Source-linked AI summary
Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, m. Cococcioni, I. Dabo, A. Dal Corso, S. Fabris, G. Fratesi, S. de Gironcoli, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari, R. M. Wentzcovitch
TL;DR
Materials simulation needed production-ready, community-accessible software beyond in-house research codes. The paper presents Quantum ESPRESSO as an open, modular suite of interoperable DFT codes, with key engines scaling to thousands of processors.
Problem
Materials simulation requires transitioning innovative in-house research codes into production tools accessible to diverse users.
Method
Quantum ESPRESSO combines modular, interoperable DFT codes using plane waves, pseudopotentials, and periodic or supercell approaches.
Results
Key engines scale on massively parallel computers to thousands of processors, with demonstrated scalability up to 4800 processors.
Takeaways & Limitations
The suite supports electronic-structure simulations across crystals, metals, insulators, liquids, amorphous materials, and finite systems.
Takeaways & Limitations
Maximum processor scaling depends on application size, available parallelism, and the numerical algorithms and pseudopotentials used.
Abstract
from arXiv · showhide
Quantum ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). Quantum ESPRESSO stands for "opEn Source Package for Research in Electronic Structure, Simulation, and Optimization". It is freely available to researchers around the world under the terms of the GNU General Public License. Quantum ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively-parallel architectures, and a great effort being devoted to user friendliness. Quantum ESPRESSO is evolving towards a distribution of independent and inter-operable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.
1. Introduction
Materials simulation is expanding through methodological innovation, increasing computing power, and widespread density-functional-theory applications, while complex multiscale problems demand modular and collaborative software. The QUANTUM ESPRESSO project presents an open-source response that gives users access to source code and development materials under core-developer coordination.
- Materials simulation is undergoing a revolution from the nanoscale to bulk materials and devices, driven by methodological and algorithmic innovation alongside increasing computer power.
- Density-functional-theory electronic-structure simulations have enabled this revolution and spread beyond a restricted core of condensed-matter theory and quantum-chemistry researchers.
- Advances in materials modeling depend on worldwide collaboration combining problem selection, theoretical insight, numerical accuracy, and algorithmic efficiency.
- Complex multiscale materials problems require modular software packages that combine methods with different accuracy and scope across distinct time and length scales.
- QUANTUM ESPRESSO embodies an open-source alternative in which a broad user community accesses source code and development materials under coordination by a smaller core-developer group.
2. The QUANTUM ESPRESSO project
QUANTUM ESPRESSO is free, open-source software comprising an integrated suite for electronic-structure calculations and materials modeling. The project combines methodological innovation, efficient and user-friendly software, massively parallel performance, and active cooperation among developers and users.
- Project goals and architecture: QUANTUM ESPRESSO is an integrated suite based on density-functional theory, plane-wave basis sets, and pseudopotentials, distributed under the GNU General Public License.Its codes support electronic-structure calculations and materials modeling.
- Project goals and architecture: The project aims to foster methodological innovation and provide a diverse community with efficient, robust, and user-friendly software implementing recent advances.It also promotes cooperation between scientists developing electronic-structure methods and users applying them to materials and devices.
- Project goals and architecture: Common input, output, and work-file formats grant interoperability among QUANTUM ESPRESSO components and support contributions from external developers.External contributors are encouraged, but not required, to use the numerical and application libraries underlying the core components.
- Performance and modularity: The PWscf and CP engines can scale on massively parallel computers up to thousands of processors.High performance is pursued in both serial and parallel execution through optimized mathematical libraries, multiple parallelization levels, and communication layers.
- Community and dissemination: qe-forge provides a dynamic web portal for active content creation and sharing, fostering coordination and integration among heterogeneous programming groups.Its services include source-code repositories, mailing lists, forums, bug tracking, file sharing, and project documentation.
- Community and dissemination: A Spring 2009 MIT test showed that web-based computational resources on Amazon EC2 were appealing compared with purchasing, maintaining, and administering computer clusters.The model used a cluster of virtual machines and supported shared access through a web interface.
3. Short description of QUANTUM ESPRESSO
QUANTUM ESPRESSO provides chemically realistic materials modeling from the nanoscale upward using DFT, plane waves, and pseudopotentials. Its capabilities span periodic, finite, magnetic, structural, dynamical, spectroscopic, transport, and response calculations, supported by interoperable data handling.
- Methods and scope: QUANTUM ESPRESSO models materials from the nanoscale upward by solving DFT problems with plane-wave basis sets and pseudopotentials for electron-ion interactions.The methods target chemically realistic modeling.
- Methods and scope: Periodic boundary conditions treat infinite crystals and enable efficient convergence for extended aperiodic systems, while supercells and density-countercharge methods handle finite systems and open boundaries.This framework supports crystals, liquids, and amorphous materials.
- Core capabilities: Core calculations include Kohn-Sham orbitals and energies, structural optimization, magnetic and spin-polarized ground states, and ab initio molecular dynamics.Structural optimization uses Hellmann-Feynman forces and stresses; molecular dynamics can use Car-Parrinello or Born-Oppenheimer approaches, including NPT variable-cell simulations.
- Advanced capabilities: Advanced capabilities include DFPT response calculations, phonons, electron-phonon and phonon-phonon interactions, transition-state searches, ballistic conductance, Wannier functions, NMR, EPR, and X-ray absorption spectra.DFPT provides second- and third-energy derivatives and static response functions such as dielectric tensors, Born effective charges, IR spectra, and Raman tensors.
- Utilities and interoperability: Post-processing utilities calculate STM images, ELF, Löwdin charges, DOS, and planar or spherical averages, while carefully designed file formats support interoperability and reproducibility.The project uses simple, reliable converters and separates potentially large data such as orbital coefficients, charge densities, and potentials into linked files.
4. QUANTUM ESPRESSO packages
Quantum ESPRESSO comprises a large, modular distribution divided into executables for different calculations. Its packages support plane-wave electronic-structure methods, Car–Parrinello dynamics, coherent electron transport, and localized-basis Hamiltonian construction.
- Distribution and modularization: The 4.1 distribution contains about 310,000 Fortran-90 lines, over 100 examples, and more than 100 tests, motivating modularization into several executables.It also includes Fortran-77, C, and Tcl code, external libraries, and approximately 10,000 lines of documentation.
- PWscf: PWscf uses iterative self-consistency and diagonalization within the plane-wave pseudopotential method, supporting NC-PPs, US-PPs, and projector augmented-wave methods.It also includes LDA and GGA functionals, spin-polarization, non-collinear magnetism, and simplified DFT + Hubbard U calculations.
- CP: CP performs Car–Parrinello ab initio molecular dynamics using norm-conserving and ultrasoft pseudopotentials, with Γ-point sampling for large systems without translational symmetry.It supports microcanonical, constant-pressure, and thermostatted dynamics, along with energy and structural minimization, NEB, and metadynamics calculations.
- PWcond: PWcond implements coherent electron transport in atomic-sized nanocontacts through the Choi–Ihm scattering approach within Landauer–Büttiker theory.The linear response ballistic conductance is proportional to electron transmission at the Fermi energy for an open quantum system connected to leads.
- Wannier functions: The Wannier code constructs a chemically accurate, transferable tight-binding Hamiltonian in a localized basis for Green’s functions, self-energies, and large-scale electronic-structure calculations.The localized representation can also support ballistic transport calculations and density-of-states determination for very large structures.
5. Parallelization
QUANTUM ESPRESSO exploits hierarchical supercomputer architectures through multiple tunable parallelization levels, distributing data and computations across processor groups. Its scalability reaches 4800 processors, while application characteristics limit scaling and OpenMP/MPI supports multicore systems and larger processor counts.
- Hierarchical parallelization: QUANTUM ESPRESSO distributes data and computations hierarchically across processors, with multiple parallelization levels tunable to the application and architecture.This design enables the main codes to run in parallel on massively parallel architectures.
- Hierarchical parallelization: Parallelization uses a hierarchy of MPI communicator groups, progressing from coarse-grained image parallelization to finer-grained tasks.Image parallelization divides processors into nimage groups, each handling one or more configuration-space images in NEB calculations.
- Scaling limits: Application structure limits scaling: k-points constrain pool size, electronic bands limit linear-algebra parallelization, and numerical algorithms scale differently.The maximum useful processor count depends on the specific application and code.
- Demonstrated scalability: 4800 processors have demonstrated excellent scalability, including cases where coarse-grained parallelization provides no benefit using only MPI.Scalability does not yet extend to tens of thousands of processors as in specially crafted codes such as QBox.
- Multicore parallelization: The current version provides partial but fully functional OpenMP parallelization for multicore CPUs, and combining OpenMP with MPI extends scalability to more processors.The developers also optimize intermediate-size simulations for medium-size clusters.
6. Perspectives and Outlook
Quantum ESPRESSO’s outlook centers on new excited-state capabilities, broader interoperability, expanded pseudopotential support, and distributed, large-scale computing infrastructures. These developments are intended to be shaped by the user community and external software contributors.
- Scientific capabilities: Future additions will emphasize excited-state calculations using TDDFT and many-body perturbation theory, including a finite-frequency TDDFT approach for optical spectra.The optical-spectra method generalizes density-functional perturbation theory to finite frequencies.
- Interoperability: External groups are expected to provide compatible and interfaceable software, expanding functionalities available to the Quantum ESPRESSO user community.Examples include yambo for many-body perturbation-theory excited-state calculations.
- Interoperability: Interoperability efforts will provide accurate specifications for data structures and file formats, interfaces with other packages, and extensions from NC-PPs to US-PPs and PAW schemes.These extensions target QUANTUM ESPRESSO components currently limited to norm-conserving pseudopotentials.
- Computing infrastructure: The increasing availability of massively parallel machines will sustain efforts toward large-scale calculations and architectures such as multicore CPUs.A mixed OpenMP-MPI approach is identified as the viable route to maximum performance on multicore CPUs.
- Computing infrastructure: The Vlab cyber-infrastructure exemplifies distributed computing through a service-oriented architecture using Quantum ESPRESSO as a back-end package and web portal.It provides distributed scientific workflows for high-pressure and temperature material properties, alongside analysis tools.
Appendix
The appendix describes algorithms used in Quantum ESPRESSO that have not been documented elsewhere.
- The appendix documents previously undescribed algorithms used in Quantum ESPRESSO.
Appendix A.1. Self-consistency
Appendix A.1 formulates Kohn–Sham self-consistency as the nonlinear fixed-point problem x = F[x] and solves it iteratively using modified Broyden mixing. It defines the squared scf norm from a Hartree-based estimate of self-consistency error and extends the algorithm to additional variables in advanced calculations.
- Fixed-point formulation: Kohn–Sham self-consistency is recast as the nonlinear fixed-point equation x = F[x], where x contains N charge-density or Kohn–Sham-potential components.F maps an input density or potential to an output vector by solving the Kohn–Sham equations.
- Iterative solution: PWscf solves the fixed-point problem iteratively with a modified Broyden algorithm using charge-density components in reciprocal space.The method constructs new search directions from prior input densities.
- Self-consistency error: The squared scf norm uses a reciprocal-space Hartree term based on ∆ρ = ρ(out) − ρ(in) to estimate self-consistent energy error.When exchange-correlation screening does not dominate electrostatic screening, this term upper-bounds the self-consistent error of the standard DFT energy.
- Mixing and preconditioning: The algorithm combines typically 4 to 8 previous input densities and can use simple, Thomas–Fermi, or local Thomas–Fermi preconditioned mixing.The new search direction may use a fraction of the optimal density difference or an approximately screened, preconditioned difference.
- Advanced calculations: For DFT+U, meta-GGA, and PAW, the vector x incorporates additional quantities, and the scf norm is modified to include their self-consistency errors.These quantities include correlated-state occupancies, kinetic energy density, and PAW projector-related terms.
Appendix A.2. Iterative diagonalization
During self-consistency, PWscf solves the generalized eigenvalue problem Hψ_i = ϵ_iSψ_i for all occupied states using iterative methods. It implements block Davidson and band-by-band conjugate-gradient minimization, with preconditioning and constraint enforcement.
- Iterative diagonalization: PWscf solves Hψ_i = ϵ_iSψ_i, i = 1, . . . , N, with generalized S-orthonormal eigenvectors using iterative methods.Both the Hamiltonian H and overlap matrix S are available as operators for calculating Hψ and Sψ products.
- Iterative diagonalization: The implemented alternatives are a block Davidson algorithm and band-by-band minimization using conjugate gradient.The conjugate-gradient approach is formulated as constrained minimization, while Davidson operates through reduced subspaces.
- Davidson: Davidson starts from orthonormalized trial orbitals, typically taken from a previous SCF, time, or optimization step, or from atomic orbitals.Residual and correction vectors expand a reduced basis in which conventional diagonalization produces updated trial eigenvectors and eigenvalues.
- Davidson: Davidson may enlarge the reduced basis progressively; this approach is typically slightly faster at the expense of larger memory usage.The enlarged basis leads to problems of increasing dimension, such as a 3N-dimensional problem, until a prefixed basis size is reached.
- Conjugate-Gradient: Conjugate-gradient iterations enforce eigenvector constraints through preconditioning, orthonormalization, normalized search directions, and Polak-Ribière updates.In practical implementation, only Pg and Ph need calculation, and only P^2 is used; a kinetic-only P^2 has proved satisfactory.
Appendix A.3. Wavefunction extrapolation
Wavefunction extrapolation generates initial guesses for molecular-dynamics and structural-relaxation calculations from prior time steps. When self-consistent wavefunctions require alignment, an overlap-based unitary transformation is constructed, with singular-value decomposition providing a simpler and more robust procedure.
- Wavefunction extrapolation: Extrapolations generate good initial wavefunction guesses at time t + dt from wavefunctions at previous time steps.They are used in molecular-dynamics runs and structural relaxations.
- Wavefunction alignment: For self-consistent calculations, the overlap matrix between consecutive wavefunction sets generates a unitary transformation aligning ψ(t + dt) to ψ(t).The transformation is based on the overlap matrix Oij between consecutive time steps.
- Wavefunction alignment: Because the overlap matrix O is not unitary, it must first be converted into a unitary matrix before applying the alignment transformation.The text notes that this conversion can use a unitarization procedure.
- SVD-based alignment: Singular-value decomposition O = vDw yields the needed unitary transformation U ≃ w†v†, with D’s eigenvalues close to 1 for very similar wavefunction sets.Here v and w are unitary, while D is diagonal and non-negative definite.
- SVD-based alignment: The SVD-based procedure is simpler than the original proposal and prevents alignment breakdown in occasional situations caused by level crossing.This is the stated robustness advantage of the procedure.
Appendix A.4. Symmetry
Quantum ESPRESSO exploits crystal symmetry through space-group operations that combine rotations and fractional translations, enabling symmetrization across the Brillouin zone. PWscf applies this to charge density, forces, and stress, while PHonon further uses the small group of q to reduce linear-response calculations and reconstruct force constants.
- Crystal symmetry: Crystal symmetry operations combine a rotation R with fractional translation f and map each atomic position to an equivalent one.The rotational parts define the crystal point group.
- Crystal symmetry: Symmetry maps Kohn–Sham orbitals at k to orbitals at the rotated Bloch vector Rk, allowing unitary mixing among degenerate states without changing physical quantities.The resulting state at Rk may have a different band index or be a unitary transformation within the same eigenvalue.
- PWscf symmetrization: PWscf symmetrizes charge density, Hellmann–Feynman forces, and stress by combining quantities evaluated on the irreducible Brillouin zone with symmetry operations and normalized k-point weights.The weights are proportional to the number of vectors in each k-point star and satisfy ∑k∈IBZ wk = 1.
- PHonon symmetry reduction: PHonon identifies the small group of q and decomposes atomic displacements into irreducible representations, whose dimensions satisfy νj ≤3 in most cases and reach 6 in some special cases.Only perturbations associated with a given irrep are needed in the self-consistent linear-response solution, and force constants across the star of q are obtained by symmetry.
Appendix A.5. Fock exchange · Commun. · Phys.
This section describes exact Fock exchange in hybrid functionals for periodic systems, including its dual-space implementation, high computational cost, Brillouin-zone sampling, and treatment of the q → 0 divergence.
- Appendix A.5. Fock exchange: Hybrid functionals include a fraction of exact, non-local Fock exchange in the exchange-correlation functional.For periodic systems, the section formulates the Fock exchange energy per unit cell.
- Appendix A.5. Fock exchange: The formulation assumes an insulating, non magnetic system and defines integrals and wavefunction normalizations over the whole crystal volume V = NΩ.Summations cover all occupied bands and all N k-points in the Brillouin zone under Born-von Kármán boundary conditions.
- Appendix A.5. Fock exchange: Auxiliary codensities are computed in real space and transformed to reciprocal space by FFT, while associated electrostatic energies are accumulated.This dual-space formalism is used to evaluate the Fock exchange term.
- Appendix A.5. Fock exchange: Applying the Fock exchange operator requires additional FFTs and real-space array multiplications repeated for every occupied band and Brillouin-zone point.These repeated operations account for the calculation’s high computational cost.
- Appendix A.5. Fock exchange: The computational cost of exact exchange is at least an order of magnitude larger than for non-hybrid calculations.The passage attributes this cost to repeating the basic operations across occupied bands and the Brillouin-zone grid.
- Appendix A.5. Fock exchange: A Γ-centered auxiliary q-point grid can reduce cost by restricting the k′ summation to k′ = k+q.Convergence with respect to this additional grid must be checked, although a coarser grid than that used for densities and potentials is often sufficient.
- Appendix A.5. Fock exchange: Regular Brillouin-zone grids cause an integrable divergence in the direct Fock-energy evaluation as q →0.The Gygi–Baldereschi procedure subtracts a term with the same divergence and adds its analytic Brillouin-zone integral separately.