The spherical-harmonics expansion is a mathematically rigorous procedure and a powerful tool for the representation of potential energy surfaces of interacting molecular systems, determining their spectroscopic and dynamical properties, specifically in van der Waals clusters, with applications also to classical and quantum molecular dynamics simulations. The technique consists in the construction (by ab initio or semiempirical methods) of the expanded potential interaction up to terms that provide the generation of a number of leading configurations sufficient to account for faithful geometrical representations. This paper reports the full general description of the method of the spherical-harmonics expansion as applied to diatomic-molecule-diatomic-molecule systems of increasing complexity: the presentation of the mathematical background is given for providing both the application to the prototypical cases considered previously (O2-O2, N2-N2, and N2-O2 systems) and the generalization to: (i) the CO-CO system, where a characteristic feature is the lower symmetry order with respect to the cases studied before, requiring a larger number of expansion terms necessary to adequately represent the potential energy surface; and (ii) the CO-HF system, which exhibits the lowest order of symmetry among this class of aggregates and therefore the highest number of leading configurations.
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