`[-](igs|intgrid|numacc)` ±*N*

This keyword (Integration Grid Selection) specifies the integration grid to be used for numerical integrations. Both "pruned" and "unpruned" grids can be specified. Pruned grids are grids that have been optimized to use the minimal number of points required to achieve a given level of accuracy. Pruned grids are used by default when available (currently defined for H through Kr).

Specific grids may be selected by giving an integer value *N* as the
argument to the option. *N* may have one of these forms:

- A small positive integer (0 ≤
*N*< 1000), which requests a pre-defined**pruned grid**, as shown in the following table: - A large positive integer of the form
*mmmlll*, which requests an**unpruned**grid with*mmm*radial shells around each atom, and a**Lebedev angular grid**in each shell, which integrates exactly all spherical harmonics of degree*L = lll*or less. The total number of integration points per atom is thus ≈*mmm*⋅(*lll*+ 1)^{2}/3. For example, to specify the (99,590) unpruned grid, use`-intgrid 99041`. The valid values of*lll*are 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 35, 41, 47, 53, 59, 65, 71, 77, 83, 89, 95, 101, 107, 113, 119, 125, 131. - A large negative integer of the form −
*mmmlll*, which requests an**unpruned**grid with*mmm*radial shells around each atom, and a**spherical product grid**having (*lll*+ 1)/2*θ*points and (*lll*+ 1)*φ*points in each shell. Again,*L = lll*is the highest order of spherical harmonics that are integrated exactly by this rule. The total number of integration points per atom is therefore*mmm*⋅(*lll*+ 1)^{2}/2. For example, this form is used to specify the (96,32,64) grid commonly cited in benchmark DFT calculations:`-intgrid −96063`.

Only one radial quadrature scheme was available in **PAMoC** versions
prior to 2012, namely the *N _{r}*-point Euler-Maclaurin
quadrature formula which, in this context, corresponds to a
(

In the current version of

Then, the integration grid selection keyword

`bck``hrf``stk``stw``arc`and`sur`-
`radrule`

- "Quadrature schemes for integrals of density functional theory"

Murray, C. W.; Handy, N. C.; Laming, G. J.*Mol. Phys.***1993**,*78*, 997-1014. - "A standard grid for density functional calculations"

Gill, P. M. W.; Johnson, B. G.; Pople, J. A.*Chem. Phys. Lett.***1993**,*209*, 506-512. - "Radial Quadrature for Multiexponential Integrands"

Gill, P. M. W.; Chien, S.-H.*J. Comput. Chem.***2003**,*24*, 732-740. - "SG-0: A Small Standard Grid for DFT Quadrature on
Large Systems"

Chien, S.-H.; Gill, P. M. W.*J. Comput. Chem.***2006**,*27*, 730-739. *(a)*"Values of the nodes and weights of ninth to seventeenth order Gauss-Markov quadrature formulae invariant under the octahedron group with inversion"

Lebedev, V.I.*USSR Comp. Math. and Math. Phys.***1975**,*15(1)*, 44-51.*Zh. vychisl. Mat. mat. Fiz.***1975**,*15(1)*, 48-54.

*(b)*"Quadratures on a sphere"

Lebedev, V.I.*USSR Comp. Math. and Math. Phys.***1976**,*16(2)*, 10-24.*Zh. vychisl. Mat. mat. Fiz.***1976**,*16(2)*, 293-306.- "Spherical quadrature formulas exact to orders 25-29"

Lebedev, V.I.*Siberian. Math. J.***1977**,*18(1)*, 99-107.*Sibirskii Matematicheskii Zhurnal***1977**,*18(1)*, 132-142. - "Quadrature formulas of orders 41, 47, and 53 for the sphere"

Lebedev, V. I.; Skorokhodov, A. L.*Russian Acad. Sci. Dokl. Math.***1992**,*45*, 587-592. - "A quadrature formula for the sphere of 59th algebraic order of
accuracy"

Lebedev, V. I.*Russian Acad. Sci. Dokl. Math.***1995**,*50*, 283-286. - "A quadrature formula for the sphere of the 131-st algebraic order
of accuracy"

Lebedev, V.I.; Laikov, D.N.*Dokl. Math.***1999**,*59*, 477-481.