Many of the integrals needed by Band are computed via numerical integration. See also: Wikipedia page on Numerical Integration.
The quality of the Becke integration grid can be changed within the
BeckeGrid Quality [Auto | Basic | Normal | Good | VeryGood | Excellent] RadialGridBoost float AtomDepQuality # Non-standard block. See details. ... End End
Type: Block Description: Options for the numerical integration grid, which is a refined version of the fuzzy cells integration scheme developed by Becke.
Type: Multiple Choice Default value: Auto Options: [Auto, Basic, Normal, Good, VeryGood, Excellent] Description: Quality of the integration grid. For a description of the various qualities and the associated numerical accuracy see reference. If ‘Auto’, the quality defined in the ‘NumericalQuality’ will be used.
Type: Float Default value: 1.0 Description: The number of radial grid points will be boosted by this factor. Some XC functionals require very accurate radial integration grids, so BAND will automatically boost the radial grid by a factor 3 for the following numerically sensitive functionals: LibXC M05, LibXC M05-2X, LibXC M06-2X, LibXC M06-HF, LibXC M06-L, LibXC M08-HX, LibXC M08-SO, LibXC M11-L, LibXC MS0, LibXC MS1, LibXC MS2, LibXC MS2H, LibXC MVS, LibXC MVSH, LibXC N12, LibXC N12-SX, LibXC SOGGA11, LibXC SOGGA11-X, LibXC TH1, LibXC TH2, LibXC WB97, LibXC WB97X, MetaGGA M06L, MetaHybrid M06-2X, MetaHybrid M06-HF, MetaGGA MVS.
Type: Non-standard block Description: One can define a different grid quality for each atom (one definition per line). Line format: ‘AtomIndex Quality’, e.g. ‘3 Good’ means that a grid of Good quality will be used for the third atom in input order. If the index of an atom is not present in the AtomDepQuality section, the quality defined in the Quality key will be used
Example: Multiresolution illustrates how to use the
- The space-partition function used in BAND differs from the one described in Ref. . The unnormalized partition function used in the program is defined as (\(\Omega_I\) is an element-dependent parameter: 0.1 Bohr for H, 0.3 Bohr for He-Xe and 0.6 Bohr for Cs-Uuo):
- The Becke grid is not very well suited to calculate Voronoi deformation density (VDD) charges. For accurate calculation of VDD charges the Voronoi integration scheme is recommended.
Radial grid of NAOs¶
RadialDefaults NR integer RMax float RMin float End
Type: Block Description: Options for the logarithmic radial grid of the basis functions used in the subprogram Dirac
Type: Integer Default value: 3000 Description: Number of radial points. With very high values (like 30000) the Dirac subprogram may not converge.
Type: Float Default value: 100.0 Unit: Bohr Description: Upper bound of the logarithmic radial grid
Type: Float Default value: 1e-06 Unit: Bohr Description: Lower bound of the logarithmic radial grid
Voronoi grid (deprecated)¶
It is possible to use an alternative numerical integration scheme to the Becke Grid, namely the Voronoi Grid.
IntegrationMethod [Becke | Voronoi]
Type: Multiple Choice Default value: Becke Options: [Becke, Voronoi] Description: Choose the real-space numerical integration method. Note: the Voronoi integration scheme is deprecated.
The options for the Voronoi Grid are specified in the
Integration AccInt float End
Type: Block Description: Options for the Voronoi numerical integration scheme. Deprecated. Use BeckeGrid instead.
Type: Float Default value: 3.5 Description: General parameter controlling the accuracy of the Voronoi integration grid. A value of 3 would be basic quality and a value of 7 would be good quality.
|||A.D. Becke, A multicenter numerical integration scheme for polyatomic molecules, Journal of Chemical Physics 88, 2547 (1988).|
|||(1, 2) M. Franchini, P.H.T. Philipsen, L. Visscher, The Becke Fuzzy Cells Integration Scheme in the Amsterdam Density Functional Program Suite, Journal of Computational Chemistry 34, 1818 (2013).|