We calculate bandgaps of 12 inorganic semiconductors and insulators composed of atoms from the first three rows of the Periodic Table using periodic equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD). Our calculations are performed with atom-centered triple-zeta basis sets and up to 64 k-points in the Brillouin zone. We analyze the convergence behavior with respect to the number of orbitals and number of k-points sampled using composite corrections and extrapolations to produce our final values. When accounting for electron–phonon corrections to experimental bandgaps, we find that EOM-CCSD has a mean signed error of −0.12 eV and a mean absolute error of 0.42 eV; the largest outliers are C (error of −0.93 eV), BP (−1.00 eV), and LiH (+0.78 eV). Surprisingly, we find that the more affordable partitioned EOM-MP2 theory performs as well as EOM-CCSD.

1.
J. P.
Perdew
, “
Density functional theory and the band gap problem
,”
Int. J. Quantum Chem.
19
,
497
(
1986
).
2.
A.
Seidl
,
A.
Görling
,
P.
Vogl
,
J. A.
Majewski
, and
M.
Levy
, “
Generalized Kohn–Sham schemes and the band-gap problem
,”
Phys. Rev. B
53
,
3764
3774
(
1996
).
3.
P.
Mori-Sánchez
,
A. J.
Cohen
, and
W.
Yang
, “
Localization and delocalization errors in density functional theory and implications for band-gap prediction
,”
Phys. Rev. Lett.
100
,
146401
(
2008
).
4.
J.
Muscat
,
A.
Wander
, and
N.
Harrison
, “
On the prediction of band gaps from hybrid functional theory
,”
Chem. Phys. Lett.
342
,
397
401
(
2001
).
5.
H.
Xiao
,
J.
Tahir-Kheli
, and
W. A.
Goddard
, “
Accurate band gaps for semiconductors from density functional theory
,”
J. Phys. Chem. Lett.
2
,
212
217
(
2011
).
6.
A. J.
Garza
and
G. E.
Scuseria
, “
Predicting band gaps with hybrid density functionals
,”
J. Phys. Chem. Lett.
7
,
4165
4170
(
2016
).
7.
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
).
8.
M. S.
Hybertsen
and
S. G.
Louie
, “
First-principles theory of quasiparticles: Calculation of band gaps in semiconductors and insulators
,”
Phys. Rev. Lett.
55
,
1418
1421
(
1985
).
9.
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
).
10.
F.
Bruneval
,
N.
Vast
, and
L.
Reining
, “
Effect of self-consistency on quasiparticles in solids
,”
Phys. Rev. B
74
,
045102
(
2006
).
11.
M.
van Schilfgaarde
,
T.
Kotani
, and
S.
Faleev
, “
Quasiparticle self-consistent GW theory
,”
Phys. Rev. Lett.
96
,
226402
(
2006
).
12.
M.
Shishkin
,
M.
Marsman
, and
G.
Kresse
, “
Accurate quasiparticle spectra from self-consistent GW calculations with vertex corrections
,”
Phys. Rev. Lett.
99
,
246403
(
2007
).
13.
W.
Chen
and
A.
Pasquarello
, “
Accurate band gaps of extended systems via efficient vertex corrections in GW
,”
Phys. Rev. B
92
,
041115
(
2015
).
14.
A. L.
Kutepov
, “
Full versus quasiparticle self-consistency in vertex-corrected GW approaches
,”
Phys. Rev. B
105
,
045124
(
2022
).
15.
C.-N.
Yeh
,
S.
Iskakov
,
D.
Zgid
, and
E.
Gull
, “
Fully self-consistent finite-temperature GW in Gaussian Bloch orbitals for solids
,”
Phys. Rev. B
106
,
235104
(
2022
).
16.
J.
McClain
,
Q.
Sun
,
G. K.-L.
Chan
, and
T. C.
Berkelbach
, “
Gaussian-based coupled-cluster theory for the ground-state and band structure of solids
,”
J. Chem. Theory Comput.
13
,
1209
1218
(
2017
).
17.
Y.
Gao
,
Q.
Sun
,
J. M.
Yu
,
M.
Motta
,
J.
McClain
,
A. F.
White
,
A. J.
Minnich
, and
G. K.-L.
Chan
, “
Electronic structure of bulk manganese oxide and nickel oxide from coupled cluster theory
,”
Phys. Rev. B
101
,
165138
(
2020
).
18.
A.
Pulkin
and
G. K.-L.
Chan
, “
First-principles coupled cluster theory of the electronic spectrum of transition metal dichalcogenides
,”
Phys. Rev. B
101
,
241113
(
2020
).
19.
K.
Laughon
,
J. M.
Yu
, and
T.
Zhu
, “
Periodic coupled-cluster Green’s function for photoemission spectra of realistic solids
,”
J. Phys. Chem. Lett.
13
,
9122
9128
(
2022
).
20.
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
).
21.
A.
Shee
and
D.
Zgid
, “
Coupled cluster as an impurity solver for Green’s function embedding methods
,”
J. Chem. Theory Comput.
15
,
6010
6024
(
2019
).
22.
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
(
2019
).
23.
M. F.
Lange
and
T. C.
Berkelbach
, “
On the relation between equation-of-motion coupled-cluster theory and the GW approximation
,”
J. Chem. Theory Comput.
14
,
4224
4236
(
2018
).
24.
M. F.
Lange
and
T. C.
Berkelbach
, “
Improving MP2 bandgaps with low-scaling approximations to EOM-CCSD
,”
J. Chem. Phys.
155
,
081101
(
2021
).
25.
J.
Tölle
and
G.
Kin-Lic Chan
, “
Exact relationships between the GW approximation and equation-of-motion coupled-cluster theories through the quasi-boson formalism
,”
J. Chem. Phys.
158
,
124123
(
2023
).
26.
A. M.
Lewis
and
T. C.
Berkelbach
, “
Ab initio linear and pump–probe spectroscopy of excitons in molecular crystals
,”
J. Phys. Chem. Lett.
11
,
2241
2246
(
2020
).
27.
X.
Wang
and
T. C.
Berkelbach
, “
Excitons in solids from periodic equation-of-motion coupled-cluster theory
,”
J. Chem. Theory Comput.
16
,
3095
3103
(
2020
).
28.
X.
Wang
and
T. C.
Berkelbach
, “
Absorption spectra of solids from periodic equation-of-motion coupled-cluster theory
,”
J. Chem. Theory Comput.
17
,
6387
6394
(
2021
).
29.
A.
Dittmer
,
R.
Izsák
,
F.
Neese
, and
D.
Maganas
, “
Accurate band gap predictions of semiconductors in the framework of the similarity transformed equation of motion coupled cluster theory
,”
Inorg. Chem.
58
,
9303
9315
(
2019
).
30.
A.
Gallo
,
F.
Hummel
,
A.
Irmler
, and
A.
Grüneis
, “
A periodic equation-of-motion coupled-cluster implementation applied to F-centers in alkaline earth oxides
,”
J. Chem. Phys.
154
,
064106
(
2021
).
31.
B. T. G.
Lau
,
B.
Busemeyer
, and
T. C.
Berkelbach
, “
Optical properties of defects in solids via quantum embedding with good active space orbitals
,” arXiv:2301.09668 (
2023
).
32.
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
).
33.
H.-Z.
Ye
and
T. C.
Berkelbach
, “
Fast periodic Gaussian density fitting by range separation
,”
J. Chem. Phys.
154
,
131104
(
2021
).
34.
H.-Z.
Ye
and
T. C.
Berkelbach
, “
Tight distance-dependent estimators for screening two-center and three-center short-range Coulomb integrals over Gaussian basis functions
,”
J. Chem. Phys.
155
,
124106
(
2021
).
35.
H.-Z.
Ye
and
T. C.
Berkelbach
, “
Correlation-consistent Gaussian basis sets for solids made simple
,”
J. Chem. Theory Comput.
18
,
1595
1606
(
2022
).
36.
Q.
Sun
,
T. C.
Berkelbach
,
N. S.
Blunt
,
G. H.
Booth
,
S.
Guo
,
Z.
Li
,
J.
Liu
,
J. D.
McClain
,
E. R.
Sayfutyarova
,
S.
Sharma
,
S.
Wouters
, and
G. K.-L.
Chan
, “
PySCF: The python-based simulations of chemistry framework
,”
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
8
,
e1340
(
2017
).
37.
S.
Goedecker
,
M.
Teter
, and
J.
Hutter
, “
Separable dual-space Gaussian pseudopotentials
,”
Phys. Rev. B
54
,
1703
1710
(
1996
).
38.
C.
Hartwigsen
,
S.
Goedecker
, and
J.
Hutter
, “
Relativistic separable dual-space Gaussian pseudopotentials from H to Rn
,”
Phys. Rev. B
58
,
3641
3662
(
1998
).
39.
Y.
Yang
,
V.
Gorelov
,
C.
Pierleoni
,
D. M.
Ceperley
, and
M.
Holzmann
, “
Electronic band gaps from quantum Monte Carlo methods
,”
Phys. Rev. B
101
,
085115
(
2020
).
40.
M.
Marsman
,
A.
Grüneis
,
J.
Paier
, and
G.
Kresse
, “
Second-order Møller–Plesset perturbation theory applied to extended systems. I. Within the projector-augmented-wave formalism using a plane wave basis set
,”
J. Chem. Phys.
130
,
184103
(
2009
).
41.
A.
Grüneis
,
M.
Marsman
, and
G.
Kresse
, “
Second-order Møller–Plesset perturbation theory applied to extended systems. II. Structural and energetic properties
,”
J. Chem. Phys.
133
,
074107
(
2010
).
42.
M. R.
Lorenz
,
R.
Chicotka
,
G. D.
Pettit
, and
P. J.
Dean
, “
The fundamental absorption edge of AlAs and AlP
,”
Solid State Commun.
8
,
693
697
(
1970
).
43.
W. Y.
Ching
,
F.
Gan
, and
M.-Z.
Huang
, “
Band theory of linear and nonlinear susceptibilities of some binary ionic insulators
,”
Phys. Rev. B
52
,
1596
1611
(
1995
).
44.
S.
Baroni
,
G.
Pastori Parravicini
, and
G.
Pezzica
, “
Quasiparticle band structure of lithium hydride
,”
Phys. Rev. B
32
,
4077
4087
(
1985
).
45.
F. C.
Brown
,
C.
Gähwiller
,
H.
Fujita
,
A. B.
Kunz
,
W.
Scheifley
, and
N.
Carrera
, “
Extreme-ultraviolet spectra of ionic crystals
,”
Phys. Rev. B
2
,
2126
2138
(
1970
).
46.
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
,
727
741
(
2021
).
47.
B.
Monserrat
,
N. D.
Drummond
, and
R. J.
Needs
, “
Anharmonic vibrational properties in periodic systems: Energy, electron–phonon coupling, and stress
,”
Phys. Rev. B
87
,
144302
(
2013
).
48.
G.
Antonius
,
S.
Poncé
,
E.
Lantagne-Hurtubise
,
G.
Auclair
,
X.
Gonze
, and
M.
Côté
, “
Dynamical and anharmonic effects on the electron–phonon coupling and the zero-point renormalization of the electronic structure
,”
Phys. Rev. B
92
,
085137
(
2015
).
49.
A.
Miglio
,
V.
Brousseau-Couture
,
E.
Godbout
,
G.
Antonius
,
Y.-H.
Chan
,
S. G.
Louie
,
M.
Côté
,
M.
Giantomassi
, and
X.
Gonze
, “
Predominance of non-adiabatic effects in zero-point renormalization of the electronic band gap
,”
npj Comput. Mater.
6
,
167
(
2020
).
50.
V.-A.
Ha
,
B.
Karasulu
,
R.
Maezono
,
G.
Brunin
,
J. B.
Varley
,
G.-M.
Rignanese
,
B.
Monserrat
, and
G.
Hautier
, “
Boron phosphide as a p-type transparent conductor: Optical absorption and transport through electron–phonon coupling
,”
Phys. Rev. Mater.
4
,
065401
(
2020
).
51.
J.
Lee
,
A.
Seko
,
K.
Shitara
,
K.
Nakayama
, and
I.
Tanaka
, “
Prediction model of band gap for inorganic compounds by combination of density functional theory calculations and machine learning techniques
,”
Phys. Rev. B
93
,
115104
(
2016
).
52.
M. J.
van Setten
,
V. A.
Popa
,
G. A.
de Wijs
, and
G.
Brocks
, “
Electronic structure and optical properties of lightweight metal hydrides
,”
Phys. Rev. B
75
,
035204
(
2007
).
53.
S.
Banerjee
and
A. Y.
Sokolov
, “
Non-Dyson algebraic diagrammatic construction theory for charged excitations in solids
,”
J. Chem. Theory Comput.
18
,
5337
5348
(
2022
).
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