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Title: Push it to the limit: Characterizing the convergence of common sequences of basis sets for intermolecular interactions as described by density functional theory

Journal Article · · Journal of Chemical Physics
DOI:https://doi.org/10.1063/1.4949536· OSTI ID:1477252
ORCiD logo [1];  [2];  [1]
  1. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States); Kavli Energy Nanosciences Institute at Berkeley, Berkeley, CA (United States)

With the aim of systematically characterizing the convergence of common families of basis sets such that general recommendations for basis sets can be made, we have tested a wide variety of basis sets against complete-basis binding energies across the S22 set of intermolecular interactions - noncovalent interactions of small and medium-sized molecules consisting of first- and second-row atoms - with three distinct density functional approximations: SPW92, a form of local-density approximation; B3LYP, a global hybrid generalized gradient approximation; and B97M-V, a meta-generalized gradient approximation with nonlocal correlation. We have found that it is remarkably difficult to reach the basis set limit; for the methods and systems examined, the most complete basis is Jensen's pc-4. The Dunning correlation-consistent sequence of basis sets converges slowly relative to the Jensen sequence. The Karlsruhe basis sets are quite cost effective, particularly when a correction for basis set superposition error is applied: counterpoise-corrected def2-SVPD binding energies are better than corresponding energies computed in comparably sized Dunning and Jensen bases, and on par with uncorrected results in basis sets 3-4 times larger. These trends are exhibited regardless of the level of density functional approximation employed. In conclusion, a sense of the magnitude of the intrinsic incompleteness error of each basis set not only provides a foundation for guiding basis set choice in future studies but also facilitates quantitative comparison of existing studies on similar types of systems.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences, and Biosciences Division
Grant/Contract Number:
AC02-05CH11231; FG02-12ER16362
OSTI ID:
1477252
Alternate ID(s):
OSTI ID: 1253656
Journal Information:
Journal of Chemical Physics, Vol. 144, Issue 19; Related Information: © 2016 Author(s).; ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 36 works
Citation information provided by
Web of Science

References (89)

Generalized Gradient Approximation Made Simple journal October 1996
Systematic optimization of long-range corrected hybrid density functionals journal February 2008
Perspectives on Basis Sets Beautiful: Seasonal Plantings of Diffuse Basis Functions journal August 2011
A geometrical correction for the inter- and intra-molecular basis set superposition error in Hartree-Fock and density functional theory calculations for large systems journal April 2012
Systematic study of basis set superposition errors in the calculated interaction energy of two HF molecules journal March 1985
Basis set convergence of molecular correlation energy differences within the random phase approximation journal February 2012
Towards a complete basis set limit of Hartree?Fock method: correlation-consistent versus polarized-consistent basis sets journal April 2005
The accurate determination of molecular equilibrium structures journal April 2001
Comparing Counterpoise-Corrected, Uncorrected, and Averaged Binding Energies for Benchmarking Noncovalent Interactions journal November 2013
Accuracy of AH n equilibrium geometries by single determinant molecular orbital theory journal January 1974
The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors journal January 2002
Fast, accurate evaluation of exact exchange: The occ-RI-K algorithm journal July 2015
Assessing electronic structure approaches for gas-ligand interactions in metal-organic frameworks: The CO 2 -benzene complex journal March 2014
Accuracy of atomization energies and reaction enthalpies in standard and extrapolated electronic wave function/basis set calculations journal June 2000
The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals journal July 2007
Self-consistent implementation of a nonlocal van der Waals density functional with a Gaussian basis set journal July 2008
Self‐consistent molecular orbital methods. XXIII. A polarization‐type basis set for second‐row elements journal October 1982
Advances in molecular quantum chemistry contained in the Q-Chem 4 program package journal September 2014
Nonlocal van der Waals density functional: The simpler the better text January 2010
Polarization-Consistent versus Correlation-Consistent Basis Sets in Predicting Molecular and Spectroscopic Properties journal March 2007
The Pseudopotential Approximation in Electronic Structure Theory journal August 2011
Statistics-based model for basis set superposition error correction in large biomolecules journal January 2012
State of the Art in Counterpoise Theory journal November 1994
Non-empirical molecular orbital calculations on the protonation of carbon monoxide journal March 1969
Gaussian basis sets for use in correlated molecular calculations. IV. Calculation of static electrical response properties journal February 1994
Self-Consistent Equations Including Exchange and Correlation Effects journal November 1965
Long-range corrected hybrid density functionals with damped atom–atom dispersion corrections journal January 2008
Extensive theoretical studies of the hydrogen‐bonded complexes (H 2 O) 2 , (H 2 O) 2 H + , (HF) 2 , (HF) 2 H + , F 2 H , and (NH 3 ) 2 journal February 1986
Hartree–Fock exchange fitting basis sets for H to Rn journal January 2007
Beyond Energies: Geometries of Nonbonded Molecular Complexes as Metrics for Assessing Electronic Structure Approaches journal March 2015
Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density journal January 1988
A fully direct RI-HF algorithm: Implementation, optimised auxiliary basis sets, demonstration of accuracy and efficiency journal August 2002
Can the Counterpoise Correction for Basis Set Superposition Effect Be Justified? journal November 2013
Effectiveness of Diffuse Basis Functions for Calculating Relative Energies by Density Functional Theory journal March 2003
An Atomic Counterpoise Method for Estimating Inter- and Intramolecular Basis Set Superposition Errors journal November 2009
Mapping the genome of meta-generalized gradient approximation density functionals: The search for B97M-V journal February 2015
New Developments in Molecular Orbital Theory journal April 1951
The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors journal October 1970
Note on an Approximation Treatment for Many-Electron Systems journal October 1934
Polarization consistent basis sets. II. Estimating the Kohn–Sham basis set limit journal May 2002
Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields journal November 1994
Efficient diffuse function-augmented basis sets for anion calculations. III. The 3-21+G basis set for first-row elements, Li-F journal October 1983
Improving the Accuracy of Hybrid Meta-GGA Density Functionals by Range Separation journal October 2011
Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules journal March 1972
Property-optimized Gaussian basis sets for molecular response calculations journal October 2010
Accurate determination of the binding energy of the formic acid dimer: The importance of geometry relaxation journal February 2014
Nonlocal van der Waals density functional: The simpler the better journal December 2010
Comparison of polarization consistent and correlation consistent basis sets for noncovalent interactions journal January 2009
Some comments on the counterpoise correction for the basis set superposition error at the correlated level journal December 1993
Density-functional exchange-energy approximation with correct asymptotic behavior journal September 1988
On the validity of the basis set superposition error and complete basis set limit extrapolations for the binding energy of the formic acid dimer journal March 2015
Basis set convergence of the coupled-cluster correction, δMP2CCSD(T): Best practices for benchmarking non-covalent interactions and the attendant revision of the S22, NBC10, HBC6, and HSG databases journal November 2011
Benchmark calculations with correlated molecular wave functions. IV. The classical barrier height of the H+H 2 →H 2 +H reaction journal May 1994
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 journal January 2006
Small Atomic Orbital Basis Set First‐Principles Quantum Chemical Methods for Large Molecular and Periodic Systems: A Critical Analysis of Error Sources journal November 2015
Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen journal January 1989
Self‐Consistent Molecular‐Orbital Methods. IX. An Extended Gaussian‐Type Basis for Molecular‐Orbital Studies of Organic Molecules journal January 1971
The basis set convergence of the density functional energy for H2 journal February 2000
A new approach to counterpoise correction to BSSE journal January 2006
Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions journal May 1992
Self‐consistent molecular orbital methods. XX. A basis set for correlated wave functions journal January 1980
A Road Map for the Calculation of Molecular Binding Energies journal October 2000
The molecular orbital theory of chemical valency VIII. A method of calculating ionization potentials journal March 1951
Electronic wave functions - I. A general method of calculation for the stationary states of any molecular system journal February 1950
Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy journal January 2005
The full versus the virtual counterpoise correction for basis set superposition error in self-consistent field calculations journal January 1986
Density‐functional thermochemistry. III. The role of exact exchange journal April 1993
Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density text January 1988
The influence of polarization functions on molecular orbital hydrogenation energies journal January 1973
ωB97X-V: A 10-parameter, range-separated hybrid, generalized gradient approximation density functional with nonlocal correlation, designed by a survival-of-the-fittest strategy journal January 2014
Atomic Shielding Constants journal July 1930
Rates of convergence and error estimation formulas for the Rayleigh–Ritz variational method journal August 1985
Gaussian basis sets for use in correlated molecular calculations. V. Core‐valence basis sets for boron through neon journal September 1995
A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions journal November 2006
Atomic orbital basis sets: Atomic orbital basis sets journal October 2012
Inhomogeneous Electron Gas journal November 1964
An Antifungal Polycyclic Tetramate Macrolactam, Heat-Stable Antifungal Factor (HSAF), Is a Novel Oxidative Stress Modulator in Lysobacter enzymogenes journal April 2021
Accurate and simple analytic representation of the electron-gas correlation energy journal June 1992
Characterizing and Understanding the Remarkably Slow Basis Set Convergence of Several Minnesota Density Functionals for Intermolecular Interaction Energies journal September 2013
Does the boys and bernardi function counterpoise method actually overcorrect the basis set superposition error? journal August 1986
Self‐consistent molecular orbital methods 25. Supplementary functions for Gaussian basis sets journal April 1984
Accurate correlated calculation of the intermolecular potential surface in the coronene dimer journal February 2010
Avogadro: an advanced semantic chemical editor, visualization, and analysis platform journal August 2012
Model for the fast estimation of basis set superposition error in biomolecular systems journal October 2011
Polarization consistent basis sets. III. The importance of diffuse functions journal November 2002
A standard grid for density functional calculations journal July 1993
Consistent structures and interactions by density functional theory with small atomic orbital basis sets journal August 2015
Polarization consistent basis sets: Principles journal November 2001
Importance of Angular Correlations between Atomic Electrons journal May 1962

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Correlation consistent basis sets designed for density functional theory: Second-row (Al-Ar) journal August 2019
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The Performance of Dunning, Jensen and Karlsruhe Basis Sets on Computing Relative Energies and Geometries datapaper December 2019
The Performance of Dunning, Jensen and Karlsruhe Basis Sets on Computing Relative Energies and Geometries datapaper November 2019
Midbond basis functions for weakly bound complexes journal February 2018
The performance of Dunning, Jensen, and Karlsruhe basis sets on computing relative energies and geometries text January 2020
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