Numerical Settings¶

Purpose: Computational parameters: meshes, basis sets, convergence, and discretization

In scope:

K-point meshes and line paths for band structures
Real-space meshes and grids
Basis set specifications: plane-wave, APW, atom-centered
Convergence thresholds and maximum iterations
Smearing functions: Fermi-Dirac, Gaussian, Methfessel-Paxton
Force calculation settings

Relationship map¶

Hold "Alt" / "Option" to enable pan & zoom

classDiagram
    class APWPlaneWaveBasisSet
    class AtomCenteredFunction
    class BasisSetComponent
    class ForceCalculations
    class KLinePath
    class KMesh
    class KSpace
    class Mesh
    class NumericalSettings
    class PlaneWaveBasisSet
    class SelfConsistency
    class Smearing
    PlaneWaveBasisSet <|-- APWPlaneWaveBasisSet
    NumericalSettings <|-- ForceCalculations
    Mesh <|-- KMesh
    NumericalSettings <|-- KSpace
    BasisSetComponent <|-- PlaneWaveBasisSet
    KMesh <|-- PlaneWaveBasisSet
    NumericalSettings <|-- SelfConsistency
    NumericalSettings <|-- Smearing
    KSpace --> KLinePath : k_line_path
    KSpace --> KMesh : k_mesh

Legend

Parent <|-- Child inheritance (Child extends Parent)

Owner --> SubSection containment/subsection

Key sections¶

Section	Description	MetaInfo
`NumericalSettings`	A base section used to define the numerical settings used in a simulation.	Open in MetaInfo browser
`Mesh`	A base section used to specify the settings of a sampling mesh.	Open in MetaInfo browser
`KMesh`	A base section used to specify the settings of a sampling mesh in reciprocal space.	Open in MetaInfo browser
`KLinePath`	A base section used to define the settings of a k-line path within a multidimensional mesh.	Open in MetaInfo browser
`KSpace`	A base section used to specify the settings of the k-space.	Open in MetaInfo browser
`Smearing`	Section specifying the smearing of the occupation numbers to either simulate temperature effects or improve SCF convergence.	Open in MetaInfo browser
`SelfConsistency`	A base section used to define the convergence settings of self-consistent field (SCF) calculation.	Open in MetaInfo browser
`ForceCalculations`	Section containing the parameters describing how a ForceField model is evaluated during a simulation.	Open in MetaInfo browser
`BasisSetComponent`	A type section denoting a basis set component of a simulation.	Open in MetaInfo browser
`PlaneWaveBasisSet`	Basis set over a reciprocal mesh, where each point $k_n$ represents a planar-wave basis function $rac{1}{\sqrt{\omega}} e^{i k_n r}$.	Open in MetaInfo browser
`APWPlaneWaveBasisSet`	A `PlaneWaveBasisSet` specialized to the APW use case.	Open in MetaInfo browser
`AtomCenteredFunction`	Specifies a single contracted basis function in an atom-centered basis set.	Open in MetaInfo browser

Quantities by section¶

`NumericalSettings`¶

Quantity	Type	Description
`name`	m_str(str)	Name of the numerical settings section. This is typically used to easy identification of the `NumericalSettings` section. Possible values: "KMesh", "FrequencyMesh", "TimeMesh", "SelfConsistency", "BasisSet".

`Mesh`¶

Quantity	Type	Description
`spacing`	Enum (shape: ['dimensionality'])	Identifier for the spacing of the Mesh. Identifier for the spacing of the Mesh. Defaults to 'Equidistant' if not defined. It can take the values: \| Name \| Description \| \| --------- \| -------------------------------- \| \| `'Equidistant'` \| Equidistant grid (also known as 'Newton-Cotes') \| \| `'Logarithmic'` \| log distance grid \| \| `'Tan'` \| Non-uniform tan mesh for grids. More dense at low abs values of the points, while less dense for higher values \|
`quadrature`	Enum	Quadrature rule used for integration of the Mesh. Quadrature rule used for integration of the Mesh. This quantity is relevant for 1D meshes: \| Name \| Description \| \| --------- \| -------------------------------- \| \| `'Gauss-Legendre'` \| Quadrature rule for integration using Legendre polynomials \| \| `'Gauss-Laguerre'` \| Quadrature rule for integration using Laguerre polynomials \| \| `'Clenshaw-Curtis'` \| Quadrature rule for integration using Chebyshev polynomials using discrete cosine transformations \| \| `'Gauss-Hermite'` \| Quadrature rule for integration using Hermite polynomials \|
`n_points`	m_int32(int32)	Number of points in the mesh.
`dimensionality`	m_int32(int32)	Dimensionality of the mesh: 1, 2, or 3. Defaults to 3.
`grid`	m_int32(int32) (shape: ['dimensionality'])	Amount of mesh point sampling along each axis. See `type` for the axes definition.
`points`	m_complex128(complex128) (shape: ['n_points', 'dimensionality'])	List of all the points in the mesh.
`multiplicities`	m_float64(float64) (shape: ['n_points'])	The amount of times the same point reappears. A value larger than 1, typically indicates a symmetry operation that was applied to the `Mesh`. This quantity is equivalent to `weights`: multiplicities = n_points * weights
`weights`	m_float64(float64) (shape: ['n_points'])	Weight of each point. A value smaller than 1, typically indicates a symmetry operation that was applied to the mesh. This quantity is equivalent to `multiplicities`: weights = multiplicities / n_points

`KMesh`¶

Quantity	Type	Description
`label`	Enum	Label used to identify the meaning of the reciprocal grid. Label used to identify the meaning of the reciprocal grid. The actual meaning of `k` vs `g` vs `q` is context-dependent, though typically: - `g` is used for the primitive vectors (typically within the Brillouin zone). - `k` for a generic reciprocal vector. - `q` for any momentum change imparted by a scattering event.
`center`	Enum	Identifier for the center of the Mesh: Identifier for the center of the Mesh: \| Name \| Description \| \| --------- \| -------------------------------- \| \| `'Gamma-centered'` \| Regular mesh is centered around Gamma. No offset. \| \| `'Monkhorst-Pack'` \| Regular mesh with an offset of half the reciprocal lattice vector. \| \| `'Gamma-offcenter'` \| Regular mesh with an offset that is neither `'Gamma-centered'`, nor `'Monkhorst-Pack'`. \|
`offset`	m_float64(float64) (shape: [3])	Offset vector shifting the mesh with respect to a Gamma-centered case (where it is defined as [0, 0, 0]).
`all_points`	m_float64(float64) (shape: ['*', 3])	Full list of the mesh points without any symmetry operations in units of the `reciprocal_lattice_vectors`. In the presence of symmetry operations, this quantity is a larger list than `points` (as it will contain all the points in the Brillouin zone).
`high_symmetry_points`	JSON	Dictionary containing the high-symmetry point labels and their values in units of `reciprocal_lattice_vectors`. Dictionary containing the high-symmetry point labels and their values in units of `reciprocal_lattice_vectors`. E.g., in a cubic lattice: high_symmetry_points = { 'Gamma': [0, 0, 0], 'X': [0.5, 0, 0], 'Y': [0, 0.5, 0], ... ]
`k_line_density`	m_float64(float64)	Amount of sampled k-points per unit reciprocal length along each axis. Contains the least precise density out of all axes. Should only be compared between calculations of similar dimensionality.

`KLinePath`¶

Quantity	Type	Description
`high_symmetry_path_names`	m_str(str) (shape: ['*'])	List of the high-symmetry path names followed in the k-line path. This quantity is directly coupled with `high_symmetry_path_value`. E.g., in a cubic lattice: `high_symmetry_path_names = ['Gamma', 'X', 'Y', 'Gamma']`.
`high_symmetry_path_values`	m_float64(float64) (shape: ['*', 3])	List of the high-symmetry path values in units of the `reciprocal_lattice_vectors` in the k-line path. This quantity is directly coupled with `high_symmetry_path_names`. E.g., in a cubic lattice: `high_symmetry_path_value = [[0, 0, 0], [0.5, 0, 0], [0, 0.5, 0], [0, 0, 0]]`.
`n_line_points`	m_int32(int32)	Number of points in the k-line path.
`points`	m_float64(float64) (shape: ['n_line_points', 3])	List of all the points in the k-line path in units of the `reciprocal_lattice_vectors`.

`KSpace`¶

Quantity	Type	Description
`reciprocal_lattice_vectors`	m_float64(float64) (shape: [3, 3])	Reciprocal lattice vectors of the simulated cell, in Cartesian coordinates and including the $2 pi$ pre-factor. The first index runs over each lattice vector. The second index runs over the $x, y, z$ Cartesian coordinates.

`Smearing`¶

Quantity	Type	Description
`name`	Enum	Smearing routine employed.

`SelfConsistency`¶

Quantity	Type	Description
`scf_minimization_algorithm`	m_str(str)	Specifies the algorithm used for self consistency minimization.
`n_max_iterations`	m_int32(int32)	Specifies the maximum number of allowed self-consistent iterations. The simulation `is_scf_converged` if the number of iterations is not larger or equal than this quantity.
`threshold_change`	m_float64(float64)	Specifies the threshold for the change between two subsequent self-consistent iterations on a given output property. The simulation `is_scf_converged` if this total change is below this threshold.
`threshold_change_unit`	m_str(str)	Unit using the pint UnitRegistry() notation for the `threshold_change`.

`ForceCalculations`¶

Quantity	Type	Description
`vdw_cutoff`	m_float64(float64)	Cutoff for calculating VDW forces.
`coulomb_type`	Enum	Method used for calculating long-ranged Coulomb forces. Method used for calculating long-ranged Coulomb forces. Allowed values are: \| Method Name \| Description \| \| ---------------------- \| ----------------------------------------- \| \| `""` \| No thermostat \| \| `"Cutoff"` \| Simple cutoff scheme. \| \| `"Ewald"` \| Standard Ewald summation as described in any solid-state physics text. \| \| `"Multi-Level Summation"` \| D. Hardy, J.E. Stone, and K. Schulten, Parallel. Comput. 35, 164\| \| `"Particle-Mesh-Ewald"` \| T. Darden, D. York, and L. Pedersen, J. Chem. Phys. 98, 10089 (1993) \| \| `"Particle-Particle Particle-Mesh"` \| See e.g. Hockney and Eastwood, Computer Simulation Using Particles, Adam Hilger, NY (1989). \| \| `"Reaction-Field"` \| J.A. Barker and R.O. Watts, Mol. Phys. 26, 789 (1973)\|
`coulomb_cutoff`	m_float64(float64)	Cutoff for calculating short-ranged Coulomb forces.
`neighbor_update_frequency`	m_int32(int)	Number of timesteps between updating the neighbor list.
`neighbor_update_cutoff`	m_float64(float64)	The distance cutoff for determining the neighbor list.

`BasisSetComponent`¶

Quantity	Type	Description
`name`	m_str(str)	Name of the basis set component.
`species_scope`	(shape: ['*'])	Reference to the section `AtomsState` specifying the localization of the basis set.
`hamiltonian_scope`	(shape: ['*'])	Reference to the section `BaseModelMethod` containing the information of the Hamiltonian term to which the basis set applies.

`PlaneWaveBasisSet`¶

Quantity	Type	Description
`cutoff_energy`	m_float64(float64)	Cutoff energy for the plane-wave basis set. The simulation uses plane waves with energies below this cutoff.
`cutoff_radius`	m_float64(float64)	Cutoff radius for the plane-wave basis set. Is the less frequently used dual to `cutoff_energy`.

`APWPlaneWaveBasisSet`¶

Quantity	Type	Description
`cutoff_fractional`	m_float64(float64)	The spherical cutoff parameter for the interstitial plane waves in the APW family. This cutoff has no units, referring to the product of the smallest muffin-tin radius and the length of the cutoff reciprocal vector ($r_{MT} * \\|K_{cut}\\|$).

`AtomCenteredFunction`¶

Quantity	Type	Description
`angular_type`	Enum	Angular basis used when expanding this shell into AOs.
`function_type`	Enum	Angular-momentum label (s, p, d, f, etc.).
`angular_momentum`	m_int32(int32)	Angular momentum quantum number ℓ.
`r_power`	m_int32(int32)	Radial power n_s for this shell's analytic form (typically 0 for GTOs).
`shell_normalization`	m_float64(float64)	Unitless normalization factor applied to each contracted atomic orbital (or shell) to satisfy the chosen normalization convention. It defines how normalized primitives are scaled when forming the final AO.
`n_primitive`	m_int32(int32)	Number of primitives in this shell. A primitive is a single uncontracted radial basis function such as one Gaussian or Slater-type orbital before contraction into a full atomic orbital.
`exponents`	m_float32(float32) (shape: ['n_primitive'])	Primitive exponents.
`contraction_coefficients`	m_float32(float32) (shape: ['n_primitive'])	Contraction coefficients for the primitives in this single-ℓ shell.
`primitive_factor`	m_float64(float64) (shape: ['n_primitive'])	Extra per-primitive multiplier (dimensionless).
`point_charge`	m_float32(float32)	Optional embedded point charge.

Numerical Settings¶

Relationship map¶

Key sections¶

Quantities by section¶

NumericalSettings¶

Mesh¶

KMesh¶

KLinePath¶

KSpace¶

Smearing¶

SelfConsistency¶

ForceCalculations¶

BasisSetComponent¶

PlaneWaveBasisSet¶

APWPlaneWaveBasisSet¶

AtomCenteredFunction¶