D. Moncrieff,et al.  A universal basis set for high-precision molecular electronic structure studies: correlation effects in the ground states of , CO, BF and , 1998 .

[56]  Mark A. Ratner,et al.  6-31G * basis set for atoms K through Zn , 1998 .

[57]  T. Noro,et al.  Contracted polarization functions for the atoms helium through neon , 1997 .

[58]  Y. Satoh,et al.  Contracted Gaussian-type basis functions revisited. III. Atoms K through Kr , 1997 .

[59]  Kirk A. Peterson,et al.  The CO molecule: the role of basis set and correlation treatment in the calculation of molecular properties , 1997 .

[60]  H. Tatewaki,et al.  Contracted Gaussian-type basis functions revisited II. Atoms Na through Ar , 1997 .

[61]  Ernest R. Davidson,et al.  Comment on ``Comment on Dunning's correlation-consistent basis sets'' , 1996 .

[62]  H. Tatewaki,et al.  CONTRACTED GAUSSIAN-TYPE BASIS FUNCTIONS REVISITED , 1996 .

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

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

[65]  K. Hirao,et al.  Comment on Dunning's correlation-consistent basis sets , 1995 .

[66]  Manuela Merchán,et al.  Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions , 1995 .

[67]  Per-Olof Widmark,et al.  Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions , 1995 .

[68]  Werner Kutzelnigg,et al.  Theory of the expansion of wave functions in a gaussian basis , 1994 .

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

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

[71]  A. Thakkar,et al.  Double and quadruple zeta contracted Gaussian basis sets for hydrogen through neon , 1993 .

[72]  Angela K. Wilson,et al.  Gaussian basis sets for use in correlated molecular calculations. IX. The atoms gallium through krypton , 1993 .

[73]  Eric Magnusson Supplementary d and f functions in molecular wave functions at large and small internuclear separations , 1993, J. Comput. Chem..

[74]  J. D. Morgan,et al.  Erratum: Rates of convergence of the partial-wave expansions of atomic correlation energies [J. Chem. Phys. 96, 4484 (1992)] , 1992 .

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

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

[77]  Werner Kutzelnigg,et al.  Rates of convergence of the partial‐wave expansions of atomic correlation energies , 1992 .

[78]  Dennis R. Salahub,et al.  Optimization of Gaussian-type basis sets for local spin density functional calculations. Part I. Boron through neon, optimization technique and validation , 1992 .

[79]  P. Taylor,et al.  Atomic Natural Orbital (ANO) Basis Sets for Quantum Chemical Calculations , 1991 .

[80]  L. Curtiss,et al.  Compact contracted basis sets for third‐row atoms: Ga–Kr , 1990 .

[81]  B. Roos,et al.  Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions , 1990 .

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

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

[84]  G. A. Petersson,et al.  A complete basis set model chemistry. I. The total energies of closed‐shell atoms and hydrides of the first‐row elements , 1988 .

[85]  Warren J. Hehre,et al.  Molecular orbital theory of the properties of inorganic and organometallic compounds 5. Extended basis sets for first‐row transition metals , 1987 .

[86]  Peter R. Taylor,et al.  General contraction of Gaussian basis sets. I. Atomic natural orbitals for first‐ and second‐row atoms , 1987 .

[87]  J. Almlöf,et al.  Energy-optimized GTO basis sets for LCAO calculations. A gradient approach , 1986 .

[88]  Wim Klopper,et al.  Gaussian basis sets and the nuclear cusp problem , 1986 .

[89]  M. Klobukowski,et al.  Well-tempered GTF basis sets for the atoms K through χe , 1985 .

[90]  M. Klobukowski,et al.  The well-tempered GTF basis sets and their applications in the SCF calculations on N2, CO, Na2, and P2 , 1985 .

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

[92]  Mark S. Gordon,et al.  Self‐consistent molecular orbital methods. XXIII. A polarization‐type basis set for second‐row elements , 1982 .

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

[94]  J. Chandrasekhar,et al.  Efficient and accurate calculation of anion proton affinities , 1981 .

[95]  S. Huzinaga,et al.  A systematic preparation of new contracted Gaussian‐type orbital sets. III. Second‐row atoms from Li through ne , 1980 .

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

[97]  Mark S. Gordon,et al.  Self-consistent molecular-orbital methods. 22. Small split-valence basis sets for second-row elements , 1980 .

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

[99]  Michael W. Schmidt,et al.  Effective convergence to complete orbital bases and to the atomic Hartree–Fock limit through systematic sequences of Gaussian primitives , 1979 .

[100]  W. Nieuwpoort,et al.  Universal atomic basis sets , 1978 .

[101]  Uniform quality Gaussian basis sets. II. Multiple optima of small Gaussian basis sets for first row elements , 1977 .

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

[103]  E. Clementi,et al.  Study of the structure of molecular complexes , 1976 .

[104]  H. Lischka,et al.  PNO-CI (pair natural-orbital configuration interaction) and CEPA-PNO (coupled electron pair approximation with pair natural orbitals) calculations of molecular systems. , 1975 .

[105]  P. Mezey,et al.  Quality of Gaussian basis sets: Direct optimization of orbital exponents by the method of conjugate gradients , 1975 .

[106]  John A. Pople,et al.  Self‐consistent molecular orbital methods. XV. Extended Gaussian‐type basis sets for lithium, beryllium, and boron , 1975 .

[107]  H. Lischka,et al.  PNO–CI (pair natural orbital configuration interaction) and CEPA–PNO (coupled electron pair approximation with pair natural orbitals) calculations of molecular systems. II. The molecules BeH2, BH, BH3, CH4, CH−3, NH3 (planar and pyramidal), H2O, OH+3, HF and the Ne atom , 1975 .

[108]  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 .

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

[110]  R. Raffenetti,et al.  General contraction of Gaussian atomic orbitals: Core, valence, polarization, and diffuse basis sets; Molecular integral evaluation , 1973 .

[111]  E. Clementi,et al.  Study of the Structure of Molecular Complexes. I. Energy Surface of a Water Molecule in the Field of a Lithium Positive Ion , 1972 .

[112]  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 .

[113]  J. Pople,et al.  Self‐Consistent Molecular‐Orbital Methods. IX. An Extended Gaussian‐Type Basis for Molecular‐Orbital Studies of Organic Molecules , 1971 .

[114]  T. H. Dunning Gaussian Basis Functions for Use in Molecular Calculations. III. Contraction of (10s6p) Atomic Basis Sets for the First‐Row Atoms , 1970 .

[115]  J. Pople,et al.  Self‐Consistent Molecular Orbital Methods. IV. Use of Gaussian Expansions of Slater‐Type Orbitals. Extension to Second‐Row Molecules , 1970 .

[116]  S. Huzinaga,et al.  Gaussian‐Type Functions for Polyatomic Systems. II , 1970 .

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

[118]  Per E. M. Siegbahn,et al.  Polarization functions for first and second row atoms in Gaussian type MO-SCF calculations , 1970 .

[119]  J. Pople,et al.  Self‐Consistent Molecular‐Orbital Methods. I. Use of Gaussian Expansions of Slater‐Type Atomic Orbitals , 1969 .

[120]  R. Stewart Small Gaussian Expansions of Atomic Orbitals , 1969 .

[121]  A. Veillard Gaussian basis set for molecular wavefunctions containing second-row atoms , 1968 .

[122]  Enrico Clementi,et al.  Atomic Screening Constants from SCF Functions , 1963 .

[123]  R. S. Mulliken Criteria for the Construction of Good Self‐Consistent‐Field Molecular Orbital Wave Functions, and the Significance of LCAO‐MO Population Analysis , 1962 .

[124]  S. F. Boys Electronic wave functions - I. A general method of calculation for the stationary states of any molecular system , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[125]  J. C. Slater Atomic Shielding Constants , 1930 .