Basis set convergence of molecular correlation energy differences within the random phase approximation.

The basis set convergence of energy differences obtained from the random phase approximation (RPA) to the correlation energy is investigated for a wide range of molecular interactions. For dispersion bound systems the basis set incompleteness error is most pronounced, as shown for the S22 benchmark [P. Jurecka et al., Phys. Chem. Chem. Phys. 8, 1985 (2006)]. The use of very large basis sets (> quintuple-zeta) or extrapolation to the complete basis set (CBS) limit is necessary to obtain a reliable estimate of the binding energy for these systems. Counterpoise corrected results converge to the same CBS limit, but counterpoise correction without extrapolation is insufficient. Core-valence correlations do not play a significant role. For medium- and short-range correlation, quadruple-zeta results are essentially converged, as demonstrated for relative alkane conformer energies, reaction energies dominated by intramolecular dispersion, isomerization energies, and reaction energies of small organic molecules. Except for weakly bound systems, diffuse augmentation almost universally slows down basis set convergence. For most RPA applications, quadruple-zeta valence basis sets offer a good balance between accuracy and efficiency.

[1]  Edward G Hohenstein,et al.  Basis set consistent revision of the S22 test set of noncovalent interaction energies. , 2010, The Journal of chemical physics.

[2]  S. Grimme,et al.  How to compute isomerization energies of organic molecules with quantum chemical methods. , 2007, The Journal of organic chemistry.

[3]  Julian Yarkony,et al.  Fast computation of molecular random phase approximation correlation energies using resolution of the identity and imaginary frequency integration. , 2010, The Journal of chemical physics.

[4]  F. Furche.  Developing the random phase approximation into a practical post-Kohn-Sham correlation model. , 2008, The Journal of chemical physics.

[5]  Dmitrij Rappoport.  Basis-set quality and basis-set bias in molecular property calculations. , 2011, Chemphyschem : a European journal of chemical physics and physical chemistry.

[6]  H. Eshuis,et al.  A parameter-free density functional that works for noncovalent interactions , 2011 .

[7]  Georg Kresse,et al.  Assessing the quality of the random phase approximation for lattice constants and atomization energies of solids , 2010 .

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

[9]  Pavel Hobza,et al.  Assessment of the MP2 method, along with several basis sets, for the computation of interaction energies of biologically relevant hydrogen bonded and dispersion bound complexes. , 2007, The journal of physical chemistry. A.

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

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

[12]  S. Grimme.  Seemingly simple stereoelectronic effects in alkane isomers and the implications for Kohn-Sham density functional theory. , 2006, Angewandte Chemie.

[13]  Stefan Grimme,et al.  The importance of inter- and intramolecular van der Waals interactions in organic reactions: the dimerization of anthracene revisited. , 2006, Angewandte Chemie.

[14]  S. F. Boys,et al.  The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors , 1970 .

[15]  H. Eshuis,et al.  Electron correlation methods based on the random phase approximation , 2012, Theoretical Chemistry Accounts.

[16]  Andreas Savin,et al.  Range-separated density-functional theory with random phase approximation applied to noncovalent intermolecular interactions. , 2014, The Journal of chemical physics.

[17]  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.

[18]  J. Ángyán,et al.  On the equivalence of ring-coupled cluster and adiabatic connection fluctuation-dissipation theorem random phase approximation correlation energy expressions. , 2010, The Journal of chemical physics.

[19]  Filipp Furche,et al.  Molecular tests of the random phase approximation to the exchange-correlation energy functional , 2001 .

[20]  Trygve Helgaker,et al.  Basis set convergence of the interaction energy of hydrogen-bonded complexes , 1999 .

[21]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

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

[23]  Alexandre Tkatchenko,et al.  Beyond the random-phase approximation for the electron correlation energy: the importance of single excitations. , 2010, Physical review letters.

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

[25]  F. Weigend,et al.  RI-MP2: first derivatives and global consistency , 1997 .

[26]  Thomas M Henderson,et al.  The ground state correlation energy of the random phase approximation from a ring coupled cluster doubles approach. , 2008, The Journal of chemical physics.

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

[28]  S. Grimme,et al.  A thorough benchmark of density functional methods for general main group thermochemistry, kinetics, and noncovalent interactions. , 2011, Physical chemistry chemical physics : PCCP.

[29]  Jirí Cerný,et al.  Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs. , 2006, Physical chemistry chemical physics : PCCP.

[30]  Amir Karton,et al.  Performance of ab initio and density functional methods for conformational equilibria of C(n)H(2n+2) alkane isomers (n = 4-8). , 2009, The journal of physical chemistry. A.

[31]  A. Savin,et al.  Range-separated density-functional theory with the random-phase approximation: Detailed formalism and illustrative applications , 2010, 1006.2061.

[32]  L. Curtiss,et al.  Assessment of Gaussian-2 and density functional theories for the computation of enthalpies of formation , 1997 .

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

[34]  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 .

[35]  S. Grimme,et al.  Double-hybrid density functionals with long-range dispersion corrections: higher accuracy and extended applicability. , 2007, Physical chemistry chemical physics : PCCP.

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

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

[38]  E. Engel,et al.  Random-phase-approximation-based correlation energy functionals: benchmark results for atoms. , 2007, The Journal of chemical physics.