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Advanced capabilities for materials modelling with Quantum ESPRESSO
P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. Buongiorno Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni, N. Colonna, I. Carnimeo, A. Dal Corso, S. de Gironcoli, P. Delugas, R. A. DiStasio, A. Ferretti, A. Floris, G. Fratesi, G. Fugallo, R. Gebauer, U. Gerstmann, F. Giustino, T. Gorni, J. Jia, M. Kawamura, H. -Y. Ko, A. Kokalj, E. Küçükbenli, M. Lazzeri, M. Marsili, N. Marzari, F. Mauri, N. L. Nguyen, H. -V. Nguyen, A. Otero-de-la-Roza, L. Paulatto, S. Poncé, D. Rocca, R. Sabatini, B. Santra, M. Schlipf, A. P. Seitsonen, A. Smogunov, I. Timrov, T. Thonhauser, P. Umari, N. Vast, X. Wu, S. Baroni
TL;DR
Quantum ESPRESSO must keep expanding its capabilities while exploiting evolving hardware and maintaining interoperability. This paper documents methodological extensions, new property calculators, improved parallelization, modularization, and software interfaces through version 6.2. The resulting suite supports a broader range of materials simulations, with improved computational performance and accuracy comparable to leading all-electron codes for curated pseudopotentials.
Problem
Quantum ESPRESSO requires continued capability expansion as computational approaches and hardware evolve, while maintaining interoperability and useful data exchange.
Method
The paper documents Quantum ESPRESSO extensions spanning methodologies, property calculators, parallelization, modularization, pseudopotential libraries, and interfaces with external software.
Results
The expanded suite provides new materials-property calculations, improved performance, and pseudopotentials whose accuracy agrees comparably with leading all-electron codes.
Takeaways & Limitations
Quantum ESPRESSO remains an open-source development platform supporting a wide range of advanced electronic-structure and materials simulations across modern computing environments.
Abstract
from arXiv · showhide
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 pseudo-potential 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 theirs 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.
I. INTRODUCTION
Quantum ESPRESSO 6.2 extends an open-source materials-simulation suite with new methodologies, property calculators, performance improvements, modularization, and interoperability. The documented advances broaden supported calculations while improving scalability and computational reach.
- Scope: Version 6.2 documents new or improved Quantum ESPRESSO capabilities beyond those described for version 4.1.The paper covers developments available through version 6.2 and excludes features already documented in the earlier reference.
- Methodological extensions: New theoretical methods include exact exchange, van der Waals functionals and corrections, Hubbard-corrected functionals, excited-state calculations, relativistic PAW, and continuum embedding.The extensions target hybrid functionals, dispersion interactions, correlated calculations, relativistic effects, and environmental modeling.
- Property calculators: New packages calculate excited-state, magnetic-resonance, electron-phonon, thermodynamic, anharmonic-force-constant, phonon-interaction, and thermal-transport properties.Examples include turboTDDFT, turboEELS, QE-GIPAW, EPW, thermo_pw, 3.q, and thermal2.
- Modularization and interoperability: The distribution was modularized and made interoperable with LAMMPS for QM-MM simulations and i-PI for molecular dynamics, including path-integral molecular dynamics.The paper also reports revised organization and redesigned data-file formats alongside these interfaces.
- Performance: Exact-exchange implementations include adaptively compressed exchange and an O(Nb) framework using maximally localized Wannier functions for hybrid-functional molecular dynamics.The Wannier representation reduces computational cost and supports exchange contributions to the stress tensor and simulations in NVE, NVT, and NPT ensembles.
- Performance: 3× to 4× speedups are reported for typical molecular calculations and up to 6× for extended systems in single-processor benchmarks.The faster algorithm preserves accuracy at convergence; the improvements extend hybrid-functional calculations to larger systems and processor counts.
2. Dispersion interactions
Quantum ESPRESSO implements non-local and pairwise approaches for dispersion interactions, with algorithms and kernel transformations that make these corrections tractable for large systems. The section also reports scaling performance and applications of TS-vdW and XDM corrections.
- Dispersion interactions arise from dynamical correlations among charge fluctuations in widely separated regions of space.
- 88% strong-scaling and 80% weak-scaling efficiencies were achieved relative to ideal efficiencies for hybrid-DFT simulations on Mira.
- Non-local van der Waals density functionals: vdW-DF separates the exchange-correlation energy into a semilocal component and a truly non-local correlation part responsible for van der Waals forces.
- Non-local van der Waals density functionals: Spline interpolation and Fourier transformation replace two spatial integrals with one Fourier-space integral, producing a considerable speedup.
- Non-local van der Waals density functionals: In large systems, the vdW-DF implementation makes compute times only insignificantly longer than standard GGA functional calculations.
- Interatomic pairwise dispersion corrections: Quantum ESPRESSO implements pairwise DFT-D2, Tkatchenko-Scheffler, and XDM corrections, with damping functions connecting short-range correlation to long-range dispersion.
- XDM performs well for lattice energies, crystal geometries, and surface adsorption energies, and supports Born-Oppenheimer and Car-Parrinello molecular dynamics at the DFT+TS-vdW level.
3. Hubbard-corrected functionals: DFT+U
DFT+U extends density-functional calculations for systems with localized, strongly correlated orbitals by adding Hubbard corrections and increasingly general formulations. Quantum ESPRESSO also provides ab initio and DFpT-based routes for calculating Hubbard parameters, reducing supercell and post-processing burdens.
- DFT+U addresses localized d- or f-like orbitals that suffer from strong self-interaction effects and poor descriptions of electronic correlations.
- The Hubbard correction adds an energy term and corresponding potential contributions to Kohn-Sham equations and derivatives such as forces and stresses.
- Quantum ESPRESSO implements an alternative DFT+U formulation for transport that incorporates the Hubbard correction directly into PAW pseudopotentials.
- DFT+U+J0 includes on-site exchange coupling J, which further stabilizes ferromagnetic ground states by penalizing anti-aligned spins on the same site.
- Calculation of Hubbard parameters: A linear-response method calculates Hubbard U ab initio, producing effective interactions consistent with the system and the ground state being corrected.
- Calculation of Hubbard parameters: DFpT-based susceptibility calculations remove periodic-system supercell calculations and their cubic cost while automating complex U-extraction post-processing.
- Calculation of Hubbard parameters: DFpT may also directly evaluate inverse susceptibilities and calculate Hubbard parameters for closed-shell systems, a known difficulty for potential-perturbation schemes.
4. Adiabatic-connection fluctuation-dissipation theory
The ACFD framework expresses exchange-correlation energy through density-response functions, enabling RPA and RPAx calculations with iterative low-mode decompositions. The implementation reduces computational prefactors and supports self-consistent EXX/RPA potentials.
- Consequences: The method treats exchange exactly, removes spurious self-interaction error, and includes long-range van der Waals interactions through nonlocal correlation.An optimized effective-potential scheme can provide self-consistent minimization of the EXX/RPA functional.
- ACFD formulation: ACFD derives the exchange-correlation energy from density linear-response functions through coupling-constant integration.The interacting system is parameterized by a scaled Coulomb interaction while maintaining the ground-state density.
- Approximations: The exact exchange-correlation kernel f_xc is unknown, so practical calculations approximate it using RPA and RPAx kernels.RPA sets f_xc to zero, whereas RPAx includes the exact-exchange kernel.
- Implementation: The ACFDT package evaluates RPA and RPAx correlation energies through iterative decompositions focused on low-lying response modes.Only a small number of eigenvalues are relevant for the correlation-energy calculation.
- Performance: 100 to 1000 times fewer operations are required than full response-matrix implementations, although the global scaling remains N^4.Different trial potentials can also be distributed efficiently across processors or processor groups.
B. Linear response and excited states without virtual orbitals
Linear-response methods in Quantum ESPRESSO extend density-functional perturbation theory to dynamical spectra without explicit virtual orbitals. Liouville-Lanczos and related iterative approaches reuse intermediate products to cover broad spectral ranges efficiently.
- DFpT foundations: DFpT represents orbital responses with generic orbitals orthogonal to occupied states and solves self-consistent Sternheimer equations.This formulation avoids expressing responses as linear combinations of large numbers of virtual orbitals.
- Dynamic response: Dynamic DFpT extends spectra calculations to sizable optical and loss-spectrum regions without explicit reference to virtual states.The extension moves beyond the static-perturbation and Born-Oppenheimer scope of conventional DFpT.
- Scope: Casida-style excited-state calculations are effective for a few excitations but are difficult to extend to continuous spectra and ionization-threshold regions.The limitation is especially relevant for extended systems and broad spectral intervals.
- Liouville-Lanczos: The Liouville-Lanczos approach reuses iterative intermediate products to construct response functions across a broad spectral range.It is based on Lanczos bi-orthogonalization and is designed for continuous spectra that are difficult to treat through a few-excitation Casida calculation.
- Broader reuse: Lanczos and multishift iterative ideas are also used for Bethe-Salpeter, polarization-propagator, and GW self-energy calculations.These approaches are exploited in multiple Quantum ESPRESSO components and other many-body implementations.
1. Static perturbations and vibrational spectroscopy
Quantum ESPRESSO extends static and dynamical linear-response capabilities for vibrational and spectroscopic properties, including correlated, spin-polarized, non-collinear, and spin-orbit-coupled systems. New DFpT+U and Lanczos-based implementations improve accessible properties and computational efficiency.
- Static perturbations and vibrational spectroscopy: DFpT+U supports Dudarev and DFT+U+J0 functionals, allowing localization effects to act selectively on phonon modes at arbitrary wave-vectors.Applications include transition-metal oxides and geophysically relevant materials.
- Static perturbations and vibrational spectroscopy: DFpT+U includes Hubbard contributions to the dynamical matrix and self-consistent density responses around the DFT+U ground state.The implementation accounts for derivatives of the Hubbard energy and uses a DFT+U unperturbed Hamiltonian.
- Static perturbations and vibrational spectroscopy: DFpT+U predictions show significantly better agreement with experiment for lattice-dynamical properties than standard LDA/GGA calculations.Reported improvements include LO-TO and magnetically induced TO splittings.
- Dynamic perturbations: Liouville-Lanczos response calculations avoid expensive Liouvillian inversion and can obtain broad frequency information from a single recursion chain.The recursion is frequency-independent, while evaluating the resulting continued fraction is fast.
- Dynamic perturbations: The dynamic-response implementation supports charge, spin, non-collinear spin-density, and spin-orbit-coupled spectroscopies.Applications include optical absorption, electron energy loss, inelastic X-ray scattering, and magnetic spectroscopies.
3. Many-body perturbation theory
Quantum ESPRESSO implements many-body perturbation methods that avoid explicit unoccupied-state calculations and target different system classes and observables. GWL and SternheimerGW provide complementary capabilities for GW, BSE, band structures, self-energies, and spectral functions.
- GW implementations: Quantum ESPRESSO’s GW approximation represents response and self-energy operators through DFpT, avoiding explicit reference to unoccupied states.This addresses the slow convergence and computational bottleneck associated with many unoccupied states in conventional GW calculations.
- GWL: GWL targets efficient GW calculations for large systems and supports optical spectra through the Bethe-Salpeter approach.It provides several polarizability bases whose dimensions can balance accuracy and computational cost.
- Scope and limitations: GWL is limited to Γ-point sampling and real wave-functions, although long-range dielectric terms can use ordinary k-point sampling.Reliable extended-material calculations can therefore use simulation cells with edges of about 20 Bohr.
- GWL: The GWL BSE implementation scales as N^3 rather than N^4 with system size N by using maximally localized Wannier functions.It can evaluate the full frequency-dependent complex dielectric function or discrete excited states.
- SternheimerGW: SternheimerGW computes frequency-dependent self-energies and quasiparticle corrections at arbitrary Brillouin-zone k-points.This enables band structures and effective masses without interpolation, while complete self-energies provide spectral functions with plasmon satellites.
C. Other spectroscopies
QE-GIPAW extends Quantum ESPRESSO for NMR, EPR, hyperfine, EFG, Mössbauer, relativistic hyperfine, and ENDOR-related calculations. Its linear-response and converse approaches support insulating, metallic, and higher-spin systems, with broader pseudopotential compatibility.
- QE-GIPAW calculates NMR chemical-shift tensors, magnetic susceptibility, EFG tensors, EPR g-tensors, and hyperfine coupling tensors.
- The package supports parameter-free g-tensors, hyperfine splittings, and ENDOR frequencies for systems with total spin S > 1/2.
- GIPAW reconstructs all-electron wavefunctions from pseudo-wavefunctions in a gauge- and translationally invariant way for uniform magnetic-field responses.
- NMR shifts and magnetic susceptibility now support any pseudization scheme and PAW, while chemical shifts can be calculated for systems with several hundreds of atoms.
- Linear response obtains insulating and metallic responses efficiently through the occupied–unoccupied completeness relation, without including virtual orbitals.
2. XSpectra: L2,3 X-ray absorption edges
XSpectra computes L2,3-edge X-ray absorption spectra as a PWscf post-processing tool and provides corrections for spectral selection, broadening, and atomic contributions. Its workflow derives the L3 edge from L2 using a statistical branching ratio and spin-orbit splitting.
- XSpectra: XSpectra has been extended to calculate X-ray absorption spectra at L2,3 edges.
- L2,3-edge construction: The L3 spectrum is obtained by multiplying the L2 spectrum by two and shifting it by the absorbing atom’s 2p spin-orbit splitting.
- L2,3-edge construction: The spin-orbit splitting can come from a relativistic all-electron calculation on an isolated atom or from experiment.
- Spectral correction: spectra correction.x removes states below a selected energy and applies more elaborate broadenings to spectra at any edge.
- Multiple atomic environments: molecularnexafs.x forms weighted sums of separate atomic contributions while accounting for environment-dependent energy references.
3. EPW: Electron-phonon coefficients from Wannier interpolation
EPW uses maximally localized Wannier functions to interpolate electron–phonon interactions from coarse to dense Brillouin-zone meshes with ab initio accuracy. It enables calculations of scattering, transport, superconductivity, and spectral properties, while retaining several implementation boundaries.
- Wannier interpolation: EPW performs ab initio electron–phonon interpolation using the localization of maximally localized Wannier functions.
- Computed properties: EPW calculates electron and phonon linewidths, electron–phonon scattering rates, coupling strengths, metallic resistivity, and superconducting properties.
- Computed properties: The package also provides Eliashberg and transport spectral functions, nesting functions, and superconducting-gap functions on the Fermi surface.
- Implementation: EPW supports electron–phonon couplings with spin-orbit coupling and exploits crystal symmetries to reduce phonon calculations to the irreducible Brillouin-zone wedge.
- Scope and scaling: EPW scales reasonably up to 2,000 cores using MPI, but does not support spin polarization, ultrasoft pseudopotentials, or PAW.
E. Multi-scale modeling
Quantum ESPRESSO broadens multiscale modeling through continuum solvation, QM–MM coupling, and relativistic PAW capabilities. The SCCS model reproduces aqueous solvation energies accurately, while the parallel QM–MM implementation removes restrictions associated with serial molecular-mechanics execution.
- Continuum solvation: The SCCS continuum-solvation model uses a smooth QM-to-continuum transition, iterative solvers, and non-electrostatic interactions.
- Continuum solvation: SCCS reproduces experimental solvation energies for neutral and charged aqueous species with accuracy comparable to or higher than state-of-the-art quantum-chemistry packages.
- Environ capabilities: Environ provides dielectric, enthalpy, cavitation, boundary-condition, dielectric-region, and smoothed-charge embedding terms compatible with multiple Quantum ESPRESSO packages.
- QM–MM coupling: The alternative parallel QM–MM implementation exchanges data through MPI in a single executable and performs as well on HPC machines as the separate QM and MM codes.
- QM–MM coupling: The parallel QM–MM approach is effective for large MM regions and can run without restrictions on any parallel machine.
- Relativistic PAW: Relativistic PAW equations provide four-component spinor pseudo-wavefunctions for electronic-structure calculations including spin-orbit coupling.
2. Electronic and structural properties in field-effect configuration
Quantum ESPRESSO extends field-effect and molecular-dynamics capabilities through periodic-boundary-condition electrostatics and an initialization procedure for Car–Parrinello electronic velocities.
- Field-effect configuration: The FET setup represents the gate as a charged plate and adds a dipolar correction to cancel the spurious field from periodic images.A potential barrier can additionally mimic the gate dielectric and prevent electron spilling toward the gate under large electron doping.
- Field-effect configuration: The gate charge is ndopA, where ndop is the doping-electron number per area and A is the unit-cell area parallel to the surface.The gate potential and barrier are specified through z- and potential-related input parameters.
- Field-effect configuration: The resulting planar-averaged potential combines gate, dipole, barrier, ionic, and Hartree contributions.Figure 3 identifies the gate, dipole, and barrier components separately and shows their sum as the total potential.
- Molecular-dynamics initialization: Car–Parrinello simulations require initial electronic velocities because they are unavailable from scratch and cannot be obtained by simple orbital finite differences.Occupied and virtual projectors, orbital energies, and the time derivative of the Kohn–Sham potential enter the formal construction.
- Molecular-dynamics initialization: The numerical procedure performs ground-state calculations at t = 0 and after a half velocity-Verlet step, then computes velocities from the orbital difference projected outside the occupied manifold.These velocities minimize their norm and therefore the initial electronic temperature.
4. Optimized tetrahedron method
Quantum ESPRESSO improves Brillouin-zone integration with an optimized tetrahedron method and advances parallelization, memory distribution, and mixed MPI–OpenMP execution for larger calculations.
- Optimized tetrahedron method: Metallic Brillouin-zone integration is difficult because the integrand is discontinuous at the Fermi level and includes Dirac delta functions.These issues affect DOS, partial DOS, and electron–phonon coupling calculations.
- Optimized tetrahedron method: The optimized tetrahedron method accounts for curvature, improving convergence over linear interpolation and extending applicability beyond DOS calculations.It supports ground-state charge density, DOS, and partial DOS calculations, as well as linear-response phonons and electron–phonon coupling.
- Parallelization: Distributed arrays and additional parallelization levels target memory and CPU bottlenecks that limit weak and strong scalability.Overlapping communication with computation and maintaining load balance are identified as key requirements for strong scalability.
- Parallelization: ELPA support improves distributed dense-matrix diagonalization performance, while band parallelization accelerates scalar-product calculations in hybrid-functional and Car–Parrinello workloads.Band parallelization is implemented in PWscf for hybrid-functional calculations and is especially important for Car–Parrinello dynamics.
- Parallelization: Quantum ESPRESSO extends explicit OpenMP parallelization beyond FFTs and can distribute Kohn–Sham orbitals in addition to plane waves.Orbital distribution is particularly useful for simulations of large cells and machines with many cores.
B. Aspects of interoperability
Quantum ESPRESSO emphasizes interoperability with external software through shared data formats, callable computational engines, APIs, and improved portable I/O. These changes support workflows ranging from excited-state and multiscale calculations to high-throughput and interactive steering.
- External interoperability: External workflows require data exchange for excited states, configuration-space sampling, quantum nuclei, multiscale simulations, high-throughput studies, and steering.These applications need scalable access to outputs, automated input generation, or finer-grained control over Quantum ESPRESSO routines.
- External interoperability: Interoperability is favored over tight integration because external software can provide specialized capabilities while using Quantum ESPRESSO as a computational engine.The interface requirements include input and output formats, installation, and calls to PWscf or CP with externally supplied atomic configurations.
- XML files with schema: Since v.6.0, the head file is a validated-schema XML file that standard tools can parse and generate.It contains run information, reproducibility data, and execution status, supporting high-throughput databases and verification.
- Large-record data file format: Distributed I/O is efficient and supports some I/O parallelization, whereas collected I/O requires reproducible ordering and careful memory and communication optimization.Distributed output requires a globally accessible file system and produces many files that are directly usable only by a compatible setup.
- Large-record data file format: The v.6.0 output directory uses collected XML data, per-k-point orbital files, and a charge- and spin-density file, with both large data types stored in reciprocal space.HDF5 output is also available in addition to Fortran binary files.
D. Organization of the distribution
Quantum ESPRESSO reorganizes its distribution into modular packages, separates algorithms from computational engines, and generalizes parallel and linear-response infrastructure. It also adds interfaces and workflow tools that improve extensibility, coupling, and automation.
- Package organization: The distribution adopts a federation of packages with a common base and separately contained additional packages instead of a monolithic organization.This restructuring addresses maintainability problems caused by uncoordinated growth and supports easier extension and debugging.
- Algorithm and engine separation: PWneb was rewritten as a separate NEB package using PWscf as its computational engine, allowing adaptation to another engine with minor effort.The separation between the NEB and self-consistency algorithms is described as nearly complete.
- External packages: PWscf and CP were adapted to work with Plumed, replacing the old internal meta-dynamics code through hook routines.Activation requires a patching process that modifies specific routines to call Plumed routines.
- Modular parallelism: A modular MPI design lets Quantum ESPRESSO routines operate within a communicator supplied by the calling code, leaving the caller’s parallelization level independent.The design supports independent calculations and external coupling, with PWneb managing NEB image parallelization outside PWscf.
- APIs and linear response: A general-purpose library exposes PWscf and CP to external Fortran, C, and C++ codes, while linear-response routines are being unified in LR Modules.The restructuring targets reuse across related linear-response problems that currently rely on many specialized routines.
- Workflow tools: AiiDA, pwtk, and related interfaces automate workflows, preserve provenance, and connect calculations into reproducible sequences.AiiDA uses directed acyclic graphs for provenance, while pwtk automates large numbers of calculations and composes tasks through Quantum ESPRESSO-like syntax.
3. QE-emacs-modes
Quantum ESPRESSO combines user-friendly editing tools, automated non-regression testing, modularization, and broad interoperability with continuing methodological and performance extensions.
- 3. QE-emacs-modes: QE-emacs-modes makes Quantum ESPRESSO input editing easier through syntax highlighting, auto-indentation, auto-completion, and utility commands.The modes recognize documented namelists, variables, cards, and options, and can insert input-file templates.
- F. Continuous Integration and testing: The test-suite runs Quantum ESPRESSO executables, extracts numerical results, compares them with reference data, and flags threshold-exceeding differences.It supports sequential or parallel tests and testing of particular code features.
- F. Continuous Integration and testing: Buildbot test farms continuously monitor the repository and test daily builds across compilers, execution modes, MPI implementations, and mathematical libraries.A subset of the suite is also used by Travis CI to identify erroneous commits and assist pull-request review.
- IV. OUTLOOK AND CONCLUSIONS: The paper presents methodological extensions, performance enhancements for parallel machines, code modularization, and interoperability within the distribution and with external software.Its outlook emphasizes code reusability, performance, reliability, adaptation to future architectures, and data exchange or cross-verification.