Exact calculation of the volume and surface area of fused hardsphere molecules with unequal atomic radii
Abstract
The volume and surface area of a fused hardsphere molecule can be calculated by the usual formula relating the union of a number of sets to their intersections. In principle, this formula includes intersections of all orders; however, we show that, by making use of the properties of certain types of double, triple, quadruple and quintuple intersection, all terms of the fifth and higher order and some terms of lower order can be eliminated from the expansion, leaving only spheres and intersections of two, three or four spheres. Analytical expressions are derived for the volumes and surface areas of intersections of two, three or four spheres with unequal radii; these expressions allow the exact calculation of the volume and surface area of any fused hardsphere molecule.
 Publication:

Molecular Physics
 Pub Date:
 1987
 DOI:
 10.1080/00268978700102951
 Bibcode:
 1987MolPh..62.1247G