Quantum Espresso Basics
Expert-defined terms from the Certificate in Quantum Espresso And VASP Theory course at HealthCareCourses (An LSIB brand). Free to read, free to share, paired with a professional course.
ABINIT – first‑principles software – A computational package that,… #
Example: ABINIT can be used to benchmark QE total‑energy calculations for silicon. Practical application: Cross‑checking phonon frequencies. Challenge: Ensuring consistent pseudopotentials across the two codes.
ACE – adaptively compressed exchange – An algorithm that accelerat… #
Example: ACE reduces the cost of HSE06 calculations on a 64‑atom supercell. Practical application: Enabling hybrid‑functional studies of defects. Challenge: Memory overhead for large systems.
Band Structure – energy‑momentum relation – The dispersion of elec… #
Example: The band structure of graphene shows Dirac cones at K. Practical application: Predicting metallic versus insulating behaviour. Challenge: Converging k‑point meshes and dealing with band‑crossing ambiguities.
Brillouin Zone – reciprocal‑space primitive cell – The Wigner‑Seit… #
Example: For a cubic lattice, the Brillouin zone is a cube centred at Γ. Practical application: Determining the minimal set of k‑points for accurate total energies. Challenge: Handling reduced symmetry in low‑symmetry crystals.
Cell Optimization – variable‑cell relaxation – A QE calculation th… #
Example: Using "vc‑relax" to find the equilibrium lattice constant of Al. Practical application: Predicting pressure‑induced phase transitions. Challenge: Choosing appropriate convergence thresholds for forces and stresses.
Charge Density – ρ(r) – The electron density obtained from the occ… #
Example: Visualising ρ(r) in VESTA reveals bonding regions in NaCl. Practical application: Constructing electrostatic potentials for surface calculations. Challenge: Achieving sufficient plane‑wave cutoff to resolve rapid density variations near nuclei.
COHP – crystal orbital Hamilton population – A post‑processing ana… #
Example: COHP analysis of Fe‑O bonds in hematite clarifies magnetic interactions. Practical application: Interpreting chemical bonding in complex oxides. Challenge: Requires accurate projections and careful selection of energy windows.
Conjugate Gradient – iterative minimisation – An algorithm used in… #
Example: The "cg" algorithm converges the wavefunctions of a 200‑atom polymer chain. Practical application: Speeding up geometry optimisations. Challenge: May stall for metallic systems with poor preconditioning.
Core‑Level Spectroscopy – X‑ray absorption, EELS – Simulations bas… #
Example: Calculating the K‑edge of carbon in diamond. Practical application: Interpreting experimental XANES spectra. Challenge: Need for accurate core‑hole pseudopotentials and large supercells.
Cutoff Energy – E cut – The maximum kinetic energy of pl… #
Example: An Ecut of 60 Ry yields converged total energies for Si. Practical application: Balancing computational cost and accuracy. Challenge: Different pseudopotentials demand different cutoffs; convergence tests are mandatory.
Density of States (DOS) – g(ε) – The distribution of electronic st… #
Example: A metallic DOS shows finite value at the Fermi level. Practical application: Estimating carrier concentrations. Challenge: Choosing appropriate smearing methods (Gaussian, Methfessel‑Paxton) to avoid artificial features.
DFT+U – Hubbard correction – An extension of DFT that adds an on‑s… #
Example: Applying U=4 eV to Ni‑d states improves band gaps of NiO. Practical application: Modelling strongly correlated oxides. Challenge: Selecting the correct U value; dependence on the chosen pseudopotential.
DFPT – density‑functional perturbation theory – A linear‑response… #
Example: Computing the phonon dispersion of MgO using "ph.X". Practical application: Predicting lattice‑thermal conductivity. Challenge: Handling metallic systems where smearing affects the response.
Dipole Correction – slab electrostatics – A technique that adds a… #
Example: Adding a dipole correction for a water‑on‑metal surface simulation. Practical application: Accurate work‑function calculations. Challenge: Determining the correct vacuum thickness and dipole plane.
Elastic Constants – C ij – Second‑order derivatives of t… #
Example: Computing C11 for cubic Fe. Practical application: Assessing mechanical stability of novel alloys. Challenge: Convergence with respect to k‑points and strain magnitude.
Electron‑Phonon Coupling (EPC) – λ, α²F(ω) – Quantifies the intera… #
Example: Using QE’s "lambda.X" to evaluate λ for MgB₂. Practical application: Estimating critical temperatures via the McMillan formula. Challenge: Dense q‑point sampling and accurate Wannier interpolation are required.
Fermi Surface – k‑space constant‑energy sheet – The set of k‑point… #
Example: Plotting the Fermi surface of Cu reveals nested sheets. Practical application: Analysing nesting‑driven instabilities. Challenge: Requires extremely fine k‑meshes and careful interpolation.
Fermi‑Level Smearing – occupancy broadening – A technique to aid S… #
Example: Methfessel‑Paxton smearing of 0.02 Ry for Al. Practical application: Stabilising metallic calculations. Challenge: Smearing influences total energies; post‑processing may need extrapolation to zero smearing.
Force Constant Matrix – Φ – The second derivative of the total ene… #
Example: Constructing Φ for a 2‑atom primitive cell of NaCl. Practical application: Building dynamical matrices for phonon dispersion. Challenge: Ensuring translational invariance and acoustic sum rule compliance.
G‑vector – reciprocal‑space plane‑wave index – The vector defining… #
Example: G‑vectors with |G|≤√(2 Ecut) are included. Practical application: controlling basis‑set size. Challenge: large G‑vectors increase memory and CPU time.
Hybrid Functionals – PBE0, HSE06 – Exchange‑correlation approximat… #
Example: HSE06 improves the band gap of GaAs from 0.5 EV (PBE) to 1.4 EV. Practical application: Accurate band‑gap predictions for semiconductors. Challenge: Computational cost scales steeply with system size; ACE or screened‑exchange techniques are needed.
In‑Plane Lattice Constant – a, b – Lattice parameters parallel to… #
Example: Setting a = b = 3.905 Å for SrTiO₃(001) slab. Practical application: Simulating strain‑engineered thin films. Challenge: Mismatch between substrate and film may require large supercells.
Input File – pw #
X, ph.X, etc. – The plain‑text file that controls a QE calculation; contains &CONTROL, &SYSTEM, &ELECTRONS, and atomic specifications. Example: The &SYSTEM block defines ecutwfc, occupations, and smearing. Practical application: Reproducible simulations. Challenge: Syntax errors and missing required flags often cause runtime failures.
K‑point Sampling – Monkhorst‑Pack grid – The discretisation of the… #
G., 6 × 6 × 6). Example: A 4 × 4 × 4 grid suffices for a 20‑atom organic crystal. Practical application: Balancing accuracy and cost. Challenge: Metallic systems need denser meshes; convergence tests are essential.
Local Density Approximation (LDA) – uniform‑electron gas – An exch… #
Example: LDA predicts a lattice constant of 4.04 Å for Al, slightly underestimated. Practical application: Quick structural optimisations. Challenge: Systematic under‑binding; fails for van‑der‑Waals systems.
Magnetic Moment – μ B – The spin polarisation per atom,… #
Example: Fe in bcc Fe carries ~2.2 ΜB. Practical application: Designing magnetic materials. Challenge: Convergence of spin density can be sensitive to initial magnetisation and smearing.
Non‑collinear Magnetism – spinor wavefunctions – An extension of s… #
Example: Modelling a spin‑spiral in Cr using "noncolin=.True.&Quot;. Practical application: Studying complex magnetic textures. Challenge: Increased computational cost and need for fully relativistic pseudopotentials.
Occupations – smearing, fixed – Specification of how electron occu… #
Example: &Quot;occupations='smearing', smearing='gaussian', degauss=0.01&Quot;. Practical application: Stabilising SCF loops. Challenge: Inappropriate smearing can distort total energies and forces.
PAW – projector‑augmented wave – A pseudopotential method that rec… #
Example: QE’s PAW dataset for Cu includes 3d and 4s valence. Practical application: High‑accuracy total‑energy differences with modest cutoffs. Challenge: Generating reliable PAW datasets; compatibility with hybrid functionals.
Phonon Dispersion – ω(q) – The variation of phonon frequencies wit… #
Example: The acoustic branches of Si show linear behaviour near Γ. Practical application: Assessing dynamical stability of new materials. Challenge: Ensuring the acoustic sum rule and dealing with imaginary modes.
Plane‑Wave Basis – Fourier expansion – The set of plane‑wave funct… #
Example: A 70 Ry cutoff yields ~10 000 plane‑waves for a 2‑atom cell. Practical application: Systematic convergence with a single parameter. Challenge: Large memory footprints for high‑cutoff calculations.
Projected Density of States (PDOS) – atom‑resolved DOS – Decomposi… #
Example: PDOS shows that O‑2p states dominate the valence band of TiO₂. Practical application: Interpreting spectroscopic data. Challenge: Selection of projection radii and orthogonalisation schemes.
Quantum ESPRESSO (QE) – open‑source DFT suite – A collection of co… #
X, ph.X, cp.X, etc.) For electronic‑structure calculations based on plane‑waves and pseudopotentials. Example: Using pw.X for ground‑state calculations, ph.X for phonons. Practical application: Research, teaching, and high‑throughput workflows. Challenge: Steep learning curve for newcomers; careful input preparation required.
Quasi‑Particle GW – self‑energy correction – A many‑body perturbat… #
Example: GW0 raises the Si band gap from 0.6 EV (PBE) to 1.1 EV. Practical application: Accurate electronic excitations. Challenge: Computationally demanding; requires well‑converged DFT starting points.
Relaxation – ionic optimisation – The process of moving atoms to m… #
Example: A "relax" run reduces forces below 0.001 Ry/Bohr for a water molecule. Practical application: Obtaining equilibrium structures. Challenge: Trapped in local minima; need for varied initial geometries.
SCF Cycle – self‑consistent field – Iterative procedure that updat… #
Example: Convergence reached when ΔE < 10⁻⁶ Ry. Practical application: Foundation of all DFT calculations. Challenge: Metallic systems may oscillate; mixing schemes (Broyden, Pulay) help.
Smearing Methods – Gaussian, Methfessel‑Paxton, Marzari‑Vanderbilt … #
Example: Methfessel‑Paxton order 1 is common for metals; Gaussian is preferred for insulators. Practical application: Improving SCF stability. Challenge: Selecting degauss small enough to avoid artificial thermal effects.
Spin‑Orbit Coupling (SOC) – relativistic interaction – Inclusion o… #
Example: SOC splits the valence band of PbTe, affecting thermoelectric properties. Practical application: Topological insulator studies. Challenge: Requires fully relativistic pseudopotentials and doubles the size of spinor wavefunctions.
Supercell – periodic expansion – A larger cell constructed from th… #
Example: A 3 × 3 × 3 Si supercell contains 216 atoms for vacancy calculations. Practical application: Defect formation energies. Challenge: Finite‑size effects and increased computational load.
Symmetry Operations – space group, point group – Transformations t… #
Example: The cubic Fm‑3m space group reduces the irreducible Brillouin zone to 1/48 of the full zone. Practical application: Speeding up calculations. Challenge: Low‑symmetry systems lose this advantage; manual symmetry input may be needed.
TDDFT – time‑dependent DFT – Extension of DFT to excited‑state dyn… #
Example: Calculating the absorption spectrum of bulk silicon. Practical application: Optical property prediction. Challenge: Requires careful treatment of local‑field effects and exchange‑correlation kernels.
U‑value – Hubbard parameter – The on‑site Coulomb interaction stre… #
Example: Linear‑response gives U = 5.3 EV for Fe‑3d in FeO. Practical application: Improving magnetic moment predictions. Challenge: Dependence on the chosen projector and basis.
Van der Waals (vdW) Corrections – D2, D3, vdW‑DF – Empirical or no… #
Example: D3 correction reduces the interlayer distance of graphite from 3.5 Å (PBE) to 3.35 Å. Practical application: Layered materials and molecular adsorbates. Challenge: Selecting the appropriate scheme for a given system.
Wavefunction – ψₙₖ(r) – The Kohn‑Sham orbital; expanded in plane‑w… #
Example: Ψₙₖ for a conduction band at the X point in Si. Practical application: Visualising orbital character. Challenge: Large data files; efficient I/O needed for post‑processing.
Wannier Functions – maximally‑localized – Real‑space orbitals obta… #
Example: Constructing Wannier90 files from QE outputs to interpolate the electron‑phonon matrix of MgB₂. Practical application: High‑resolution Fermi surfaces. Challenge: Disentanglement of bands and choice of initial projections.
XC Functional – exchange‑correlation – Approximation for the many‑… #
Example: PBE improves lattice constants over LDA for most metals. Practical application: Selecting a functional that balances accuracy and cost. Challenge: No universal functional; benchmarking is essential.
Zero‑Point Energy (ZPE) – phonon ground‑state energy – The quantum… #
Example: ZPE correction of ~0.05 EV for H₂ adsorption on Pt. Practical application: Accurate thermochemistry. Challenge: Requires full phonon calculations, increasing computational expense.
k‑point Mesh – Monkhorst‑Pack, Gamma‑centered – The grid of recipr… #
Example: A 8 × 8 × 8 Gamma‑centered mesh for a cubic perovskite. Practical application: Systematic convergence studies. Challenge: Metallic systems often need denser meshes; non‑orthogonal cells may require custom grids.
Linear‑Response Theory – DFPT, susceptibility – Framework that com… #
Example: Calculating dielectric constants via "ph.X" linear‑response. Practical application: Efficient phonon and EPC calculations. Challenge: Implementation limited to perturbations that preserve periodicity.
Magnetisation Density – m(r) – Difference between spin‑up and spin… #
Example: M(r) shows localized moments on Mn atoms in MnO. Practical application: Designing spintronic devices. Challenge: Convergence of spin density can be slower than charge density.
Metadynamics – enhanced sampling – A technique to explore free‑ene… #
Example: Metadynamics used to discover new Si polymorphs. Practical application: Overcoming kinetic barriers in structure prediction. Challenge: Choice of collective variables and bias parameters.
Non‑Self‑Consistent Field (NSCF) – band‑structure run – A calculat… #
Example: NSCF run on a 24 × 24 × 24 mesh to generate DOS. Practical application: High‑resolution electronic spectra. Challenge: Must ensure the SCF density is fully converged.
Occupancy Smearing – degauss, smearing type – Parameter controllin… #
Example: Degauss = 0.02 Ry for Al with Methfessel‑Paxton smearing. Practical application: Reducing charge sloshing. Challenge: Too large a degauss artificially raises electronic temperature.
PAW Dataset – pseudopotential file – Contains atomic data for the… #
Example: Cu.Paw file includes 3d and 4s channels. Practical application: High‑accuracy total‑energy differences with moderate cutoffs. Challenge: Compatibility with specific XC functionals and hybrid calculations.
Projector Augmented‑Wave (PAW) – all‑electron reconstruction – Met… #
Example: PAW reproduces core‑level binding energies within 0.1 EV. Practical application: Reliable forces for transition‑metal oxides. Challenge: Generating robust PAW datasets for rare‑earth elements.
Quantum ESPRESSO (QE) Modules – pw #
X, ph.X, cp.X, etc. – Individual executables each dedicated to a specific task: Pw.X for ground‑state DFT, ph.X for phonons, cp.X for Car‑Parrinello MD, etc. Example: Running "pw.X -in scf.In > scf.Out" for an SCF calculation. Practical application: Modular workflow design. Challenge: Mastering the correct input syntax for each module.
Reciprocal Lattice – b₁, b₂, b₃ – Vectors defining the periodicity… #
Example: For a cubic lattice a, the reciprocal vectors have magnitude 2π/a. Practical application: Constructing Brillouin‑zone paths. Challenge: Low‑symmetry cells may produce awkward reciprocal vectors, requiring custom mesh generation.
Relaxation Algorithm – CG, BFGS, FIRE – Numerical methods employed… #
Example: BFGS often converges faster for organic molecules than CG. Practical application: Efficient geometry optimisation. Challenge: Poor initial guesses can stall the optimizer; switching algorithms may help.
Self‑Interaction Error (SIE) – DFT limitation – The spurious inter… #
Example: SIE causes underestimation of band gaps in ZnO. Practical application: Motivates use of hybrid functionals or DFT+U. Challenge: Quantifying SIE for a given system is non‑trivial.
Spin‑Polarised Calculation – collinear magnetism – DFT run where s… #
Example: Setting "starting_magnetization(1)=0.5&Quot; for Fe in QE. Practical application: Modelling ferromagnets and antiferromagnets. Challenge: Convergence may be sensitive to the initial magnetisation and smearing.
Supercell Convergence – finite‑size effects – The process of incre… #
Example: Vacancy formation energy in Si converges within 0.02 EV at a 3 × 3 × 3 supercell. Practical application: Reliable defect energetics. Challenge: Computational cost grows rapidly with cell size.
Surface Slab Model – vacuum, dipole correction – A periodic slab r… #
Example: A 5‑layer Si(111) slab with 15 Å vacuum. Practical application: Adsorption studies and work‑function calculations. Challenge: Ensuring sufficient slab thickness and vacuum; dipole correction may be required for polar surfaces.
Symmetry‑Reduced k‑Points – irreducible Brillouin zone – The subse… #
Example: A 6 × 6 × 6 mesh reduces to 48 irreducible points for a cubic crystal. Practical application: Reducing computational effort. Challenge: Low symmetry leads to many irreducible points; manual symmetry specification may be needed.
Time‑Step (MD) – Car‑Parrinello, Born‑Oppenheimer – The interval b… #
Example: A 0.12 Fs time‑step is typical for Car‑Parrinello MD of water. Practical application: Simulating finite‑temperature behaviour. Challenge: Too large a step leads to energy drift; too small increases cost.
Totally‑Symmetric Representation – Γ representation – The irreduci… #
Example: The A₁g mode in Si belongs to the totally‑symmetric representation. Practical application: Raman activity prediction. Challenge: Assigning correct representations for low‑symmetry crystals.
Ultra‑Soft Pseudopotentials (USPP) – Vanderbilt type – Pseudopoten… #
Example: USPP for Ti reduces Ecut from 80 Ry (norm‑conserving) to 40 Ry. Practical application: Large‑scale simulations of transition‑metal compounds. Challenge: May introduce ghost states if not carefully generated.
Van der Waals Density Functional (vdW‑DF) – non‑local correlation … #
Example: VdW‑DF2 improves interlayer spacing of MoS₂ compared with PBE. Practical application: Layered heterostructures and physisorption. Challenge: Higher computational cost and occasional over‑binding.
Wavefunction Cutoff – ecutwfc – Parameter specifying the kinetic‑e… #
Example: Ecutwfc = 60 Ry for Si leads to converged forces. Practical application: Primary convergence parameter. Challenge: Must be accompanied by a higher cutoff for charge density (ecutrho ≈ 4 × ecutwfc for norm‑conserving pseudopotentials).
Wannier90 Interface – post‑processing tool – A code that reads QE… #
Example: Using "pw2wannier90.X" to generate input for Wannier90. Practical application: High‑resolution band structures and electron‑phonon coupling. Challenge: Selecting disentanglement windows; ensuring smooth gauge.
Zero‑Temperature Approximation – static lattice – The assumption t… #
Example: DFT total energies are often reported at 0 K. Practical application: Baseline for formation‑energy calculations. Challenge: ZPE and finite‑temperature contributions may be non‑negligible for light atoms.
k‑point Weight – integration coefficient – The factor assigned to… #
Example: In a 4 × 4 × 4 mesh, the Γ point may have weight = 1/64. Practical application: Accurate total‑energy and DOS calculations. Challenge: Automatic weight generation may fail for distorted cells; manual correction sometimes needed.