Theoretical calculations were correlated to elucidate the interface interaction between thiol groups of host-guest systems and gold cluster. The 1-octanethiol molecule acts as guest into α-cyclodextrin host to form a supramolecular complex in which is stabilizing gold clusters. The intermolecular interaction and the vibrational frequencies nature between a host-guest system and gold cluster were elucidated by a theoretical point of view at the MP2, SCS-MP2, and PBE-D3 methods. It is showing a van der Waals interaction and a good vibrational frequencies correlation.