11.1.4 grid_set_angular: set parameters for angular grids

      subroutine grid_get_angular (record,aqu,lmin,lmax,crowd,acca)
      subroutine grid_set_angular (record,aqu,lmin,lmax,crowd,acca)
      implicit double precision (a-h,o-z)
      character *(*) aqu
      integer lmin(0:*),lmax(0:*)

Specify the details of the angular quadrature scheme. The default choice for aqu is 'LEBEDEV' (ie. as in A. D. Becke, J. Chem. Phys. 88 (1988) 2547) which provides angular grids of octahedral symmetry. The alternative choice for aqu is 'LEGENDRE' which gives Gauss-Legendre quadrature in $\theta$ and simple quadrature in $\phi$, as defined by C. W. Murray, N. C. Handy and G. J. Laming, Mol. Phys. 78 (1993) 997. Each type of grid specifies a family of which the various members are characterized by a single quantum number $l$; spherical harmonics up to degree $l$ are integrated exactly. lmin and lmax specify allowed ranges of $l$ for hydrogen/helium, first row, second row, and other elements respectively. As the Lebedev grids have particular values of $l$ associated with each grid, if the value of $l$ is not one of the set implemented in MOLPRO (9, 11, 13, 15, 17, 19, 23, 29, 41, 47, 53), then $l$ is increased to give the next largest angular grid available. Requesting Lebedev grids with $l \lt 9$ results in an appropriate Gauss-Legendre grid. In general, different radial points will have different $l$, and in the absence of any moderation described below, will be taken from lmax.

crowd is a parameter to control the reduction of the degree of quadrature close to the nucleus, where points would otherwise be unnecessarily close together; larger values of crowd mean less reduction thus larger grids. A very large value of this parameter, or, conventionally, setting it to zero, will switch off this feature.

acca is a target energy accuracy. It is used to reduce $l$ for a given radial point as far as possible below lmax but not lower than lmin. The implementation uses the error in the angular integral of the kernel of the Slater-Dirac exchange functional using a sum of approximate atomic densities. If acca is zero, the global threshold is used instead, or else it is ignored.