A common way to evaluate electronic integrals for polyatomic molecules is to use Becke’s partitioning scheme (Becke and Chem, 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.

评估多原子分子电子积分的一种常用方法是使用Becke的分配方案（Becke和Chem，1988年）以及以每个原子位点为中心的重叠网格。Becke方案是为在远距离下快速掉落的集成物（例如那些近似绑定电子态的集成物）设计的。但是，当应用于电子连续体中的状态时，Becke方案收敛速度较慢，并且是高度冗余的。在这里，我们介绍了Becke方案的修改版本，该版本适用于电子连续体的功能，例如涉及分子光电离和电子-分子散射的那些，并且可以确保收敛性和效率与计算结合态时所实现的收敛性和效率相当。在此修改方案中，Becke分区中已经存在的原子量在距其各自原子核数键长的范围内平滑关闭，并由渐近unit重进行补充。原子积分在以每个原子为中心的小球形网格上进行评估，其尺寸与相应原子量的支持相对应。间隙和远距离区域的剩余积分通过中央主栅格进行评估。通过评估包含高斯型轨道和 尺寸与相应原子量的支持相称。间隙和远距离区域的剩余积分通过中央主栅格进行评估。通过评估包含高斯型轨道和 尺寸与相应原子量的支持相称。间隙和远距离区域的剩余积分通过中央主栅格进行评估。通过评估包含高斯型轨道和原子位点上的汤川势以及以主网格为中心的球形贝塞尔函数。这些功能代表了在多原子分子中实际电子散射和光电离计算中遇到的功能。