Quantum Chemistry at ANU

The roots (*x*_{i}) and weights (*a*_{i})
for *n*-point quadrature on [0,1] with the weight function ln^{2}*x*
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 *r*^{2} can be found from these using

*r*_{i} = − *R* ln *x*_{i}
*w*_{i} = *R*^{3} (*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