Lebedev Quadrature

A large amount of work has been done on quadrature schemes to exactly integrate spherical harmonics over a sphere [136,137,138,139]. The most popular are those by Lebedev [140,141,142,143] which use quadratures based on the octahedral group. A Lebedev grid of degree L exactly integrates all spherical harmonics of degree L or less. The number of grid points, NP(L) required is approximately
$$\begin{align}\mathrm{NP}(L) \approx \frac{(L+1)^{2}}{3}. \end{align}$$
Lebedev grids are currently available up to degree L=53 (974 grid points), although Q-CHEM has only up to degree L=29 (302 grid points).