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DFTInts

Table of contents

Details

The DFTINTS input section specifies details of the integration grid used in density functional theory calculations. The DFTINTS section is optional. ChronusQ uses a molecular grid composed of superimposed atomic grids scaled by the Becke weighting scheme.1 The atomic grids are products of Lebedev spherical grids2 for angular integration and a one dimensional Euler-Maclaurin grid3,4 for the radial integration.

Keywords

Keyword Type Description Default
EPS Double precision float Screening tolerance on the DFT grid 10^{-12}
NANG Integer Number of angular points in DFT grid 302
NRAD Integer Number of radial points in DFT grid 100
NMACRO Integer Number of radial shells in each DFT batch 4

The NANG Keyword

ChronusQ uses Lebedev spherical grids for the angular portion of the atomic grids.1,2 These grids integrate spherical harmonics up to a given order (based on the number of points in the grid) and have octahedral symmetry. Because of these constraints, only grids with a certain number of points are permitted. These are the Lebedev grids currently available in ChronusQ:

  • Low accuracy: 6, 14, 26, 38, 50, 74, 86, 110, 146, 170
  • Moderate accuracy: 194, 230, 266, 302 (Default)
  • High accuracy: 590, 974

Setting NANG to any of the numbers above will use that Lebedev grid for angular integration.

The NRAD Keyword

ChronusQ uses an Euler-Maclaurin scheme for radial integration. This scheme uses equidistant points on the interval [0, 1] that are mapped to the interval [0, \infty).3,4 Any number of points can be used, specified by the NRAD keyword.

The NMACRO Keyword

The NMACRO keyword controls the number of radial shells per parallel batch during the integration. For most cases, the default is sufficient. If specifying number of radial shells with NRAD, the user should be sure that NRAD is evenly divisible by NMACRO for highest efficiency.

Example

High accuracy grid

[DFTInts]
NRad = 300
NAng = 974
NMacro = 12

Small grid

This is related to the "SG-1" grid5 but using the same Lebedev grid across all radial shells.

[DFTInts]
NRad = 50
NAng = 194
NMacro = 10

References

  1. Becke, A. D. (1988). A multicenter numerical integration scheme for polyatomic molecules. The Journal of chemical physics, 88(4), 2547-2553. ↩

  2. Lebedev, V. I. (1976). Quadratures on a sphere. USSR Computational Mathematics and Mathematical Physics, 16(2), 10-24. ↩

  3. Murray, C. W., Handy, N. C., & Laming, G. J. (1993). Quadrature schemes for integrals of density functional theory. Molecular Physics, 78(4), 997-1014. ↩

  4. Johnson, B. G. (1995). (Development, implementation and applications of efficient methodologies for density functional calculations.)[https://doi.org/10.1016/S1380-7323(05)80036-6] In Theoretical and computational chemistry (Vol. 2, pp. 169-219). Elsevier. ↩

  5. Gill, P. M., Johnson, B. G., & Pople, J. A. (1993). A standard grid for density functional calculations. Chemical Physics Letters, 209(5-6), 506-512. ↩