Gaussian multipoles (differentiated Gaussian functions) are used to de
scribe molecular charge densities. Their use simplifies considerably t
he calculation of the first-order Coulomb interaction energy between p
airs of molecules, which is an important part of the intermolecular po
tential. Methods are developed for expressing the charge densities of
linear molecules economically and accurately using Gaussian multipoles
. Partial-wave expansions are calculated for the first-order Coulomb i
nteraction energies of H-2-He, N-2-He, CO-He, H-2-H-2, N-2-N-2 and CO-
H-2, and their convergence is discussed as a function of molecular ani
sotropy and intermolecular separation. It is confirmed that the multip
ole approximation is very inaccurate for physically important dimer se
parations.