  A common way to evaluate electronic integrals for polyatomic molecules is to
use Becke's partitioning scheme [J. Chem. Phys.88, 2547 (1988)] in conjunction
with overlapping grids centered at each atomic site. The Becke scheme was
designed for integrands that fall off rapidly at large distances, such as those
approximating bound electronic states. When applied to states in the electronic
continuum, however, Becke scheme exhibits slow convergence and it is highly
redundant. Here, we present a modified version of Becke scheme that is
applicable to functions of the electronic continuum, such as those involved in
molecular photoionization and electron-molecule scattering, and which ensures
convergence and efficiency comparable to those realized in the calculation of
bound states. In this modified scheme, the atomic weights already present in
Becke's partition are smoothly switched off within a range of few bond lengths
from their respective nuclei, and complemented by an asymptotically unitary
weight. The atomic integrals are evaluated on small spherical grids, centered
on each atom, with size commensurate to the support of the corresponding atomic
weight. The residual integral of the interstitial and long-range region is
evaluated with a central master grid. The accuracy of the method is
demonstrated by evaluating integrals involving integrands containing Gaussian
Type Orbitals and Yukawa potentials, on the atomic sites, as well as spherical
Bessel functions centered on the master grid. These functions are
representative of those encountered in realistic electron-scattering and
photoionization calculations in polyatomic molecules.
