Roots and Weights for MultiExp Quadrature

The roots (x_i) and weights (a_i) for n-point quadrature on [0,1] with the weight function ln²x can be seen by entering a value of n (1-26, 30, 35, 40, 45, 50).

The roots (r_i) and weights (w_i) for n-point quadrature on [0,∞) with the weight function r² can be found from these using

r_i = − R ln x_i         w_i = R³ (a_i / x_i)

where R is a scale factor indicating the "extent" of the integrand. For DFT calculations, the R value should be comparable to the size of the atom.

See: P.M.W. Gill and S.H. Chien, J. Comput. Chem. 24 (2003) 732-740