We present a quasiparticle self-consistent GW (QSGW) implementation for periodic systems based on crystalline Gaussian basis sets. Our QSGW approach is based on a full-frequency analytic continuation GW scheme with Brillouin zone sampling and employs the Gaussian density fitting technique. We benchmark our QSGW implementation on a set of weakly correlated semiconductors and insulators as well as strongly correlated transition metal oxides, including MnO, FeO, CoO, and NiO. The band gap, band structure, and density of states are evaluated using finite size corrected QSGW. We find that although QSGW systematically overestimates the bandgaps of the tested semiconductors and transition metal oxides, it completely removes the dependence on the choice of density functionals and provides a more consistent prediction of spectral properties than G0W0 across a wide range of solids. This work paves the way for utilizing QSGW in ab initio quantum embedding for solids.
REFERENCES
1.
L.
Hedin
, “New method for calculating the one-particle Green’s function with application to the electron-gas problem
,” Phys. Rev.
139
, A796
–A823
(1965
).2.
W.
Hanke
and L. J.
Sham
, “Many-particle effects in the optical excitations of a semiconductor
,” Phys. Rev. Lett.
43
, 387
–390
(1979
).3.
G.
Strinati
, H. J.
Mattausch
, and W.
Hanke
, “Dynamical aspects of correlation corrections in a covalent crystal
,” Phys. Rev. B
25
, 2867
–2888
(1982
).4.
M. S.
Hybertsen
and S. G.
Louie
, “Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies
,” Phys. Rev. B
34
, 5390
–5413
(1986
).5.
F.
Aryasetiawan
and O.
Gunnarsson
, “The GW method
,” Rep. Prog. Phys.
61
, 237
(1998
).6.
D.
Golze
, M.
Dvorak
, and P.
Rinke
, “The GW compendium: A practical guide to theoretical photoemission spectroscopy
,” Front. Chem.
7
, 377
(2019
).7.
X.
Ren
, P.
Rinke
, C.
Joas
, and M.
Scheffler
, “Random-phase approximation and its applications in computational chemistry and materials science
,” J. Mater. Sci.
47
, 7447
–7471
(2012
).8.
W.
Kohn
and L. J.
Sham
, “Self-consistent equations including exchange and correlation effects
,” Phys. Rev.
140
, A1133
–A1138
(1965
).9.
M.
Shishkin
and G.
Kresse
, “Implementation and performance of the frequency-dependent GW method within the PAW framework
,” Phys. Rev. B
74
, 035101
(2006
).10.
X.
Gonze
, B.
Amadon
, P.-M.
Anglade
, J.-M.
Beuken
, F.
Bottin
, P.
Boulanger
, F.
Bruneval
, D.
Caliste
, R.
Caracas
, M.
Côté
, T.
Deutsch
, L.
Genovese
, P.
Ghosez
, M.
Giantomassi
, S.
Goedecker
, D. R.
Hamann
, P.
Hermet
, F.
Jollet
, G.
Jomard
, S.
Leroux
, M.
Mancini
, S.
Mazevet
, M. J. T.
Oliveira
, G.
Onida
, Y.
Pouillon
, T.
Rangel
, G.-M.
Rignanese
, D.
Sangalli
, R.
Shaltaf
, M.
Torrent
, M. J.
Verstraete
, G.
Zerah
, and J. W.
Zwanziger
, “ABINIT: First-principles approach to material and nanosystem properties
,” Comput. Phys. Commun.
180
, 2582
–2615
(2009
).11.
J.
Deslippe
, G.
Samsonidze
, D. A.
Strubbe
, M.
Jain
, M. L.
Cohen
, and S. G.
Louie
, “BerkeleyGW: A massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures
,” Comput. Phys. Commun.
183
, 1269
–1289
(2012
).12.
A.
Marini
, C.
Hogan
, M.
Grüning
, and D.
Varsano
, “yambo: An ab initio tool for excited state calculations
,” Comput. Phys. Commun.
180
, 1392
–1403
(2009
).13.
M.
Govoni
and G.
Galli
, “Large scale GW calculations
,” J. Chem. Theory Comput.
11
, 2680
–2696
(2015
).14.
A.
Gulans
, S.
Kontur
, C.
Meisenbichler
, D.
Nabok
, P.
Pavone
, S.
Rigamonti
, S.
Sagmeister
, U.
Werner
, and C.
Draxl
, “Exciting: A full-potential all-electron package implementing density-functional theory and many-body perturbation theory
,” J. Phys.: Condens. Matter
26
, 363202
(2014
).15.
F.
Hüser
, T.
Olsen
, and K. S.
Thygesen
, “Quasiparticle GW calculations for solids, molecules, and two-dimensional materials
,” Phys. Rev. B
87
, 235132
(2013
).16.
C.
Friedrich
, S.
Blügel
, and A.
Schindlmayr
, “Efficient implementation of the GW approximation within the all-electron FLAPW method
,” Phys. Rev. B
81
, 125102
(2010
).17.
T.
Zhu
and G. K. L.
Chan
, “All-electron Gaussian-based G0W0 for valence and core excitation energies of periodic systems
,” J. Chem. Theory Comput.
17
, 741
(2021
).18.
X.
Ren
, F.
Merz
, H.
Jiang
, Y.
Yao
, M.
Rampp
, H.
Lederer
, V.
Blum
, and M.
Scheffler
, “All-electron periodic G0W0 implementation with numerical atomic orbital basis functions: Algorithm and benchmarks
,” Phys. Rev. Mater.
5
, 13807
(2021
).19.
F.
Bruneval
and M. A. L.
Marques
, “Benchmarking the starting points of the GW approximation for molecules
,” J. Chem. Theory Comput.
9
, 324
–329
(2013
).20.
T.
Körzdörfer
and N.
Marom
, “Strategy for finding a reliable starting point for G0W0 demonstrated for molecules
,” Phys. Rev. B
86
, 041110
(2012
).21.
W.
Chen
and A.
Pasquarello
, “Band-edge positions in GW: Effects of starting point and self-consistency
,” Phys. Rev. B
90
, 165133
(2014
).22.
F.
Caruso
, P.
Rinke
, X.
Ren
, M.
Scheffler
, and A.
Rubio
, “Unified description of ground and excited states of finite systems: The self-consistent GW approach
,” Phys. Rev. B
86
, 81102
(2012
).23.
F.
Caruso
, P.
Rinke
, X.
Ren
, A.
Rubio
, and M.
Scheffler
, “Self-consistent GW: All-electron implementation with localized basis functions
,” Phys. Rev. B
88
, 075105
(2013
).24.
A. L.
Kutepov
, “Self-consistent solution of Hedin’s equations: Semiconductors and insulators
,” Phys. Rev. B
95
, 195120
(2017
).25.
M.
Grumet
, P.
Liu
, M.
Kaltak
, J.
Klimeš
, and G.
Kresse
, “Beyond the quasiparticle approximation: Fully self-consistent GW calculations
,” Phys. Rev. B
98
, 155143
(2018
).26.
C.-N.
Yeh
, S.
Iskakov
, D.
Zgid
, and E.
Gull
, “Fully self-consistent finite-temperature GW in Gaussian Bloch orbitals for solids
,” arXiv:2206.07660 (2022
).27.
M.
Shishkin
and G.
Kresse
, “Self-consistent GW calculations for semiconductors and insulators
,” Phys. Rev. B
75
, 235102
(2007
).28.
S. V.
Faleev
, M.
Van Schilfgaarde
, and T.
Kotani
, “All-electron self-consistent GW approximation: Application to Si, MnO, and NiO
,” Phys. Rev. Lett.
93
, 126406
(2004
).29.
M.
Van Schilfgaarde
, T.
Kotani
, and S.
Faleev
, “Quasiparticle self-consistent GW theory
,” Phys. Rev. Lett.
96
, 226402
(2006
).30.
T.
Kotani
, M.
Van Schilfgaarde
, and S. V.
Faleev
, “Quasiparticle self-consistent GW method: A basis for the independent-particle approximation
,” Phys. Rev. B
76
, 165106
(2007
).31.
M.
Shishkin
, M.
Marsman
, and G.
Kresse
, “Accurate quasiparticle spectra from self-consistent GW calculations with vertex corrections
,” Phys. Rev. Lett.
99
, 246403
(2007
).32.
F.
Bruneval
, N.
Vast
, and L.
Reining
, “Effect of self-consistency on quasiparticles in solids
,” Phys. Rev. B
74
, 045102
(2006
).33.
F.
Bruneval
and M.
Gatti
, “Quasiparticle self-consistent GW method for the spectral properties of complex materials
,” Top. Curr. Chem.
347
, 99
–136
(2014
).34.
W.
Chen
and A.
Pasquarello
, “Accurate band gaps of extended systems via efficient vertex corrections in GW
,” Phys. Rev. B
92
, 041115
(2015
).35.
D.
Deguchi
, K.
Sato
, H.
Kino
, and T.
Kotani
, “Accurate energy bands calculated by the hybrid quasiparticle self-consistent GW method implemented in the ecalj package
,” Jpn. J. Appl. Phys.
55
, 051201
(2016
).36.
F.
Kaplan
, M. E.
Harding
, C.
Seiler
, F.
Weigend
, F.
Evers
, and M. J.
Van Setten
, “Quasi-particle self-consistent GW for molecules
,” J. Chem. Theory Comput.
12
, 2528
–2541
(2016
).37.
A.
Förster
and L.
Visscher
, “Low-order scaling quasiparticle self-consistent GW for molecules
,” Front. Chem.
9
, 698
(2021
).38.
M. J.
Van Setten
, R.
Costa
, F.
Viñes
, and F.
Illas
, “Assessing GW approaches for predicting core level binding energies
,” J. Chem. Theory Comput.
14
, 877
–883
(2018
).39.
Q.
Sun
, X.
Zhang
, S.
Banerjee
, P.
Bao
, M.
Barbry
, N. S.
Blunt
, N. A.
Bogdanov
, G. H.
Booth
, J.
Chen
, Z.-H.
Cui
, J. J.
Eriksen
, Y.
Gao
, S.
Guo
, J.
Hermann
, M. R.
Hermes
, K.
Koh
, P.
Koval
, S.
Lehtola
, Z.
Li
, J.
Liu
, N.
Mardirossian
, J. D.
McClain
, M.
Motta
, B.
Mussard
, H. Q.
Pham
, A.
Pulkin
, W.
Purwanto
, P. J.
Robinson
, E.
Ronca
, E. R.
Sayfutyarova
, M.
Scheurer
, H. F.
Schurkus
, J. E. T.
Smith
, C.
Sun
, S.-N.
Sun
, S.
Upadhyay
, L. K.
Wagner
, X.
Wang
, A.
White
, J. D.
Whitfield
, M. J.
Williamson
, S.
Wouters
, J.
Yang
, J. M.
Yu
, T.
Zhu
, T. C.
Berkelbach
, S.
Sharma
, A. Y.
Sokolov
, and G. K.-L.
Chan
, “Recent developments in the PySCF program package
,” J. Chem. Phys.
153
, 024109
(2020
).40.
X.
Ren
, P.
Rinke
, V.
Blum
, J.
Wieferink
, A.
Tkatchenko
, A.
Sanfilippo
, K.
Reuter
, and M.
Scheffler
, “Resolution-of-identity approach to Hartree–Fock, hybrid density functionals, RPA, MP2 and GW with numeric atom-centered orbital basis functions
,” New J. Phys.
14
, 053020
(2012
).41.
J.
Wilhelm
, M.
Del Ben
, and J.
Hutter
, “GW in the Gaussian and plane waves scheme with application to linear acenes
,” J. Chem. Theory Comput.
12
, 3623
–3635
(2016
).42.
Q.
Sun
, T. C.
Berkelbach
, J. D.
McClain
, and G. K.-L.
Chan
, “Gaussian and plane-wave mixed density fitting for periodic systems
,” J. Chem. Phys.
147
, 164119
(2017
).43.
H. J.
Vidberg
and J. W.
Serene
, “Solving the Eliashberg equations by means of N-point Padé approximants
,” J. Low Temp. Phys.
29
, 179
–192
(1977
).44.
P.
Pulay
, “Convergence acceleration of iterative sequences. The case of scf iteration
,” Chem. Phys. Lett.
73
, 393
–398
(1980
).45.
T. H.
Dunning
, “Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
,” J. Chem. Phys.
90
, 1007
–1023
(1989
).46.
D. E.
Woon
and T. H.
Dunning
, “Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon
,” J. Chem. Phys.
98
, 1358
–1371
(1993
).47.
B. P.
Prascher
, D. E.
Woon
, K. A.
Peterson
, T. H.
Dunning
, and A. K.
Wilson
, “Gaussian basis sets for use in correlated molecular calculations. VII. Valence, core-valence, and scalar relativistic basis sets for Li, Be, Na, and Mg
,” Theor. Chem. Acc.
128
, 69
–82
(2011
).48.
C.
Hättig
, “Optimization of auxiliary basis sets for RI-MP2 and RI-CC2 calculations: Core-valence and quintuple-ζ basis sets for H to Ar and QZVPP basis sets for Li to Kr
,” Phys. Chem. Chem. Phys.
7
, 59
–66
(2005
).49.
F.
Weigend
, A.
Köhn
, and C.
Hättig
, “Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations
,” J. Chem. Phys.
116
, 3175
–3183
(2002
).50.
R. A.
Kendall
, T. H.
Dunning
, and R. J.
Harrison
, “Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions
,” J. Chem. Phys.
96
, 6796
–6806
(1992
).51.
K. A.
Peterson
and C.
Puzzarini
, “Systematically convergent basis sets for transition metals. II. Pseudopotential-based correlation consistent basis sets for the group 11 (Cu, Ag, Au) and 12 (Zn, Cd, Hg) elements
,” Theor. Chem. Acc.
114
, 283
–296
(2005
).52.
D.
Figgen
, G.
Rauhut
, M.
Dolg
, and H.
Stoll
, “Energy-consistent pseudopotentials for group 11 and 12 atoms: Adjustment to multi-configuration Dirac–Hartree–Fock data
,” Chem. Phys.
311
, 227
–244
(2005
).53.
C.
Hartwigsen
, S.
Goedecker
, and J.
Hutter
, “Relativistic separable dual-space Gaussian pseudopotentials from H to Rn
,” Phys. Rev. B
58
, 3641
–3662
(1998
).54.
J.
VandeVondele
, M.
Krack
, F.
Mohamed
, M.
Parrinello
, T.
Chassaing
, and J.
Hutter
, “Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach
,” Comput. Phys. Commun.
167
, 103
–128
(2005
).55.
J. P.
Perdew
, K.
Burke
, and M.
Ernzerhof
, “Generalized gradient approximation made simple
,” Phys. Rev. Lett.
77
, 3865
(1996
).56.
C.
Adamo
and V.
Barone
, “Toward reliable density functional methods without adjustable parameters: The PBE0 model
,” J. Chem. Phys.
110
, 6158
–6170
(1999
).57.
O.
Madelung
, Semiconductors: Data Handbook
, 3rd ed. (Springer-Verlag
, New York
, 2004
).58.
T.
Chiang
, K.
Frank
, H.
Freund
, A.
Goldmann
, F. J.
Himpsel
, U.
Karlsson
, R.
Lecky
, and W.
Schneider
, Electronic Structure of Solids: Photoemission Spectra and Related Data
(Springer
, 1989
).59.
R. C.
Whited
, C. J.
Flaten
, and W. C.
Walker
, “Exciton thermoreflectance of MgO and CaO
,” Solid State Commun.
13
, 1903
–1905
(1973
).60.
N.
Schwentner
, F.-J.
Himpsel
, V.
Saile
, M.
Skibowski
, W.
Steinmann
, and E. E.
Koch
, “Photoemission from rare-gas solids: Electron energy distributions from the valence bands
,” Phys. Rev. Lett.
34
, 528
–531
(1975
).61.
D. R.
Hamann
and D.
Vanderbilt
, “Maximally localized Wannier functions for GW quasiparticles
,” Phys. Rev. B
79
, 045109
(2009
).62.
G.
Knizia
, “Intrinsic atomic orbitals: An unbiased Bridge between quantum theory and chemical concepts
,” J. Chem. Theory Comput.
9
, 4834
–4843
(2013
).63.
Z.-H.
Cui
, T.
Zhu
, and G. K.-L.
Chan
, “Efficient implementation of ab initio quantum embedding in periodic systems: Density matrix embedding theory
,” J. Chem. Theory Comput.
16
, 119
–129
(2020
).64.
J.
van Elp
, R. H.
Potze
, H.
Eskes
, R.
Berger
, and G. A.
Sawatzky
, “Electronic structure of MnO
,” Phys. Rev. B
44
, 1530
–1537
(1991
).65.
H. K.
Bowen
, D.
Adler
, and B. H.
Auker
, “Electrical and optical properties of FeO
,” J. Solid State Chem.
12
, 355
–359
(1975
).66.
J.
van Elp
, J. L.
Wieland
, H.
Eskes
, P.
Kuiper
, G. A.
Sawatzky
, F. M. F.
de Groot
, and T. S.
Turner
, “Electronic structure of CoO, Li-doped CoO, and LiCoO2
,” Phys. Rev. B
44
, 6090
–6103
(1991
).67.
G. A.
Sawatzky
and J. W.
Allen
, “Magnitude and origin of the band gap in NiO
,” Phys. Rev. Lett.
53
, 2339
–2342
(1984
).68.
S.
Mandal
, K.
Haule
, K. M.
Rabe
, and D.
Vanderbilt
, “Systematic beyond-DFT study of binary transition metal oxides
,” npj Comput. Mater.
5
, 115
(2019
).69.
C.
Rödl
, F.
Fuchs
, J.
Furthmüller
, and F.
Bechstedt
, “Quasiparticle band structures of the antiferromagnetic transition-metal oxides MnO, FeO, CoO, and NiO
,” Phys. Rev. B
79
, 235114
(2009
).70.
T.
Zhu
and G. K.-L.
Chan
, “Ab initio full cell GW+DMFT for correlated materials
,” Phys. Rev. X
11
, 021006
(2021
).71.
T.
Zhu
, C. A.
Jiménez-Hoyos
, J.
McClain
, T. C.
Berkelbach
, and G. K.-L.
Chan
, “Coupled-cluster impurity solvers for dynamical mean-field theory
,” Phys. Rev. B
100
, 115154
(2019
).72.
T.
Zhu
, Z.-H.
Cui
, and G. K.-L.
Chan
, “Efficient formulation of ab initio quantum embedding in periodic systems: Dynamical mean-field theory
,” J. Chem. Theory Comput.
16
, 141
–153
(2020
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
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