Convergence behavior of RPA renormalized many-body perturbation theory Understanding why low-order, non-perturbative expansions work Jefferson E. Bates , Jonathon Sensenig, Niladri Sengupta, & Adrienn Ruzsinszky Department of Physics, Temple University August 20, 2017 Jefferson E. Bates (Temple Univ.) RPAr Convergence 08/20/2017 1 / 14
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Convergence behavior of RPA renormalized many-bodyperturbation theory
Understanding why low-order, non-perturbative expansions work
Jefferson E. Bates, Jonathon Sensenig,Niladri Sengupta, & Adrienn Ruzsinszky
Department of Physics, Temple University
August 20, 2017
Jefferson E. Bates (Temple Univ.) RPAr Convergence 08/20/2017 1 / 14
Introduction & Background
Electronic Instabilities
N2 dissociation with EXX kernel
Treating exchange to ∞-order causes instabilities even in simple systems.Renormalized perturbation theories offer robust solution.
Colonna, Hellgren, de Gironcoli Phys. Rev. B 90, 125150 (2014)
Jefferson E. Bates (Temple Univ.) RPAr Convergence 08/20/2017 2 / 14
Petersilka, Gossmann, and Gross, Phys. Rev. Lett. 76, 1212(1996)Lein, Gross, and Perdew, Phys. Rev. B 61, 13431 (2000)Colonna, Hellgren, de Gironcoli Phys. Rev. B 90, 125150 (2014)Erhard, Bleiziffer, Gorling Phys. Rev. Lett. 117, 143002 (2016)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4q (a.u.)
0.06
0.05
0.04
0.03
0.02
0.01
0.00
ε c(q
) (a.
u.)
RPAexact
HEG correlation energy per particle ; rs = 4
Jefferson E. Bates (Temple Univ.) RPAr Convergence 08/20/2017 5 / 14
Introduction & Background ACFDT & RPA
Applications of RPA
Why RPA?
naturally incorporates dispersion
applicable to small-gap systems(metals)
EXX part is self-interaction free
less expensive than CCSD(T)
Shortcomings:
overestimates EC
tendency to underbind
self-correlation error
more expensive than semilocalDFT∗
Typically more accurate than semilocalfunctionals for:
basic properties of molecules & solids
adsorption of molecules on metal surfaces
adsorption of graphene on metal surfaces
binding energies & distances for weaklybound complexes
binding energies of layered materials
reaction energies & barriers, catalysisHarl, Schimka, Kresse, Phys. Rev. B 81, 115126 (2010)Lebegue et al. Phys. Rev. Lett. 105, 196401 (2010)Schimka et al. Nat. Mater. 9, 741 (2010)Bjorkman, Gulans, Krasheninnikov, Nieminen, Phys. Rev. Lett. 108,235502 (2012)Eshuis, Furche J. Phys. Chem. Lett. 2, 983 (2011)Olsen, Thygesen Phys. Rev. B 87, 075111 (2013)Schimka et al. Phys Rev. B 87, 214102 (2013)Burow, Bates, Furche, Eshuis J. Chem. Theory Comput. 10, 180(2014)Bao et al. ACS Catal. 5, 2070 (2015)Waitt, Ferrara, Eshuis J. Chem. Theory Comput. 12, 5350 (2016)
Jefferson E. Bates (Temple Univ.) RPAr Convergence 08/20/2017 6 / 14
yields RPAr power series for ∆E bRPAC , with the n-th order term
∆E RPAr-nC [fxc ] = −
∫ 1
0
dα
∫ ∞0
du
2π〈V (χαf αxc )n χα〉
Both RPA and beyond-RPA correlation are obtained in a single calculation!
RPAr1 : χα ≈ χα + χαf αxc χα
eliminates electronic instabilities
preserves RPA’s static correlation
has analytic α integral for x-like f αxc
dominant (∼ 90%) part of ∆E bRPAC
RPAr-n : nth-order terms
do they converge?
relative contributions?
kernel dependent?
system dependent?Bates, Furche J. Chem. Phys. 139, 171103 (2013)Colonna, Hellgren, de Gironcoli Phys. Rev. B 90, 125150 (2014)Bates, Laricchia, and Ruzsinszky, Phys. Rev. B 93, 045119 (2016)Bates, Sensenig, Ruzsinszky Phys. Rev. B 95, 195158 (2017)
Jefferson E. Bates (Temple Univ.) RPAr Convergence 08/20/2017 9 / 14