Noncovalent interactions are prevalent in crystal packing and supramolecular chemistry. Directional noncovalent interactions such as donor-acceptor bonds (e.g., hydrogen, chalcogen, and pnictogen bonds) as well as nondirectional forces (such as dispersion) come together to stabilize supramolecular assemblies by striking a delicate energetic balance. Typically, a two-pronged approach employing experimental X-ray structures and gas phase quantum chemical modeling has been used to understand and design supramolecular architectures. Drawing from recent advances in molecular crystal modeling with dispersion corrected density functional theory (DFT), we propose in this article a combination of qualitative noncovalent index (NCI) analysis and periodic and gas phase DFT calculations on substitutional crystal analogues to unravel the dominant interactions in a particular crystal packing. We illustrate the possibilities of this approach by studying three crystal packings of epoxydihydroarsanthrene analogues that present a complex combination of donor-acceptor interactions including pnictogen-pnictogen, pnictogen-π, and pnictogen-chalcogen. We show that, in these crystals, the chalcogen-pnictogen interaction dominates over the pnictogen-pnictogen and pnictogen-π. In the latter, the role of donor and acceptor is reversed depending on the interacting moieties. Multiple chalcogen-pnictogen interactions necessitate larger donor atoms, such as sulfur. These observations explain and rationalize the experimentally observed crystal structures.