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Title: Push it to the limit: comparing periodic and local approaches to density functional theory for intermolecular interactions

Abstract

With the aim of systematically comparing two popular approaches to density functional theory–all-electron calculations with local basis sets, and periodic calculations employing plane wave basis sets and norm-conserving pseudopotentials–we have computed complete-basis binding energies across the S22 set of intermolecular interactions, a dataset consisting of noncovalent interactions of small- and medium-sized molecules containing first- and second-row atoms, using the Troullier-Martins norm-conserving pseudopotentials with SPW92, a local spin-density approximation; and PBE, a generalised gradient approximation. Here, we have found that it is challenging to reach the basis set limit with these periodic calculations; for the methods and systems examined, a minimum vacuum distance of 30 Å between a system and its nearest images is necessary–unless some form of dipole correction is employed–as is a kinetic energy cutoff of at least 80 Ry. The trends in convergence with respect to vacuum size and kinetic energy cutoff are largely independent of the level of density functional approximation employed. A sense of the impact of each hyperparameter on basis set error provides a foundation for ensuring quality calculations in future studies and allows us to quantify the basis set errors incurred in existing studies on similar systems.

Authors:
 [1];  [1];  [2]
  1. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Molecular Foundry
  2. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1814759
Grant/Contract Number:  
AC02-05CH11231; FG02-12ER16362
Resource Type:
Accepted Manuscript
Journal Name:
Molecular Physics
Additional Journal Information:
Journal Volume: 117; Journal Issue: 9-12; Journal ID: ISSN 0026-8976
Publisher:
Taylor & Francis
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; Intermolecular interactions; density functional theory; basis set limit; plane waves; atomic orbitals

Citation Formats

Witte, Jonathon, Neaton, Jeffrey B., and Head-Gordon, Martin. Push it to the limit: comparing periodic and local approaches to density functional theory for intermolecular interactions. United States: N. p., 2018. Web. doi:10.1080/00268976.2018.1542164.
Witte, Jonathon, Neaton, Jeffrey B., & Head-Gordon, Martin. Push it to the limit: comparing periodic and local approaches to density functional theory for intermolecular interactions. United States. https://doi.org/10.1080/00268976.2018.1542164
Witte, Jonathon, Neaton, Jeffrey B., and Head-Gordon, Martin. Thu . "Push it to the limit: comparing periodic and local approaches to density functional theory for intermolecular interactions". United States. https://doi.org/10.1080/00268976.2018.1542164. https://www.osti.gov/servlets/purl/1814759.
@article{osti_1814759,
title = {Push it to the limit: comparing periodic and local approaches to density functional theory for intermolecular interactions},
author = {Witte, Jonathon and Neaton, Jeffrey B. and Head-Gordon, Martin},
abstractNote = {With the aim of systematically comparing two popular approaches to density functional theory–all-electron calculations with local basis sets, and periodic calculations employing plane wave basis sets and norm-conserving pseudopotentials–we have computed complete-basis binding energies across the S22 set of intermolecular interactions, a dataset consisting of noncovalent interactions of small- and medium-sized molecules containing first- and second-row atoms, using the Troullier-Martins norm-conserving pseudopotentials with SPW92, a local spin-density approximation; and PBE, a generalised gradient approximation. Here, we have found that it is challenging to reach the basis set limit with these periodic calculations; for the methods and systems examined, a minimum vacuum distance of 30 Å between a system and its nearest images is necessary–unless some form of dipole correction is employed–as is a kinetic energy cutoff of at least 80 Ry. The trends in convergence with respect to vacuum size and kinetic energy cutoff are largely independent of the level of density functional approximation employed. A sense of the impact of each hyperparameter on basis set error provides a foundation for ensuring quality calculations in future studies and allows us to quantify the basis set errors incurred in existing studies on similar systems.},
doi = {10.1080/00268976.2018.1542164},
journal = {Molecular Physics},
number = 9-12,
volume = 117,
place = {United States},
year = {Thu Nov 08 00:00:00 EST 2018},
month = {Thu Nov 08 00:00:00 EST 2018}
}

Works referenced in this record:

Generalized Gradient Approximation Made Simple
journal, October 1996

  • Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
  • Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
  • DOI: 10.1103/PhysRevLett.77.3865

Nonlocal van der Waals density functional made simple and efficient
journal, January 2013


Systematic optimization of long-range corrected hybrid density functionals
journal, February 2008

  • Chai, Jeng-Da; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 128, Issue 8
  • DOI: 10.1063/1.2834918

Property-optimized Gaussian basis sets for molecular response calculations
journal, October 2010

  • Rappoport, Dmitrij; Furche, Filipp
  • The Journal of Chemical Physics, Vol. 133, Issue 13
  • DOI: 10.1063/1.3484283

Survival of the most transferable at the top of Jacob’s ladder: Defining and testing the ω B97M(2) double hybrid density functional
journal, June 2018

  • Mardirossian, Narbe; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 148, Issue 24
  • DOI: 10.1063/1.5025226

MN15-L: A New Local Exchange-Correlation Functional for Kohn–Sham Density Functional Theory with Broad Accuracy for Atoms, Molecules, and Solids
journal, February 2016

  • Yu, Haoyu S.; He, Xiao; Truhlar, Donald G.
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 3
  • DOI: 10.1021/acs.jctc.5b01082

GW 100: Benchmarking G0W0 for molecular systems
text, January 2015

  • van Setten, M. J.; Caruso, F.; Sharifzadeh, S.
  • Universität Regensburg
  • DOI: 10.5283/epub.33561

van der Waals density functional made accurate
journal, March 2014


Daubechies wavelets as a basis set for density functional pseudopotential calculations
journal, July 2008

  • Genovese, Luigi; Neelov, Alexey; Goedecker, Stefan
  • The Journal of Chemical Physics, Vol. 129, Issue 1
  • DOI: 10.1063/1.2949547

Benchmarking Calculated Lattice Parameters and Energies of Molecular Crystals Using van der Waals Density Functionals
journal, July 2014

  • Carter, Damien J.; Rohl, Andrew L.
  • Journal of Chemical Theory and Computation, Vol. 10, Issue 8
  • DOI: 10.1021/ct500335b

Density-functional exchange-energy approximation with correct asymptotic behavior
journal, September 1988


“Lagrange Functions”: A Family of Powerful Basis Sets for Real-Space Order- N Electronic Structure Calculations
journal, October 2004


Benchmark calculations with correlated molecular wave functions. IV. The classical barrier height of the H+H 2 →H 2 +H reaction
journal, May 1994

  • Peterson, Kirk A.; Woon, David E.; Dunning, Thom H.
  • The Journal of Chemical Physics, Vol. 100, Issue 10
  • DOI: 10.1063/1.466884

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

  • Jurečka, Petr; Šponer, Jiří; Černý, Jiří
  • Physical Chemistry Chemical Physics, Vol. 8, Issue 17, p. 1985-1993
  • DOI: 10.1039/B600027D

Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
journal, January 1989

  • Dunning, Thom H.
  • The Journal of Chemical Physics, Vol. 90, Issue 2
  • DOI: 10.1063/1.456153

Periodic boundary conditions in ab initio calculations
journal, February 1995


An all‐electron numerical method for solving the local density functional for polyatomic molecules
journal, January 1990

  • Delley, B.
  • The Journal of Chemical Physics, Vol. 92, Issue 1
  • DOI: 10.1063/1.458452

Comparing Counterpoise-Corrected, Uncorrected, and Averaged Binding Energies for Benchmarking Noncovalent Interactions
journal, November 2013

  • Burns, Lori A.; Marshall, Michael S.; Sherrill, C. David
  • Journal of Chemical Theory and Computation, Vol. 10, Issue 1
  • DOI: 10.1021/ct400149j

Push it to the limit: Characterizing the convergence of common sequences of basis sets for intermolecular interactions as described by density functional theory
journal, May 2016

  • Witte, Jonathon; Neaton, Jeffrey B.; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 144, Issue 19
  • DOI: 10.1063/1.4949536

Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions
journal, May 1992

  • Kendall, Rick A.; Dunning, Thom H.; Harrison, Robert J.
  • The Journal of Chemical Physics, Vol. 96, Issue 9
  • DOI: 10.1063/1.462569

How Large is the Elephant in the Density Functional Theory Room?
journal, August 2017


Achieving Linear Scaling for the Electronic Quantum Coulomb Problem
journal, January 1996


Use of the rVV10 Nonlocal Correlation Functional in the B97M-V Density Functional: Defining B97M-rV and Related Functionals
journal, December 2016

  • Mardirossian, Narbe; Ruiz Pestana, Luis; Womack, James C.
  • The Journal of Physical Chemistry Letters, Vol. 8, Issue 1
  • DOI: 10.1021/acs.jpclett.6b02527

The Elephant in the Room of Density Functional Theory Calculations
journal, March 2017

  • Jensen, Stig Rune; Saha, Santanu; Flores-Livas, José A.
  • The Journal of Physical Chemistry Letters, Vol. 8, Issue 7
  • DOI: 10.1021/acs.jpclett.7b00255

Reproducibility in density functional theory calculations of solids
journal, March 2016


Accuracy of Several Wave Function and Density Functional Theory Methods for Description of Noncovalent Interaction of Saturated and Unsaturated Hydrocarbon Dimers
journal, June 2012

  • Granatier, Jaroslav; Pitoňák, Michal; Hobza, Pavel
  • Journal of Chemical Theory and Computation, Vol. 8, Issue 7
  • DOI: 10.1021/ct300215p

Advances in molecular quantum chemistry contained in the Q-Chem 4 program package
journal, September 2014


Filtering a distribution simultaneously in real and Fourier space
journal, March 2006


Large-scale ab initio simulations based on systematically improvable atomic basis
preprint, January 2015


Electronic wave functions - I. A general method of calculation for the stationary states of any molecular system
journal, February 1950

  • Boys, S. F.
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 200, Issue 1063, p. 542-554
  • DOI: 10.1098/rspa.1950.0036

The Pseudopotential Approximation in Electronic Structure Theory
journal, August 2011


The Gaussian and augmented-plane-wave density functional method for ab initio molecular dynamics simulations
journal, December 1999

  • Lippert, Gerald; Hutter, Jürg; Parrinello, Michele
  • Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 103, Issue 2
  • DOI: 10.1007/s002140050523

Daubechies wavelets as a basis set for density functional pseudopotential calculations
text, January 2008


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

  • Chai, Jeng-Da; Head-Gordon, Martin
  • Physical Chemistry Chemical Physics, Vol. 10, Issue 44
  • DOI: 10.1039/b810189b

Efficient pseudopotentials for plane-wave calculations
journal, January 1991


A multicenter numerical integration scheme for polyatomic molecules
journal, February 1988

  • Becke, A. D.
  • The Journal of Chemical Physics, Vol. 88, Issue 4
  • DOI: 10.1063/1.454033

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

  • Weigend, Florian; Ahlrichs, Reinhart
  • Physical Chemistry Chemical Physics, Vol. 7, Issue 18, p. 3297-3305
  • DOI: 10.1039/b508541a

A plane-wave pseudopotential description of charged clusters
journal, December 1999

  • Nogueira, F.; Martins, J. L.; Fiolhais, C.
  • The European Physical Journal D, Vol. 9, Issue 1
  • DOI: 10.1007/s100530050431

Density‐functional thermochemistry. III. The role of exact exchange
journal, April 1993

  • Becke, Axel D.
  • The Journal of Chemical Physics, Vol. 98, Issue 7, p. 5648-5652
  • DOI: 10.1063/1.464913

Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals
journal, April 2017


The Elephant in the Room of Density Functional Theory Calculations
text, January 2017


libvdwxc: a library for exchange–correlation functionals in the vdW-DF family
journal, June 2017

  • Larsen, Ask Hjorth; Kuisma, Mikael; Löfgren, Joakim
  • Modelling and Simulation in Materials Science and Engineering, Vol. 25, Issue 6
  • DOI: 10.1088/1361-651X/aa7320

Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
text, January 1988

  • Robert, Parr,; Chengteh, Lee,; Weitao, Yang,
  • The University of North Carolina at Chapel Hill University Libraries
  • DOI: 10.17615/zrp0-ry04

Why the Standard B3LYP/6-31G* Model Chemistry Should Not Be Used in DFT Calculations of Molecular Thermochemistry: Understanding and Correcting the Problem
journal, November 2012

  • Kruse, Holger; Goerigk, Lars; Grimme, Stefan
  • The Journal of Organic Chemistry, Vol. 77, Issue 23
  • DOI: 10.1021/jo302156p

Quantum Theory of Molecules and Solids Vol. 4: The Self‐Consistent Field for Molecules and Solids
journal, December 1974

  • Slater, J. C.; Phillips, James C.
  • Physics Today, Vol. 27, Issue 12
  • DOI: 10.1063/1.3129035

Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
journal, January 1988


Atomic Shielding Constants
journal, July 1930


GW 100: A Plane Wave Perspective for Small Molecules
journal, January 2017

  • Maggio, Emanuele; Liu, Peitao; van Setten, Michiel J.
  • Journal of Chemical Theory and Computation, Vol. 13, Issue 2
  • DOI: 10.1021/acs.jctc.6b01150

Ab initio pseudopotentials for electronic structure calculations of poly-atomic systems using density-functional theory
journal, June 1999


Higher-accuracy van der Waals density functional
journal, August 2010


GW 100: Benchmarking G 0 W 0 for Molecular Systems
journal, November 2015

  • van Setten, Michiel J.; Caruso, Fabio; Sharifzadeh, Sahar
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 12
  • DOI: 10.1021/acs.jctc.5b00453

Assessment of two hybrid van der Waals density functionals for covalent and non-covalent binding of molecules
journal, June 2017

  • Berland, Kristian; Jiao, Yang; Lee, Jung-Hoon
  • The Journal of Chemical Physics, Vol. 146, Issue 23
  • DOI: 10.1063/1.4986522

Effective empirical corrections for basis set superposition error in the def2-SVPD basis: gCP and DFT-C
journal, June 2017

  • Witte, Jonathon; Neaton, Jeffrey B.; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 146, Issue 23
  • DOI: 10.1063/1.4986962

A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions
journal, November 2006

  • Zhao, Yan; Truhlar, Donald G.
  • The Journal of Chemical Physics, Vol. 125, Issue 19, Article No. 194101
  • DOI: 10.1063/1.2370993

Comparative Study of Selected Wave Function and Density Functional Methods for Noncovalent Interaction Energy Calculations Using the Extended S22 Data Set
journal, July 2010

  • Gráfová, Lucie; Pitoňák, Michal; Řezáč, Jan
  • Journal of Chemical Theory and Computation, Vol. 6, Issue 8
  • DOI: 10.1021/ct1002253

Searching for DFT-based methods that include dispersion interactions to calculate the physisorption of H2 on benzene and graphene
journal, June 2017

  • Cabria, I.; López, M. J.; Alonso, J. A.
  • The Journal of Chemical Physics, Vol. 146, Issue 21
  • DOI: 10.1063/1.4984106

Inhomogeneous Electron Gas
journal, November 1964


An Introduction to Coupled Cluster Theory for Computational Chemists
book, January 2000

  • Crawford, T. Daniel; Schaefer, Henry F.; Lipkowitz, Kenny B.
  • Reviews in Computational Chemistry: Lipkowitz/Reviews
  • DOI: 10.1002/9780470125915.ch2

Mapping the genome of meta-generalized gradient approximation density functionals: The search for B97M-V
journal, February 2015

  • Mardirossian, Narbe; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 142, Issue 7
  • DOI: 10.1063/1.4907719

ω B97M-V: A combinatorially optimized, range-separated hybrid, meta-GGA density functional with VV10 nonlocal correlation
journal, June 2016

  • Mardirossian, Narbe; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 144, Issue 21
  • DOI: 10.1063/1.4952647

Accurate and simple analytic representation of the electron-gas correlation energy
journal, June 1992


Large-scale ab initio simulations based on systematically improvable atomic basis
journal, February 2016


Ab initio molecular-dynamics simulations of Si clusters using the higher-order finite-difference-pseudopotential method
journal, October 1994


Filtering a distribution simultaneously in real and Fourier space
text, January 2005


Periodic local Møller–Plesset second order perturbation theory method applied to molecular crystals: Study of solid NH3 and CO2 using extended basis sets
journal, April 2010

  • Maschio, Lorenzo; Usvyat, Denis; Schütz, Martin
  • The Journal of Chemical Physics, Vol. 132, Issue 13
  • DOI: 10.1063/1.3372800

Cryscor: a program for the post-Hartree–Fock treatment of periodic systems
journal, January 2012

  • Pisani, Cesare; Schütz, Martin; Casassa, Silvia
  • Physical Chemistry Chemical Physics, Vol. 14, Issue 21
  • DOI: 10.1039/c2cp23927b

C RYSTAL14 : A program for the ab initio investigation of crystalline solids
journal, March 2014

  • Dovesi, Roberto; Orlando, Roberto; Erba, Alessandro
  • International Journal of Quantum Chemistry, Vol. 114, Issue 19
  • DOI: 10.1002/qua.24658

Avogadro: an advanced semantic chemical editor, visualization, and analysis platform
journal, August 2012

  • Hanwell, Marcus D.; Curtis, Donald E.; Lonie, David C.
  • Journal of Cheminformatics, Vol. 4, Issue 1
  • DOI: 10.1186/1758-2946-4-17

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

  • Jensen, Frank
  • The Journal of Chemical Physics, Vol. 116, Issue 17
  • DOI: 10.1063/1.1465405

Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields
journal, November 1994

  • Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.
  • The Journal of Physical Chemistry, Vol. 98, Issue 45, p. 11623-11627
  • DOI: 10.1021/j100096a001

Polarization consistent basis sets. III. The importance of diffuse functions
journal, November 2002

  • Jensen, Frank
  • The Journal of Chemical Physics, Vol. 117, Issue 20
  • DOI: 10.1063/1.1515484

Role of Stone-Wales defects on the interfacial interactions among graphene, carbon nanotubes, and Nylon 6: A first-principles study
journal, August 2018

  • Jha, Sanjiv K.; Roth, Michael; Todde, Guido
  • The Journal of Chemical Physics, Vol. 149, Issue 5
  • DOI: 10.1063/1.5032081

Polarization consistent basis sets: Principles
journal, November 2001

  • Jensen, Frank
  • The Journal of Chemical Physics, Vol. 115, Issue 20
  • DOI: 10.1063/1.1413524

Improving the Accuracy of Hybrid Meta-GGA Density Functionals by Range Separation
journal, October 2011

  • Peverati, Roberto; Truhlar, Donald G.
  • The Journal of Physical Chemistry Letters, Vol. 2, Issue 21
  • DOI: 10.1021/jz201170d

Works referencing / citing this record:

Modeling halogen bonding with planewave density functional theory: Accuracy and challenges
journal, April 2019

  • Ang, Shi Jun; Ser, Cher Tian; Wong, Ming Wah
  • Journal of Computational Chemistry, Vol. 40, Issue 20
  • DOI: 10.1002/jcc.25835