A hierarchy of simplified Hartree-Fock (HF), density functional theory (DFT) methods, and their combinations has been recently proposed for the fast electronic structure computation of large systems. The covered methods are a minimal basis set Hartree–Fock (HF-3c), a small basis set global hybrid functional (PBEh-3c), and its screened exchange variant (HSE-3c), all augmented with semiclassical correction potentials. Here, we extend their applicability to inorganic covalent and ionic solids as well as layered materials. The new methods have been dubbed HFsol-3c, PBEsol0-3c, and HSEsol-3c, respectively, to indicate their parent functional as well as the correction potentials. They have been implemented in the CRYSTAL code to enable routine application for molecular as well as solid materials. We validate the new methods on diverse sets of solid state benchmarks that cover more than 90 solids ranging from covalent, ionic, semi-ionic, layered, and molecular crystals. While we focus on structural and energetic properties, we also test bandgaps, vibrational frequencies, elastic constants, and dielectric and piezoelectric tensors. HSEsol-3c appears to be most promising with mean absolute error for cohesive energies and unit cell volumes of molecular crystals of 1.5 kcal/mol and 2.8%, respectively. Lattice parameters of inorganic solids deviate by 3% from the references, and vibrational frequencies of α-quartz have standard deviations of 10 cm−1. Overall, this shows an accuracy competitive to converged basis set dispersion corrected DFT with a substantial increase in computational efficiency.

1.
K.
Burke
, “
Perspective on density functional theory
,”
J. Chem. Phys.
136
(
15
),
150901
(
2012
).
2.
R. J.
Maurer
,
C.
Freysoldt
,
A. M.
Reilly
,
J. G.
Brandenburg
,
O. T.
Hofmann
,
T.
Bjöorkman
,
S.
Lebègue
, and
A.
Tkatchenko
, “
Advances in density-functional calculations for materials modeling
,”
Annu. Rev. Mater. Res.
49
,
1
30
(
2019
).
3.
E.
Caldeweyher
and
J. G.
Brandenburg
, “
Simplified DFT methods for consistent structures and energies of large systems
,”
J. Phys.: Condens. Matter
30
,
213001
(
2018
).
4.
S.
Ehrlich
,
A. H.
Göller
, and
S.
Grimme
, “
Towards full quantum-mechanics-based protein–ligand binding affinities
,”
ChemPhysChem
18
,
898
905
(
2017
).
5.
S.
Rösel
,
H.
Quanz
,
C.
Logemann
,
J.
Becker
,
E.
Mossou
,
L.
Cañadillas-Delgado
,
E.
Caldeweyher
,
S.
Grimme
, and
P. R.
Schreiner
, “
London dispersion enables the shortest intermolecular hydrocarbon H⋯H contact
,”
J. Am. Chem. Soc.
139
(
22
),
7428
7431
(
2017
).
6.
T. A.
Schaub
,
R.
Sure
,
F.
Hampel
,
S.
Grimme
, and
M.
Kivala
, “
Quantum chemical dissection of the shortest P=O⋯I halogen bond: The decisive role of crystal packing effects
,”
Chem. Eur. J.
23
(
24
),
5687
5691
(
2017
).
7.
M.
Cutini
,
B.
Civalleri
, and
P.
Ugliengo
, “
Cost-effective quantum mechanical approach for predicting thermodynamic and mechanical stability of pure-silica zeolites
,”
ACS Omega
4
,
1838
1846
(
2019
).
8.
J.
Klimeš
and
A.
Michaelides
, “
Perspective: Advances and challenges in treating van der Waals dispersion forces in density functional theory
,”
J. Chem. Phys.
137
,
120901
(
2012
).
9.
K.
Berland
,
V. R.
Cooper
,
K.
Lee
,
E.
Schröder
,
T.
Thonhauser
,
P.
Hyldgaard
, and
B. I.
Lundqvist
, “
van der Waals forces in density functional theory: A review of the vdW-DF method
,”
Rep. Prog. Phys.
78
,
066501
(
2015
).
10.
S.
Grimme
,
A.
Hansen
,
J. G.
Brandenburg
, and
C.
Bannwarth
, “
Dispersion-corrected mean-field electronic structure methods
,”
Chem. Rev.
116
,
5105
5154
(
2016
).
11.
H.
Kruse
and
S.
Grimme
, “
A geometrical correction for the inter-and intra-molecular basis set superposition error in Hartree-Fock and density functional theory calculations for large systems
,”
J. Chem. Phys.
136
,
154101
(
2012
).
12.
R.
Sure
and
S.
Grimme
, “
Corrected small basis set Hartree-Fock method for large systems
,”
J. Comput. Chem.
34
,
1672
1685
(
2013
).
13.
S.
Grimme
,
J. G.
Brandenburg
,
C.
Bannwarth
, and
A.
Hansen
, “
Consistent structures and interactions by density functional theory with small atomic orbital basis sets
,”
J. Chem. Phys.
143
,
054107
(
2015
).
14.
J. G.
Brandenburg
,
E.
Caldeweyher
, and
S.
Grimme
, “
Screened exchange hybrid density functional for accurate and efficient structures and interaction energies
,”
Phys. Chem. Chem. Phys.
18
,
15519
15523
(
2016
).
15.
J. G.
Brandenburg
,
C.
Bannwarth
,
A.
Hansen
, and
S.
Grimme
, “
B97-3c: A revised low-cost variant of the B97-D density functional method
,”
J. Chem. Phys.
148
,
064104
(
2018
).
16.
M.
Cutini
,
B.
Civalleri
,
M.
Corno
,
R.
Orlando
,
J. G.
Brandenburg
,
L.
Maschio
, and
P.
Ugliengo
, “
Assessment of different quantum mechanical methods for the prediction of structure and cohesive energy of molecular crystals
,”
J. Chem. Theory Comput.
12
,
3340
3352
(
2016
).
17.
R.
Dovesi
,
V. R.
Saunders
,
C.
Roetti
,
R.
Orlando
,
C. M.
Zicovich-Wilson
,
F.
Pascale
,
B.
Civalleri
,
K.
Doll
,
N. M.
Harrison
,
I. J.
Bush
,
P.
D’Arco
,
M.
Llunell
,
M.
Causà
,
Y.
Noël
,
L.
Maschio
,
A.
Erba
,
M.
Rerat
, and
S.
Casassa
, CRYSTAL17 (
Universitá di Torino
,
Torino
,
2017
).
18.
A.
Grüneich
and
B. A.
Heß
, “
Choosing GTO basis sets for periodic HF calculations
,”
Theor. Chem. Acc.
100
,
253
263
(
1998
).
19.
F.
Jensen
, “
Analysis of energy-optimized Gaussian basis sets for condensed phase density functional calculations
,”
Theor. Chem. Acc.
132
,
1380
(
2013
).
20.
J. P.
Perdew
,
A.
Ruzsinszky
,
G. I.
Csonka
,
O. A.
Vydrov
,
G. E.
Scuseria
,
L. A.
Constantin
,
X.
Zhou
, and
K.
Burke
, “
Restoring the density-gradient expansion for exchange in solids and surfaces
,”
Phys. Rev. Lett.
100
,
136406
(
2008
).
21.
L.
Schimka
,
J.
Harl
, and
G.
Kresse
, “
Improved hybrid functional for solids: The HSEsol functional
,”
J. Chem. Phys.
134
,
024116
(
2011
).
22.
P.
Pernot
,
B.
Civalleri
,
D.
Presti
, and
A.
Savin
, “
Prediction uncertainty of density functional approximations for properties of crystals with cubic symmetry
,”
J. Phys. Chem. A
119
,
5288
5304
(
2015
).
23.
J. M.
Crowley
,
J.
Tahir-Kheli
, and
W. A.
Goddard
 III
, “
Resolution of the band gap prediction problem for materials design
,”
J. Phys. Chem. Lett.
7
,
1198
1203
(
2016
).
24.
A. J.
Garza
and
G. E.
Scuseria
, “
Predicting band gaps with hybrid density functionals
,”
J. Phys. Chem. Lett.
7
,
4165
4170
(
2016
).
25.
S.
Grimme
,
J.
Antony
,
S.
Ehrlich
, and
H.
Krieg
, “
A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu
,”
J. Chem. Phys.
132
,
154104
(
2010
).
26.
S.
Grimme
,
S.
Ehrlich
, and
L.
Goerigk
, “
Effect of the damping function in dispersion corrected density functional theory
,”
J. Comput Chem.
32
,
1456
1465
(
2011
).
27.

The basis sets for H, N, and O were not modified in the present work to keep results as much as possible consistent with original composite methods.

28.
R.
Dovesi
,
A.
Erba
,
R.
Orlando
,
C. M.
Zicovich-Wilson
,
B.
Civalleri
,
L.
Maschio
,
M.
Rérat
,
S.
Casassa
,
J.
Baima
,
S.
Salustro
 et al, “
Quantum-mechanical condensed matter simulations with CRYSTAL
,”
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
8
,
e1360
(
2018
).
29.
C.
Pisani
,
R.
Dovesi
, and
C.
Roetti
,
Hartree-Fock Ab Initio Treatment of Crystalline Systems
, Lecture Notes in Chemistry Vol. 48 (
Springer Verlag
,
Heidelberg
,
1988
).
30.
R.
Orlando
,
M.
De La Pierre
,
C. M.
Zicovich-Wilson
,
A.
Erba
, and
R.
Dovesi
, “
On the full exploitation of symmetry in periodic (as well as molecular) self-consistent-field ab initio calculations
,”
J. Chem. Phys.
141
,
104108
(
2014
).
31.
A.
Erba
,
J.
Baima
,
I.
Bush
,
R.
Orlando
, and
R.
Dovesi
, “
Large-scale condensed matter DFT simulations: Performance and capabilities of the CRYSTAL code
,”
J. Chem. Theory Comput.
13
,
5019
5027
(
2017
).
32.
J.
Rezác
,
K.
E Riley
, and
P.
Hobza
, “
S66: A well-balanced database of benchmark interaction energies relevant to biomolecular structures
,”
J. Chem. Theory Comput.
7
,
2427
2438
(
2011
).
33.
A.
Otero-De-La-Roza
and
E. R.
Johnson
, “
A benchmark for non-covalent interactions in solids
,”
J. Chem. Phys.
137
,
054103
(
2012
).
34.
A. M.
Reilly
and
A.
Tkatchenko
, “
Seamless and accurate modeling of organic molecular materials
,”
J. Phys. Chem. Lett.
4
,
1028
1033
(
2013
).
35.
P.
Hao
,
Y.
Fang
,
J.
Sun
,
G. I.
Csonka
,
P. H. T.
Philipsen
, and
J. P.
Perdew
, “
Lattice constants from semilocal density functionals with zero-point phonon correction
,”
Phys. Rev. B
85
,
014111
(
2012
).
36.
M. F.
Peintinger
,
D. V.
Oliveira
, and
T.
Bredow
, “
Consistent Gaussian basis sets of triple-zeta valence with polarization quality for solid-state calculations
,”
J. Comput. Chem.
34
,
451
459
(
2013
).
37.

Reference data adopted in the POB dataset were not back-corrected to estimate the athermal limit. Therefore, it should be expected that the computed equilibrium unit cell volumes are slightly underestimated with respect to experimental data, which is indeed the case for HFsol-3c, PBEsol-3c, and HSEsol-3c.

38.
L.
Spanu
,
S.
Sorella
, and
G.
Galli
, “
Nature and strength of interlayer binding in graphite
,”
Phys. Rev. Lett.
103
,
196401
(
2009
).
39.
Y.
Baskin
and
L.
Meyer
, “
Lattice constants of graphite at low temperatures
,”
Phys. Rev.
100
(
2
),
544
(
1955
).
40.
G.
Sansone
,
A. J.
Karttunen
,
D.
Usvyat
,
M.
Schütz
,
J. G.
Brandenburg
, and
L.
Maschio
, “
On the exfoliation and anisotropic thermal expansion of black phosphorus
,”
Chem. Commun.
54
,
9793
9796
(
2018
).
41.
G.
Sansone
,
L.
Maschio
,
D.
Usvyat
,
M.
Schütz
, and
A.
Karttunen
, “
Toward an accurate estimate of the exfoliation energy of black phosphorus: A periodic quantum chemical approach
, “
J. Phys. Chem. Lett.
7
,
131
136
(
2015
).
42.
G. A.
Lager
,
J. D.
Jorgensen
, and
F. J.
Rotella
, “
Crystal structure and thermal expansion of α-SiO2 at low temperatures
,”
J. Appl. Phys.
53
,
6751
6756
(
1982
).
43.
R.
Tarumi
,
K.
Nakamura
,
H.
Ogi
, and
M.
Hirao
, “
Complete set of elastic and piezoelectric coefficients of α-quartz at low temperatures
,”
J. Appl. Phys.
102
,
113508
(
2007
).
44.
L.
Levien
,
C.
T Prewitt
, and
D. J.
Weidner
, “
Structure and elastic properties of quartz at pressure
,”
Am. Miner.
65
,
920
930
(
1980
).
45.
C. M.
Zicovich-Wilson
,
F.
Pascale
,
C.
Roetti
,
V. R.
Saunders
,
R.
Orlando
, and
R.
Dovesi
, “
Calculation of the vibration frequencies of α-quartz: The effect of Hamiltonian and basis set
,”
J. Chem. Phys.
25
,
1873
1881
(
2004
).
46.
E.
Caldeweyher
,
C.
Bannwarth
, and
S.
Grimme
, “
Extension of the D3 dispersion coefficient model
,”
J. Chem. Phys.
147
,
034112
(
2017
).
47.
E.
Caldeweyher
,
S.
Ehlert
,
A.
Hansen
,
H.
Neugebauer
,
S.
Spicher
,
C.
Bannwarth
, and
S.
Grimme
, “
A generally applicable atomic-charge dependent London dispersion correction
,”
J. Chem. Phys.
150
(
15
),
154122
(
2019
).
48.
B. M.
Axilrod
and
E.
Teller
, “
Interaction of the van der Waals type between three atoms
,”
J. Chem. Phys.
11
,
299
300
(
1943
).
49.
Y.
Muto
, “
Force between nonpolar molecules
,”
J. Phys. Math. Soc. Jpn.
17
,
629
631
(
1943
).

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