We present a novel formulation for the intermolecular interaction tensor, which is used to describe the long-range electrostatic, induction, and dispersion interactions. Our formulation is based on concepts drawn from combinatorial analysis and Clifford calculus and enables us to present the interaction tensor in a form that is simple to use and suitable for both numerical and symbolic analyses. We apply the derived formulas to calculate the long-range interaction coefficients in hydrogen and coinage metal (Cu, Ag, and Au) clusters. The electronic structure calculations are performed at the CCSD(T) level, with triple-zeta and quadruple-zeta basis sets. The multipole moments and dispersion coefficients are obtained as fits to the derived interaction formulas. The most important interaction parameters are obtained accurately and are in good agreement with other results.