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GPAW: An open Python package for electronic-structure calculations

Jens Jørgen Mortensen, Ask Hjorth Larsen, Mikael Kuisma, Aleksei V. Ivanov, Alireza Taghizadeh, Andrew Peterson, Anubhab Haldar, Asmus Ougaard Dohn, Christian Schäfer, Elvar Örn Jónsson, Eric D. Hermes, Fredrik Andreas Nilsson, Georg Kastlunger, Gianluca Levi, Hannes Jónsson, Hannu Häkkinen, Jakub Fojt, Jiban Kangsabanik, Joachim Sødequist, Jouko Lehtomäki, Julian Heske, Jussi Enkovaara, Kirsten Trøstrup Winther, Marcin Dulak, Marko M. Melander, Martin Ovesen, Martti Louhivuori, Michael Walter, Morten Gjerding, Olga Lopez-Acevedo, Paul Erhart, Robert Warmbier, Rolf Würdemann, Sami Kaappa, Simone Latini, Tara Maria Boland, Thomas Bligaard, Thorbjørn Skovhus, Toma Susi, Tristan Maxson, Tuomas Rossi, Xi Chen, Yorick Leonard A. Schmerwitz, Jakob Schiøtz, Thomas Olsen, Karsten Wedel Jacobsen, Kristian Sommer Thygesen

arXiv:2310.14776v2cond-mat.mtrl-sciphysics.comp-ph

TL;DR

The paper reviews GPAW as a platform for electronic-structure calculations spanning response, excitation, magnetism, and real-time methods. Its multi-basis design and modular implementations support broad applications, while some approaches retain explicit scope limitations.

  • Problem

    Electronic-structure studies require computational methods covering response functions, excitations, magnetism, and dynamics beyond ground-state calculations.

  • Method

    The paper reviews GPAW’s implementations across complementary basis representations and application-specific electronic-structure methodologies.

  • Results

    GPAW supports GW band structures, BSE optical excitations, direct optimization of localized excited states, real-time TDDFT, magnetic-response methods, and related materials calculations.

  • Takeaways & Limitations

    Combining basis representations within a single run renders GPAW versatile and provides a platform for implementing diverse electronic-structure methods.

  • Takeaways & Limitations

    Self-consistent non-collinear Kohn–Sham calculations are presently restricted to LDA, while ALDA cannot account for excitons in extended systems.

Abstract

from arXiv · show

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE) providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation (BSE), variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support of GPU acceleration has been achieved with minor modifications of the GPAW code thanks to the CuPy library. We end the review with an outlook describing some future plans for GPAW.

I. INTRODUCTION

GPAW is an open-source Python electronic-structure package combining PAW-based DFT with three complementary wave-function representations. Its ASE integration, modular design, and broad feature set support both flexible calculations and new methodological development.

  • GPAW originated as a Python multigrid solver for PAW-based DFT and evolved into a full-featured electronic-structure package.
  • The three representations are complementary and can be combined within a single run, making GPAW highly versatile.
  • The package supports advanced methods including GW, BSE, time-dependent DFT, magnetic calculations, localized excitations, defects, and electron-related response properties.
  • GPAW’s Python and ASE integration exposes calculation data and permits inspection or modification of key quantities during execution.User code can be inserted into the self-consistent-field loop for custom workflows and diagnostics.
  • GPAW supports plane-wave, finite-difference real-space, and numerical atom-centered-orbital representations with distinct accuracy, boundary-condition, and system-size trade-offs.PW and FD modes favor accuracy, while LCAO enables calculations on systems exceeding ten thousand atoms.
  • GPAW’s new design improves feature implementation, while mode-specific functionality means users must choose PW, FD, or LCAO according to accuracy and resources.Production calculations are currently recommended with the old code, whereas new features are developed on the new code.

B. Numerical implementation

GPAW represents smooth wave functions with plane waves, finite differences on uniform grids, or numerical atom-centered orbitals. Its numerical implementation combines SCF eigensolvers, density mixing, Poisson solvers, and PAW-based reconstruction tools.

  • GPAW offers plane-wave and LCAO basis representations alongside a finite-difference representation of the kinetic-energy operator on a uniform Cartesian grid.
  • PAW tools interpolate pseudo wave functions to fine real-space grids and add corrections needed to represent all-electron behavior near nuclei.
  • All-electron electrostatic potentials can be calculated for transmission electron microscopy simulations that assess valence-bonding effects beyond isolated-atom models.
  • PW and FD modes use iterative diagonalization with density mixing, whereas LCAO mode uses full Hamiltonian diagonalization.
  • Each SCF step updates the wave-function subspace, solves the eigensystem, updates eigenvalues and occupations, then mixes and symmetrizes the density.
  • GPAW provides direct Fourier-based and iterative multigrid Poisson solvers, with iterative methods potentially more efficient for larger systems.
  • Boundary conditions and occupation schemes can be selected for system dimensionality and electronic structure, including multipole corrections for molecular dipoles.

4. Updating wavefunctions in dynamics

GPAW updates wave functions after small atomic displacements by moving nearby charge contributions, accelerating iterative FD and PW calculations. Direct minimization offers an alternative SCF strategy with lower usual effort and broader applicability, but finite-temperature occupations remain unsupported.

  • Updating wavefunctions in dynamics: Rigidly moving local wave-function projections provides an improved guess after small atomic displacements in FD and PW modes.The approach relies on nearby charge moving with the atom.
  • Updating wavefunctions in dynamics: The update can double-count contributions because partial waves on different atoms are not orthonormal, making the resulting wave functions partly unphysical.
  • Updating wavefunctions in dynamics: The update could be improved by using the LCAO basis and overlap matrix to prevent double-counting.
  • Direct minimization: Direct minimization avoids Hamiltonian diagonalization at every step and usually requires less computational effort than conventional eigensolver and density-mixing routines.It is applicable to GPAW’s orbital representations and to finite or extended systems.
  • Direct minimization: The current direct-minimization implementation does not support finite-temperature occupation distributions and therefore requires a finite band gap.

9. GPU implementation

GPAW’s GPU implementation combines CuPy, vendor libraries, and manually written kernels to support NVIDIA and AMD hardware. Current GPU use is limited to PW-mode total-energy calculations with LDA/GGA, while multi-GPU execution uses MPI.

  • GPU implementation: GPAW targets NVIDIA and AMD GPUs through CUDA and HIP backends using manually written kernels, GPU libraries, and CuPy.CuPy provides a NumPy-like GPU-array interface that hides many hardware details from users.
  • GPU implementation: CPU quantities use NumPy arrays while GPU calculations use CuPy arrays in the rewritten ground-state code.
  • GPU implementation: At present, GPUs support total-energy calculations with LDA/GGA in PW mode.
  • GPU implementation: Multiple GPUs are supported through MPI, with one GPU assigned to each MPI rank.GPU-aware MPI enables direct GPU-to-GPU communication without unnecessary host-CPU memory copies.
  • Exchange–correlation support: The broader GPAW framework provides multiple exchange–correlation functionals and corrections, including LDA/GGA/MGGA, van der Waals, GLLBsc, DFT+U, and hybrid approaches.
  • Exchange–correlation support: Range-separated functionals divide exchange into short-range and long-range components controlled by mixing parameters and a decay parameter γ.LCY-PBE applies Hartree–Fock exchange at long range, whereas HSE reverses the short- and long-range treatment.

5. SIC

GPAW implements self-interaction correction and Bayesian exchange–correlation ensembles alongside broader electronic-structure and optimization capabilities. These methods can improve selected results, but their reliability depends on the functional, ensemble coverage, and implementation scope.

  • SIC: GPAW provides a fully self-consistent, variational Perdew–Zunger self-interaction correction with atomic forces available in all three basis representations.
  • SIC: PZ-SIC subtracts each occupied orbital density’s self-Coulomb and self-exchange–correlation contributions, making the energy non-invariant under occupied-orbital unitary transformations.
  • SIC: PZ-SIC gives accurate results in cases where common Kohn–Sham functionals fail, including the Mn dimer, α-quartz defect states, and molecular excitation energies.
  • BEEF: Bayesian error ensembles vary XC-model parameters so the most likely model fits benchmark data while ensemble spread reflects deviations from the benchmark.BEEF-vdW, mBEEF, and mBEEF-vdW implement this error-estimation approach in GPAW.
  • BEEF: Ensemble-based error estimates can be poor when every included functional describes the target property poorly, such as oxide band gaps or van der Waals bonding with only GGA functionals.
  • ASE integration: GPAW supplies energies and forces as a black-box calculator to ASE, which performs geometry optimization, reaction-path calculations, and molecular dynamics.
  • ASE integration: Bayesian-optimization workflows using GPAW-generated databases and surrogate potential-energy surfaces achieved speed-ups of several orders of magnitude in finding optimal structures.

A. Spin–orbit coupling

GPAW treats spin–orbit coupling through non-selfconsistent post-processing or fully self-consistent calculations, supporting band structures, magnetic anisotropy, non-collinear magnetism, and orbital magnetization. Applications include WS2 band splitting, Cr2O3 spin flop, and orbital-magnetization calculations using PAW-based methods.

  • Spin–orbit coupling: Non-selfconsistent spin–orbit eigenenergies are obtained by diagonalizing the full Hamiltonian in a scalar-relativistic orbital basis.This is a fast post-processing step requiring projector overlaps, although convergence with respect to included scalar-relativistic states remains necessary.
  • Spin–orbit coupling: 0.45 eV valence-band splitting occurs at the K point of WS2, while spin degeneracy remains along the Γ-M line.The splitting is attributed to strong spin–orbit coupling from W atoms; Γ-M remains invariant under two non-commuting mirror symmetries.
  • Magnetic anisotropy: Magnetic anisotropy can be evaluated by rotating magnetic moments and comparing the resulting Kohn–Sham eigenvalues.The magnetic force theorem motivates this non-selfconsistent treatment for magnetic materials.
  • Self-consistent non-collinear magnetism: Self-consistent non-collinear magnetism is implemented within LDA, while the PAW formalism permits fully non-collinear treatment without intra-atomic collinearity.The present self-consistent generalization is restricted to LDA because GGA formulations face formal and numerical problems.
  • Orbital magnetization: PAW-based orbital magnetization requires broken time-reversal symmetry and can include spin–orbit coupling self-consistently or through collinear post-processing.For bcc-Fe, fcc-Ni, fcc-Co, and hcp-Co, PAW-ACA results mainly improve over MT-ACA and show decent agreement with modern-theory results.
  • Constant B-field: 6 T marks the Cr2O3 spin-flop transition from Sz to Sx alignment in LDA+U with U = 2 eV.The transition occurs when Zeeman energy overcomes anisotropy, and the post-flop canting is roughly 1°.

E. Spin spirals

GPAW evaluates non-collinear magnetic states through generalized-Bloch spin spirals and determines their energetics and orientations. Its response-function framework extends these calculations to electronic screening and optical properties.

  • Spin-spiral method: GPAW evaluates planar spin-spiral energies within the chemical unit cell using the Generalized Bloch Theorem.For each wave vector q, the self-consistent generalized-Bloch problem yields the corresponding spin-spiral energy.
  • NiBr2 results: The NiBr2 monolayer has an incommensurate spin-spiral ground state, with a local Ni magnetic moment that varies only weakly with q.The ground-state wave vector is approximately Q ≃[0.1, 0.1, 0].
  • NiBr2 results: Spin–orbit coupling selects the spiral orientation by minimizing the non-self-consistent projected spin–orbit energy.The spiral-plane normal n is perpendicular to Q in the NiBr2 ground state, corresponding to a cycloidal spiral.
  • Electronic response: Linear-response calculations obtain susceptibilities from Kohn–Sham orbitals, eigenvalues, and occupations, then include interactions through a Dyson-like equation with Hartree-XC kernels.GPAW supports RPA, ALDA, rALDA, and bootstrap kernel treatments.
  • Electronic response: In periodic systems, GPAW Fourier-transforms the susceptibility into a plane-wave matrix equation diagonal in q and evaluates reciprocal-space quantities using PAW corrections and FFTs.Special treatment cancels the divergent Coulomb contribution in the optical limit.

2. Spectral representation

GPAW represents frequency-dependent response functions either by direct frequency evaluation or through a spectral function and Hilbert transform. Its dielectric calculations use integration schemes whose convergence differs substantially between semiconductors and metals.

  • Spectral representation: GPAW evaluates the Kohn–Sham susceptibility directly at selected frequencies or through a spectral function followed by a Hilbert transform.The spectral-function route is usually faster but more memory-intensive and permits tetrahedron integration for improved k-point convergence.
  • Dielectric function: GPAW extracts optical absorption and electron energy-loss spectra from the macroscopic dielectric function, including local-field corrections.The susceptibility can be evaluated using RPA, ALDA, rALDA, or bootstrap exchange-correlation kernels.
  • Spectral representation: The tetrahedron method linearly interpolates eigenvalues and matrix elements, whereas point integration replaces the energy delta function with a smeared Lorentzian.This distinction controls how Brillouin-zone sampling errors appear in the dielectric function.
  • Dielectric function: For Si, both integration methods agree as ω →0, but tetrahedron integration avoids the higher-frequency unphysical oscillations caused by finite k-point sampling.Si has no low-energy excitations, so its dielectric function has zero imaginary part and a flat real part at low frequencies.
  • Dielectric function: For metallic Ag, the difference between point and tetrahedron integration is more pronounced because k-point convergence is slower.Point-integration results eventually approach tetrahedron results only with increased k-point sampling and higher computational cost.

D. Magnetic response

GPAW computes transverse magnetic susceptibilities and analyzes their spectra as collective magnons and Stoner excitations. It also maps the response to Heisenberg exchange parameters, while exposing the limits of localized-spin descriptions for itinerant magnets.

  • Magnetic susceptibility: For collinear systems without spin–orbit coupling, transverse spin susceptibility decouples from charge and longitudinal-spin responses.In the ALDA, the transverse Dyson equation becomes scalar for spins polarized along z.
  • Magnetic susceptibility: GPAW calculates transverse magnetic susceptibility in a plane-wave basis and derives a spectral function that governs energy dissipation from induced spin changes.The spectrum separates excitations that lower or raise the spin projection by one unit.
  • Magnetic excitations: The transverse spectrum contains collective spin-wave excitations, or magnons, and a Stoner continuum of opposite-spin electron–hole pairs.Plane-wave spectral output can be compared directly with inelastic neutron-scattering cross sections.
  • Magnetic excitations: Magnon dispersions are extracted from peaks in the spectrum diagonal, while majority and minority eigenmodes separate individual magnon lineshapes from the many-body Stoner continuum.This enables studies of nonanalytic dispersion, magnetic phase transitions, and collective modes inside the Stoner continuum.
  • Liechtenstein MFT: GPAW computes Heisenberg exchange parameters from the reactive static Kohn–Sham susceptibility and the exchange-correlation magnetic field using Liechtenstein’s magnetic force theorem.Users can choose spherical, cylindrical, or parallelepipedic magnetic-site configurations of variable size.
  • Liechtenstein MFT: For hcp-Co, magnetic-force-theorem magnon dispersions agree excellently with LR-TDDFT except for the optical mode along K–M–Γ.The Heisenberg model misses fine structure and Kohn anomalies arising from overlap with the Stoner continuum.

E. GW approximation

GPAW supports G0W0 quasiparticle calculations and BSE-based optical and magnetic excitation analyses. Its implementations include full-frequency self-energy evaluation, low-dimensional Coulomb truncation, and parallelized BSE construction.

  • GW approximation: GPAW supports standard G0W0 quasiparticle calculations using first-order perturbation theory for the linearized quasiparticle equation.
  • GW approximation: Spin-polarized G0W0 calculations are supported through the spin-indexed quasiparticle formulation.
  • GW approximation: The GW self-energy uses full-frequency integration along the real axis, providing numerical accuracy and access to the full spectral function.
  • GW approximation: For low-dimensional systems, truncated Coulomb interactions remove periodic-image screening, while special q = 0 treatment improves k-point convergence.
  • GW approximation: GPAW’s GW self-energy matrix elements agree strikingly with corresponding results from the Yambo GW code.
  • Bethe–Salpeter Equation: BSE calculations provide excitonic optical spectra and can also yield plasmon and magnon dispersions at finite q.

H. Raman spectrum

GPAW computes Raman spectra through electron–phonon coupling and Raman tensors, using resonant and non-resonant formulations. Its implementation includes polarization-resolved spectra, second-order optical response, SHG, and shift-current calculations.

  • Raman spectrum: Raman spectra describe inelastic light scattering in which vibrational modes are excited within the material.
  • Raman spectrum: The Stokes Raman intensity depends on phonon frequencies, Bose–Einstein occupations, light polarization vectors, and Raman tensors.
  • Raman spectrum: GPAW computes Raman tensors with the Kramers–Heisenberg–Dirac method or time-dependent third-order perturbation theory.
  • Raman spectrum: A polarization-resolved Raman spectrum of bulk 2H-MoS2 was computed at an incident wavelength of 488 nm using only the resonant term.
  • Nonlinear optical response: GPAW implements second-order optical response, including second-harmonic generation and shift-current tensors.
  • Nonlinear optical response: The nonlinear-response implementation requires time-reversal symmetry, limiting these calculations to non-magnetic systems.

VII. REAL-TIME TDDFT

GPAW’s real-time TDDFT propagates time-dependent Kohn–Sham states in finite-difference and LCAO modes. Users can apply customized pulses, record observables, and continue calculations in short wall-time-limited chunks.

  • Real-time propagation: RT-TDDFT is implemented in finite-difference and LCAO modes and can model molecules in strong fields.
  • Real-time propagation: The method requires non-periodic boundary conditions and can be combined with hybrid quantum-classical modeling of molecule–plasmon interactions.
  • Real-time propagation: Starting from a ground state, GPAW propagates the time-dependent Kohn–Sham equation while updating the density-dependent Hamiltonian after each step.
  • Real-time propagation: Users can define external potentials including delta-kicks and Gaussian pulses.
  • Analysis and workflow: A time-dependent dipole moment from a delta-kick can be Fourier-transformed to obtain a photoabsorption spectrum.
  • Analysis and workflow: Continuation and time-limiter features support running propagations in short chunks on shared high-performance resources.

A. Kohn–Sham decomposition

GPAW uses time-dependent Kohn–Sham density matrices to analyze observables and excitation processes. The section also outlines applications, implementation limits, and known shortcomings of linear-response and variational excited-state methods.

  • Kohn–Sham decomposition: The time-dependent Kohn–Sham density matrix is a central quantity for computing observables and can be evaluated efficiently in LCAO mode.
  • Kohn–Sham decomposition: Fourier-transformed induced density matrices can be decomposed into electron–hole contributions for energy-resolved analyses of polarizability.
  • Kohn–Sham decomposition: Density-matrix decompositions support analyses of hot-carrier generation in plasmonic nanostructures and nanoparticle interfaces.
  • Applications: ECD calculations require delta-kicks in all three Cartesian directions and are supported in both finite-difference and LCAO modes.
  • Radiation reaction: Radiative losses can be included without additional computational cost for systems with analytically known Green’s tensors, while 3D free-space and cavity functionality remains under development.
  • Excited-state limitations: Linear-response TDDFT tends to fail for charge-transfer, Rydberg, and doubly excited states, while variational excited-state calculations can suffer from collapse and convergence issues.

1. Direct orbital optimization

GPAW uses direct orbital optimization to obtain variational excited states while reducing variational collapse, and applies these calculations across molecules, solvated systems, solids, polarization, and response-related properties.

  • Direct orbital optimization: Direct-optimization methods use saddle-point search strategies to improve convergence to excited-state solutions over conventional SCF eigensolvers with MOM.DO-MOM and DO-GMF provide alternative optimization strategies; DO-GMF guarantees convergence to an nth-order saddle point but requires partial Hessian diagonalization.
  • Direct orbital optimization: DO-MOM is available with LCAO, real-space-grid, and plane-wave basis sets, with basis-dependent orbital optimization procedures.LCAO calculations optimize orbital-rotation variables, whereas grid and plane-wave calculations additionally use an outer minimization over reference orbitals.
  • Applications: Variational excited-state calculations cover systems from gas-phase or solvated molecules to solids because direct optimization combines robustness with selectable basis sets.Applications include charge-transfer excitations, solvated photoinduced structural dynamics, and solid-state defect excitations.
  • Applications: For the negatively charged nitrogen-vacancy center in diamond, plane-wave calculations with several density functionals found the correct ordering of excited states in a supercell of up to 511 atoms.The defect is described as a prototypical system for quantum applications.
  • Polarization: GPAW evaluates formal polarization changes along adiabatic paths and applies this framework to ferroelectrics such as tetragonal KNbO3 and 2D GeS.For GeS, the reported spontaneous polarization is 490 pC/m, while the electronic 2D polarizabilities reported for GeS and MoS2 are 3.75 Å and 6.19 Å, respectively.

B. Berry phases and band topology

GPAW uses Berry phases to analyze band topology and supports Wannier-function construction, point-defect energetics, and symmetry representations of electronic states.

  • Berry phases and band topology: Berry-phase evolution across the Brillouin zone provides a route to identifying quantum spin Hall and Chern-insulator topology in the presence of spin–orbit coupling.GPAW handles the required smooth gauge for spinor Bloch states with a parallel-transport algorithm.
  • Berry phases and band topology: For 1T’-MoS2, time-reversal symmetry makes the Berry phases at Γ and Y two-fold degenerate, diagnosing the quantum spin Hall insulating state.The cited passage connects this diagnostic to gapless edge states.
  • Wannier functions: Wannier functions are localized electronic states obtained by unitary transformation of Bloch eigenstates that minimizes their spatial extent.GPAW and ASE can construct partially occupied Wannier functions for entangled bands and non-periodic systems.
  • Wannier functions: GPAW includes PAW-based tools for constructing partially occupied Wannier functions and improving Wannierization robustness with a spread-distribution penalty term.The method extends maximally localized Wannier functions to entangled bands and non-periodic systems.
  • Defects and symmetry: For hBN defects, HSE06 calculations reproduce condition-dependent defect stability and charge-transition levels for CN and CB.CB is lower under N-rich conditions, CN is favorable under N-poor conditions, and the reported transitions are 3.73 eV and 3.26 eV above or within the band gap, respectively.
  • Defects and symmetry: GPAW automatically assigns point-group symmetry representations to molecular and extended-system Kohn–Sham wavefunctions for analyzing band degeneracies and dipole-transition selection rules.The analysis outputs irreducible-representation weights for each eigenstate and can restrict the wavefunction to a local region.

F. Band-structure unfolding

GPAW provides band-structure unfolding across its three wave-function representations and includes the QEH model for dielectric response in layered 2D heterostructures, alongside solvent and electrochemical interfaces.

  • Band-structure unfolding: Band-structure unfolding maps supercell bands into the primitive-cell Brillouin zone, making electronic structures from enlarged cells easier to compare.Supercells contain more bands in a smaller Brillouin zone than primitive cells.
  • Band-structure unfolding: GPAW unfolds supercell band structures in real-space-grid, plane-wave, and LCAO modes without explicitly calculating overlaps between supercell and primitive-cell wavefunctions.The unfolded result is represented through a spectral function.
  • The QEH model: The QEH model calculates dielectric response and excitations in vertical stacks of two-dimensional van der Waals materials by coupling dielectric building blocks for individual layers.The building blocks are derived from ab initio RPA density-response functions and combined through electrostatic coupling.
  • The QEH model: For stacked MoS2/WSe2 heterostructures, the static dielectric function increases with layer number and approaches a bulk limit.The layer dependence can be used to investigate interlayer and intralayer excitonic properties and band-edge renormalization.
  • Solvent models: GPAW models solvent effects with a position-dependent continuum permittivity, retaining nearly vacuum-level computational cost while enabling solvation free-energy calculations and electrolyte-interface potentials.The implementation supports neutral and ionic species, periodic surfaces, and electrochemical reaction simulations.
  • Solvent models: Constant-potential surface simulations use grand-potential energies consistent with forces, while GPAW supports purely implicit and hybrid explicit-implicit solvents.Excess charge can be localized on one surface side using a one-sided jellium region and dipole correction.
  • Solvent models: GPAW implements real-space constrained DFT for diabatic or charge/spin-localized states across isolated molecules and one-, two-, or three-dimensional periodic systems.The implementation supplies tools for Marcus-theory transfer-rate parameters in molecular, surface, and bulk systems.

K. Orbital-free DFT

GPAW’s orbital-free DFT implementation combines PAW and real-space methods to provide all-electron values with linear scaling, while the review also outlines magnetic-property tools and future development boundaries.

  • K. Orbital-free DFT: Orbital-free DFT models the kinetic energy as a direct functional of the electron density and uses a Kohn–Sham-like equation for the square root of that density.The scheme approximately enforces the Pauli principle through averaged quantum effects.
  • K. Orbital-free DFT: GPAW’s PAW-based orbital-free DFT accesses all-electron values with computational time scaling linearly with system size.The implementation reports a mean absolute error of 10 meV per atom against reference all-electron values.
  • K. Orbital-free DFT: The orbital-free PAW implementation supports assessment of density functionals, including studies of large-Z and semiclassical limits.All-electron values are used to identify high-performing orbital-free DFT functionals.
  • Magnetic properties: GPAW computes zero-field splitting and hyperfine coupling from electronic spin densities and magnetic interactions using PAW-based quantities.The zero-field-splitting tensor is evaluated in reciprocal space, while hyperfine coupling includes isotropic contact and anisotropic dipolar contributions.
  • Outlook and scope: Future development includes parallelized plane-wave hybrid functionals, LCAO hybrid and GW methods, self-consistent and vertex-corrected GW, and constrained RPA.The accuracy of LCAO-based GW with a limited basis remains unclear.
  • Outlook and scope: Current PAW potentials date from 2009, and new soft and norm-conserving potentials are under development.Norm-conserving potentials are intended for response-function calculations.
  • Outlook and scope: GPU acceleration currently covers standard ground-state calculations, while compatibility with advanced features such as linear response and GW is anticipated.The CuPy library simplifies porting GPAW components to GPUs.
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