Electrostatic Damping Functions and the Penetration Energy

The use of damping functions to correct the multipole expansion at short-range is explored. Damping functions for the terms in the multipole expansion can be determined ab initio as a linear combination of analytic functions of the separation between sites, but there are additional short-range terms that have different angular dependence. The approach provides a detailed ab initio description of the penetration energy correction to the multipole expansion in an easily comprehensible form.