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New grids for three-dimensional numerical integration are introduced. They include a new mapping for radial integration of the Gauss–Chebyshev type which seems to surpass in accuracy the existing integration schemes as proposed by Becke J. Chem. Phys. 88, 2547 (1988), Murray et al. Mol. Phys. 78, 997 (1993), or Gill et al. Chem. Phys. Lett. 209, 506 (1993). Lebedev grids are employed for spherical integration. Open ended quadrature schemes are presented using the efficient Lobatto formula for the θ integration. These grids are employed for self-consistent density functional calculations using local approximation and nonlocal corrections and are implemented into the program package turbomole. The results of grid tests and demonstrative applications of energy and especially analytical gradient calculations are given.
Treutler et al. (Sun,) studied this question.