  The MultiExp Gaussian quadrature rule proposed by Gill and Chien has many
compelling properties for the integration of radial integrands encountered in
electronic structure, but thus far has only been computed up to N = 50, with
some nontrivial holes in the existing tables for 27 <= N < 50. In this work, a
simple recipe is developed to compute the MultiExp Gaussian quadrature for
larger N at close to the double precision machine epsilon. Notably, this recipe
uses only double precision operations, so no computer algebra systems or
arbitrary precision libraries are needed. There are three primary outcomes: (A)
The MultiExp tables for all N <= 1000 are presented in a supplement to this
report - these might prove useful in building better medium and high quality
density functional theory quadrature grids (B) these tables are compared to the
known Gill and Chien tables with excellent agreement obtained modulo a
noticeable problem with the weights of the largest N = 50 Gill and Chien table
and (C) it may be the case that the Boley-Golub plus extremely high-order
Gauss-Legendre quadrature approximation recipe developed in this work could be
used to automatically derive other quadrature rules throughout electronic
structure theory and beyond.
