Ab initio MP2/aug'-cc-pVTZ calculations have been carried out to investigate the six unique cyclic quaternary complexes FH:FH:FH:FH, FH:FH:FH:FCl, FH:FH:FCl:FCl, FH:FCl:FH:FCl, FH:FCl:FCl:FCl, and FCl:FCl:FCl:FCl stabilized by F-H center dot center dot center dot F hydrogen bonds and F-CI center dot center dot center dot F halogen bonds. The binding energies of these complexes decrease as the number of FH molecules decreases, and therefore as the number of hydrogen bonds decreases, indicating that hydrogen bonds are primarily responsible for stabilities. Nonadditivities of binding energies are synergistic for complexes with 4, 3, and 2 FH molecules, but antagonistic for those with 1 and 0 FH molecules. In addition to depending on changes in F-F, F-H, and F-Cl distances, complex binding energies are also influenced by two sets of angular parameters. These include the external F-F-F angles which must sum to 360 degrees in these cyclic structures, and the internal H-F-F angles for hydrogen bonds and F- Cl-F angles for halogen bonds, which measure the deviation from linearity of these bonds. Transition structures present the barriers to converting an equilibrium structure to an equivalent equilibrium structure on the potential surfaces. These barriers increase as the number of FH molecules decreases. EOM-CCSD spin-spin coupling constants (2h)J(F-F) across hydrogen bonds in complexes tend to increase with decreasing F-F distance. They increase dramatically in transition structures, but show no dependence on the F-F distance. The one-bond coupling constants (1h)J(F-H) are relatively small and negative in complexes, increase dramatically, and are positive in transition structures. (1)J(F-H) values are greatest for the covalent F-H bond. Coupling constants (1x)J(F-Cl) across halogen bonds are relatively small and positive in complexes, and increase dramatically in transition structures. The largest values of (1)J(F-Cl) are found for covalent bonds.