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Advanced capabilities for materials modelling withQuantum ESPRESSO
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2017
J. Phys.: Condens. Matter
29
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1© 2017 IOP Publishing Ltd Printed in the UKJournal of Physics: Condensed Matter
Advanced capabilities for materials modelling with Q
UANTUM
ESPRESSO
P Giannozzi
1
, O Andreussi
2
,
9
, T Brumme
3
, O Bunau
4
, M Buongiorno Nardelli
5
, M Calandra
4
, R Car
6
, C Cavazzoni
7
, D Ceresoli
8
, M Cococcioni
9
, N Colonna
9
, I Carnimeo
1
, A Dal Corso
10
,
32
, S de Gironcoli
10
,
32
, P Delugas
10
, R A DiStasio Jr
11
, A Ferretti
12
, A Floris
13
, G Fratesi
14
, G Fugallo
15
, R Gebauer
16
, U Gerstmann
17
, F Giustino
18
, T Gorni
4
,
10
, J Jia
11
, M Kawamura
19
, HY Ko
6
, A Kokalj
20
, E K
üçü
kbenli
10
, M Lazzeri
4
, M Marsili
21
, N Marzari
9
, F Mauri
22
, N L Nguyen
9
, HV Nguyen
23
, A OterodelaRoza
24
, L Paulatto
4
, S Ponc
é
18
, D Rocca
25
,
26
, R Sabatini
27
, B Santra
6
, M Schlipf
18
, A P Seitsonen
28
,
29
, A Smogunov
30
, I Timrov
9
, T Thonhauser
31
, P Umari
21
,
32
, N Vast
33
, X Wu
34
and S Baroni
10
1
Department of Mathematics, Computer Science, and Physics, University of Udine, via delle Scienze 206, I33100 Udine, Italy
2
Institute of Computational Sciences, Universit
à
della Svizzera Italiana, Lugano, Switzerland
3
WilhelmOstwaldInstitute of Physical and Theoretical Chemistry, Leipzig University, Linn
é
str. 2, D04103 Leipzig, Germany
4
IMPMC, UMR CNRS 7590, Sorbonne Universit
é
sUPMC University Paris 06, MNHN, IRD, 4 Place Jussieu, F75005 Paris, France
5
Department of Physics and Department of Chemistry, University of North Texas, Denton, TX, United States of America
6
Department of Chemistry, Princeton University, Princeton, NJ 08544, United States of America
7
CINECA
—
Via Magnanelli 6/3, I40033 Casalecchio di Reno, Bologna, Italy
8
Institute of Molecular Science and Technologies (ISTM), National Research Council (CNR), I20133 Milano, Italy
9
Theory and Simulation of Materials (THEOS), and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), Ecole Polytechnique F
é
d
é
rale de Lausanne, CH1015 Lausanne, Switzerland
10
SISSAScuola Internazionale Superiore di Studi Avanzati, via Bonomea 265, I34136 Trieste, Italy
11
Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853, United States of America
12
CNR Istituto Nanoscienze, I42125 Modena, Italy
13
School of Mathematics and Physics, College of Science, University of Lincoln, United Kingdom
14
Dipartimento di Fisica, Universit
à
degli Studi di Milano, via Celoria 16, I20133 Milano, Italy
15
ETSF, Laboratoire des Solides Irradi
é
s, Ecole Polytechnique, F91128 Palaiseau cedex, France
16
The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, I34151 Trieste, Italy
17
Department Physik, Universit
ä
t Paderborn, D33098 Paderborn, Germany
18
Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
19
The Institute for Solid State Physics, Kashiwa, Japan
20
Department of Physical and Organic Chemistry, Jo
ž
ef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
21
Dipartimento di Fisica e Astronomia, Universit
à
di Padova, via Marzolo 8, I35131 Padova, Italy
22
Dipartimento di Fisica, Universit
à
di Roma La Sapienza, Piazzale Aldo Moro 5, I00185 Roma, Italy
23
Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Hanoi, Vietnam
24
Department of Chemistry, University of British Columbia, Okanagan, Kelowna BC V1V 1V7, Canada
25
Universit
é
de Lorraine,
CRM
2
, UMR 7036, F54506 Vandoeuvrel
è
sNancy, France
26
CNRS,
CRM
2
, UMR 7036, F54506 Vandoeuvrel
è
sNancy, France
27
Orionis Biosciences, Newton, MA 02466, United States of America
28
Institut f
ü
r Chimie, Universit
ä
t Zurich, CH8057 Z
ü
rich, Switzerland
29
D
é
partement de Chimie,
É
cole Normale Sup
é
rieure, F75005 Paris, France
30
SPEC, CEA, CNRS, Universit
é
ParisSaclay, F91191 GifSurYvette, France
31
Department of Physics, Wake Forest University, WinstonSalem, NC 27109, United States of America
1361648X/17/465901+30$33.00https://doi.org/10.1088/1361648X/aa8f79J. Phys.: Condens. Matter
29
(2017) 465901 (30pp)
P Giannozzi
et al
2
32
CNRIOM DEMOCRITOS, Istituto Ofﬁcina dei Materiali, Consiglio Nazionale delle Ricerche, Italy
33
Laboratoire des Solides Irradi
é
s,
É
cole Polytechnique, CEADRFIRAMIS, CNRS UMR 7642, Universit
é
ParisSaclay, F91120 Palaiseau, France
34
Department of Physics, Temple University, Philadelphia, PA 191221801, United States of AmericaEmail: paolo.giannozzi@uniud.itReceived 5 July 2017, revised 23 September 2017Accepted for publication 27 September 2017Published 24 October 2017
Abstract
Quantum ESPRESSO
is an integrated suite of opensource computer codes for quantum simulations of materials using stateoftheart electronicstructure techniques, based on densityfunctional theory, densityfunctional perturbation theory, and manybody perturbation theory, within the planewave pseudopotential and projectoraugmentedwave approaches.
Quantum ESPRESSO
owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core opensource development platform to implement their ideas. In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software.Keywords: densityfunctional theory, densityfunctional perturbation theory, manybody perturbation theory, ﬁrstprinciples simulations(Some ﬁgures may appear in colour only in the online journal)
1. Introduction
Numerical simulations based on densityfunctional theory (DFT) [1, 2] have become a powerful and widely used tool
for the study of materials properties. Many such simulations are based upon the
‘
planewave pseudopotential method
’
, often using ultrasoft pseudopotentials [3] or the projector augmented wave method (PAW) [4] (in the following, all of these modern developments will be referred to under the generic name of
‘
pseudopotentials
’
). An important role in the diffusion of DFTbased techniques has been played by the availability of robust and efﬁcient software implementations [5], as is the case for Q ESPRESSO, which is an opensource software distribution
—
i.e.
an integrated suite of codes
—
for electronicstructure calculations based on DFT or manybody perturbation theory, and using planewave basis sets and pseudo potentials [6].
The core philosophy of
Quantum ESPRESSO
can be summarized in four keywords: openness, modularity, efﬁciency, and innovation. The distribution is based on two core packages,
PWscf
and
CP
, performing selfconsistent and moleculardynamics calculations respectively, and on additional packages for more advanced calculations. Among these we quote in particular:
PHonon
, for linearresponse calculations of vibrational properties;
os roc
, for data analysis and postprocessing;
atomic
, for pseudopotential generation;
XSpectra
, for the calculation of xray absorption spectra;
GIPAW
, for nuclear magnetic resonance and electron paramagn etic resonance calculations.In this paper we describe and document the novel or improved capabilities of
Quantum ESPRESSO
up to and including version 6.2. We do not cover features already present in v.4.1 and described in [6], to which we refer for further details. The list of enhancements includes theoretical and methodological extensions but also performance enhancements for current parallel machines and modularization and extended interoperability with other software.Among the theoretical and methodological extensions, we mention in particular:
•
Fast implementations of exact (Fock) exchange for hybrid functionals [7, 42
–
44]; implementation of nonlocal van der Waals functionals [9] and of explicit corrections for van der Waals interactions [10
–
13]; improvement and extensions of Hubbardcorrected functionals [14, 15].
•
Excitedstate calculations within timedependent densityfunctional and manybody perturbation theories.
•
Relativistic extension of the PAW formalism, including spin
–
orbit interactions in densityfunctional theory [16, 17].
•
Continuum embedding environments (dielectric solvation models, electronic enthalpy, electronic surface tension, periodic boundary corrections) via the
Environ
module [18, 19] and its timedependent generalization [20].
Several new packages, implementing the calculation of new properties, have been added to
Quantum ESPRESSO
. We quote in particular:
J. Phys.: Condens. Matter
29
(
2017
) 465901
P Giannozzi
et al
3
•
turboTDDFT
[21
–
24] and
turboEELS
[25, 26], for
excitedstate calculations within timedependent DFT (TDDFT), without computing virtual orbitals, also interfaced with the
Environ
module (see above).
•
QEGIPAW
, replacing the old
GIPAW
package, for nuclear magnetic resonance and electron paramagnetic resonance calculations.
•
EPW
, for electron
–
phonon calculations using Wannierfunction interpolation [27].
•
GWL
and
SternheimerGW
for quasiparticle and excitedstate calculations within manybody perturbation theory, without computing any virtual orbitals, using the Lanczos biorthogonalization [28, 29] and multishift
conjugategradient methods [30], respectively.
•
thermo_pw
, for computing thermodynamical properties in the quasiharmonic approximation, also featuring an advanced masterslave distributed computing scheme, applicable to generic highthroughput calculations [31].
•
d3q
and
thermal2
, for the calculation of anharmonic 3body interatomic force constants, phononphonon interaction and thermal transport [32, 33].
Improved parallelization is crucial to enhance performance and to fully exploit the power of modern parallel architectures. A careful removal of memory bottlenecks and of scalar sections of code is a prerequisite for better and extending scaling. Signiﬁcant improvements have been achieved, in particular for hybrid functionals [34, 35].
Complementary to this, a complete pseudopotential library,
pslibrary
, including fullyrelativistic pseudopotentials, has been generated [36, 37]. A curation effort [38] on all the pseudo
potential libraries available for
Quantum ESPRESSO
has led to the identiﬁcation of optimal pseudopotentials for efﬁciency or for accuracy in the calculations, the latter delivering an agreement comparable to any of the best allelectron codes [5]. Finally, a signiﬁcant effort has been dedicated to modularization and to enhanced interoperability with other software. The structure of the distribution has been revised, the code base has been reorganized, the format of data ﬁles redesigned in line with modern standards. As notable examples of interoperability with other software, we mention in particular the interfaces with the
LAMMPS
molecular dynamics (MD) code [39] used as molecularmechanics
‘
engine
’
in the
Quantum ESPRESSO
implementation of the QM
–
MM methodology [40], and with the
i
−
PI
MD driver [41], also featuring pathintegral MD.All advances and extensions that have not been documented elsewhere are described in the next sections. For more details on new packages we refer to the respective references.The paper is organized as follows. Section 2 contains a description of new theoretical and methodological developments and of new packages distributed together with
Quantum ESPRESSO
. Section 3 contains a description of improvements of parallelization, updated information on the philosophy and general organization of
Quantum ESPRESSO
, notably in the ﬁeld of modularization and interoperability. Section 4 contains an outlook of future directions and our conclusions.
2. Theoretical, algorithmic, and methodological extensions
In the following, CGS units are used, unless noted otherwise.
2.1. Advanced functionals2.1.1. Advanced implementation of exact (Fock) exchange and hybrid functionals.
Hybrid functionals are already the
de facto
standard in quantum chemistry and are quickly gaining popularity in the condensedmatter physics and computational materials science communities. Hybrid functionals reduce the selfinteraction error that plagues lowerrung exchangecorrelation functionals, thus achieving more accurate and reliable predictive capabilities. This is of particular importance in the calculation of orbital energies, which are an essential ingredient in the treatment of band alignment and charge transfer in heterogeneous systems, as well as the input for higherlevel electronicstructure calculations based on manybody perturbation theory. However, the widespread use of hybrid functionals is hampered by the often prohibitive computational requirements of the exactexchange (Fock) contribution, especially when working with a planewave basis set. The basic ingredient here is the action
(ˆ
V
x
φ
i
)(
r
)
of the Fock operator
ˆ
V
x
onto a (singleparticle) electronic state
φ
i
, requiring a sum over all occupied Kohn
–
Sham (KS) states
{
ψ
j
}
. For spinunpolarized systems, one has:
(ˆ
V
x
φ
i
)(
r
) =
−
e
2
j
ψ
j
(
r
)
d
r
′
ψ
∗
j
(
r
′
)
φ
i
(
r
′
)

r
−
r
′

,
(1)where
−
e
is the charge of the electron. In the srcinal algorithm [6] implemented in
PWscf
, selfconsistency is achieved via a double loop: in the inner one the
ψ
’
s entering the deﬁnition of the Fock operator in equation (1) are kept ﬁxed, while the outer one cycles until the Fock operator converges to within a given threshold. In the inner loop, the integrals appearing in equation (1):
v
ij
(
r
) =
d
r
′
ρ
ij
(
r
′
)

r
−
r
′

,
ρ
ij
(
r
) =
ψ
∗
i
(
r
)
φ
j
(
r
)
,
(2)are computed by solving the Poisson equation in reciprocal space using fast Fourier transforms (FFT). This algorithm is straightforward but slow, requiring
O
(
N
b
N
k
)
2
FFTs, where
N
b
is the number of electronic states (
‘
bands
’
in solidstate parlance) and
N
k
the number of
k
points in the Brillouin zone (BZ). While feasible in relatively small cells, this unfavorable scaling with the system size makes calculations with hybrid functionals challenging if the unit cell contains more than a few dozen atoms.To enable exactexchange calculations in the condensed phase, various ideas have been conceived and implemented in recent
Quantum ESPRESSO
versions. Code improvements aimed at either optimizing or better parallelizing the standard algorithm are described in section 3.1. In this section we describe two important algorithmic developments in
Quantum ESPRESSO
, both entailing a signiﬁcant reduction in the computational effort: the
adaptively compressed
J. Phys.: Condens. Matter
29
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2017
) 465901
P Giannozzi
et al
4
exchange
(ACE) concept [7] and a linearscaling (
O
(
N
b
)
) framework for performing hybridfunctional
ab initio
molecular dynamics using maximally localized Wannier functions (MLWF) [42
–
44].
2.1.1.1. Adaptively compressed exchange.
The simple formal derivation of ACE allows for a robust implementation, which applies straightforwardly both to isolated or aperiodic systems (
Γ
−
only sampling of the BZ, that is,
k
=
0
) and to periodic ones (requiring sums over a grid of
k
points in the BZ); to norm conserving and ultrasoft pseudopotentials or PAW; to spinunpolarized or polarized cases or to noncollinear magnetization. Furthermore, ACE is compatible with, and takes advantage of, all available parallelization levels implemented in
Quantum ESPRESSO
: over plane waves, over
k
points, and over bands.With ACE, the action of the exchange operator is rewritten as

ˆ
V
x
φ
i
≃
jm

ξ
j
M
−
1
jm
ξ
m

φ
i
,
(3)where

ξ
i
=
ˆ
V
x

ψ
i
and
M
jm
=
ψ
j

ξ
m
. At selfconsistency, ACE becomes exact for
φ
i
’
s in the occupied manifold of KS states. It is straightforward to implement ACE in the doubleloop structure of
PWscf
. The new algorithm is signiﬁcantly faster while not introducing any loss of accuracy at convergence. Benchmark tests on a single processor show a
3
×
to
4
×
speedup for typical calculations in molecules, up to
6
×
in extended systems [45].An additional speedup may be achieved by using a reduced FFT cutoff in the solution of Poisson equations. In equation (1), the exact FFT algorithm requires a FFT grid containing
G
vectors up to a modulus
max
=
2
c
, where
G
c
is the largest modulus of
G
vectors in the planewave basis used to expand
ψ
i
and
φ
j
, or, in terms of kinetic energy cutoff, up to a cutoff
E
x
=
4
E
c
, where
E
c
is the planewave cutoff. The presence of a
1
/
G
2
factor in the reciprocal space expression suggests, and experience conﬁrms, that this condition can be relaxed to
E
x
∼
2
E
c
with little loss of precision, down to
E
x
=
E
c
at the price of increasing somewhat this loss [46]. The kineticenergy cutoff for Fockexchange computations can be tuned by specifying the keyword
ecutfock
in input.Hybrid functionals have also been extended to the case of ultrasoft pseudopotentials and to PAW, following the method of [47]. A large number of integrals involving augmentation charges
q
lm
are needed in this case, thus offsetting the advantage of a smaller planewave basis set. Better performances are obtained by exploiting the localization of the
q
lm
and computing the related terms in real space, at the price of small aliasing errors.These improvements allow to signiﬁcantly speed up a calcul ation, or to execute it on a larger number of processors, thus extending the reach of calculations with hybrid functionals. The bottleneck represented by the sum over bands and by the FFT in equation (1) is however still present: ACE just reduces the number of such expensive calculations, but does not eliminate them. In order to achieve a real breakthrough, one has to get rid of delocalized bands and FFTs, moving to a representation of the electronic structure in terms of localized orbitals. Work along this line using the
selected column density matrix
localization scheme [48, 49] is ongoing. In the
next section we describe a different approach, implemented in the code, based on maximally localized Wannier functions (MLWF).
2.1.1.2. Ab initio molecular dynamics using maximally local ized Wannier functions.
The
CP
code can now perform highly efﬁcient hybridfunctional
ab initio
MD using MLWFs [50]
{
ϕ
i
}
to represent the occupied space, instead of the canonical KS orbitals
{
ψ
i
}
, which are typically delocalized over the entire simulation cell. The MLWF localization procedure can be written as a unitary transformation,
ϕ
i
(
r
) =
j
U
ij
ψ
j
(
r
)
, where
U
ij
is computed at each MD time step by minimizing the total spread of the orbitals via a secondorder damped dynamics scheme, starting with the converged
U
ij
from the previous time step as initial guesses [51].The natural sparsity of the exchange interaction provided by a localized representation of the occupied orbitals (at least in systems with a ﬁnite band gap) is efﬁciently exploited during the evaluation of exactexchange based applications (
e.g.
hybrid DFT functionals). This is accomplished by computing each of the required pairexchange potentials
v
ij
(
r
)
(corresponding to a given localized pairdensity
ρ
ij
(
r
)
) through the numerical solution of the Poisson equation:
∇
2
v
ij
(
r
) =
−
4
πρ
ij
(
r
)
,
ρ
ij
(
r
) =
ϕ
∗
i
(
r
)
ϕ
j
(
r
)
(4)using ﬁnite differences on the realspace grid. Discretizing the Laplacian operator (
∇
2
) using a 19point centraldifference stencil (with an associated
O
(
h
6
)
accuracy in the grid spacing
h
), the resulting sparse linear system of equations is solved using the conjugategradient technique subject to the boundary conditions imposed by a multipolar expansion of
v
ij
(
r
)
:
v
ij
(
r
) =
4
π
lm
Q
lm
2
l
+
1
Y
lm
(
θ
,
φ
)
r
l
1
,
Q
lm
=
d
r
Y
∗
lm
(
θ
,
φ
)
r
l
ρ
ij
(
r
)
(5)in which the
Q
lm
are the multipoles describing
ρ
ij
(
r
)
[42
–
44].Since
v
ij
(
r
)
only needs to be evaluated for
overlapping pairs
of MLWFs, the number of Poisson equations that need to be solved is substantially decreased from
O
(
N
2
b
)
to
O
(
N
b
)
. In addition,
v
ij
(
r
)
only needs to be solved on a subset of the realspace grid (that is in general of ﬁxed size) that encompasses the overlap between a given pair of MLWFs. This further reduces the overall computational effort required to evaluate exactexchange related quantities and results in a linearscaling (
O
(
N
b
)
) algorithm. As such, this framework for performing exactexchange calculations is most efﬁcient for nonmetallic systems (
i.e.
systems with a ﬁnite band gap) in which the occupied KS orbitals can be efﬁciently localized.The MLWF representation not only yields the exactexchange energy
E
xx
,
E
xx
=
−
e
2
ij
d
r
ρ
ij
r
v
ij
r
,
(6)
J. Phys.: Condens. Matter
29
(
2017
) 465901