Efficient molecular numerical integration schemes

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Abstract
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 t u r b o m o l e. The results of grid tests and demonstrative applications of energy and especially analytical gradient calculations are given.