Revisiting the extrapolation of correlation energies to complete basis set limit

The extrapolation scheme of correlation energy is revisited to evaluate the complete basis set limit from double‐zeta (DZ) and triple‐zeta levels of calculations. The DZ level results are adjusted to the standard asymptotic behavior with respect to the cardinal number, observed at the higher levels of basis sets. Two types of adjusting schemes with effective scaling factors, which recover errors in extrapolations with the DZ level basis set, are examined. The first scheme scales the cardinal number for the DZ level energy, while the second scheme scales the prefactor of the extrapolation function. Systematic assessments on the Gaussian‐3X and Gaussian‐2 test sets reveal that these calibration schemes successfully and drastically reduce errors without additional computational efforts. © 2015 Wiley Periodicals, Inc.

[1]  M. Head‐Gordon,et al.  A fifth-order perturbation comparison of electron correlation theories , 1989 .

[2]  D. Feller.  Benchmarks of improved complete basis set extrapolation schemes designed for standard CCSD(T) atomization energies. , 2013, The Journal of chemical physics.

[3]  W. Kutzelnigg,et al.  Møller-plesset calculations taking care of the correlation CUSP , 1987 .

[4]  Angela K. Wilson,et al.  Gaussian basis sets for use in correlated molecular calculations. VI. Sextuple zeta correlation consistent basis sets for boron through neon , 1996 .

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

[6]  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 .

[7]  Edward F. Valeev,et al.  Analysis of the errors in explicitly correlated electronic structure theory. , 2005, Physical chemistry chemical physics : PCCP.

[8]  G. A. Petersson,et al.  A Comparison of Model Chemistries , 1995 .

[9]  D. Tew,et al.  New correlation factors for explicitly correlated electronic wave functions. , 2005, The Journal of chemical physics.

[10]  R. Metzger,et al.  Piecewise polynomial configuration interaction natural orbital study of 1 s2 helium , 1979 .

[11]  Donald G. Truhlar,et al.  Basis-set extrapolation , 1998 .

[12]  P. Piecuch,et al.  Extrapolating potential energy surfaces by scaling electron correlation at a single geometry , 2006 .

[13]  Jae Shin Lee,et al.  Basis set and correlation dependent extrapolation of correlation energy , 2003 .

[14]  S. J. Cole,et al.  Towards a full CCSDT model for electron correlation , 1985 .

[15]  P. Piecuch,et al.  Extrapolating potential energy surfaces by scaling electron correlation: isomerization of bicyclobutane to butadiene. , 2008, The Journal of chemical physics.

[16]  A. Varandas.  Extrapolating to the one-electron basis-set limit in electronic structure calculations. , 2007, The Journal of chemical physics.

[17]  Wim Klopper,et al.  Wave functions with terms linear in the interelectronic coordinates to take care of the correlation cusp. I. General theory , 1991 .

[18]  C. Schwartz,et al.  Importance of Angular Correlations between Atomic Electrons , 1962 .

[19]  Generalized uniform singlet- and triplet-pair extrapolation of the correlation energy to the one electron basis set limit. , 2008, The journal of physical chemistry. A.

[20]  R. Hill,et al.  Rates of convergence and error estimation formulas for the Rayleigh–Ritz variational method , 1985 .

[21]  Trygve Helgaker,et al.  Basis-set convergence of correlated calculations on water , 1997 .

[22]  A. J. C. Varandas,et al.  Møller–Plesset perturbation energies and distances for HeC20 extrapolated to the complete basis set limit , 2009, J. Comput. Chem..

[23]  L. Curtiss,et al.  Gaussian-3X (G3X) theory : use of improved geometries, zero-point energies, and Hartree-Fock basis sets. , 2001 .

[24]  D. Bakowies.  Extrapolation of electron correlation energies to finite and complete basis set targets. , 2007, The Journal of chemical physics.

[25]  Matthew L. Leininger,et al.  Psi4: an open‐source ab initio electronic structure program , 2012 .

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

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

[28]  J. C. Slater.  A Simplification of the Hartree-Fock Method , 1951 .

[29]  A. Varandas.  Basis-set extrapolation of the correlation energy , 2000 .

[30]  Krishnan Raghavachari,et al.  Gaussian-2 theory for molecular energies of first- and second-row compounds , 1991 .

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

[32]  A. Varandas,et al.  Narrowing the error in electron correlation calculations by basis set re-hierarchization and use of the unified singlet and triplet electron-pair extrapolation scheme: application to a test set of 106 systems. , 2014, The Journal of chemical physics.

[33]  Kirk A. Peterson,et al.  Benchmark calculations with correlated molecular wave functions. IV. The classical barrier height of the H+H2→H2+H reaction , 1994 .

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

[35]  Edward F. Valeev,et al.  Explicitly correlated R12/F12 methods for electronic structure. , 2012, Chemical reviews.

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

[37]  S. H. Vosko,et al.  Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis , 1980 .

[38]  G. A. Petersson,et al.  Complete basis set correlation energies. IV. The total correlation energy of the water molecule , 1985 .

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

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

[41]  Trygve Helgaker,et al.  Basis-set convergence in correlated calculations on Ne, N2, and H2O , 1998 .

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

[43]  F. Manby,et al.  An explicitly correlated second order Møller-Plesset theory using a frozen Gaussian geminal. , 2004, The Journal of chemical physics.

[44]  Seiichiro Ten-no,et al.  Initiation of explicitly correlated Slater-type geminal theory , 2004 .

[45]  Werner Kutzelnigg,et al.  r12-Dependent terms in the wave function as closed sums of partial wave amplitudes for large l , 1985 .