Energy vs. density on paths toward more exact density functionals

Physical Chemistry Chemical Physics : PCCP
Kasper P Kepp

Abstract

Recently, the progression toward more exact density functional theory has been questioned, implying a need for more formal ways to systematically measure progress, i.e. a "path". Here I use the Hohenberg-Kohn theorems and the definition of normality by Burke et al. to define a path toward exactness and "straying" from the "path" by separating errors in ρ and E[ρ]. A consistent path toward exactness involves minimizing both errors. Second, a suitably diverse test set of trial densities ρ' can be used to estimate the significance of errors in ρ without knowing the exact densities which are often inaccessible. To illustrate this, the systems previously studied by Medvedev et al., the first ionization energies of atoms with Z = 1 to 10, the ionization energy of water, and the bond dissociation energies of five diatomic molecules were investigated using CCSD(T)/aug-cc-pV5Z as benchmark at chemical accuracy. Four functionals of distinct designs was used: B3LYP, PBE, M06, and S-VWN. For atomic cations regardless of charge and compactness up to Z = 10, the energy effects of the different ρ are <4 kJ mol-1(chemical accuracy) defined here as "normal", even though these four functionals ranked very differently in the previous test. Thus, ...Continue Reading

References

Oct 28, 1996·Physical Review Letters·J P PerdewM Ernzerhof
Jan 11, 2007·The Journal of Chemical Physics·Kasper P JensenUlf Ryde
Oct 16, 2008·Inorganic Chemistry·Kasper P Jensen
Sep 3, 2013·Physical Review Letters·Min-Cheol KimKieron Burke
Feb 12, 2014·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Roberto Peverati, Donald G Truhlar
Jan 7, 2017·Science·Michael G MedvedevKonstantin A Lyssenko
May 4, 2017·Annual Review of Physical Chemistry·Adam WassermanKieron Burke
May 12, 2017·Journal of Chemical Theory and Computation·Tim Gould

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Citations

Oct 10, 2019·Chemphyschem : a European Journal of Chemical Physics and Physical Chemistry·Klaus A Moltved, Kasper P Kepp
Jul 3, 2020·The Journal of Chemical Physics·Klaus A Moltved, Kasper P Kepp
May 22, 2021·The Journal of Physical Chemistry. a·Carlos Martín-Fernández, Jeremy N Harvey
May 31, 2018·Journal of Chemical Theory and Computation·Klaus A Moltved, Kasper P Kepp
Dec 9, 2020·Journal of Chemical Theory and Computation·Philip Jakobsen, Frank Jensen
Mar 19, 2019·The Journal of Physical Chemistry. a·Klaus A Moltved, Kasper P Kepp
Mar 22, 2018·Journal of Chemical Theory and Computation·Diptarka Hait, Martin Head-Gordon
Oct 20, 2018·The Journal of Physical Chemistry Letters·Eunji SimKieron Burke

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Software Mentioned

SVWN
M06
Turbomole
def2

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