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  Journal of Physics: Condensed Matter PAPER Advanced capabilities for materials modelling withQuantum ESPRESSO To cite this article: P Giannozzi et al   2017 J. Phys.: Condens. Matter    29  465901 View the article online for updates and enhancements. Related content QUANTUM ESPRESSO: a modular andopen-source software project forquantumsimulations of materialsPaolo Giannozzi, Stefano Baroni, NicolaBonini et al.-Electronic structure calculations withGPAW: a real-space implementation of theprojectoraugmented-wave methodJ Enkovaara, C Rostgaard, J J Mortensenet al.-exciting: a full-potential all-electronpackage implementing density-functionaltheory and many-body perturbation theoryAndris Gulans, Stefan Kontur, ChristianMeisenbichler et al.- Recent citations Clean Os(0001) electronic surface states:a first-principle fully relativisticinvestigationAndrea Urru and Andrea Dal Corso- This content was downloaded from IP address 128.112.123.238 on 17/01/2018 at 19:34  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 , H-Y 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 , H-V Nguyen 23 , A Otero-de-la-Roza 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, I-33100 Udine, Italy 2  Institute of Computational Sciences, Universit à  della Svizzera Italiana, Lugano, Switzerland 3  Wilhelm-Ostwald-Institute of Physical and Theoretical Chemistry, Leipzig University, Linn é str. 2, D-04103 Leipzig, Germany 4  IMPMC, UMR CNRS 7590, Sorbonne Universit é s-UPMC University Paris 06, MNHN, IRD, 4 Place Jussieu, F-75005 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, I-40033 Casalecchio di Reno, Bologna, Italy 8  Institute of Molecular Science and Technologies (ISTM), National Research Council (CNR), I-20133 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, CH-1015 Lausanne, Switzerland 10  SISSA-Scuola Internazionale Superiore di Studi Avanzati, via Bonomea 265, I-34136 Trieste, Italy 11  Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853, United States of America 12  CNR Istituto Nanoscienze, I-42125 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, I-20133 Milano, Italy 15  ETSF, Laboratoire des Solides Irradi é s, Ecole Polytechnique, F-91128 Palaiseau cedex, France 16  The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, I-34151 Trieste, Italy 17  Department Physik, Universit ä t Paderborn, D-33098 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, I-35131 Padova, Italy 22  Dipartimento di Fisica, Universit à  di Roma La Sapienza, Piazzale Aldo Moro 5, I-00185 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, F-54506 Vandoeuvre-l è s-Nancy, France 26  CNRS, CRM 2 , UMR 7036, F-54506 Vandoeuvre-l è s-Nancy, France 27  Orionis Biosciences, Newton, MA 02466, United States of America 28  Institut f  ü r Chimie, Universit ä t Zurich, CH-8057 Z ü rich, Switzerland 29  D é partement de Chimie, É cole Normale Sup é rieure, F-75005 Paris, France 30  SPEC, CEA, CNRS, Universit é  Paris-Saclay, F-91191 Gif-Sur-Yvette, France 31  Department of Physics, Wake Forest University, Winston-Salem, NC 27109, United States of America 1361-648X/17/465901+30$33.00https://doi.org/10.1088/1361-648X/aa8f79J. Phys.: Condens. Matter 29  (2017) 465901 (30pp)  P Giannozzi et al  2 32  CNR-IOM DEMOCRITOS, Istituto Officina dei Materiali, Consiglio Nazionale delle Ricerche, Italy 33  Laboratoire des Solides Irradi é s, É cole Polytechnique, CEA-DRF-IRAMIS, CNRS UMR 7642, Universit é  Paris-Saclay, F-91120 Palaiseau, France 34  Department of Physics, Temple University, Philadelphia, PA 19122-1801, United States of AmericaE-mail: 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 open-source computer codes for quantum simulations of materials using state-of-the-art electronic-structure techniques, based on density-functional theory, density-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudopotential and projector-augmented-wave 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 open-source 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: density-functional theory, density-functional perturbation theory, many-body perturbation theory, first-principles simulations(Some figures may appear in colour only in the online journal) 1. Introduction Numerical simulations based on density-functional 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 ‘ plane-wave 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 DFT-based techniques has been played by the availability of robust and efficient software implementa-tions [5], as is the case for Q󰁵󰁡󰁮󰁴󰁵󰁭 ESPRESSO, which is an open-source software distribution — i.e.  an integrated suite of codes — for electronic-structure calculations based on DFT or many-body perturbation theory, and using plane-wave 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 self-consistent and molecular-dynamics calculations respectively, and on additional packages for more advanced calculations. Among these we quote in particular: PHonon , for linear-response calculations of vibrational properties; os roc , for data analysis and postprocessing; atomic , for pseudopotential generation; XSpectra , for the calculation of x-ray absorp-tion spectra; GIPAW , for nuclear magnetic resonance and elec-tron 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 pre-sent in v.4.1 and described in [6], to which we refer for fur-ther details. The list of enhancements includes theoretical and methodological extensions but also performance enhance-ments 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 non-local van der Waals functionals [9] and of explicit corrections for van der Waals interactions [10 – 13]; improvement and extensions of Hubbard-corrected functionals [14, 15].   •  Excited-state calculations within time-dependent density-functional and many-body perturbation theories.  •  Relativistic extension of the PAW formalism, including spin – orbit interactions in density-functional 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 time-dependent 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 excited-state calculations within time-dependent DFT (TDDFT), without computing virtual orbitals, also inter-faced with the Environ  module (see above).  •   QE-GIPAW , replacing the old GIPAW  package, for nuclear magnetic resonance and electron paramagnetic resonance calculations.  •   EPW , for electron – phonon calculations using Wannier-function interpolation [27].  •   GWL  and SternheimerGW  for quasi-particle and excited-state calculations within many-body perturbation theory, without computing any virtual orbitals, using the Lanczos bi-orthogonalization [28, 29] and multi-shift conjugate-gradient methods [30], respectively.  •   thermo_pw , for computing thermodynamical proper-ties in the quasi-harmonic approximation, also featuring an advanced master-slave distributed computing scheme, applicable to generic high-throughput calculations [31].  •   d3q   and thermal2 , for the calculation of anharmonic 3-body interatomic force constants, phonon-phonon interaction and thermal transport [32, 33]. Improved parallelization is crucial to enhance performance and to fully exploit the power of modern parallel architec-tures. A careful removal of memory bottlenecks and of scalar sections of code is a pre-requisite for better and extending scaling. Significant improvements have been achieved, in par-ticular for hybrid functionals [34, 35]. Complementary to this, a complete pseudopotential library, pslibrary , including fully-relativistic 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 deliv-ering an agreement comparable to any of the best all-electron 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 re-organized, the format of data files re-designed in line with modern standards. As notable exam-ples of interoperability with other software, we mention in particular the interfaces with the LAMMPS  molecular dynamics (MD) code [39] used as molecular-mechanics ‘ engine ’  in the Quantum ESPRESSO  implementation of the QM – MM methodology [40], and with the i − PI  MD driver [41], also featuring path-integral MD.All advances and extensions that have not been docu-mented 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 devel-opments and of new packages distributed together with Quantum ESPRESSO . Section 3 contains a descrip-tion of improvements of parallelization, updated infor-mation on the philosophy and general organization of Quantum ESPRESSO , notably in the field of modulari-zation 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 condensed-matter physics and computational materials science communities. Hybrid functionals reduce the self-interaction error that plagues lower-rung exchange-corre-lation functionals, thus achieving more accurate and reliable predictive capabilities. This is of particular importance in the calculation of orbital energies, which are an essential ingredi-ent in the treatment of band alignment and charge transfer in heterogeneous systems, as well as the input for higher-level electronic-structure calculations based on many-body pertur-bation theory. However, the widespread use of hybrid func-tionals is hampered by the often prohibitive computational requirements of the exact-exchange (Fock) contribution, espe-cially when working with a plane-wave basis set. The basic ingredient here is the action (ˆ V   x φ i )( r )  of the Fock operator ˆ V   x  onto a (single-particle) electronic state φ i , requiring a sum over all occupied Kohn – Sham (KS) states { ψ  j } . For spin-unpolarized 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 algo-rithm [6] implemented in PWscf , self-consistency is achieved via a double loop: in the inner one the ψ ’ s entering the defi-nition 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 solid-state 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 exact-exchange calculations in the condensed phase, various ideas have been conceived and implemented in recent Quantum ESPRESSO  versions. Code improve-ments aimed at either optimizing or better parallelizing the standard algorithm are described in section 3.1. In this sec-tion we describe two important algorithmic developments in Quantum ESPRESSO , both entailing a significant reduc-tion in the computational effort: the adaptively compressed J. Phys.: Condens. Matter 29  ( 2017 ) 465901  P Giannozzi et al  4 exchange  (ACE) concept [7] and a linear-scaling ( O (  N  b ) ) framework for performing hybrid-functional ab initio  molec-ular 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 spin-unpolarized or polarized cases or to non-collinear mag-netization. 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 self-consistency, ACE becomes exact for φ i ’ s in the occupied manifold of KS states. It is straightforward to implement ACE in the double-loop structure of PWscf . The new algorithm is significantly faster while not introducing any loss of accuracy at conv-ergence. 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 equa-tion (1), the exact FFT algorithm requires a FFT grid con-taining G -vectors up to a modulus max  =  2  c , where G c  is the largest modulus of G -vectors in the plane-wave 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 plane-wave 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 kinetic-energy cutoff for Fock-exchange 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 advan-tage of a smaller plane-wave basis set. Better performances are obtained by exploiting the localization of the q lm  and com-puting 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 func-tionals. 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 local-ized 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 hybrid-functional ab initio  MD using MLWFs [50] { ϕ i }  to represent the occupied space, instead of the canoni-cal 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 second-order 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 exact-exchange based applica-tions ( e.g.  hybrid DFT functionals). This is accomplished by computing each of the required pair-exchange potentials v ij ( r )  (corresponding to a given localized pair-density 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 real-space grid. Discretizing the Laplacian operator ( ∇ 2 ) using a 19-point central-differ-ence stencil (with an associated O ( h 6 )  accuracy in the grid spacing h ), the resulting sparse linear system of equations is solved using the conjugate-gradient 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 real-space grid (that is in general of fixed size) that encom-passes the overlap between a given pair of MLWFs. This further reduces the overall computational effort required to evaluate exact-exchange related quantities and results in a linear-scaling ( O (  N  b ) ) algorithm. As such, this framework for performing exact-exchange calculations is most efficient for non-metallic 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 exact-exchange energy  E  xx ,  E  xx  = − e 2  ij    d r ρ ij  r  v ij  r  ,  (6) J. Phys.: Condens. Matter 29  ( 2017 ) 465901
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